Fatigue performance of metal additive manufacturing: a comprehensive overview

ABSTRACT

Fatigue life assessment of metal additive manufacturing (AM) products has remained challenging due to the uncertainty of as–built defects, heterogeneity of the microstructure, and residual stress. In the past few years, many works have been conducted to develop models in order to predict fatigue life of metal AM samples by considering the existence of AM inherent defects. This review paper addresses the main issues regarding fatigue assessment of metal AM parts by considering the effect of defects and post processing strategies. Mechanisms that are contributing to the failure of metal AM samples are categorized and discussed in detail. Several modelling approaches exist in the case of fatigue life prediction. The common fatigue models that are compatible with AM properties are thoroughly explained by discussing the previous works and highlighting their major conclusions. In addition, the use of machine learning is identified as the future of metal AM fatigue life assessment due to their high performance. The main challenge of today's fatigue and fracture community was identified as the fatigue life estimation of complex geometries with the presence of different types of defects, anisotropic microstructure, and complex state of residual stress. This work proposes the available approaches to tackle this challenge.

KEYWORDS:

• Metal additive manufacturing, fatigue life assessment, defect-based fatigue model, fatigue crack propagation, continuum damage mechanics, multistage modelling, defect detection

1. Introduction

Metal additive manufacturing (AM) is an emerging technology with high potential in producing functional and complex components. This technology enables new opportunities to manufacture components that have not been possible by means of conventional manufacturing (CM) processes. Moreover, less manufacturing lead time, waste material, and required tools for fabrication through the AM methods paved the way toward producing complex parts with less effort. For example, topology-optimised components can be produced without considering several time-consuming and complex processing stages. This capability gains significance because of today’s constant need to improve the functionality and performance of mechanical components and reduce their weight at the same time. Advancements in AM technology requires accurate prediction of the mechanical performance of materials, especially for aviation components. Among the mechanical properties of materials, fatigue life has attracted significant attention due to its relation with the service life of the component. It has been reported that metal AM products have lower fatigue strength compared to wrought materials due to their unfavourable as-built condition [1,2]; thus, a proper solution is of significance. Many studies have been implemented on the effect of defects and post-treatments on the fatigue life of metal AM components; however, lack of broadness and consistency in the literature make it hard to catch up with the research trend. On the other hand, the diversity and development of methods for fatigue life prediction of metal AM materials give rise to confusion and uncertainty in selecting the proper approach for analyses.

Fatigue life is defined as the number of cycles that a component can survive under a specific cyclic loading, and generally described by the S-N curve. Fatigue life basically depends on several factors such as defects size and distribution, surface roughness, residual stress, applied stress amplitude, microstructure, environmental effects, specimen size, and local stress concentration (i.e. notch sensitivity). At high stress levels, the material is experiencing severe plastic strain, which causes failure after a few hundreds to thousands of cycles. This phenomenon is also known as the low-cycle fatigue (LCF) that is essential for industries such as aerospace, where cyclic loading under high stress conditions is commonplace. At lower stress levels, no macro-plastic strain occurs; instead, the whole sample is gone through elastic strain (including local micro-plastic strain), which is responsible for the material failure. This mechanism is also known as the high-cycle fatigue (HCF) that covers thousands to the commonly agreed two million cycles in most structural materials. At low stress levels, an asymptotic behaviour indicates the fatigue limit of the material below which the failure will not occur. This specific stress level for each material is called the fatigue limit. The main cause of failure during LCF and HCF is different, while the contribution of defects is dominant in both cases [3]. The third fatigue life regime is the very high cycle fatigue (VHCF) that deals with stresses significantly lower than the fatigue limit of the material and the material could generally survive up to 10⁸ cycles. The dominant failure mechanism at such conditions is microstructural imperfections or impurities. In order to obtain a broad understanding of the material behaviour under cyclic loading, it is necessary to investigate all three fatigue regimes.

There are several major research groups that are specifically active in the field of fatigue and fracture of AM components. Among them, Beretta et al. have mainly focused on the damage-tolerant design and probabilistic fatigue life estimation [4–6]. In this approach, the inherent defects are considered as stress-rising locations that reduce the fatigue strength of the material. Berto et al. have considered notched specimens and the effect of geometry on the stress concentration of metal AM materials [7–9]. Fatemi et al. have investigated defect-based fatigue life assessment including notched specimens, under multi-axial loading conditions [10–12]. Shamsaei et al. aimed at fatigue life improvements by post-processing and process parameter optimisation, as well as development of microstructure-based models for crack initiation and growth [13–16]. Withers et al. have focused on the effect of manufacturing defects on fatigue performance of AM parts and fatigue crack growth (FCG) monitoring by means of synchrotron X-ray diffraction [17–19]. They further put emphasise on the development of machine learning (ML) models for fatigue life prediction based on the synchrotron X-ray diffraction data [20,21]. Du Plessis et al. mainly work on the defect distribution and characterisation using the μCT technique [22–24]. Qian et al. have investigated the effect of microstructure features and post-processing on the FCG and fatigue life (especially in the VHCF regime) of AM products from experimental and numerical aspects [25–27].

In recent years, a number of review papers have been published addressing different aspects of fatigue and fracture of metal AM; however, none of them gave a comprehensive insight to the field. Tang et al. [28] discussed the existing predictive models for metal AM components with more focus on the empirical models. Awd et al. [29] concentrated on the review of the FEM-based, physical, empirical, and data-driven models; however, left the FCG models untouched. Foti et al. [11] established a valuable insight into the multi-axial failure and fatigue life predictive models. Sanaei and Fatemi [30], and Zerbst et al. [31] provided in-detail information on the effect of defects on fatigue life and FCG behaviour of metal AM components with more emphasise on L-PBF process. Ye et al. [32] and Maleki et al. [33] put effort on gathering studies related to the effect of post-processing on the fatigue properties of metal AM components. Nevertheless, fatigue and fracture of metal AM is a rapidly growing field, which requires extensive knowledge of previous works and research gaps to conduct novel experiments. Thus, frequent review papers are necessary to summarise the recent advancements in this field and guide new researchers toward the latest trend.

In this paper, a comprehensive review of recently published works on the fatigue and fracture of metal AM components, is presented. Since this study addresses the fundamental aspects of fatigue assessment and failure mechanisms, no distinctions are considered between different AM-based methods; however, efforts are made to include results from all the available AM-based processes in order to deliver a more comprehensive discussion. In Section 2, the factors that reduce fatigue life including surface roughness, defects, residual stress, and microstructural heterogeneity are discussed in detail. Section 3 highlights the effect of post-processing on fatigue life of AM materials and provides comparison with the wrought counterparts. The correlations between the AM microstructural features and fatigue crack behaviour are addressed in section 4. Section 5 covers the classification and description of fatigue life prediction models under damage-tolerant design, common defect characterisation methods, multi-stage models, and artificial intelligence-based life prediction studies. Section 6 is dedicated to fatigue life assessment of complex specimens such as notched test samples and topology-optimised functional parts. In the final section, the current status in the study of fatigue and fracture of metal AM components is demonstrated, and the potential research opportunities are highlighted.

2. Fatigue failure mechanisms in metal AM

There are four types of defects inherent to the metal AM processes that can significantly reduce the mechanical properties of AM components. Fatigue behaviour of AM components has several distinctions from the conventionally-manufactured (CM) counterparts. Complex thermodynamics and high cooling rate in AM processes as opposed to stable and slow cooling process in CM metals form large-scale heterogeneity that causes variation in FCG even in a single component [34,35]. Moreover, localised heat source and directional cooling process generates tensile residual stress that forms a pre-stressed state especially within the (sub)surface region [36]. On the other hand, large defects (i.e. 50 to 250 μm) and as-built rough surface (up to 30 μm) significantly reduce fatigue strength of AM components and shorten the service life of the components [37,38]. Several studies compared the fatigue performance of AM components with their wrought counterparts to investigate the causes for lower fatigue life in AM parts. The main reason for pre-mature failure in AM components is related to the presence of defects. Defects can reduce fatigue strength to 50% of wrought material [39]. Especially, concerning the as-built condition of AM components, the effect of each type of defect on the mechanical properties of the product should be determined. Akgun et al. [40] highlighted that the fatigue life of wrought Ti-6Al-4V was generally higher than the polished AM counterpart due to the presence of smaller defects, which required higher stress to initiate failure. Concli et al. [41] reported fairly similar fatigue endurance limit for as-machined L-PBF of 17–4PH to the wrought material, while the as-built specimens achieved about 25% lower fatigue limit. The following sub-sections deal with the cause and effect of each defect type, namely surface roughness and subsurface defects, internal defects, residual stress, and microstructural heterogeneity, from the fatigue and failure perspective and provide results in comparison to the wrought materials.

2.1. Surface roughness and sub-surface defects

Surface quality has a major impact on the mechanical performance and lifespan of metal AM components [42]. Inherent high surface roughness in metal AM components causes less fatigue life than the wrought counterparts. The severity of surface roughness of metal AM components is considerably affected by the key process parameters, namely layer thickness, hatch spacing, laser scan speed, laser power, and build angle [43]; however, several other parameters was discussed to be effective [44].

(Sub)surface defects are another concern regarding the surface integrity of metal AM parts. Sub-surface defects are similar to the internal defects in terms of size and shape; however, their severity is much higher due to higher stress concentration factor [45]. Therefore, they are classified as the surface defects rather than internal defects. These defects can be considered as deep and sharp micro-notches, which are critical spots in favour of crack initiation [46]. Figure 1(a–f) shows fatigue failure cases due to (sub)surface defects for different AM and wrought materials. As shown, the sub-surface defects are the main failure initiation locations that causes reduction in fatigue life of metal AM specimens. Therefore, regardless of the other factors, elimination of sub-surface defects can lead to a better fatigue performance, especially in the LCF regime.

Figure 1. Examples of fatigue failure from surface defects for different L-PBF and wrought materials: (a, d) Ti-6Al-4V, (b, e) SS17-4PH, and (c, f) Inconel 718 [35].

Many studies have been shown that for almost all the as-built specimens, failure initiates from the surface critical locations [42,45,47]. The most common failure mechanisms from the surface are lack of fusion (LoF) pores at free surfaces, and multiple-site crack initiations from surface roughness [48]. It was reported that the probability of LoF occurrence on the surface is between 37 to 85% [48]; thus, the as-built samples are likely to fail from the critical LoF defect on the surface. It is obvious that although the effect of surface LoF is more drastic than the surface roughness, the difference in fatigue strength is not much. In other words, the effect of a 400μm deep LoF is similar to 20μm surface roughness. Molaei et al. [49] believe that the aspect ratio (i.e. the ratio of the minor axis to the major axis) of surface irregularities is more influential than the depth of the features. As the occurrence probability of LoF defects on the surface of small-size samples is lower, it is observed that the small size sample most likely to fail from the surface roughness. On the other hand, Yadollahi et al. [50,51] observed that the effect of depth of the defect is more detrimental in comparison to the aspect ratio. Edwards et al. [52] reported lower fatigue life for vertically-built Ti-6Al-4V specimens due to higher surface roughness (Ra = 39μm) compared to horizontally-built specimens (Ra = 30μm). They also showed that the effect of internal defects is dominant in machined samples. Stern et al. [53] observed that almost all the as-built L-PBF AISI 316 uniaxial fatigue test coupons failed from the surface irregularities. Based on the provided evidence, surface roughness and surface defects are the major factors in the fatigue performance of metal AM components. Concli et al. [41] demonstrated that surface machined L-PBF 17–4PH specimens contained more scatter in HCF results compared to the as-build ones due to the uncertainty of defect distribution and failure location.

In a series of studies, Fatemi et al. [49,54,55] investigated the effect of surface roughness and internal defects on fatigue life in various loading conditions (i.e. axial, torsion, and combined). They found that the concentration of defects near the surface is detrimental to fatigue life in all loading conditions. Sanaei and Fatemi [47] confirmed for R = 1 and 0.1 that higher average surface roughness, Ra leads to lower fatigue life, as shown in Figure 2(a, b). However, many researchers agree that regardless of the defect size, sub-surface LoF defects are the most critical locations for crack initiation [3,56–58]. Thus, it is not the best choice to blame arithmetic surface roughness Ra or Sa for surface failure [59]. In fact, it was shown that the Rv or Sv, which are defined as the depth of the deepest valley on the surface, represents a better correlation between the surface measurements and fatigue data [3,60]. Lee et al. [61] performed an in-depth investigation on the as-built and half-polished specimens and carried out fatigue tests in order to determine the correlation between fatigue performance and the conventional surface roughness parameters. They first found that there are some hidden cavities under the partially-melted powders, which cannot be detected using optical measurements. They also confirmed that the Sv surface parameter can represent the correlation between the as-built surface roughness and fatigue life with a high confidence coefficient (R²= 0.99); however, for the half-polished samples the regression coefficient fell down to R²= 0.708. They proposed hybrid parameters Sv+S_mode and Sv+S_mode×S_ku×S_sk, which increased the confidence coefficient for all samples (as-built and half-polished) up to R²= 0.978. The results show a better prediction of fatigue life, as shown in Figure 2(c, d).

Figure 2. The relationship between the $\sqrt{\mathrm{Ra}}$, and fatigue life of L-PBF Ti-6Al-4V at (a) R = -1, and (b) R = 0.1 [47]; Surface roughness versus reversals to failure for: (c) Conventional roughness representation (Rv and Sv), and (d) The hybrid roughness parameters (Orange points: Sv + S_mode and blue points: Sv + S_mode×S_ku×S_sk) [61].

2.2. Internal defects

Internal defects are divided into three main types, namely porosity, LoF, and micro cracks. The generation of such defects is directly governed by the process parameters, powder quality, and machine stability. Therefore, it is crucial to understand the effect of process parameters on the formation of these defects and eliminate them as much as possible. The shape and size of these defects can drastically affect the fatigue performance of AM materials.

Porosity is generated in spherical or keyhole shapes. Spherical and keyhole porosities can be up to 80 μm in diameter and are identified as less vital due to the lower stress concentration effect [62]. On the other hand, LoF defects induce from unmelted powders can be catastrophic based on their size, and orientation. The LoF defects are irregular but it was shown that their direction is along the scan pattern [63]. This fact creates the worst-case scenario for the mechanical performance of the component because directional defects could significantly reduce the load-bearing cross-section area of the component.

