×

Elastic field prediction for a welding repaired material using a semi-analytical method. (English) Zbl 1481.74202

Summary: Material mismatch between the welding bead and its surrounding matrix has been known to cause stress concentration due to incompatible deformation, and/or even crack regeneration, thus greatly affecting the performance of a welding repaired material. In this paper, a semi-analytical method (SAM) is developed to tackle problems for material mismatch in a welding repaired material with free surface under remote tensile loading. The heterogeneous welding bead is modeled by a homogeneous base material containing unknown eigenstrains through the equivalent inclusion method; after which a numerical discretization is adopted and the eigenstrains within each computational element are determined by iteratively solving a set of linear equations with the assistance of conjugate gradient method. Stress field arising from the eigenstrains can be obtained by employing previously derived influence coefficients. The SAM is then examined by a simple finite element model and utilized to analyze influences of material properties, aspect ratio, angle of differently shaped welding bead and interactions among multiple welding beads on the stress distribution. The SAM may have potential applications in dealing with problems related to residual stress in welded material due to eigenstrains.

MSC:

74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Guo, W.; Ding, N.; Liu, L.; Xu, N.; Li, N.; Zhang, F.; Chen, L., Stress corrosion cracking of a 304 stainless steel elbow, J. Fail. Anal. Prev., 20, 483-493 (2020)
[2] Salviato, M.; Zappalorto, M.; Maragoni, L., Exact solution for the mode III stress fields ahead of cracks initiated at sharp notch tips, Eur. J. Mech. A-Solid, 72, 88-96 (2018) · Zbl 1406.74604
[3] Zhao, X.; Xu, L.; Jing, H.; Han, Y.; Zhao, L., A strain-based fracture assessment for offshore clad pipes with ultra undermatched V groove weld joints and circumferential surface cracks under large-scale plastic strain, Eur. J. Mech. A-Solid, 74, 403-416 (2019)
[4] Mikami, Y.; Nakamura, T.; Mochizuki, M., Numerical investigation of the influence of heat source modeling on simulated residual stress distribution in weaving welds, Weld. World, 60, 41-49 (2016)
[5] Lavigne, O.; Gamboa, E.; Luzin, V.; Law, M. J.E. F.A., Analysis of intergranular stress corrosion crack paths in gas pipeline steels; straight or inclined?, Eng. Fail. Anal., 85, 26-35 (2018)
[6] Wei, X.; Ling, X.; Zhang, M., Influence of surface modifications by laser shock processing on the acid chloride stress corrosion cracking susceptibility of AISI 304 stainless steel, Eng. Fail. Anal., 91, 165-171 (2018)
[7] Jiang, W.; Liu, Z.; Gong, J.; Tu, S., Numerical simulation to study the effect of repair width on residual stresses of a stainless steel clad plate, Int. J. Pres. Ves. Pip., 87, 457-463 (2010)
[8] Huilin, Z.; Changjiang, W.; Xuemei, Y.; Xinsheng, W.; Ran, L., Automatic welding technologies for long-distance pipelines by use of all-position self-shielded flux cored wires, Nat. Gas Ind. B, 1, 113-118 (2014)
[9] Muhammad, N. A.; Wu, C., Evaluation of capabilities of ultrasonic vibration on the surface, electrical and mechanical behaviours of aluminium to copper dissimilar friction stir welds, Int. J. Mech. Sci., 183, Article 105784 pp. (2020)
[10] Salerno, G.; Bennett, C.; Sun, W.; Becker, A., Residual stress analysis and finite element modelling of repair-welded titanium sheets, Weld. World, 61, 1211-1223 (2017)
[11] Sun, T.; Roy, M.; Strong, D.; Simpson, C.; Withers, P.; Prangnell, P., Weld zone and residual stress development in AA7050 stationary shoulder friction stir T-joint weld, J. Mater. Process. Tech., 263, 256-265 (2019)
[12] Li, Y.; Ren, X.; He, J.; Zhang, Z., Effect of thermal residual stresses on ductile-to-brittle transition of a bi-material specimen by using the CAFE method, Eur. J. Mech. A-Solid, 80, Article 103889 pp. (2020) · Zbl 1473.74034
