Numerical investigation of residual ultimate strength of dented metallic pipes subjected to pure bending

Figures & data

Figure 1. Sketch of a plain dent on pipe surface: (a) dent cross-section; (b) top view. (This figure is available in colour online.)

Figure 2. Sketch of dented pipe subjected to pure bending moment.

Figure 3. FEA model of dented pipe: (a) general mesh distribution; (b) refined dent region. (This figure is available in colour online.)

Table 1. Principal dimension of pipe models for simulation.

Pipe type	Diameter D (mm)	Thickness t (mm)	Length L0(mm)	D/t	L0/D	Material
Seamless	168.3	7.9	720	21.3	4.28	Q345 (GB/T 1591 2008)

Figure 4. The fitted true stress-strain curve for numerical investigation. (This figure is available in colour online.)

Figure 5. Configuration of four-point bending test set-up in laboratory. (This figure is available in colour online.)

Figure 6. Dent damage from both test and numerical models: (a) artificial dent damage on specimen; (b) dent damage on numerical model. (This figure is available in colour online.)

Table 2. Summary of both test and simulation results on dented specimens (dimension unit: mm; angle unit: degree; dents are on the compression side of specimens).

				Dent	Dent	BM (test)	BM (FEA)	Discrepancy	κ(test)	κ(FEA)	Discrepancy
S.N.	D	t	D/t	(ld × wd × dd)	angle	(kNm)	(kNm)	(%)	(1/m)	(1/m)	(%)
S2N1	169.21	8.25	20.51	89 × 68 × 10.3	90	92.57	91.75	−0.89%	0.154	0.124	−19.48%
S2N2	168.23	8.13	20.69	100 × 75 × 10.3	90	93.55	87.53	−6.44%	0.109	0.108	−0.92%
S2N3	169.38	7.90	21.44	130 × 60 × 10.3	45	91.65	92.25	0.66%	0.158	0.122	−22.79%
S2N5	168.74	8.15	20.70	110 × 85 × 10.3	90	90.97	87.00	−4.36%	0.164	0.101	−38.42%

Figure 7. Comparison of failure mode between test and simulation (S2N1). (This figure is available in colour online.)

Figure 8. (a) Sketch of representative paths on specimen surface (S2N1); (b) four stages during the loading procedure; (c) strain along the longitudinal path AB; (d) strain along the hoop path CD. (This figure is available in colour online.)

Figure 9. Comparison between numerical and test results in terms of bending moment-curvature diagram for specimens with dent: (a) specimen S2N2 with 90° dent on compression side; (b) specimen S2N3 with 45° dent on compression side; (c) specimen S2N5 with 90° dent on compression side. (This figure is available in colour online.)

Figure 10. The first eigenvalue-buckling mode of a perfect pipe subjected to pure bending. (This figure is available in colour online.)

Figure 11. Bending moment-curvature diagram of a pipe with varying of initial imperfection (no dent damage). (This figure is available in colour online.)

Figure 12. The bending capacity of a dented pipe with varying of D/t. (This figure is available in colour online.)

Figure 13. Bending moment-curvature diagram with varied diameter-to-thickness ratio (D/t). (This figure is available in colour online.)

Figure 14. Membrane stress distribution of a dented pipe with different diameter-to-thickness ratio at the ultimate bending point. (This figure is available in colour online.)

Figure 15. Bending moment-curvature diagram of pipes with varying of the dent location (l_d = 100 mm, w_d = 60 mm). (This figure is available in colour online.)

Figure 16. The bending capacity of a dented pipe with varying of dent rotation angle. (This figure is available in colour online.)

Figure 17. (a) Membrane stress distribution of a dented pipe with dent rotation angle θ_d = 45° at the ultimate bending point; (b) membrane stress distribution of a dented pipe with dent rotation angle θ_d = 90° at the ultimate bending point. (This figure is available in color online.)

Figure 18. Equivalent plastic strain (PEEQ) of a dented pipe with varying of dent rotation angle (θ_d) at the ultimate bending point. (This figure is available in color online.)

Figure 19. The structural response in terms of bending capacity and maximum lateral displacement of pipe with varying of different parameters: (a) dented pipe with varying of dent depth; (b) dented pipe with varying of dent length; (c) dented pipe with varying of dent width. (This figure is available in colour online.)

Figure 20. Lateral displacement distribution of a dented pipe with the varied dent depth d_d at the residual limit point. (This figure is available in color online.)

Table 3. Residual ultimate strength of pipes with varying of dent depth.

	l′d = 100 mm, wd = 60 mm
	dd/t
Capacity	0.13	0.25	0.38	0.51	0.76	1.01	1.27	0.1.39	1.52	1.65	1.77	1.90
Mcr/My	1.279	1.277	1.246	1.222	1.161	1.150	1.100	1.10	1.110	1.104	1.100	1.098
Ulateral/t	0.13	0.13	0.11	0.15	0.12	0.22	0.22	0.33	0.33	0.35	0.36	0.37

Table 4. Residual ultimate strength of pipes with varying of dent length.

	dd = 10 mm, wd = 60 mm
Capacity	0.389	0.776	1.164	1.551	1.939	2.327	2.715	3.103	3.491	3.878	4.266	5.042
Mcr/My	1.374	1.393	1.335	1.285	1.261	1.236	1.214	1.172	1.152	1.100	1.078	1.040
Ulateral/t	0.48	0.54	0.34	0.26	0.23	0.26	0.26	0.28	0.29	0.22	0.22	0.23

Table 5. Residual ultimate strength of pipes with varying of dent width.

	dd = 10 mm, l′d = 100 mm
Capacity	0.397	0.795	1.192	1.589	1.986	2.384	2.781	3.178	3.576	3.973	4.370	5.165
Mcr/My	1.145	1.133	1.125	1.096	1.122	1.100	1.105	1.134	1.120	1.151	1.135	1.175
Ulateral/t	0.20	0.32	0.32	0.25	0.30	0.22	0.21	0.26	0.21	0.26	0.21	0.26

Figure 21. Comparison of model accuracy: (a) comparison between predictions and both test and simulation results (M_cr/M_i); (b) prediction of strength with varying of dent parameter (λ_l).

GB/T 1591., 2008. 低合金高强度结构钢 [High strength low alloy structural steels]. China: Chinese National Standard. Chinese.

 Google Scholar