Micro cracks can be induced due to inappropriate process parameter selection, low heat conductivity, or residual stress [64]. Furthermore, the effect of solid phase change, could accelerate micro crack generation during solidification. Such cracking mechanism contributes to the wide range of alloying elements with different solidus temperatures, which resulted in phase concentration, brittleness, and cracking [65].

After the elimination of surface irregularities, the effect of internal defects on fatigue life is dominant. Among internal defects, large LoF defects with sharp corners and low aspect ratios are critical [66]. Also note that the closer the defect is to the surface, the more critical the defect condition gets. In this essence, Romano et al. [67] studied the effect of deep and shallow machining (0.5 mm, and 3 mm, respectively) on the defect distribution and fatigue performance. They found that even shallow machining can improve HCF performance, while there was no further improvement for deep machining as the sub-surface defects were completely eliminated. Fleishel et al. [68] investigated the effect of EBM defects on fatigue life by intentionally altering process parameters to produce LoF defects at different locations. This conclusion is important because it shows that the size of the initial sample does not matter as long as the subsurface defects are eliminated through sufficient machining. Note that they eliminated the effect of residual stress and microstructure anisotropy by performing a two-stage heat treatment (HT) prior to the machining process. They also observed that in absence of LoF defects, even a small spherical pore (20–30 μm) can be a crack initiation site.

2.3. Build orientation

The effect of build orientation can be discussed in the course of anisotropic microstructure of metal AM components, surface roughness distinction, or the directionality of LoF defects. The overhang features and unsupported surfaces generally possess higher surface roughness [69]. Furthermore, Nezhadfar et al. [70] found that the defect content may vary depending on the build orientation. Shrestha et al. [71] investigated the effect of directional manufacturing on fatigue behaviour of the L-PBF 316L in both as-built and machined conditions. They obtained that the fatigue resistance of the horizontal specimens is higher, while the diagonal specimens possess the lowest fatigue resistance in both as-built and machined conditions. This trend is mainly derived from the high projected defect area perpendicular to the load direction, excessive surface roughness, and easier grain boundary sliding. Thus, the directional manufacturing may lead to anisotropic defect orientation, as well as anisotropic microstructural orientation. Based on their findings, build orientation has more impact on HCF, where the effect of defects in fatigue failure is significant. Doh et al. [72] showed that the vertical specimens had lower fatigue lives than the horizontal ones in the as-built condition (Figure 3(a)). It was further demonstrated that microstructural homogenisation during HT reduced the effect of directional fatigue behaviour of L-PBF maraging steel, especially after the removal of surface roughness (Figure 3(b, c)). After HT and machining (Figure 3(d)), the effect of surface roughness, heterogeneous microstructure, and residual stress was eliminated; therefore, the only effective factor was the cross-section area of the internal defects with respect to the loading direction. In this case, there was only a slight difference between the fatigue life of vertical and horizontal specimens. Note that the LCF of AM specimens was similar to the wrought material; however, in the HCF region, lower fatigue performance was obtained from the AM samples due to the effect of internal defects. By considering the effect of defects and microstructure, Yadollahi et al. [73] observed a relatively similar LCF behaviour for vertical and horizontal test samples after HT, which is a result of anisotropy compensation. Zhang et al. [74] confirmed that the fatigue life of horizontal samples is higher than vertical ones for L-PBF SS304L due to the combined effect of surface roughness, effective area of defects, residual stress, and grain orientation.

Figure 3. Experimental fatigue life data of metal AM specimen according to build orientations: (a) specimen as printed, (b) specimen as printed with heat treatment, (c) specimen as printed with machining, and (d) specimen as printed with heat-treated machining [72].

On the contrary, Xu et al. [75] observed no distinctive difference between the fatigue limit of vertical, diagonal, and horizontal samples made from AlSi10Mg during the rotary bending fatigue test. The reason for the very low fatigue limit is reported to be the initiation of multiple cracks on the surface and their coalescence, which significantly reduces the fatigue limit of the material. Bača et al. [76] showed that the vertical samples possess lower fatigue performance simply due to higher defect area perpendicular to the loading direction. Wu et al. [19] demonstrated that although the failure mechanism in vertical and horizontal L-PBF AlSi10Mg was from the (sub)surface LoFs, the horizontal samples showed higher HCF performance. The reason was larger projected defects in the vertically-produced specimens that reduced the fatigue strength, as shown in Figure 4(a, b). Beretta et al. [77] investigated the effect of as-build surface roughness of L-PBF AlSi10Mg resulted from different build orientations on fatigue life. Their results revealed a strong correlation between the build orientation, surface roughness, and fatigue life, as summarised in Figure 4(c, d). Furthermore, Parvez et al. [78] proved that the S-N curve of the diagonal specimens is somewhere between the vertical and horizontal specimens.

Figure 4. (a) Probabilistic Kitagawa-Takahashi diagram of the material described by the El-Haddad formulation considering the expected defect distribution (b) S-N curve for vertical and horizontal specimens [19]; (c) Surface textures of different series obtained by CT scans over the notch region, and (d) Fatigue test data [77].

Andreau et al. [79] showed that the size of internal defects should be 4–10 times larger than surface defects to become critical. Also noted that the crack growth rate is lower for internal defects than the surface defects due to the environmental effects [80]. The direction of LoF defects is affected by the laser movement; thus, they are mainly elongated perpendicular to the build direction, which makes the life of vertical samples shorter [30]. It is believed that by a decrease in the average critical defect size at a constant stress level, the fatigue life of metal AM components increases [81]. Identified failure mechanisms from defects are: (1) LoF pores at or near the free surface (Figure 5(a)), (2) LoF pores in the bulk (Figure 5(b)), (3) gas pores at or near the free surface (Figure 5(c)), and (4) gas pores in the bulk (Figure 5(d)) [48]. It should be noted that in the HCF regime internal defects gain importance even in presence of a rough surface due to the low-stress level. Although Du et al. [82] revealed that the failure mechanism was LoF defects on the surface in both LCF and HCF, the internal defects was the dominant failure mechanism in very high-cycle fatigue (VHCF) regime. They also showed that the failure mechanism is not dependent on the stress ratio (R) for LCF and HCF. Table 1 categorised the failure mechanisms in small and standard fatigue test samples in both as-built and machined conditions.

Figure 5. Examples of various failure mechanisms from defects for L-PBF machined specimen: (a) LoF pores at the free surface, (b) LoF pores in the bulk, (c) Gas pores at the free surface, and (d) Gas pores in the bulk [48].

Table 1. A summary of the number of specimens in which the different crack initiation mechanisms were observed for the different specimen types and sizes [48].

Geometry	LoF pore on surface	LoF pore in bulk	Gas pore on surface	Gas pore in bulk	Surface roughness
Standard size machined	10	8	2	0	0
Small size machined	7	5	4	3	0
Standard size As-built	12	0	0	0	2
Small size As-built	7	0	0	0	8

On the other hand, Solberg et al. [83] observed that the failure mechanism in high stress levels (i.e. LCF regime and even static tensile behaviour) is internal defects, while by a transition from LCF to HCF failure mechanism shifts to surface in L-PBF 316L. Note that the porosity rate of their samples was higher than the other spotted studies. Thus, a kind of competition exists between the surface and internal failure mechanisms. Syed et al. [84] observed that even though larger artificial defects (∼200 μm) were seeded within the bulk material, the majority of samples failed from the surface and sub-surface defects. A new approach was proposed by Hamidi Nasab et al. [85], which takes the effect of surface roughness and internal defects into account, simultaneously. They found that by considering a control volume that carries over 90% of maximum applied stress, and performing size analysis, the probability of failure initiation mechanism can be obtained. Their results seem satisfactory; however, they were unable to predict the location of failure initiation. Sanaei and Fatemi [81] showed that the extreme value statistics is a powerful tool in order to determine the critical defect size. Note that the fatigue data related to machined samples showed higher scatter than the as-built samples due to various mechanisms of failure [48]. To obtain more consistent results from the S-N curve, Le et al. [48] proposed to use the ‘corrected stress, S_max’ introduced in [86] through Eq. 1, where $\sqrt{\mathrm{are}{a}_i}$ is the average pore size for each defect category, and $s^{\mathrm{\prime }}$ is a non-linear weight factor related to the pore size. Figure 6(a, b) shows the uncorrected and corrected S-N curves for different pore sizes. (1) $\mathrm{Corrected}{S}_{\max }=S_{\max }{\left({\displaystyle \frac{\sqrt{\mathrm{area}}}{\mathrm{average}\sqrt{\mathrm{are}{a}_i}}}\right)}^{s^{\mathrm{\prime }}}$(1)

Figure 6. Uncorrected and corrected S-N curves of machined specimens for the crack initiation mechanism related to: (a) LoF pores on surface, and (b) LoF pores in bulk [48].

Murakami et al. [87] proposed dividing the stress amplitude, σ by the fatigue limit σ_w in order to reduce the S-N curve experimental data. Li et al. [88] formulated the improved backward statistical inference approach (ISIA) using the modified distribution coefficients for modern axle materials and weldments in order to find a better fitting parameters to describe fatigue life through the S-N curve. A more comprehensive effective stress parameter was introduced by Qu et al. [89], where $\alpha =0.226+\mathrm{HV}\times {10}^{-4}$, R is the stress ratio, $\sqrt{\mathrm{are}{a}_E}$ and $\mathrm{\Delta }{K}_E$ is the effective defect area and corresponding stress intensity factor. Obtained stress from Equation (2) could significantly reduce the S-N curve scatter resulted from the defect distribution and size. (2) $\sigma ={\displaystyle \frac{\mathrm{\Delta }{K}_E}{\mathrm{HV}\times {\left(\sqrt{\mathrm{are}{a}_E}\right)}^{\frac{1}{3}}\times {(1-R/2)}^{\alpha }}}$(2)

2.4. Residual stress

Metal AM processes use high-power laser or electron beam that travels within each layer of the component to form the whole geometry. This procedure results in localised heat accumulation, which leads to high thermal stress. This thermal stress is converted to residual stress due to very high solidification rate (∼10⁶ K/s) during the manufacturing process. Thus, process parameters gain importance in this case. Due to the uniform heating and cooling cycle in the EBM process, the product has negligible residual stress, which is not detrimental for fatigue life. On the other hand, the L-PBF process produces high tensile residual stress on the free-surfaces, which is critical for fatigue crack initiation [90]. Residual stress is in compressive form within the bulk material of L-PBF components. Note that compressive residual stress provides crack closure and extend fatigue life. Tensile residual stress on the surface can be transformed to compressive form by applying optimised surface treatment [91]. It is impossible to solely investigate the effect of residual stress due to the existence of pores in as-build samples and the stress-relieving effect of healing post-processes (e.g. HIP) after post-treatments. Leuders et al. [92] asserted that pores are responsible for the crack initiation phase, while the fatigue crack propagation is dependent on the residual stress. As they showed, the subsurface (100 μm in depth) residual stress can be up to three times higher than the surface residual stress. It is challenging to specifically identify the effect of residual stress on fatigue life due to the limitations in measuring internal residual stress. There are several HT strategies, such as VSR (Vacuum stress relief), prior to part removal that assist stress relaxation.

By comparing the fatigue performance of as-built and stress-relieved samples from an identical batch, one can obtain an estimation for the effect of residual stress on the fatigue life of metal AM parts. Note that only an estimation could be achieved due to the very low repeatability of the structural and microstructural condition of samples even in the same batch. In this case, Lai et al. [93] confirmed that the stress-relieving HT can significantly improve fatigue life by eliminating residual stress. Furthermore, they showed that the effect of stress-relieving is almost similar to machining in the case of surface residual stress removal. In their study, polished samples showed relatively lower fatigue performance, which is asserted to be due to the effect of tensile residual stress on the surface, and undoubtedly surface defects. Note that the machined + polished samples showed a large scatter due to the variation in failure mechanisms from the internal defects as discussed earlier.

2.5. Microstructural anisotropy

The complex thermodynamics during the AM processes causes large-scale microstructural heterogeneity that complicates the evaluation of the effect of microstructure on fatigue life and FCG behaviour of the AM materials [94]. Due to the localised heat on the constructing surface of the part, a temperature gradient forms within the section, which mainly dissipated along the Z axis to the build platform [95]. This phenomenon produces a columnar microstructure in line with the heat dissipation direction. Thus, directional microstructure leads to anisotropic material properties, which makes the material behaviour difficult to predict. The level of anisotropy is directly related to the input heat, which is governed by the process parameters [96]. For example, a higher cooling rate in Ti-6Al-4V alloy leads to a fully martensitic microstructure, which is not favourable from the fatigue resistance aspect [97]. Hence, many studies categorised α-phase as a type of microstructural defect due to its brittle behaviour [98]. Moreover, the β-phase was considered detrimental in the reduction of crack propagation resistance of Ti-6Al-4V alloy, especially for vertical specimens [99].

Beard et al. [100] found that the vertical L-PBF SS316L samples show better fatigue performance in the LCF regime in comparison to diagonal samples due to finer grains and shorter slip path. Liang et al. [101] showed that by decreasing the build angle from 90 to 0 degrees the fatigue performance of SS316L was increased. It was also demonstrated that the dominant failure mechanism for vertical samples was defects, while the horizontal samples tended to fail from microstructure features. Zhou et al. [102] also found the same conclusion for the WAAM Al-Mg Alloy. Ghorbanpour et al. [103] produced gradient microstructure by changing the laser power throughout the layers. It was shown that the defect generation, microstructure grain size crystallographic textures, precipitates, and Laves phases are affected by changing the laser power, which directly affected fatigue life and FCG behaviour of Inconel 718.