[13] Konjatić, P.; Kozak, D.; Gubeljak, N., The influence of the weld width on fracture behaviour of the heterogeneous welded joint, Key Eng. Mater., Trans. Tech. Publ., 367-370 (2012)
[14] Hyde, T.; Williams, J.; Becker, A.; Sun, W., A review of the finite element analysis of repaired welds under creep conditions, Rev. FE Anal. Repaired Welds OMMI, 2 (2003)
[15] Feng, H.; Lam, Y. C.; Zhou, K.; Kumar, S. B.; Wu, W., Elastic-plastic behavior analysis of an arbitrarily oriented crack near an elliptical inhomogeneity with generalized Irwin correction, Eur. J. Mech. A-Solid, 67, 177-186 (2018) · Zbl 1406.74113
[16] Xu, G.; Guo, Q.; Hu, Q.; Pan, H.; Qian, H.; Du, B., Numerical and Experimental Analysis of Dissimilar Repair Welding Residual Stress in P91 Steel Considering Solid-State Phase Transformation, J. Mater. Eng. Perform., 28, 5734-5748 (2019)
[17] Hu, Z. X.; Zhao, J. P.; Zhang, Y. J., Numerical Simulation of Residual Stress in P91 Repair Welding Incorporating Martensitic Transformation, Key Eng. Mater., Trans. Tech. Publ., 416-423 (2019)
[18] Jun, H. K.; Kim, D. W.; Jeon, I. S.; Lee, S. H.; Chang, Y. S., Investigation of residual stresses in a repair-welded rail head considering solid-state phase transformation, Fatigue Fract. Eng. M, 40, 1059-1071 (2017)
[19] Hemmesi, K.; Mallet, P.; Farajian, M., Numerical evaluation of surface welding residual stress behavior under multiaxial mechanical loading and experimental validations, Int. J. Mech. Sci., 168, Article 105127 pp. (2020)
[20] Dong, P., On repair weld residual stresses and significance to structural integrity, Weld. World, 62, 351-362 (2018)
[21] Song, S.; Dong, P., Residual stresses at weld repairs and effects of repair geometry, Sci. Technol. Weld. Joi, 22, 265-277 (2017)
[22] Kabo, E.; Ekberg, A.; Maglio, M., Rolling contact fatigue assessment of repair rail welds, Wear, 436, Article 203030 pp. (2019)
[23] Jun, H.-K.; Seo, J.-W.; Jeon, I.-S.; Lee, S.-H.; Chang, Y.-S., Fracture and fatigue crack growth analyses on a weld-repaired railway rail, Eng. Fall Anal., 59, 478-492 (2016)
[24] Charkhi, M.; Akbari, D., Experimental and numerical investigation of the effects of the pre-heating in the modification of residual stresses in the repair welding process, Int. J. Pres. Ves. Pip., 171, 79-91 (2019)
[25] Xia, J.; Jin, H., Numerical analysis for controlling residual stresses in welding design of dissimilar materials girth joints, Int. J. Precis. Eng. Man, 19, 57-66 (2018)
[26] Salerno, G.; Bennett, C.; Sun, W.; Becker, A.; Palumbo, N.; Kelleher, J.; Zhang, S. Y., On the interaction between welding residual stresses: a numerical and experimental investigation, Int. J. Mech. Sci., 144, 654-667 (2018)
[27] Hertelé, S.; O’Dowd, N.; Van Minnebruggen, K.; Verstraete, M.; De Waele, W., Fracture mechanics analysis of heterogeneous welds: validation of a weld homogenisation approach, Procedia Mater. Sci., 3, 1322-1329 (2014)
[28] Hertelé, S.; De Waele, W.; Verstraete, M.; Denys, R.; O’Dowd, N., J-integral analysis of heterogeneous mismatched girth welds in clamped single-edge notched tension specimens, Int. J. Pres. Ves. Pip., 119, 95-107 (2014)
[29] Leitao, C.; Zhang, B. K.; Padmanabhan, R.; Rodrigues, D., Influence of weld geometry and mismatch on formability of aluminium tailor welded blanks: numerical and experimental analysis, Sci. Technol. Weld. Joi, 16, 662-668 (2011)
[30] Chen, G.; Wang, G.; Xuan, F.; Tu, S., Mismatch effect in creep properties on creep crack growth behavior in welded joints, Mater. Des., 63, 600-608 (2014)
[31] Štefane, P.; Naib, S.; Hertelé, S.; De Waele, W.; Gubeljak, N., Crack tip constraint analysis in welded joints with pronounced strength and toughness heterogeneity, Theor. Appl. Frac. Mec., 103, Article 102293 pp. (2019)
