Numerical analysis on the SIF of internal surface cracks in steel pipes reinforced with CRS subjected to bending

Figures & data

Figure 1. The schematic of the FE model and the 4-point bending setup.

Figure 2. The location of the surface crack and the parameters of the surface crack.

Figure 3. (a) Global mesh of the FE model and the CFRP reinforcement; (b) illustration of the surface cracked area by splitting the pipe.

Figure 4. (a) Surface crack modelling module; (b) the mesh around the surface crack.

Figure 5. Wrapping pattern including longitudinal direction (L) and hoop direction (H).

Table 1. Detail information of the phase one FE models.

Index	D	t	Le	Li	Wrapping scheme (see in Figure 5.)
P	101.6	4.0	1200	500	\
P-R1	101.6	4.0	1200	500	L-H-L
P-R2	101.6	4.0	1200	500	L-L-H

Note: ‘P’ is the unreinforced pipe model. ‘P-R1’ and ‘P-R2’ are two CFRP reinforced pipes by two different wrapping schemes. The ‘L’ and ‘H’ of the wrapping scheme mean longitudinal wrapping and hoop wrapping respectively. For instance, ‘L-H-L’ stands for longitudinal wrapping for the first and third layer, while hoop wrapping for the second layer. All units in this table are in ‘mm’.

Table 2. Material properties of the adhesive and CFRP (Kabir et al. 2016).

Material	E1 (Pa)	E2 (Pa)	G12 (Pa)	G13 (Pa)	G23 (Pa)	T (Pa)	Nu
Adhesive	$2.86\times {10}^9$	$2.86\times {10}^9$	\	\	\	$46\times {10}^6$	0.35
CFRP	$205\times {10}^9$	$25\times {10}^9$	1	1	$3.0\times {10}^9$	$4.9\times {10}^9$	0.33

Note: E_i is the elastic modulus of fibre along the i direction, G_ij is the shear modulus, Nu is the Passion’s ratio.

Figure 6. Numerical and experimental (Kabir et al. 2016) load–displacement response of P, and (a) P-R1, (b) P-R2.

Table 3. Detail information of phase two FE models.

Index	D (mm)	t (mm)	c (mm)	a (mm)	Li (mm)	Le (mm)	${\sigma }_{\max }$ (MPa)	${\sigma }_{\min }$ (MPa)
PI-1	102.0	8.1	22.75	4.5	245	1000	200.0	20.0
PI-2	102.0	8.1	6.0	3.0	245	1000	210.0	21.0
PI-3	102.0	8.1	5.0	5.0	245	1000	325.0	32.5
PI-4	102.0	8.1	18.25	3.0	245	1000	200.0	20.0
PI-5	102.0	12.7	6.0	6.0	245	1000	220.0	22.0
PI-6	102.0	12.7	6.0	3.0	245	1000	261.0	26.1

Figure 7. The procedure of evaluating surface crack growth.

Figure 8. Comparison between the experimental results (Yoo and Ando 2000) and FE results: (a) a/c versus a/t ratio; (b) fatigue life.

Figure 9. The global equivalent stress distribution of the pipe.

Figure 10. The equivalent stress distribution around the surface crack on the pipe internal surface.

Figure 11. The comparison results between the un-reinforced FE model ‘PI-6’ and the CRS reinforced FE model ‘PI-R’: (a) crack growth rate along depth direction; (b) crack growth rate along length direction; (c) a/c versus a/t ratio.

Figure 12. The normalised SIF result of FE models with different bond length: (a) normalised SIF along the crack front; (b) normalised SIF of the deepest point.

Table 4. Specimen configuration of steel pipes with various diameters and thickness, and the SIF decrease.

External diameter (mm)	102.0			168.3			219.1				273.0
Bond length (mm)	100	150	200	100	150	200	100	150	200	300	100	150	200	300
SIF decrease (%)	11.7	12.7	12.6	7.6	11.6	11.0	5.3	9.3	10.4	9.9	3.4	7.9	9.6	9.0

Note: The percentage of SIF decrease is the reduction of each model towards the corresponding model without CRS.

Figure 13. The normalised SIF result of FE models with different numbers of composite layer: (a) normalised SIF along the crack front; (b) normalised SIF of the deepest point.

Figure 14. The normalised SIF result of FE models with different CFRP modulus: (a) normalised SIF along the crack front; (b) normalised SIF of the deepest point.

Figure 15. The normalised SIF result of FE models with different adhesive thickness: (a) normalised SIF along the crack front; (b) normalised SIF of the deepest point.

Figure 16. The stress distribution in the adhesive layer with different thickness.

Figure 17. The normalised SIF result of FE models by using different types of adhesive: (a) normalised SIF along the crack front; (b) normalised SIF of the deepest point.

Figure 18. The stress distribution in the adhesive layer using different types of adhesive.

Table 5. Material properties of different type of adhesive (Kabir et al. 2016).

Adhesive type	E (Pa)	T (Pa)
MBrace saturant	$2.86\times {10}^9$	$46\times {10}^6$
Araldite K630	$6.50\times {10}^9$	$33\times {10}^6$
Sikadur 330	$4.82\times {10}^9$	$31.28\times {10}^6$

Figure 19. Wrapping scheme: (1) longitudinal and hoop wrapping; (2) inversely diagonal wrapping pattern.

Figure 20. The normalised SIF result of FE models with different CFRP wrapping orientation: (a) normalised SIF along the crack front; (b) normalised SIF of the deepest point.

Table 6. Specimen configuration of steel pipes with different aspect ratios.

Model No.	a (mm)	c (mm)	a/c	SIF decrease
1	3.0	12.0	0.25	13.15%
2	3.0	6.0	0.5	12.98%
3	4.5	6.0	0.75	12.92%
4	6.0	6.0	1.0	13.22%
5	6.0	4.5	1.5	13.13%
6	6.0	3.0	2.0	13.10%

Figure 21. The normalised SIF result of FE models by using on one layer of GFRP laminate: (a) normalised SIF along the crack front; (b) normalised SIF of the deepest point.

Table 7. Material properties of the GFRP material.

Fibre type	E1 (Pa)	E2 (Pa)	G12 (Pa)	G13 (Pa)	G23 (Pa)	T (Pa)	Nu
GFRP	$35\times {10}^9$	$35\times {10}^9$	$4.7\times {10}^9$	$3.5\times {10}^9$	$4.7\times {10}^9$	$1.1\times {10}^9$	0.33

Table 8. Specimen configuration of steel pipes with various dimensions, and the results of the SIF decrease.

Model No.	D (mm)	t (mm)	D/t	SIF decrease
1	168.3	10.97	15.34	23.58%
2	168.3	12.70	13.25	22.70%
3	168.3	14.27	11.79	19.55%
4	168.3	18.26	9.22	16.16%
5	168.3	21.95	7.67	13.89%
6	219.1	12.70	17.25	18.63%
7	273.0	12.70	21.50	15.71%
8	323.8	12.70	25.40	13.64%

Kabir MH, Fawzia S, Chan THT, Gamage JCPH, Bai JB. 2016. Experimental and numerical investigation of the behaviour of CFRP strengthened CHS beams subjected to bending. Eng Struct. 113:160–173. doi: 10.1016/j.engstruct.2016.01.047

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Yoo Y, Ando K. 2000. Circumferential inner fatigue crack growth and penetration behaviour in pipe subjected to a bending moment. Fatigue Fract Eng Mater Struct. 23:1–8. doi: 10.1046/j.1460-2695.2000.00248.x

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