The scan pattern determines the sequence of re-heating at each layer; therefore, it also has significant effect on microstructural evolution and fatigue life. Yu et al. [104] employed zigzag laser scanning strategy and cross-hatching layer scanning strategy, and obtained different grain structures. It was shown that the melt pool boundaries have better strain compatibility in comparison to the grain boundaries and is less susceptible to fatigue crack initiation. In most cases, individual laser tracks simultaneously contain columnar and equiaxed grains that are connected to the neighbouring tracks. Pham et al. [105] reported large columnar grain structure for the middle region of each laser tracks that was elongated throughout several layers in the build direction. By travelling from the middle to the melt pool boundaries columnar grains are getting smaller and eventually transformed to equiaxed grains. The reason for this phenomenon is the higher cooling rate of melt pool boundaries that leads to cellular or equiaxed grain structures [106]. Since the columnar grains have more FCG resistivity in the perpendicular direction, they can promote fatigue life. On the other hand, cellular grain structure has more ductility that can also delay fatigue crack initiation and prolong the fatigue life. Therefore, both grain structures work together to enhance fatigue life of AM components to even higher number of cycles than the wrought counterparts. In this regard, Cui et al. [107] showed superior fatigue strength of AM SS316L came from the pre-existing high-density dislocations within the cellular microstructure. Nevertheless, due to the complex heat distribution during the AM process, it is not always possible to account for all the microstructural variations in the case of fatigue life determination; thus, a representative microstructure could be nominated from the critical section of the specimen for analysis.

The effect of microstructural anisotropy gains more significance in HCF due to the major contribution of microstructure in fatigue life. Nicoletto [108] proposed a test procedure based on the Schenk–Erlinger cyclic plane-bending machine to capture the effect of directionality on the fatigue life with lower cost and effort. The obtained results were further compared to the results from the literature and showed good agreement. Zhang et al. [109] employed various HT strategies in order to study the effect of microstructure on the fatigue life of L-PBF Ti-6Al-4V. It was demonstrated that all the applied HTs promoted fatigue performance especially in the LCF regime. Unlike the HCF regime, large scatter was observed in the LCF regime for all the HT strategies, which represented the effect of defects on the pre-mature failure of samples.

In the absence of surface and internal defects, microstructure inhomogeneity is governing the fatigue performance; however, the effect of microstructure anisotropy is less pronounced in the presence of defects [52]. For example, in the case of post-processed AM Ti-6AL-4V with no critical surface and internal defects, needle-like martensitic facets and clusters can cause fatigue crack initiation at the VHCF regime [98]. Figure 7(a–d) shows a fatigue failure due to the unfavourable microstructural conditions in L-PBF Ti-6AL-4V alloy. Liu et al. [110] provided in-depth understanding on the fatigue crack initiation and fatigue life of Ti-6Al-4V in the VHCF regime. Crack initiation location was identified to be the internal defects and microstructural impurities that contained fine granular area (FGA). Note that the type of fatigue test is contributing to the failure mechanism. Sun et al. [111] reported lower fatigue performance in the VHCF regime for the rotary bending fatigue test in comparison with ultrasonic fatigue testing. According to their study, during the rotary bending fatigue test, cracks tend to initiate from the surface, while in the ultrasonic fatigue test internal microstructural features like fish-eye-like pattern or fine granular area morphology is responsible for crack initiation. It should be noted that the microstructure anisotropy of metal AM components have almost no impact on fatigue crack initiation; however, fatigue crack propagation may significantly affect by the microstructural properties of the material.

Figure 7. Internal fatigue crack initiation from inclined α-phases in the VHCF regime. The crack initiating clusters of α-phase: (a, b) Crack initiation at 20μm beneath the surface (σ_a = 471 MPa, N_f = 1.8×10⁸), (c, d) Internal crack initiation (σ_a= 471 MPa, N_f = 4.6×10⁸) [98].

It should be noted that by close control on defect induction and microstructure evolution, it is possible to obtain superior fatigue life, especially in the HCF regime. Chen et al. [112] showed how fine grain formation in 13Cr4Ni Martensitic Stainless Steel during WAAM process lead to higher HCF life in comparison to forged counterparts. Zhang et al. [113] obtained higher fatigue life by refining grain structure through addition of boron to titanium alloy when producing L-DED samples. The reason for higher fatigue life was the crack initiation resistivity of fine grain structure. Razavi and Berto [114] also reported higher fatigue life for L-DED Ti-6Al-4V in comparison to forged alloy due to the presence of fine basket-weave α and columnar β phases.

3. Effect of post-processing on fatigue life

Post-treatment methods can be divided into surface-based treatments and bulk treatments. Figure 8 demonstrates the available surface-based treatments. Bulk post-treatments include any type of HT strategies and the hot isostatic pressing (HIP) process. In general, any action that reduces component’s surface roughness or internal defects has a positive effect on fatigue life. For example, it was shown that machining can improve fatigue strength up to 30 and 50 percent in bending and axial fatigue tests, respectively, while polished surfaces had been shown to be even more effective than machining [52,115]. Nakatani et al. [116] showed that polished HIPed specimens possess nearly three times higher fatigue limit than the as-built samples. Lesseur et al. [117] reported that the artificial defects within the bulk material of L-PBF and EBM specimens were completely eliminated after the HIP process; however, it was not effective for near-surface defects. In the LCF regime, the main failure mechanism is from the surface; thus, by removing surface roughness and residual stress through machining, LCF can be significantly improved [118]. Konečná et al. [119] observed improved LCF and HCF performance after grinding. Another study showed that the sand blasting (SB) process is more effective than micromachining and grinding on the fatigue performance of Ti-6Al-4V parts due to applying compressive residual stress on the surface [120]. Yu et al. [121] also showed that the SB has impact on LCF and HCF regimes, and convert the main fracture mechanism from surface to the subsurface defects.

Figure 8. Surface post-treatment methods based on their characteristics [33].

From another approach, any action that generates obstacles on the crack growth path can improve the fatigue performance of metal AM components. In this case, generating surface and subsurface compressive residual stress can be helpful in preventing early crack initiation. For instance, shot peening (SP) of L-PBF AlSi10Mg showed higher surface microhardness and rotating HCF life [122]. Balbaa et al. [123] also revealed that the SP process shows its merit in HCF regime of L-PBF Inconel 625 and Inconel 718. Furthermore, Jin et al. [124] found that the laser shock peening (LSP) process has significant impact on HCF behaviour of EBM Ti–6Al–4, while it has minor effect on LCF. Figure 9(c, d) show the generated residual stress and resulting fatigue life of as-built, HIPed, SPed, and tribo-finished (TFed) Ti-6Al-4V material produced via L-PBF, respectively. It is obvious that SP has also a significant effect on LCF. Furthermore, electropolished samples showed the same improvement for both LCF and HCF regimes. TF process had similar effect as per HIP process; however, it is important to understand the differences in failure mechanisms. In another study, SPed specimen was compared to chemically-polished (CP), laser polished (LP), and as-built specimens [125]. According to their results, SPed specimens possess the highest fatigue limit, and after that LPed and CPed specimens failed at slightly lower stresses, while the as-built specimens showed a relatively much lower fatigue limit stress (See Figure 9(a)). The ultrasonic nano-crystal surface modification (UNSM) method can also promote fatigue performance as shown in Figure 9(b) [126]. This method has significant impact on LCF due to the generation of compressive residual stress on the surface, as well as closing surface defects. Karimbaev et al. [127] showed that the UNSM method also has positive effect on HCF behaviour of laser metal deposition (LMD) Inconel 718. Based on the fractographic images in Figure 9(e), after TF and electropolishing, the failure was still initiated from the surface; however, the residual compressive stress after SP eliminates surface crack initiation. Persenot et al. [128] reported a 60% increase in fatigue strength of EBMed Ti-6Al-4V after 30 minutes of chemical etching due to the surface roughness reduction. Chemical polishing is also proved to be effective in fatigue life improvement up to 60% regarding the duration and the type of chemical solution [129].

Figure 9. (a) fatigue behaviour after CP, SP and LP [125]; (b) S–N curves from rotation bending fatigue tests of AM Ti-6Al-4V before and after UNSM [126]; (c) residual stress distribution, (d) S-N curves, and (e) fractographic SEM images for as-built, TFed, electropolished, and SPed samples [130].

Based on a comprehensive study by Kahlin et al. [131], a wide range of fatigue limit data for various post-treated and as-built L-PBF and EBM specimens were gathered. They confirmed that the as-built specimens cannot satisfy the expectations of wrought materials; however, even a single post-treatment strategy can boost the fatigue performance of metal AM parts. Among all post-treatment methods, the combination of machining and HIP showed the highest effectiveness. It is obvious that this combination eliminates the surface roughness and surface defects, as well as the internal defects without any significant changes in microstructure. When machining is not applicable, SP and SB can provide a very smooth surface roughness along with compressive residual stress, which completely eliminates the crack initiation from the surface. Aside from that, SP and solo LSP can be effective to some extent. On the other hand, Kahlin et al. [131] observed a lower fatigue limit for LPed specimens even in comparison with the as-built Ti-6Al-4V specimens. The reason is reported to be a result of near-surface phase transformation to martensitic ά without the existence of the β phase, which causes embrittlement in the near-surface region. As the notch sensitivity is higher for the high-hardness materials, the risk of crack initiation dramatically increased. It is also stated that the laser re-melting has a positive impact on fatigue life; however, the degree of improvement requires in-depth study. Note that due to the scatter in data, it is not possible to distinguish which post-processing strategy had higher improvement in LCF or HCF. Uzan et al. [122] showed that mechanical or electrolyte polishing after SP can improve HCF, it had slight effect on LCF regime.

Surface-based post-treatments are mainly employed in order to improve surface roughness, and preferably induce compressive surface residual stress, which reduces crack initiation probability from the surface. LPS and SP are considered the most effective surface-based methods in order to improve fatigue performance as they can reduce surface roughness, as well as generating compressive residual stress. Chemical-based treatments are also effective in surface roughness reduction but their contribution to fatigue life enhancement is not fully addressed. LP may not be a wise choice for Ti-6Al-4V due to the local microstructural evolution and high hardness generation, which leads to a brittle microstructure and lower fatigue life. Novel surface finishing methods such as dry mechanical-electrochemical polishing or magnetic abrasive flow machining are efficient, while they are not limited by complexity of components.

Bulk HT strategies for AM materials can be divided into four categories: (1) Stress-relieving annealing, (2) recrystallization (homogenisation), (3) solution treatment, and (4) aging. The main function of these processes is modifying the microstructure and eliminating microstructural anisotropy, as well as neutralising the residual stress. Based on specific requirements, researchers employed these heat treatments in order to achieve their desirable microstructure and mechanical properties.

Leuders et al. [92] found that HT can extend the threshold stress intensity factor of Ti-6Al-4V from 1.4 MPa.m^0.5–6.1 MPa.m^0.5 when a suitable temperature was set. Their results also showed that the mean fatigue life increased from 27000 cycles to 93000 cycles for HT at 800°C and 290000 cycles for HT at 1050°C. In the case of aging post-treatment, Solberg et al. [132] found that a multi-stage HT strategy (‘first 1 hour at 1095°C followed by air cooling to room temperature, then double ageing, first 8 hours at 720°C followed by furnace cooling at 50°C/h until 620°C and aged for 8 hours’) can improve HCF behaviour of the L-PBF Inconel 718. In the case of L-DED method, Ren et al. [133] reported improvement in LCF behaviour of Ti-6Al-4V after HT. On the other hand, there are studies that showed HT has no significant impact on fatigue life. In general, proper HT is beneficial for fatigue life extension unless surface roughness remains at the as-built condition. Balachandramurthi et al. [134] reported no fatigue life improvement after a multistage HT strategy due to high surface roughness and internal defects. However, near-wrought fatigue performance was obtained after performing deep machining (6 mm), followed by the mentioned complex HTand HIP. Yadollahi et al. [35] observed no improvement in HCF behaviour of stainless steel 17-4 after solution annealing and peak-aging. The reason is reported to be the existence of large defects within the sub-surface region of the material.

There are also several cases that reported decrease in fatigue performance after HT. Leuders et al. [135] showed that HT can extend the ductility of L-PBF Ti-6Al-4V; however, it has negative impact on the HCF behaviour of the material due to significant microstructural changes. They also observed negative effect of the HIP process on the tensile and HCF of the L-PBF 316L in comparison with the as-built condition due to the microstructure evolution. Similar results were obtained for Ti-6Al-4V and 316L by Cutolo et al. [136], as shown in Figure 10(a, b). Zhang et al. [137] reported that various HT strategies changed the size and morphology of Si element, which leads to a decrease in fatigue property of L-PBF AlSi10Mg. However, the HIP process showed a significant improvement in the HCF regime (see Figure 10(c, d)) [138]. In the case of LCF, Aydinoz et al. [139] showed that the HIP process has no significant impact on the fatigue life of L-PBF Inconel 718 due to undesirable changes in microstructure. Their results indicate that it is important to employ the HIP process at the appropriate temperature and pressure to minimise the internal defects, as well as not affect the microstructure. Günther et al. [98] showed that fatigue performance of HIPed Ti-6Al-4V is considerably higher due to the pore closure effect, and also comparable with the wrought material in the VHCF region. Furthermore, based on the mentioned study by Leuders et al. [92], HIPed Ti-6Al-4V did not fail after 2×10⁶ cycles at 600 MPa. Based on the recommendations notified by Sanaei and Fatemi [30], the HIP process should be performed at lower temperatures and higher pressure. HIP process is also capable of eliminating the effect of directional properties. Note that the HIP process may not also be effective when the failure mechanism is from the surface [41,140]. As demonstrated by Molaei et al. [55], combination of machining and HIP can eliminate the effect of down-skin surface roughness, as well as directional microstructure, and obtain wrought-like fatigue performance for L-PBF Ti-6Al-4V material. Gheysen et al. [141] also reported exceptional fatigue life improvement for L-PBF Al-Mg alloy after the HIP. Qin et al. [142] witnessed significant HCF improvement after the HIP process on the L-PBF Al–4.74Mg–0.70Sc–0.32Zr alloy as a result of defect reduction.

Figure 10. Effect of HT and HIP on fatigue performance of different materials: (a, b) HT and HIP for Ti-6Al-4V and 316L [136]; (c) HT for L-PBF AlSi10Mg [137]; (d) HIP for L-PBF AlSi10Mg [138].