[32] Ran, M.-M.; Sun, F.-F.; Li, G.-Q.; Kanvinde, A.; Wang, Y.-B.; Xiao, R. Y., Experimental study on the behavior of mismatched butt welded joints of high strength steel, J. Constr. Steel Res., 153, 196-208 (2019)
[33] Zhou, Q.; Jin, X.; Wang, Z.; Wang, J.; Keer, L. M.; Wang, Q., Numerical EIM with 3D FFT for the contact with a smooth or rough surface involving complicated and distributed inhomogeneities, Tribol. Int., 93, 91-103 (2016)
[34] Jacq, C.; Nelias, D.; Lormand, G.; Girodin, D., Development of a three-dimensional semi-analytical elastic-plastic contact code, J. Tribol., 124, 653-667 (2002)
[35] Eshelby, J. D., The determination of the elastic field of an ellipsoidal inclusion, and related problems, P. Roy. Soc. A-Math Phys., 241, 376-396 (1957) · Zbl 0079.39606
[36] Eshelby, J. D., The elastic field outside an ellipsoidal inclusion, P. Roy. Soc. A-Math Phy., 252, 561-569 (1959) · Zbl 0092.42001
[37] Phan-Thien, N.; Kim, S., Microstructures in elastic media: principles and computational methods (1994), Oxford University Press: Oxford University Press New York · Zbl 0908.73003
[38] Zhou, K.; Chen, W. W.; Keer, L. M.; Ai, X.; Sawamiphakdi, K.; Glaws, P.; Wang, Q. J., Multiple 3D inhomogeneous inclusions in a half space under contact loading, Mech. Mater., 43, 444-457 (2011)
[39] Zhou, K.; Keer, L. M.; Wang, Q. J., Semi-analytic solution for multiple interacting three-dimensional inhomogeneous inclusions of arbitrary shape in an infinite space, Int. J. Numer. Meth. Eng., 87, 617-638 (2011) · Zbl 1242.74022
[40] Yang, W.; Huang, Y.; Zhou, Q.; Wang, J.; Jin, X.; Keer, L. M., Parametric study on stressed volume and its application to the quantification of rolling contact fatigue performance of heterogeneous material, Tribol. Int., 107, 221-232 (2017)
[41] Yang, W.; Zhou, Q.; Huang, Y.; Wang, J.; Jin, X.; Chen, W. W.; Keer, L. M.; Wang, Q. J., A thermoelastic contact model between a sliding sphere and a stationary half space distributed with spherical inhomogeneities, Tribol. Int., 131, 33-44 (2019)
[42] Yang, W.; Zhou, Q.; Wang, J.; Khoo, B. C.; Phan-Thien, N., Equivalent inclusion method for arbitrary cavities or cracks in an elastic infinite/semi-infinite space, Int. J. Mech. Sci., 195, Article 106259 pp. (2021)
[43] Chiu, Y., On the internal stresses in a half plane and a layer containing localized inelastic strains or inclusions, J. Appl. Mech., 47, 313-318 (1980) · Zbl 0491.73018
[44] Jin, X.; Keer, L. M.; Wang, Q., New Green’s function for stress field and a note of its application in quantum-wire structures, Int. J. Solids Struct., 46, 3788-3798 (2009) · Zbl 1176.74044
[45] Chiu, Y. P., On the stress field and surface deformation in a half space with a cuboidal zone in which initial strains are uniform, J. Appl. Mech.-T ASME, 45, 302-306 (1978) · Zbl 0386.73004
[46] Wang, Z.; Jin, X.; Zhou, Q.; Ai, X.; Keer, L. M.; Wang, Q., An efficient numerical method with a parallel computational strategy for solving arbitrarily shaped inclusions in elastoplastic contact problems, J. Tribol., 135, Article 031401 pp. (2013)
[47] Polonsky, I. A.; Keer, L. M., A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques, Wear, 231, 206-219 (1999)
[48] Liu, S.; Wang, Q.; Liu, G., A versatile method of discrete convolution and FFT (DC-FFT) for contact analyses, Wear, 243, 101-111 (2000)
[49] Zhou, Q.; Jin, X.; Wang, Z.; Wang, J.; Keer, L. M.; Wang, Q., Numerical implementation of the equivalent inclusion method for 2D arbitrarily shaped inhomogeneities, J. Elast., 118, 39-61 (2015) · Zbl 1305.74085
[50] Johnson, K. L., Contact mechanics (1987), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0599.73108
[51] Ni, J.; Zhuang, X.; Abdel Wahab, M., Review on the prediction of residual stress in welded steel components, CMC-Comput. Mater. Conf., 62, 495-523 (2020)
[52] Mura, T., Micromechanics of defects in solids (2013), Springer Science & Business Media: Springer Science & Business Media Dordrecht
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.