A non-local damage model for the fatigue behaviour of metallic polycrystals

ABSTRACT

The development of fatigue damage in metallic materials is a complex process influenced by both intrinsic (e.g. texture, defects) and extrinsic (e.g. loading mode, frequency) factors. To better understand this process, some efforts have been made to develop microstructure-sensitive models that consider the impact of microstructural heterogeneities on the formation of fatigue cracks. An important limitation of such models is their inability to describe the transition between the nucleation and growth stages in a consistent thermodynamic framework. To circumvent this limitation, a constitutive model, which is appropriate for the description of both nucleation and early growth, is proposed. For this purpose, non-local damage mechanics is used to construct a set of constitutive relations that explicitly considers the progressive stiffness reduction due to the formation of fatigue cracks. Specifically, a damage variable is attached to each slip system, which allows considering both the anisotropic aspect of fatigue damage and closure effects. The spatial gradients of the damage variables are treated as additional state variables to account for the increase of surface energy associated with the formation of fatigue cracks. For the evolution equations to be compatible with the second law of thermodynamics, a modified form of the entropy production inequality is adopted. For illustration purposes, the non-local damage model is implemented in a spectral solver. Some numerical examples are then presented. These examples allow discussing the ability of the proposed model to describe the impact of loading conditions and pre-existing defects on the fatigue behaviour of metallic polycrystals.

KEYWORDS:

• Damage
• fatigue
• polycrystalline metals
• thermodynamics
• FFT

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1 $\left[\mathbf{\bullet }\right]$ denotes the jump of • across an interface.

2 The spatial and frequency forms of a given field Z are differentiated with notations $Z\left(\mathit{X}\right)$ and $Z\left(\mathit{\xi }\right)$.

3 The average dissipated energy density per loading cycle $w_d$ is given by $w_d\left(\mathit{X}\right)=\oint {\rho }_0\left(\mathit{X}\right)d(\mathit{X},t)\mathrm{d}t$.