To summarise the effect of bulk HT on the fatigue life of metal AM structures, it can be concluded that every HT strategy that leads to an increase in the ductility of the material can improve LCF, while it damages HCF due to the recrystallization effect. Nevertheless, recrystallization is beneficial for obtaining isotropic microstructure. Moreover, HT does not have any impact on defects; therefore, only the HIP process with optimised parameters can significantly delay failure by extending the crack initiation regime, especially in HCF. For LCF design, the crack propagation regime is dominant; therefore, it is more favourable to preserve the equiaxed and occasional columnar microstructure. Stress-relieving HT eliminates tensile residual stress and removes the pre-load at the crack tip. Aging treatment causes solid-solution precipitation that aids fatigue performance by increasing the strength and crack growth resistivity of the material. The optimum HT strategy should be designed based on the material in a way to eliminate residual stress and directional properties, as well as to stabilise secondary phases and brittle intermetallics. Thus, a tailored HT strategy should be determined for each material. The best strategy is to employ a surface-based treatment based on the availability and applicability (preferably those which produces compressive residual stress), along with HIP process in order to eliminate both surface and bulk defects. Only in such condition a wrought-like performance can be expected.

Table 2 gives an insight to the current stage in data availability on fatigue life of post-processed metal AM components. Although there have been several studies on the effect of various post-processing strategies on the surface roughness and defect condition of metal AM components, the actual relationship between the selected post-process and fatigue life of the component is unclear. This lack of information amplifies by evaluating contradicting results. Note that in some cases no improvement observed after some post-treatments. The reason is that the fatigue behaviour of metal AM parts depends on several parameters and the exact relationship between the parameters and fatigue life could not be easily formulated. Thus, there are several opportunities to study the effect of each post-treatment technique in detail to understand the actual contribution of each method to the fatigue performance of the metal AM components.

Table 2. Summary of the available post-processing strategies for bulk metal AM components along with the capabilities in removing surface defects and their available test data.

Principle	Method	Achievable surface roughness (Ra)	Surface compressive stress	Complex geometries	Effect on LCF Effect on HCF	Effect on FCG	Fatigue limit (L-PBF)	References
Machining-based methods	Milling	0.3 μm	no	no	yes yes	no	125-200%	[52,54,143]
	Grinding	8.6 nm	no	no	yes yes	no	64%	[119]
Rotary-based methods	Tumble finishing (tribofinishing)	18.9 μm	yes	applicable	no yes	no	50%	[125]
	Dry mechanical-electrochemical polishing	0.8 μm	no	applicable	no information	no	no	[144]
Polishing-based methods	Conventional polishing	0.1-0.16 μm	no	no	yes yes	no	70%	[115,116,143]
	Magnetically driven abrasive polishing	4 μm	no	applicable	no information	no	no	[145]
	Hydrodynamic cavitation abrasive finishing (HCAF)	44 μm	no	applicable	no information	no	no	[146]
	Ultrasonic cavitation abrasive finishing (UCAF)	3.8 μm	no	applicable	yes yes	no	no	[147]
Laser-based methods	Laser micro machining	0.82 μm	no	no	no information	no	no	[148]
Chemical-based methods	Chemical etching	2 μm	no	applicable	yes yes	no	40-60%	[128]
	Chemical machining	2 μm	no	applicable	no information	no	no	[149]
	Chemical brightening	6 μm	no	applicable	no information	no	no	[150]
	Chemical polishing	0.29-0.51 μm	no	applicable	yes yes	no	60%	[122]
	Electrochemical polishing (ECP)	0.10-1.30 μm	no	applicable	no information	no	no	[151]
Impact-based methods	Shot peening (SP)	4.5 μm	yes	no	yes yes	yes	64-100%	[122,123]
	Sandblasting (SB)	10.1 μm	yes	no	yes yes	yes	100%	[125]
	Cavitation peening (CP)	17 μm	yes	no	yes yes	no information	100%	[125]
	Ultrasonic nanocrystal surface modification (UNSM)	9.0 μm	yes	no	yes yes	no information	200%	[127]
	Laser shock peening (LSP)	no information	yes	no	yes yes	yes	20%	[124]
	Laser re-melting	1.5 μm	no	no	no information	yes	no	[152]
	Laser polishing (LP)	1.77 μm	no	no	no no	no information	-50%	[131]
	Heat treatment	-	no	applicable	yes yes	yes	20-70%	[92,153]
	Hot isostatic pressing (HIP)	-	no	applicable	yes yes	yes	200%	[154]

4. Effect of defects on fatigue crack growth

Metal AM components should be designed in a way to perform their tasks even in presence of structural defects; therefore, damage tolerance analysis of components gains importance. All the inherent defects in metal AM parts contribute to the fatigue crack behaviour of these materials. Brandão et al. [155] compared FCG rate and the threshold stress intensity factor, Δk_th of L-PBF Ti-6Al-4V with forged, bar, and cast alloys. Their results revealed that the FCG rate is fairly similar for L-PBF, forged, and cast alloys, while it is slower than the bar alloy. Edwards et al. [156] observed a slower FCG rate for EBM Ti-6Al-4V and L-PBF Ti-6Al-4V in the Paris region compared to the wrought counterpart as a result of a fine and columnar grain structure. On the contrary, Leuders et al. [156,157] reported a faster FCG rate for as-built L-PBF Ti-6Al-4V in comparison with the conventional material. They revealed that porosity and residual stress are responsible for faster FCG rate, as restated in [158]. The reason for this inconsistency is the sensitivity of the macro and microstructural features to the process parameters (e.g. laser power and speed, layer thickness, scan pattern, etc.). Thus, similar FCG resistance to the wrought materials (or even better) can be obtained for metal AM parts by performing effective post-processing such as the HIP and stress-relieving HT to eliminate internal defects and residual stress, while maintaining the fine microstructure [30].

Surface roughness seems to have no effect on the FCG rate. Zhang et al. [159] reported no significant change in the FCG rate of as-built, heat-treated, and HIPed samples, before and after surface machining, as shown in Figure 11(c–e). However, after HT or HIP (Figure 11(a, b), the FCG rate was significantly reduced due to the stress relaxation defect elimination. On the other hand, Yang et al. [160] showed that the effect of HT on the FCG can also be destructive if an inappropriate HT strategy is taken.

Figure 11. FCG rate versus Δk_th for Ti-6Al-4V in different conditions [159].

In general, internal defects have a slight impact on the FCG direction and FCG rate; however, large LoF defects may cause multiple-site crack initiation, which leads to crack coalescence and significantly increases the FCG rate, as previously observed by Molaei et al. [161] for fatigue testing under axial-torsion loading condition. VanSickle et al. [162] reported that fatigue cracks tend to propagate towards the nearby voids. Furthermore, they observed premature failure due to the concentration of defect clusters near the crack tip. In contrast, Leuders et al. [92] showed that the effect of pores is not significant on the FCG threshold and FCG rate by comparing the heat-treated and HIPed samples. Thus, although the clusters of defects can accelerate the FCG, their impact is less than residual stress and microstructure. Several studies [159,163,164] verified that the LoF defects do not have any significant effect on the FCG rate except minor acceleration in the vicinity of defects. Thus, the significant role of LoF defects is their contribution to early-stage fatigue crack initiation, as well as producing scatter in test data. Also note that the FCG rate is lower for cracks initiated from internal defects than the surface defects due to the environmental effects [80]. Andreau et al. [165] also tested this argument by comparing the FCG results under air and argon testing conditions. It was found that the crack propagation mechanism was intergranular for air atmosphere tests, which represented open cracks. On the other hand, testing under argon gas showed that the crack propagation mechanism from internal defects was intragranular. Poulin et al. [166] reported crack retardation as a result of a large and elongated LoF defect perpendicular to the FCG path for L-PBF Inconel 625 with 3% porosity. Their findings also revealed that the FCG rate in the Paris-Erdogan regime is identical for HIPed and stress-relieved vertical samples. Although the projected area of defects was maximum in this direction, the same FCG behaviour was observed after eliminating the effect of residual stress, which again emphasises the negligibility of the effect of defects on the FCG rate.

Residual stress seems to play a major role in FCG behaviour of the AM structures. As previously demonstrated, residual stress within the bulk AM components is in compressive form; thus, it has a crack closure effect on the crack tip. Abdul Syed et al. [167] showed that the stress-relieving HT leads to a lower FCG rate. Leuders et al. [92] believe that pores are responsible for the crack initiation phase, while the fatigue crack propagation is dependent on the state of residual stress. As they showed that the subsurface residual stress (approximately up to 100 μm in depth) can be up to three times higher than the surface residual stress, it is challenging to actually identify the effect of residual stress on fatigue life due to the limitations of measuring internal residual stress. Based on a study by Zhang et al. [159], EBM Ti-6Al-4V products that were manufactured under vacuum and at 700°C, contained almost no residual stress, and thus, near-cast fracture toughness (102 MPa.m^0.5), and similar FCG as heat-treated and HIPed L-PBF Ti-6Al-4V were measured. Santos et al. [168] reported a lower FCG rate for heat-treated L-PBF maraging steel. Based on their findings, HT decreased FCG rate by relaxing residual stress, as well as grain orientation correction.

Furthermore, the microstructure effect is also significant in the case of FCG behaviour of the AM materials [92]. Nezhadfar et al. [169] reported transformation of mode I FCG to mode II as a result of columnar grains elongated parallel to the loading direction, as shown in Figure 12(a–e). VanSickle et al. [162] also proved that the FCG direction is along the ά laths and deflect at prior β grain boundaries. Xu et al. [170] observed a zigzag FCG path in the small-crack growth region due to the basket-weave α+β microstructure in L-PBF Ti-6Al-4V; however, the effect of microstructure anisotropy can be ignored in the long-crack growth region. Santos et al. [168] also reported a zigzag fashion with a width of one or two grain size for FCG of as-built maraging steel, which reveals that the crack propagated throughout the boundaries of the deposited layers. Tarik Hasib et al. [171] showed that the martensitic microstructure in Ti-6Al-4V only affects the FCG resistance at growth rates less than ∼10⁻⁷ mm/cycle. Furthermore, they proved that the larger the martensitic lath thickness is, the higher the FCG resistance gets. However, for some alloys like AlSi12, Siddique et al. [172] showed that the grain coarsening, which occurred by heating the build platform during manufacturing, does not have any effect on the FCG rate in the Paris region, while it can improve fatigue crack resistance in stage I, which is probably because of lower tensile residual stress in the subsurface region.

Figure 12. (a) Schematic of crack growth behaviour through columnar grains at location 1 and 2 of L-PBF 17-4PH, (b, c) Fracture surface at location 1, (d, e) Fracture surface at location 2 [169].

Riemer et al. [173] and Leuders et al. [92] studied the effect of microstructure orientation on FCG of L-PBF 316L. They found a close correlation between the FCG rate, FCG direction, and microstructure orientation. They also showed that the threshold stress intensity factor is higher when the FCG direction is elongated along the grain boundaries (i.e. parallel to the build direction). Thus, the FCG rate is faster in vertical samples. As shown in Figure 13(a–d), FCG rate decreased, when the crack direction is parallel to the build direction due to the lower grain boundary spacing. Note that based on their microstructural investigations after HT at 650°C no significant changes occurred in terms of grain size and orientation of L-PBF 316L; thus, the same FCG behaviour was observed for the as-built and heat-treated samples. For L-PBF Ti-6Al-4V, HT at 850°C increased threshold stress intensity due to the elimination of α phase, however it almost had no effect on FCG rate. After the HIP, FCG rate was decreased and higher threshold stress intensity was achieved. On the other hand, after the HIP process at 1150°C, recrystallization occurred and higher FCG rate was observed. Hu et al. [174] and Galarraga et al. [175] showed that the FCG rate for the horizontal L-PBF Inconel 625 samples are faster than the vertical counterparts due to the elongated grains in vertical samples, which makes it harder for the crack to propagate. Sun et al. [176] reported similar FCG for the vertical and horizontal samples, while the diagonal sample showed a slower FCG rate. Thus, FCG depends on the build orientation, material type, grain size and orientation.

Figure 13. FCG curves for L-PBF 316L in different conditions: (a) Perpendicular to the build direction, and (b) Parallel to the build direction [173]; FCG curves for L-PBF Ti-6Al-4V in different conditions: (c) Perpendicular to the build direction, and (d) Parallel to the build direction [92].

Fracture toughness is the resistivity of the material toward crack propagation. It was shown that the fracture toughness increases by an increase in the α lamella width for Ti-6Al-4V alloy due to the existence of larger barriers on the crack propagation path [177]. Zhang et al. [159] showed that the fracture toughness of L-PBF Ti-6Al-4V could be considerably improved by stress-relaxation and microstructure evolution. Based on their experiments, HT and HIP can increase fracture toughness from 35.9 to 46.5 MPa.m^0.5 to 120.18–135.98 MPa.m^0.5, and 115.11–122.92 MPa.m^0.5, respectively, which are higher than the wrought and cast Ti-6Al-4V (approximately 65 MPa.m^0.5 and 107–109 MPa.m^0.5, respectively) [178]. In the case of Inconel 718, FCG resistance of L-PBF samples is relatively lower than the wrought counterparts. The lower Δk_th in L-PBF samples contributes to a lower boron content, smaller grain size, and residual stress [179]. Surprisingly, the effect of defect closure during the HIP process seems to have no positive impact on fracture toughness, while grain morphology and build orientation affect the fracture toughness and FCG direction [180]. Edwards et al. [157] showed that the fracture toughness is higher when the crack is perpendicular to the build direction. Thus, the microstructure grain size and orientation are the most influential factors that affecting fracture toughness of metal AM components. Fracture toughness can also be determined using finite element analysis (FEM). Kalita and Jayaganthan [181] employed ABAQUS software to determine fracture toughness and J-integral for AM 17-4PH stainless steel samples using two-dimensional and three-dimensional elastic-plastic simulation and reached a good agreement with the experimental results.

FCG behaviour of metallic materials can be described through linear elastic fracture mechanics (LEFM) equations. As demonstrated earlier, Paris law is applicable only for the steady-state crack growth, while there are other equations capable of representing the behaviour of material in all the fatigue failure regimes. The NASGRO equation is one of the most common methods to describe the crack growth behaviour with respect to the number of cycles. The NASGRO equation also considers the stress ratio, which provides a more accurate results in comparison to the Paris law. This equation has been employed for several AM materials in the literature. Jones et al. [182] applied the NASGRO equation to describe FCG of AM Ti-6Al-4V and Milled Annealed Ti-6Al-4V, and found that both materials have fairly the same crack growth behaviour. Iliopoulos et al. [183] also successfully represented the FCG of AM Ti-6Al-4V, SS316L, and AerMet 100 steel using the NASGRO equation. Macallister et al. [184] investigated the NASGRO parameters for L-PBF Ti-6Al-4V in the as-built, stress-relieved, and duplex annealed state in various directions and highlighted that the effect of material anisotropy can be well-described through different NASGRO parameters. The utilisation of NASGRO equation in defect-based modelling of fatigue life will be discussed in the following sections.

5. Fatigue models for metal additive manufacturing

The study of fatigue behaviour for metal AM components is challenging due to the complex geometry of components, unpredictable defect occurrence, directional grain orientation, and complex state of residual stress. Due to the difficulties in finding the critical section in terms of defect content, residual stress, and surface roughness, a clear guideline for production of test coupons that correctly resembles the manufacturing conditions of actual component is necessary. NASA recently developed a set of standards for the components that are produced via the L-PBF process for spaceflight applications in which they recommended manufacturing of some tensile and fatigue test coupons in the same batch of actual components as the witness coupons for testing and performance evaluation [164]. However, it is not possible to accurately estimate the integrity of the actual part from a few simple specimens. Therefore, in general, conventional methods cannot accurately determine the life of metal AM components. Countless studies have been done on metal AM samples in order to establish S-N curves for various materials. However, due to the randomness of structural and microstructural defects, a unified conclusion has not been drawn yet. A more accurate approach is to develop phenomenological and empirical models that take the effect of metal AM’s unique features into account in order to estimate fatigue life. In this section, available models are categorised based on the logic behind them and proper discussions are provided to explain the current status in terms of accuracy and applicability.

5.1. Phenomenological and empirical models

Due to the inevitable presence of defects and their negative impact on the fatigue life of metal AM components, defect-based models are developed to take the effect of size and location of defects on fatigue life into account. This approach was mainly developed due to the lack of information that can be obtained from a typical S-N curve. Many researchers concluded that a defect-based fatigue model in the frame of LEFM would be capable of predicting fatigue life of metal AM components accurately [3,185]. They believe that the effect of defects and surface roughness are detrimental; thus, stress-life and strain-life approaches cannot fully describe the fatigue life of metal AM components. Berrios et al. [186] proposed a procedure to determine the NASGRO parameters for mixed-mode loading through a hybrid experimental and numerical method. Gupta et al. [187] employed the NASGRO equation to estimate the FCG behaviour of short crack via ANSYS SMART. Ferreira et al. [188] modelled cyclic plastic deformation for L-PBF Ti-6Al-4V using FEM and evaluated the sensitivity of the model to the stress ratio. Thus, FEM is an efficient tool for determining LEFM-based parameters of the model.

A semi-empirical fracture mechanics-based model had been developed by Murakami et al. [189,190] in 1985 that considered the effect of defect size and location for the determination of fatigue life. This model was first developed for low and medium hardness steels, and later, proved to be applicable for other alloys such as Ti-6Al-4V or Inconel 718 with minor changes [116,191–193]. Based on this approach, the fatigue limit of steels with HV<400 can be determined from the square root of the area of the projected critical defect perpendicular to the loading direction, and the hardness of the material as an indicator for mechanical and microstructural properties of the material, as shown in Equation (3). C₁ is an indication for the location of the critical defect and its value is 1.43, 1.41, or 1.56 for surface defects (or surface roughness), defects with contact to the surface, and internal defects, respectively. This approach requires the identification of the most critical defect at which the crack initiation has started. According to the LEFM, the most critical defect is the one with the highest stress intensity factor, which is the largest LoF defect that would probably occur within the surface or subsurface of the specimen. As will be discussed, the distribution of the maximum defect can be estimated using the statistical methods such as the Gumbel extreme value distribution function [190]. (3) ${\sigma }_w={\displaystyle \frac{C_1(\mathrm{HV}+120)}{{\left(\sqrt{\mathrm{area}}\right)}^{\frac{1}{6}}}}$(3)

It is also possible to estimate the threshold stress intensity factor through this method, as shown in Equation (4), where Y is equal to 0.65 for surface defects, and 0.5 for internal defects. Note that the effective defect size should be considered according to Figure 14. (4) $\mathrm{\Delta }K=Y\mathrm{\Delta \sigma }\sqrt{\pi \sqrt{\mathrm{area}}}$(4)

Figure 14. Regularisation criteria for critical defects in fatigue modelling: (a) a surface defect, (b) a near-surface defect, (c) multiple surface defects, and (d) multiple near-surface defects [17].

Furthermore, the NASGRO equation can be modified to include Murakami’s $\sqrt{\mathrm{area}}$ approach: (5) $N_{\mathrm{LC}}={\int }_{a_i}^{a_c}\left\{{\left(1-\frac{\mathrm{\Delta }{K}_{\mathrm{th}}}{\mathrm{\Delta }K}\right)}^{-p}{C}^{-1}{\left[\left(\frac{1-f}{1-R}\right)\mathrm{\Delta }K\right]}^{-m}{\left(1-\frac{K_{\max }}{K_{\mathrm{IC}}}\right)}^q\right\}\mathrm{da}$(5) where $a_c$ and $a_i$ are the final and initial crack length, $f$ is the crack opening function [194], R is the stress ratio, C, m, p, q are the fitting parameters according to the FCG rate curve, and $\mathrm{\Delta }K$ is the stress intensity factor. According to the Murakami’s approach, $a_i$ is the largest defect that initiates the crack propagation. It was shown that the performance of the NASGRO equation can be improved for short crack growth by considering the Murakami’s $\sqrt{\mathrm{area}}$ parameter [194].

This method is also applicable for metal AM samples. Hu et al. [185] showed that using Equation (4) instead of global applied stress, can reduce scatter of experimental test data in the S-N curve because the stress intensity factor considers defect size and location. It is also highlighted that the effect of the crack tip plastic zone can be captured as a part of the initial crack size ($a_i=0.5d+r_p)$ [185]. Masuo et al. [140] and Yamashita et al. [193] used Murakami’s method for L-PBF Ti-6Al-4V and Inconel 718, respectively, for predicting the lower band of fatigue limit. Nevertheless, this method lacks reliability when the failure mechanism is LoF defects, because it is not considering stress concentration due to the sharp corners of the defects. Based on this method, the effective area of defects is presented via a spherical estimation of the actual defect, as shown in Figure 14(a–d). Gunther et al. [98] employed the Murakami’s approach along with the Weibull statistical method to estimate the effect of defects on fatigue life and achieved reasonable accuracy. Sheridan et al. [195] combined the Murakami’s equations with Paris law and obtained a defect-based model for fatigue life of L-PBF Inconel 718. Romano et al. [164] showed that the Murakami’s approach is a precise and robust method in order to predict the initial failure location by knowing the $\sqrt{\mathrm{area}}$ parameter, location of the defect (i.e. surface or internal), and the effective stress within the cross-section of the defect. Note that this method may not be capable of considering the effect of small-sized defects exist in HIPed samples [196]. Ogawahara and Sasaki [197] evaluate the cross-section of fatigue test samples by cutting and employing the Gumbel distribution curves to identify the largest internal defect. They further used a modified version of the Murakami’s equation to estimate fatigue limit of the L-PBF Inconel 718. Yamashita et al. [193] also applied the Murakami’s parameter to establish a relationship between the critical defect size and fatigue life of the L-PBF Inconel 718. Rigon and Meneghetti [198] proposed an empirical bi-parametric model based on the grain size and the Vickers hardness (HV) value to estimate the fully-reversed stress intensity factor for long cracks, for wrought and AM steel samples. Beretta et al. [199] proved that the Murakami’s approach is applicable for AlSi10Mg and Ti-6Al-4V produced by either AM or conventional methods.

Further modifications to the equivalent defect size have been done by other researchers. Yin and Li [200] came up with a novel model based on the Murakami’s approach that took advantage of fracture mechanics phenomenon and fatigue limit of the materials to determine the number of cycles to failure for defined stress amplitude. Muhammad et al. [201] showed that the _Murakami’s $\sqrt{\mathrm{area}}$ for surface defects of HT SS17-4PH in as-built and machined surface conditions can be estimated as $d\sqrt{10}$, where d is the width of the area covering the post-contour process on the circular fracture surface of the specimen (typically between 60 and 80 μm for L-PBF). Liang et al. [101] used the square root of the product of minimum and maximum fretting dimensions of the maximum defect as the equivalent defect size. Dastgerdi et al. [202] proposed $\left(\sqrt{\mathrm{are}{a}_D}+\sqrt{\mathrm{are}{a}_R}+d_{R-D}\right)$ as the effective defect size by considering surface roughness and sub-surface defect. In this definition, $\sqrt{\mathrm{are}{a}_D}$ and $\sqrt{\mathrm{are}{a}_R}$ are the prospective internal and equivalent surface roughness defect size, respectively. The $d_{R-D}$ is the shortest distance between two adjacent defects. They further modified the Murakami’s equation for fatigue limit to include stress ratio as: (6) ${\sigma }_w={\displaystyle \frac{1.43(\mathrm{HV}+120)}{{\left(\sqrt{\mathrm{area}}\right)}^{\frac{1}{6}}}{\left[{\displaystyle \frac{1-R}{2}}\right]}^{\alpha }}$(6) where $\mathrm{HV}$ (kgf/mm²) is the Vickers hardness, $R=\frac{{\sigma }_{\min }}{{\sigma }_{\max }}$ and $\alpha =0.226+\mathrm{HV}\times {10}^{-4}$.

Afazov et al. [203] proposed a relationship between the defect factor (d), the defect size (D) and location from the surface (L), as presented in Equation (7). (7) $d=1-{\displaystyle \frac{1}{1+(0.06/D)}+{\displaystyle \frac{1}{0.9\ln (1+1/D+15D)+(D/4L)}}}$(7)

The defect factor, d can also be related to stress concentration factor k_t through $d=\frac{1}{k_t}$; thus, the actual stress in the vicinity of defects can be estimated. This model led to reliable results for machined L-PBF AlSi10Mg samples that were subjected to the rotational bending loading. Chan and Peralta-Duran [204] proposed another crack nucleation model shown in Figure 15(a, b) considering the stress concentration factor and the ratio of valley depth (R_v) to valley spacing ($\lambda$_i). It was found that the worst case for crack initiation occurred at $R_v/{\lambda }_i=1$ and $k_t=3$ for LCF of AM Inconel 718. (8) $k_t=1+2{\left[{\displaystyle \frac{2}{1+{({\lambda }_i/R_v)}^2}}\right]}^{0.5}$(8)

Figure 15. Worst-case threshold stress plots for surface notches in AM materials: (a) ΔS_th vs k_t plot, and (b) ΔS_th vs $R_v/{\lambda }_i$ plot [204].

Another semi-empirical criterion is based on defect tolerant design, which uses the Kitagawa-Takahashi (KT) diagram, as shown schematically in Figure 16(a). Based on the KT diagram, fatigue endurance limit is related to the crack size through fatigue crack growth threshold to define the area of non-propagating cracks, which leads to infinite fatigue life. El Haddad et al. [205] proposed a smooth transition from short crack to long crack growth (coloured line in Figure 16(a)). They introduced an intrinsic crack length, to overcome the limitations of LEFM, which is defined as: (9) $a_{0,H}={\displaystyle \frac{1}{\pi }{\left({\displaystyle \frac{\mathrm{\Delta }{K}_{\mathrm{th},\mathrm{lc}}}{Y.\mathrm{\Delta }{\sigma }_e}}\right)}^2}$(9)

Figure 16. The KT diagram showing fatigue limit range variation with defect size: (a) Schematic, (b) El-Haddad verification for conventionally-manufactured specimens [207]; (c, d) L-PBF AlSi10Mg and L-PBF Ti-6Al-4V [199]; and (e) CM and AM Inconel 718 [209].

The $a_{0,H}$ is the threshold length at which the crack enters the long crack region, and the endurance limit stress range is dependent to the crack size can be calculate from: (10) $\mathrm{\Delta }{\sigma }_{\mathrm{th}}(a_{0,H})={\displaystyle \frac{\mathrm{\Delta }{K}_{\mathrm{th},\mathrm{lc}}}{Y.\sqrt{\pi .(a+a_{0,H})}}}$(10) where $\mathrm{\Delta }{K}_{\mathrm{th},\mathrm{lc}}$ is the fatigue crack growth threshold for long crack (related to the microstructure and process parameters [206]), $\mathrm{\Delta }{\sigma }_e$ is the endurance limit for polished defect-free sample, and Y is the geometry factor of crack. By combining Murakami’s approach and the El Haddad model, the relationship between the defect size and fatigue limit can be expressed as: (11) $\mathrm{\Delta }{\sigma }_w=\mathrm{\Delta }{\sigma }_{w0}\sqrt{{\displaystyle \frac{\sqrt{\mathrm{are}{a}_0}}{\sqrt{\mathrm{area}}+\sqrt{\mathrm{are}{a}_0}}}}$(11) and, (12) $\mathrm{\Delta }{k}_{\mathrm{th}}=\mathrm{\Delta }{k}_{\mathrm{th},\mathrm{lc}}\sqrt{{\displaystyle \frac{\sqrt{\mathrm{are}{a}_0}}{\sqrt{\mathrm{area}}+\sqrt{\mathrm{are}{a}_0}}}}$(12) where, (13) $\sqrt{\mathrm{are}{a}_0}={\displaystyle \frac{1}{\pi }{\left({\displaystyle \frac{\mathrm{\Delta }{k}_{\mathrm{th},\mathrm{lc}}}{Y\mathrm{\Delta }{\sigma }_{w0}}}\right)}^2}$(13)

In these relations, $\sqrt{\mathrm{area}}>10\sqrt{\mathrm{are}{a}_0}$ [205]. Figure 16(b) shows the verification of the El-Haddad approach for conventionally-manufactured specimens [207]. Sheridan [208] modified the El-Haddad approach based on Equation (13) to include the effect of stress ratio and expand its application for a wider range of damage-tolerant design frameworks. Bereta et al. [199] and Yang et al. [209] verified the applicability of the KT diagram for defect-tolerant design of L-PBF AlSi10Mg, Ti-6Al-4V, and Inconel 718, as shown in Figure 16(c–e).

Le et al. [86] employed the KT diagram to establish a link between the defects and fatigue failure of the L-PBF Ti-6Al-4V samples. They further applied two fracture mechanics-based approaches (i.e. Paris law and Caton et al. [210]) in order to obtain a generalised KT diagram, which showed a good agreement with the experimental results. Meneghetti et al. [211] used a combination of the KT and the Murakami’s approach for investigating the effect of defects on the fatigue strength of maraging steel produced via the L-PBF process. Note that the KT approach may yield conservative results due to the produced fine grains during laser-assisted production [212]. Sheridan et al. [213] also took a combined Murakami and El-Haddad approach to explain the effect of defect size and location on the scatter of test data when plotting a typical S-N curve. Niu et al. [214] implemented El-Haddad defect tolerant approach, along with extreme value statistics in order to identify the killer defect and estimate fatigue life based on its size. The allowable defect size can be determined according to Eq. 14 below [214]: (14) $\mathrm{\Delta }{\sigma }_w={\displaystyle \frac{{\vartheta }_3\times \mathrm{\Delta }{\sigma }_{w0}}{k_f(1+3\mathrm{CV})}\times \sqrt{{\displaystyle \frac{\sqrt{\mathrm{are}{a}_0}}{\sqrt{\mathrm{area}}+\sqrt{\mathrm{are}{a}_0}}}}}$(14) where $\mathrm{\Delta }{\sigma }_w$ is the fatigue strength (stress range), $\mathrm{\Delta }{\sigma }_{w0}$ is the fatigue strength in the absence of defects, $\sqrt{\mathrm{area}}$ is the effective defect size, and $\sqrt{\mathrm{are}{a}_0}$ is the El-Haddad material size parameter.

Moquin et al. [215] employed El-Haddad’s approach for damage tolerant design verification of L-PBF Ti–6Al–4 V and determined the critical defect size of 200 μm for the LCF regime. Critical $\sqrt{\mathrm{are}{a}_0}$ defect size for horizontal L-PBF Ti-6Al-4V specimens was 30 μm in the HCF regime [216]. For L-PBF Scalmalloy®, an intrinsic defect size of 20 μm was obtained from the KT diagram below which only microstructural-dominated failure occurred [217]. In regard to additively-repaired components, Scott-Emuakpor et al. [218] established an assessing criteria for HCF of repaired turbine engine components by means of the WAAM and LP-DED processes. The intrinsic defect size for the DED Ti-6Al-4V was 80 μm based on the El-Haddad approach.

Concli et al. [206] set up the KT-diagram for the L-PBF 316L and AlSi10Mg in as-built condition. The surface roughness was considered as shallow defect with the size of $\sqrt{10}{R}_v$ and the defect size as $\sqrt{\mathrm{area}}$. It was shown that the El-Haddad approach provided a non-conservative result; however, by considering the combined effect of surface roughness and the critical sub-surface defect, the results were well-fitted to the model. Cersullo et al. [219] developed a stress–life–defect size model based on the El-Haddad’s approach for AM Ti-6Al-4V and Inconel 718 using artificial defects and literature experimental data. Recently, Intishar Nur et al. [220] introduced a correction factor to the El-Haddad model in order to match the experimental test data for L-PBF AlSi10Mg with the KT diagram. Tenkamp et al. [221] successfully integrated El-Haddad’s KT diagram for HCF and VHCF life of die-cast AlSi7Mg0.3 and AM AlSi12. Zerbst et al. [94] also expanded understanding of safe life design through the use of the KT diagram and El-Haddad’s approach for the L-PBF process. Therefore, El-Haddad’s approach proved to be effective for describing the correlation between pore size and fatigue limit for a wide range of materials and processing methods. Gao et al. [99] applied the El-Haddad model to the projected defect size from the XCT data and obtained a conservative estimation of failure for horizontal and vertical specimens.

Apart from the empirical models introduced based on the defect size, several other models have been introduced by considering the effect of other contributing factors in fatigue life of metal AM components. Wu et al. [222] modified their Tanaka–Mura–Wu model, which was initially based on the dislocation pileup by taking the effect of microstructure and surface roughness into account and proposed an equation to calculate fatigue limit according to the roughness factor, Rs and a microstructure factor, M. It was shown that the reduction in fatigue endurance limit caused by microstructure factor is 1.5–2 times lower than the wrought counterpart. This reduction was explained by the presence of pores and LoF defects. The proposed model was successful in describing fatigue behaviour of machined, HIPed, and as-built L-PBF samples, as well as the wrought material. One major drawback of using the defect-based models is that it is not possible to directly consider the effect of microstructure features such as the grain size and orientation, as well as the residual stress.

On the other hand, combining defect-based models with probabilistic methodology enables accounting for various factors including variability in material properties, geometric features, and operational conditions. Haridas et al. [223] developed a probabilistic defect-based model to predict the fatigue life of AM materials by considering the combined effect of grain-defect features. Tognan and Salvati [224] applied a probabilistic Monte Carlo simulation approach to determine El Haddad’s parameters for damage-tolerant design based on the literature test data. The proposed approach took advantage of Logistic Regression (LR) and Maximum a Posteriori (MAP) as well-known machine learning algorithms in order to probabilistically evaluating the El Haddad’s parameters (ΔK_th,lc and Δσ_w).

5.2. Critical defect detection for damage-tolerant design

Since the reliability of the damage-tolerant and fracture mechanics-based models depends on the accuracy of critical defect determination, this section discusses the three most common methods for precise defect sizing methods apart from the typical fractography-based measurements. The first method is to seed artificial defects with known dimensions in order to reduce uncertainty in failure location and facilitate the establishment of the KT diagram. The second method is the estimation of the critical defect using a few data known as the RVE based on the probabilistic models. The third approach is to take μCT from the most critical cross-section or the whole specimen and determine the most critical defect based on the size and location.

5.2.1. Artificially-seeded defect

Artificial defects can significantly facilitate the production of the KT diagram. These engineered defects can be produced during the AM process or conventional methods such as machining or drilling [225]. Bonneric et al. [226] designed artificial defects with known dimensions on the surface of the specimens and determined El-Haddad’s $\sqrt{\mathrm{are}{a}_0}$ parameter, which was further verified by the literature results. The KT diagram can effectively reduce the scatter in test data. Syed et al. [84] took the same approach and predicted the fatigue limit for L-PBF Ti-6Al-4V alloy with as-machined surface. The spherical defects were seeded 200 μm beneath the surface and in the bulk material. The accuracy and sizing of the artificial defects were evaluated via XCT analysis. The obtained KT diagram was planned to be used for the design and approval of components according to the applied stress and defect size. Benedetti and Santus [227] established a KT diagram for defective AM specimens by introducing the critical defect at the V-notch. It was shown that rounded V-notch can simplify the fatigue tests by reducing the experimental uncertainty. Stern et al. [228] employed cubic artificial defects in the centre of smooth specimens in order to determine the parameters of KT diagram. However, due to the failure from the surface of specimens, this approach was not successful at stablishing an accurate KT diagram. Morishita et al. [229] also highlighted the challenges involved with the failure initiation from an arbitrary internal defect. Therefore, several internal defects with known size (400–1000 μm) and location were introduced in order to programme failure from internal artificial defects. The actual size and location of seeded defects were measured through μCT. It was shown that all the prepared test specimens were failed from the intentional defects and the fatigue life showed reduction by increasing the defect size.

5.2.2. Probabilistic critical defect estimation

It is known that the fatigue of metal AM components is governed by the defects, and the size and random distribution of defects cause scatter in test results [230]. Probabilistic models are designed to capture scatter in data, which is mainly induced by various failure mechanisms in metal AM components. Such models provide useful estimations for the range of possible fatigue lives and the probability of failure based on defect size and distribution. The most common distribution functions are Poisson, Weibull, Gamma, Gumbel, and Lognormal [39]. Statistical methods have been used in order to determine the distribution and size of defects within the critical sections of metal AM components. Then, the most critical defect based on the effective size would be introduced as the killer defect. In the statistical approach, defects are estimated by the largest circle that surrounds the defect area; thus, the shape of defect has not been considered in this methodology. Kousoulas et al. [231] compared the results of different functions for L-PBF SS316L and found that the results of all the four functions yielded high R values (R>0.975).

Among all the available probabilistic models, the extreme value statistics (EVS) has been revealed to be suitable for metal AM components. The EVS deals with the analysis of random values that are far from the expected value of their probability distribution [232]. Thus, this method is capable of estimating the largest expected defect within the component based on empirical observations. As the largest defect is mainly the source of failure, it would be helpful to identify the largest defect within the component. Kakiuchi et al. [39] estimated the maximum defect size and employed the Murkami’s approach to predict fatigue strength of conventionally manufactured and AM Ti-6Al-4V. The obtained results showed an acceptable agreement with the experimental data. Two sampling strategies can be used for the EVS: (1) block maxima (BM), and (2) peaks-over-threshold (POT). In the BM method, the specimen is divided into smaller blocks, and the maximum defect size in each block is identified. However, in the POT method, defects larger than a defined threshold are identified. The POT method is more efficient when it comes to the XCT data, due to higher data acquisition through XCT. A schematic of these two sampling methods is presented in Figure 17(a, b).

Figure 17. (a) Block maxima sampling, and (b) Peaks-over-threshold sampling [232].

The data from the BM method can be described using the Gumbel distribution, which is the largest extreme value distribution. (15) $F_{\mathrm{Gumbel}}(x,\delta ,\lambda )=\exp \left(-\exp \left(-{\displaystyle \frac{x-\lambda }{\delta }}\right)\right)$(15) where λ and δ are the location and scale parameters respectively. These parameters can then be evaluated from the BM sampled data using data analysis techniques. The maximum expected value to be sampled in an associated material volume (V) can be calculated using the characteristic maximum value for the Gumbel distribution [232]: (16) ${\hat{x}}_{\mathrm{Gumbel}}(V)=\hat{\lambda }-\hat{\delta }.\log \left[-\log \left(1-{\displaystyle \frac{V_0}{V}}\right)\right]$(16) where $\hat{\lambda }$ and $\hat{\delta }$ are the evaluated location and scale parameters and V₀ is the investigated material volume.

The POT data can be represented using the Generalized Pareto Distribution (GPD). (17) $F_{\mathrm{GPD}}(x,u,\sigma )=1-\exp \left(-{\displaystyle \frac{x-u}{\sigma }}\right)$(17) where u is the location (cut-off) parameter and σ is the scale parameter. These parameter are then fit to the POT sampled data, but in practice the location parameter u is the same as the POT cut-off value, and thus, it needs to be set before σ can be evaluated [232]. The characteristic maximum value for the GPD is: (18) ${\hat{x}}_{\mathrm{GPD}}(V)=\hat{u}+\hat{\sigma }.\log (\mathrm{\rho V})$(18) where $\hat{u}$ and $\hat{\sigma }$ are the evaluated location and scale parameters and $\rho$ is the volumetric density of the POT sampled distribution. This density is simply the number of POT sampled defects (N) divided by the investigated material volume $\rho$ = N/V [232]. Bhandari et al. [233] rewrote Eq. 18 by using the $\sqrt{\mathrm{area}}$ approach and obtain: (19) $F\left(\sqrt{\mathrm{area}}\right)=\exp \left[-\exp \left[-\left(-\sqrt{\mathrm{are}{a}_i}\right)-{\displaystyle \frac{\lambda }{\beta }}\right]\right]$(19) where $\sqrt{\mathrm{area}}$ is the random variate, $\lambda$ and $\beta$ are the location and the shape parameters, respectively. The probability density distribution function is given by: (20) $G\left(\sqrt{\mathrm{area}}\right)={\displaystyle \frac{1}{\beta }\left[\exp \left(-{\displaystyle \frac{\sqrt{\mathrm{area}}-\lambda }{\beta }}\right)\right]\exp \left[-\exp \left(-{\displaystyle \frac{\sqrt{\mathrm{area}}-\lambda }{\beta }}\right)\right]}$(20)

This equation can further be employed in order to calculate the actual stress at the critical defect using Equation (4).

The EVS method has been used in several studies as a tool for fatigue life estimation of the L-PBF components. Romano et al. [234,235] applied the EVS method to tomographic measurements for analysing the X-ray data. They took μCT from a complex bracket manufactured through the L-PBF process and estimated the extreme defect using the EVS method. Their results revealed that this method is capable of robustly estimating the size of the killer defect at the fracture surface of the witnessed samples. They also proposed a probabilistic approach to estimate the fatigue life of a complex component based on the analysis of elemental failure in presence of the critical defect [236]. This approach is highly desirable for rapid fatigue life estimation of complex components using limited data. Sanaei and Fatemi [81] applied a combination of POT sampling strategy and generalised pareto distribution (GPD) to calculate the maximum prospective defect size for L-PBF Ti-6Al-4V and 17-4PH. Stopka et al. [237] proposed a model based on the crystal plasticity finite element method (CPFEM) to determine the fatigue indicator parameter (FIP). They found that the number of grains in the representative volume elements (RVEs) is important for model convergence. Niu et al. [214,238] employed a combination of the EVS and the weakest-link theory to establish a probabilistic fatigue life estimation by considering the size effect and scatter in test results. Further, a link was established between the probabilistic fatigue life estimation and defect-tolerant design, which indicates the reliability and robustness of this method. Deng et al. [239] utilised the EVS to estimate the maximum effective defect size for a part-scale volume based on a sub-volume measurement and found that the estimation error is less than 10%. Siddique et al. [240] developed a stochastic method for prediction of fatigue life of L-PBF AlSi12 by using the weakest-link theory including two-parameter Weibull distribution for fatigue life (N_f) as: (21) $f(N_f)=\alpha .\beta .N_f^{\beta -1}.e^{-\alpha .N_f^{\beta }}$(21) where α and β were determine from the maximum likelihood method.

Probabilistic defect size estimation provides supplementary information for defect-based models in order to obtain a more accurate prediction without going through intensive testing procedure.

5.2.3. X-ray-based defect detection methods

The in-situ and ex-situ μCT has been widely used in defect detection and fatigue test monitoring of AM components [235]. Since this method has been utilised in many studies as an essential tool for fatigue analysis, this section is dedicated to the applications of the μCT technique in fatigue life estimation.

The ex-situ μCT setup can be used for the evaluation of defect density, pore size and morphology, and surface roughness evaluations [241]. Du Plessis [242] analysed the defect distribution of specimens that were produced through different laser powers. The results in Figure 18(a–h) show the μCT results emphasising on the importance of proper laser power to avoid LoF defects. Leuders et al. [243] investigated the relationship between porosity, stress concentration, and fatigue performance of L-PBF Ti-6Al-4V in the as-built and HIP conditions. Vayssette et al. [244] developed a numerical model of surface roughness based on μCT to predict HCF cracks. Senck et al. [245] used μCT to evaluate defect distribution in a topology-optimised aluminum bracket manufactured through the L-PBF method. Knowing the size and location of defects enables the use of semi-empirical models such as Murakami’s or the KT diagram in order to predict fatigue strength of the component. Further, the data can be directly used to train ML algorithms in order to establish a nondestructive prediction of fatigue life. CT data can be effectively utilised for probabilistic fatigue life prediction. Niu et al. [214] employed the EVS theory and the KT diagram combined with the CT data in order to correlate defect size and fatigue strength.

Figure 18. (a-h) 3D porosity distributions in the central 1 mm of each of the samples at increasing power. The images (b)–(h) are all to the same colour scale maximally 0.1 mm [242]; (e) 3D renderings of FCG at 810 MPa stress [246].

On the other hand, in-situ μCT has exceptional capability to monitor crack initiation and propagation within the specimen with high resolution. This data can give better understanding of the failure mechanisms inside the sample, and also act as a verification method for the computational and theoretical frameworks. Hu et al. [185] employed synchrotron radiation μCT (SR-μCT) to evaluate L-PBF defect size and distribution for the determination of the critical ones. The critical defect size was plugged into the NASGRO model to predict life under cyclic loadings. Qian [17] monitored single and multiple-site crack initiation from LoF defects within the (sub)surface region of L-PBF AlSi10Mg during the HCF test. A numerical simulation was developed to predict the FCG and was successfully verified with the XCT data. Wu et al. [246,247] employed a time-lapse SR-μCT setup along with typical microscopic analysis in order to monitor fatigue crack propagation during the LCF testing of L-PBF Ti-6Al-4V. The results revealed that the crack initiation location may not always occur at the defective locations, especially for miniature test specimens with few defects; therefore, microstructural impurities should be also added to the equivalent defect size in case of using the KT diagram. Figure 18(i) shows the result of one of the test trials. It was also highlighted that the SR-μCT setup enables the investigation of complex interaction of defects, intermetallics, and surface roughness in failure progress.

5.3. Microstructure and multistage fatigue models

Microstructure-based models deal with the fatigue damage that is initiated from various microstructural features and propagated as small and long cracks through the sample. McDowell et al. [248] initially developed a microstructure-based model for HCF of the cast aluminum sample subjected to multiaxial loading but it could be extended to other materials and loading conditions in both LCF and HCF regimes. The foundation of multistage fatigue (MSF) approach is based on multiscale finite element method (FEM) analyses containing microstructure and macrostructure characteristics of the material. Therefore, understanding of FEM and theoretical models are prerequisites. This model uses the effect of microplasticity and crystallographic orientation on crack tip displacement as the driving force in order to predict fatigue life. Based on this model, fatigue life is divided into four stages $N_{\mathrm{Total}}=N_{\mathrm{inc}}+N_{\mathrm{MSC}}+N_{\mathrm{PSC}}+N_{\mathrm{LC}}$, where $N_{\mathrm{Total}}$ is the total fatigue life, $N_{\mathrm{inc}}$ is the number of cycles corresponds to crack incubation (i.e. initiation and early propagation within the micro notches at defects), $N_{\mathrm{MSC}}$ is the number of cycles for microstructurally small crack propagation, $N_{\mathrm{PSC}}$ is the number of cycles for physically small crack propagation, and finally, $N_{\mathrm{LC}}$ is the number of cycles for long crack propagation. Each term is governed by a proper formulation for various materials as described in the literature [249–251]. The crack incubation stage is based on the modified Coffin-Manson law. Fatemi and Socie [252] proposed a FIP that includes the maximum plastic shear strain during the cycle-by-cycle loading process, material yield strength, and stress amplitude to determine the $N_{\mathrm{inc}}$: (22) $\mathrm{FI}{P}_{\max }={\gamma }_f(2N_{\mathrm{inc}}{)}^b$(22) where ${\gamma }_f$ and b are fitting parameters of HCF data. The MSC/PSC regimes are governed by crack tip displacement (CTD), while the long crack (LC) stage is based upon a modified Paris Law. It is also possible to integrate the finite element models for each regime. In some studies, the $N_{\mathrm{MSC}}$ or $N_{\mathrm{PSC}}$ terms were ignored due to their negligible contribution to the total life.

Continuum damage mechanics (CDM) accounts for the accumulation of damage in a material as a result of cyclic loading; therefore, it is suitable for microstructural and multi-stage modelling. This method can be used to predict the fatigue life of materials and components under both LCF and HCF conditions [253]. The main advantage of CDM over the fracture mechanics-based approaches is that the latter is not accurately applicable for the crack initiation stage; thus, the CDM is applicable for multi-scale fatigue modelling. Although the crack initiation life is rarely significant in the case of metal AM components, the discussion is made for the sake of completeness. In the field of CDM, several damage sensitive models have been developed for LCF and HCF so far [254–257]; however, the impact of AM defects and microstructure features should be specifically investigated. Zhang et al. [258] established a model based on CDM, crystal plasticity, and the theory of critical distances (TCD) for a test sample containing several drilled holes to act as the stress concentration regions. The model account for the effect of microstructure anisotropy according to the single crystal Ni-based superalloy. Furthermore, the constitutive equations applied in FEM in order to study HCF. Zhan et al. [259] developed a CDM-based model by considering the effect of AM key process parameters in the frame of volumetric energy density for uniaxial and multiaxial loading conditions. The proposed model was validated with experimental data and showed good correlation for common AM alloys (i.e. SS316L, Ti6Al4 V, and AlSi10Mg). Pei et al. [260] quantified the effect of microstructural features, including porosity and precipitates to the damage evolution of the L-PBF Inconel 718 alloy and found that the effect of defects on the damage evolution is dominant. Faghihi et al. [261] established a probabilistic design framework by using the results of fatigue test data and a CDM-based model, to quantify uncertainties in experimental data and computational model for fatigue life prediction of structural components. It was shown that the Bayesian method is capable of calibrating the computational model beyond the test range and making design-related decision-making under uncertainty possible.

The FEM is a powerful tool for studying fatigue behaviour of metal AM materials, especially using the multi-scale fatigue analysis. FEM should be integrated with theoretical models to effectively predict fatigue life of metals. There are a vast number of studies that applied previously-developed crack propagation models to metal AM components using FEM. Based on various assumptions, researchers have studied fatigue cracks from different approaches. Hybrid models are combinations of different fatigue modelling approaches in order to obtain a more reliable and robust results. There are several combinations of FEM with microstructural models, defect-based models, empirical and, CDM models. Using FEM for fatigue assessment can provide a more accurate prediction of the fatigue behaviour of a material or structure than individual models.

In general, numerical simulation of fatigue cracks consists of two phases: (1) crack nucleation, and (2) crack propagation. Crack nucleation can be modelled using the CDM approach, which considers micromechanics of the structure. CDM requires a RVE and a damage model in order to model the effect of crack nucleation within the material. For the second phase, the cohesive zone method (CZM) or extended finite element method (XFEM) can be used to model crack propagation. The commercial FEM packages such as ABAQUS and ANSYS have built-in modules for crack propagation analysis based on CZM and XFEM; however, they only operate based on the Paris law. Through these modules, the crack tip and its propagation domain should be initially defined. However, in order to model crack initiation based on the CDM approach, subroutines are required to define the damage model.

Wang et al. [262] proposed a damage evolution model based on the CDM and the irreversible thermodynamics for LCF analyses, and implemented that in ABAQUS using a UMAT subroutine. Burr et al. [263] studied the performance of numerical modelling for EBM lattice structures based on a damage accumulation law and achieved reasonable accuracy. Liang et al. [264] used FEM to study the effect of defects and grain morphology on HCF of conventional SS316L. They used two non-local methods to model HCF and compared their results to the experimental data. They noted that the microstructure modelling is important in the case of understanding the effect of defects on fatigue life. Dinh et al. [265] proposed a fatigue model that could robustly capture the effect of high surface roughness on fatigue crack initiation of L-PBF Ti-6Al-4V alloy through nonlinear FE. They employed an in-house code to calculate the FIP from the FE analyses. Vayssette et al. [244] introduced a methodology based on surface profilometry and XCT to investigate the effect of surface roughness on the HCF by means of FEM. The method was able to predict the fatigue life of as-built samples; however, the computational cost of the process is high. Afroz et al. [266] also used μCT data to establish a FEM model to determine the effect of defect size and location on fatigue life through the Murakami’s approach.

Wan et al. [267] developed a multi-scale model based on FEM and CDM, which was capable of accounting for the effect of gas porosity and build orientation. Pei et al. [268] took a plastic strain energy damage model for LCF of L-PBF Inconel 718, which could also be used for monotonic loading condition. Microstructure features including pores and precipitates were also taken into account to obtain satisfactory agreement with the experimental results.

The MSF modelling can be applied to both conventional and metal AM components, while considering the effect of microstructure changes [269]. However, very little effort has been done in the case of MSF development for metal AM parts. Xue et al. [270] and Torries et al. [271] employed the MSF model to study fatigue behaviour of the laser engineered net shaping (LENS) SS316L and Ti-6AL-4V, respectively, by considering cyclic plasticity. They used optical microscopy and μCT for their observations, and characterised defects based on their size, location, and the nearest neighbourhood features. Torries et al. [271] showed that the density of pores and their impact on failure can produce deviations in the MSF model. Note that MSF models should be calibrated based on the material and corresponding microstructure. Thus, developing such models are challenging for metal AM materials due to the anisotropic and heterogeneous nature of them. Torries and Shamsaei [272] studied the effect of grain structure on the fatigue behaviour of metal AM structures using a microstructure-sensitive model. The developed model was calibrated using two different microstructures that were generated through different process parameters. The results of experimental data fell within the predicted lower and upper limit of the proposed model.

Cao et al. [273] employed crystal plasticity in FEM with a stored energy density criterion to investigate fatigue crack nucleation behaviour of L-PBF AlSi10Mg and quantify fatigue life by considering different types of defects. It was shown that the crack nucleation is sensible to both keyhole defect and LoF; however, the impact of LoF defect is more significant. Figure 19(a–h) show the distributions of plastic strain accumulation and stored energy density at the 20th cycle in gas/keyhole pore microstructure at different cyclic loading levels. Krishnamoorthi et al. [274] introduced a microstructure-based fatigue model for L-PBF Ti-6AL-4V by considering the role of prior β boundaries using crystal plasticity and the critical accumulated plastic strain energy density (APSED). It was shown that the impact of prior β grain boundaries and their orientation is vital to fatigue performance of metal AM samples. Luo et al. [275] used μCT data to reconstruct different defect geometries in order to be employed in a MSF framework based on crystal plasticity for HCF assessment. The model well-reflected the fatigue life scatter resulted from different defect types. Qu et al. [89] took the effect of defects and microstructure into account and came up with two microstructure-sensitive fatigue models for brittle and ductile fracture provided in Equation (23). (23) $N_f=\{\begin{array}{c}{\displaystyle \frac{1}{2}{\left({\displaystyle \frac{Y\times \mathrm{\Delta }{\sigma }_0\sqrt{\pi }{\left(\sqrt{\mathrm{are}{a}_E}\right)}^{1/6}}{(171.03-0.3156\mathrm{HV})\times \mathrm{HV}\times {(1-R/2)}^{\alpha }}}\right)}^{1/0.18}}\\ {\displaystyle \frac{1}{2}{\left({\displaystyle \frac{Y\times \mathrm{\Delta }{\sigma }_0\sqrt{\pi }{\left(\sqrt{\mathrm{are}{a}_E}\right)}^{1/6}}{(129.78-0.3099\mathrm{HV})\times \mathrm{HV}\times {(1-R/2)}^{\alpha }}}\right)}^{1/0.12}}\end{array}$(23)

Figure 19. The distributions of plastic strain accumulation and stored energy density at the 20th cycle in gas/keyhole pore microstructure at different cyclic loading levels: (a, e) σ_max= 0.7σ_0.2NP, (b, f) σ_max= 0.8σ_0.2NP, (c, g) σ_max= 0.9σ_0.2NP, and (d, h) σ_max= 1.0σ_0.2NP [273].

where all the parameters are defined in the previous sections. The first equation in Equation (23) corresponds to brittle cracking mode controlled by stress concentration of defect edge (SCDE), and the second one is used for the ductile cracking mode controlled by fatigue damage behaviour in local microstructures (FDLM).

5.4. Artificial intelligence-assisted models

Artificial neural network (ANN) and machine learning (ML) are also capable of integration with the previous approaches. Salvati et al. [276] developed a defect-based physics-informed machine learning (PiNN) framework to predict fatigue life of defective components. This approach is based on the definition of a size indicator consists of the volume of the defect and its projection onto the normal with respect to the applied load. This parameter was further transformed to the $\sqrt{\mathrm{area}}$ parameter to be used in fracture mechanics approach. Experimental data were used to train an ANN algorithm, which can be used for structural design purposes. Wang et al. [277] proposed a loss function within a defect driven PiNN methodology as an indicator for the effect of defect size and population on fatigue life. The proposed model achieved higher accuracy in comparison to the results from the fracture mechanics-based data driven PiNN, which was dependent on the employed fracture mechanics model. One major issue with the data-driven approaches is the high number of required data to reach a sufficient accuracy. Therefore, physics-guided machine learning frameworks, which combined physics-based models and ML algorithms is recommended in order to reach better estimation with limited data [278]. Wang et al. [279] showed that the utilisation of the physics-informed probabilistic neural network (PiPNN) accounts for the involved uncertainty introduced by the microstructural inhomogeneity and gives a better prediction of the fatigue life of AM specimens. Chen and Liu [280] established a PiPNN model in order to relate fatigue life directly to the process parameters (i.e. scanning speed, laser power, hatch space, layer thickness, heat temperature, and heat time) for L-PBF Ti-6Al-4V. The response of the developed model with different data sets was recorded and verified the reliability of the predictions.

Zhan et al. [281] employed CDM and ML to establish a data-driven fatigue life prediction model for metal AM components. For the theoretical aspect, fatigue damage analysis and life prediction of two titanium alloys are carried out using damage mechanics-based fatigue models and random forest model. The computational aspect consists of the numerical implementation of the damage mechanics-based fatigue models and the development of the random forest (RF) model. The authors added extra features to their model to take the effect of process parameters (i.e. laser power, scan speed, hatch space, layer thickness) on the fatigue life into consideration and predict the number of cycles to failure based on the designed process parameters [282]. Ciampaglia et al. [283] also developed a ML model to predict the effect of process and post-processing parameters on the fatigue life of metal AM parts. Wang et al. [284] established a methodology for fatigue life determination of AM components by considering defect density using CDM and ML. The system vector machine (SVM) and RF techniques were used for fatigue life prediction based on the experimental data. The SVM algorithm combined with CDM-sensitive features showed a better prediction performance. However, the work only considered defect density, which cannot fully represent the state of the material in terms of sensitivity to damage and failure. Horňas et al. [285] investigated the effect of defect distribution provided by μCT data on fatigue life using the common ML algorithms, namely ANN, RF, and SVM. All the results lay within ±5% deviation from the equity line that was plotted from the experimental and predicted data. Bao et al. [21] highlighted the accuracy and effectiveness of the SVM when trained with the synchrotron X-ray tomography data. Peng et al. [20] employed the extreme gradient boosting model to investigate the prediction accuracy of fatigue life of L-PBF AlSi10Mg alloy by considering the effect of the applied stress, critical defects (morphology, location, and projected area). The results of the proposed model were compared to the Murakami’s model and proved to be reliable. Zhang et al. [286] involved the AM effects in a CDM-based model and calculated the corresponding fatigue lives using FEM. Afterwards, common ML algorithms were trained using more than 500 data sets. The results were showed the sensitivity of ML algorithms to the design of levels and trees; thus, a proper design can accurately predict the fatigue life based on the available data sets. It is also possible to estimate fatigue life from the manufacturing process parameters by employing ML. Tridello et al. [287] developed a ML algorithm that predicts defect population and size distribution of metal AM samples from the process parameter set, and used the data for fatigue life estimation. Psihoyos et al. [288] also implemented similar methodology by predicting defects based on the thermal history of produced parts.

6. Fatigue studies on complex mechanical components

The majority of fatigue studies have been implemented on the standard samples with simplified geometries and under specific processing conditions. However, it is necessary to evaluate how the obtained results can be extended to various mechanical components, especially the topologically optimised components that were produced through the metal AM processes. Due to the geometrical complexity of most of the mechanical components, smooth specimens cannot fully represent actual material behaviour under complex conditions. Therefore, a notch with particular geometry is commonly introduced in the middle section of the smooth test specimen to simulate the worst-case scenario for fatigue crack initiation and propagation through excessive stress concentration. The geometry and type of the notch should be selected according to the geometry of the critical section of actual component. The typical notch geometries and how they affect the fatigue life for L-PBF Inconel 718 are shown in Figure 20(a, b), respectively. Therefore, as the radius of the notch decreases for a constant stress amplitude, the severity of stress concentration gets worse and the fatigue life decreases [7]. It was shown that the same trend rules for wrought and DED specimens [114]. In the case of metal AM test specimens deep surface cavities can also act as micro-notches; nevertheless, this section discussed the effect of intentional notches on the fatigue life.

Figure 20. (a) Common notch geometries in fatigue testing, and (b) fatigue life test data for notched and unnotched L-PBF Inconel 718 [289].

Solberg et al. [7–9,132] studied the effect of notch geometry on the fatigue life of as-built L-PBF specimens. Figure 21 summarises the fundamental results of their study. It was found that there is a relationship between the notch geometry and the failure location. Furthermore, in the case of as-built notched specimens, the down-skin region of the notch possesses higher surface roughness and is more likely to initiate failure than the centre of the notch, as shown in Figure 21(a–d) [7,8]. The deviation is particularly interesting in the semi-circle (Blunt) notch, as shown in Figure 21(e). Kahlin et al. [290] also determined the combined effect of surface roughness and notch stress concentration factor on the fatigue life of EBM and L-PBF Ti-6Al-4V. It was found that the fatigue notch factor for the two manufacturing processes is relatively similar (K_f-EBM: 6.64, and K_f-LPBF: 6.15). Razavi et al. [291,292] revealed that the rough surface in smooth specimens caused a small notch sensitivity factor for the semicircular and V-notched L-PBF Ti-6Al-4V specimens. Nicoletto et al. [293] reported the correlation of the fatigue notch factor with build orientation and notch geometry. In other studies [294,295], the effect of surface roughness on smooth and notched L-PBF AlSi10Mg and Inconel 718 specimens was investigated. The results showed the negative impact of the down-skin surface on the fatigue performance of notched specimens. Afkhami et al. [296] studied more diverse configurations of notch geometry in the as-built condition and provided a more comprehensive understanding of the correlation between the notch geometry and stress concentration. It was found that the inherent (sub)surface defects play a crucial role in the failure initiation location of notched specimens. A modification of Murakami’s approach yielded reliable results based on the experimental data. Further, the aforementioned Solberg-Berto diagram that was initially developed for Inconel 718 [7], proved to be applicable for the tool steel 18Ni300 material as well. Molaei et al. [297] compared the multi-axial fatigue life of notched Ti-6Al-4V and 17-4PH stainless steel produced via the L-PBF with their wrought counterparts. The results revealed that the type of loading, surface roughness, and notch condition have a crucial impact on the deviation of metal AM components from the wrought counterparts.

Figure 21. (a, b) Cross section of a AM notched geometry subjected to fatigue loading, (c) Generalised notch geometry with dimensions, (d) Schematic illustration of a AM notched geometry with higher surface roughness in the down-skin, and (e) Schematics of initial diagram developed for AM Inconel 718 [7].

Beretta et al. [298] linked the fatigue life of test coupons to a representative mechanical component manufactured via L-PBF and elaborated on how the defects and residual stress can affect test specimens, as well as a complex geometry. Figure 22(a–d) show how failure from internal defects can induce scatter in test data of an actual bracket as previously discussed for smooth test specimens. On the other hand, failure from the as-built surface showed lower but consistent results. It is promising to find that the stress analysis using the FEM can effectively predict failure locations. Kishore et al. [299] proposed a framework for fatigue life evaluation of complex geometries produced via metal AM processes. However, this framework is not fully reliable as it only considers surface roughness. Raičević et al. [300] investigated the fatigue life of a topology-optimised torque link as a part of the nose landing gear of aircraft using the improved FEM method to understand the effect of the inherent residual stress of AM components. Boursier Niutta et al. [301] developed a fatigue design of AM components through topology optimisation using two different defect-driven approaches. In the first approach, defect distribution and the marginal P-S-N curves were employed in order to predict fatigue life, while, the second approach modelled the size effect by considering the non-local stress distribution. The optimal design was determined through an iterative methodology based on the state of the stress within the current design. Margetin et al. [302] assessed the fatigue life of a bicycle frame produced via L-PBF AlSi10Mg. FEM was employed for stress analysis, determination of the critical locations, and multi-axial fatigue life assessment. It was pointed out that the fatigue performance of AM components is lower than the cast counterparts which limits its use. The involved scatter in the experimental data was also processed using the statistical approach. Schnabel et al. [303] subjected a component-like structure to cyclic loading to investigate the effect of geometrical complexity on the fatigue life of L-PBF AlSi10Mg. It was shown that there are several factors contributing to the failure of a component. It was surprising that even the same batch of components with the same processing parameters may fail from different locations due to the random distribution of defects.

Figure 22. The summary of fatigue life assessment of a bracket produced via the L-PBF: (a) S-N curve of the bracket in the as-built and machined conditions, (b) S-N curve of the cylindrical test specimen, (c, d) Defect distributions for the machined and as-built specimens [298].

7. Discussions and challenges

Fatigue and fracture analysis of metal AM components is challenging due to the presence and random distribution of inherent defects and microstructural heterogeneity. It was shown that the surface roughness and (sub)surface defects have higher stress concentration factors and oxidation risks in comparison to internal defects making them more critical than the internal discontinuities; therefore, they are the main failure mechanisms in the as-built specimens. The internal failure generally activates in low-stress levels (denoted by HCF and VHCF), and the distribution of internal defects causes scatter in the S-N curve representation. Thus, normalisation of S-N curve is required to obtain a better fit. Structural defects with less than 1% population seem to have no sensible impact on the FCG rate; however, it was found that the internal defects tend to attract the crack tip and generate multiple-crack sites.

The effect of microstructure features on fatigue behaviour falls behind the structural defects due to the high probability of pre-mature failure from surface irregularities or internal defects. The effect of microstructure heterogeneity and unfavourable phases is rather complex but generally results in lower fatigue life in comparison to the wrought counterparts. The non-uniform and sharp grain boundaries, along with low ductility in AM microstructures are the main reasons for this deviation from the wrought behaviour. However, oriented grains along the build direction promote crack resistivity of the material in the vertical direction. FCG rate and direction are generally governed by microstructural grain size and their orientation; meaning that the elongated grains can significantly increase the FCG resistivity. The orientation of FCG is mainly in line with the weakest boundary, which is generally elongated throughout the cooling direction of the material during production. Thus, the anisotropy of AM components can drastically damage the FCG resistance of the products.

Residual stress forms a pre-stressed region near the surface of specimens, which reduces the fatigue life of metal AM components, especially in the initiation stage. The residual stress distribution is directly affected by the process parameters and cooling rate of the component. Several numerical tools are available to estimate the distribution of residual stress and deformation, based on the selected process parameters. As discussed, residual stress in the subsurface region is in tensile form, which causes crack opening with even a low applied stress. However, residual stress is generally in compressive form within the internal regions; thus, it causes crack closure and FCG rate reduction.

Post-processing strategies are employed to improve the fatigue performance of metal AM components by eliminating defects, relaxing residual stress, and removing unfavourable microstructural features. Surface treatment strategies such as machining, tribofinishing, and chemical etching improve fatigue life by removing excessive surface roughness, while laser shock peening, shot peening, sand blasting, and ultrasonic nano-crystal surface modification reduce surface roughness, as well as transform the tensile residual stress into compressive form, which encloses the surface defects and promotes fatigue life. On the other hand, optimised heat-treatment strategies can be employed to modify grain size and contributing phases to increase fatigue resistivity. Furthermore, the HIP process is capable of curing internal defects but it has no impact on surface and subsurface defects; thus, the machining process or other surface treatment strategies should be coupled with the HIP to maximise performance.

Damage-tolerant models have been developed in order to match with the AM inherent conditions and take the effect of defect size and location into account. Through these models, the effective stress intensity factor in the vicinity of the critical defect can be determined, which results in a more accurate estimation of fatigue life. The Murakami’s equivalent defect size proved to be a conservative method for the determination of stress intensity factor based on the defect size and location; however, it should also be modified for anisotropic microstructures. The Kitagawa-Takahashi diagram and El-Haddad’s modification provide a deeper understanding of the fatigue life and damage-tolerant design.

It is possible to investigate the effect of defect type, microstructure anisotropy, and microplastic cyclic deformation using the CDM approach. In order to implement CDM for a material, a proper model should be established and implemented using finite elements. The main drawback of this approach is the high computational cost, which generally limits the size of the model. In most cases, a 2D model is established instead of a 3D analysis to reduce the simulation cost. Furthermore, the development of parallel and high-performance computing methods can accelerate the solution of complex CDM models, as well as promote the accuracy and efficiency of numerical methods.

Numerical and ML-based methods are developed to reduce the intensive testing procedure and organise their results in a systematic way. The combination of ML with CDM and FEM provides a powerful tool that is capable of predicting the fatigue life of metal AM components based on the accuracy and comprehensiveness of the constitutive damage model. The model can contain information from the loading condition, microstructure heterogeneity, defect population and distribution, and residual stress. It is now possible to directly relate these factors to the process parameters and obtain a rough estimation of the fatigue life based on the selected process parameters. Obviously, the next step should be the generalisation and improvement of such models by considering laboratory-produced samples, as well as actual industrial components. This seems to be the only path to predict the fatigue life of metal AM components without going through hundreds of hours of testing and characterisation.

Future works on fatigue life prediction in metal AM involve life estimation of topology-optimised components with complex states of residual stress, surface roughness, and defect distribution, which requires a high level of expertise and accuracy to handle. The ultimate goal is to find a correlation between the process parameters and the fatigue life of metal AM components. The aim of the fatigue community is to restrict the number of tests due to the high cost of sample production and testing. In order to reach this goal, in-situ process monitoring data along with the ex-situ defect and distortion information from the actual component can be used to establish fatigue predictive models based on ML algorithms. This goal can be only achieved through the use of thermal history information or synchrotron XCT in order to estimate residual stress and defect locations. Alternatively, ex-situ μCT can be employed in order to characterise the critical defect in the whole component, and provide sufficient data for the training stage. Further, a ML algorithm coupled with a theoretical or empirical model can be employed to predict fatigue life. Note that the accuracy of different ML algorithms is not the same; therefore, several algorithms should be tested on the collected data and validated using fracture-mechanics or defect-based approaches. Recently, the effect of microstructure heterogeneity has also been included in ML-based fatigue algorithms; however, further developments are required to establish benchmarks for different materials and loading conditions.

8. Conclusions

This paper provides a comprehensive overview of the fatigue performance of metal AM and reveals the evolving landscape of this technology in the realm of structural integrity. The study delves into various aspects, including material properties, process parameters, post-processing, and modelling techniques, shedding light on the intricate interplay influencing fatigue behaviour. As we navigate the complexities of AM in fatigue analysis, it becomes evident that the technology holds great promise, offering unique opportunities for innovation in design and production. Our findings underscore the importance of continued research and development to achieve more reliable fatigue life predictions, fulfilling the requirements of industries ranging from aerospace to biomedical. This work contributes to the growing body of knowledge in fatigue of metal AM, providing a foundation for future advancements and fostering a deeper understanding of the fatigue performance of components produced through AM.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability

The data that support the findings of this study are available from the corresponding author, BK, upon reasonable request.

Additional information

Funding

This study was carried out under the Scientific and Technological Council of Turkey (TUBITAK) Technology and Innovation Support Program [grant number: 5158001].