Journal of Applied and Computational Mechanics

Application of a Generalized Isotropic Yield Criterion to Determining Limit Load Solutions for Highly Undermatched Welded Bars in Tension

Document Type : Research Paper

Authors

1 Ishlinsky Institute for Problems in Mechanics RAS, 101-1 Prospect Vernadskogo, Moscow, 119526, Russian Federation

2 School of Mechanical Engineering and Automation, Beihang University, No. 37 Xueyuan Road, Beijing, 100191, China

3 Department of Civil Engineering, RUDN University, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

4 Department of Applied Informatics and Intelligent Systems in Humanities, RUDN University, 6 Miklukho-Maklaya St, Moscow, 117198, Russian Federation

Abstract

The limit load is an important input parameter of analytical flaw assessment procedures. The accuracy of limit load solutions affects the accuracy of these procedures. The present paper evaluates the influence of a class of the work functions involved in the upper bound theorem on the upper bound limit load of a round highly undermatched tensile bar. It is assumed that the weld contains a crack. The boundary value problem is axisymmetric. The work functions considered cover the entire range of physically reasonable yield criteria, assuming the material is isotropic and incompressible. The kinematically admissible velocity field chosen accounts for some features of the real velocity field. In particular, the kinematically admissible velocity field is singular near the interface between the base material and weld. As a result, the new solution predicts a more accurate limit load than available solutions for the von Mises and Tresca yield criteria. Moreover, the effect of the generalized yield criterion associated with the work functions above on the limit load is shown.

Keywords

Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Schwalbe, K.-H., Kalluri, S., McGaw, R.M., Neimitz, A., Dean, S.W. On the Beauty of Analytical Models for Fatigue Crack Propagation and Fracture—A Personal Historical Review, Journal of ASTM International, 7, 2010, 102713, doi:10.1520/JAI102713.
[2] Zerbst, U., Madia, M., Analytical Flaw Assessment, Engineering Fracture Mechanics, 187, 2018, 316–367, doi:10.1016/j.engfracmech.2017.12.002.
[3] Konjatic, P., Katinic, M., Kozak, D., Gubeljak, N., Yield Load Solutions for SE(B) Fracture Toughness Specimen with I-Shaped Heterogeneous Weld, Materials, 15, 2021, 214, doi:10.3390/ma15010214.
[4] Njock Bayock, F., Kah, P., Mvola, B., Layus, P., Effect of Heat Input and Undermatched Filler Wire on the Microstructure and Mechanical Properties of Dissimilar S700MC/S960QC High-Strength Steels, Metals, 9, 2019, 883, doi:10.3390/met9080883.
[5] Zhao, H., Li, X., Lie, S.T., Strain-Based Fracture Assessment for an Interface Crack in Clad Pipes under Complicated Loading Conditions, Ocean Engineering, 198, 2020, 106992, doi:10.1016/j.oceaneng.2020.106992.
[6] Tümer, M., Warchomicka, F.G., Pahr, H., Enzinger, N., Mechanical and Microstructural Characterization of Solid Wire Undermatched Multilayer Welded S1100MC in Different Positions, Journal of Manufacturing Processes, 73, 2022, 849–860, doi:10.1016/j.jmapro.2021.11.021.
[7] Miloševic, N.Z., Sedmak, A.S., Bakic, G.M., Lazic, V., Miloševic, M., Mladenovic, G., Maslarevic, A., Determination of the Actual Stress–Strain Diagram for Undermatching Welded Joint Using DIC and FEM, Materials, 14, 2021, 4691, doi:10.3390/ma14164691.
[8] Kim, Y.-J., Schwalbe, K.-H., Compendium of Yield Load Solutions for Strength Mis-Matched DE(T), SE(B) and C(T) Specimens, Engineering Fracture Mechanics, 68, 2001, 1137–1151, doi:10.1016/S0013-7944(01)00016-9.
[9] Hao, S., Cornec, A., Schwalbe, K.H., Plastic stress-strain fields and limit loads of a plane strain cracked tensile panel with a mismatched welded joint, International Journal of Solids and Structures, 34(3), 1997, 297–326, doi:10.1016/S0020-7683(96)00021-2.
[10] Drucker, D.C., Prager, W., Greenberg, H.J., Extended Limit Design Theorems for Continuous Media, Quarterly of Applied Mathematics, 9, 1952, 381–389, doi:10.1090/qam/45573.
[11] Hill, R., The Mathematical Theory of Plasticity, Clarendon Press, Oxford, UK, 1950.
[12] Hill, R., Lee, E.H., Tupper, S.J., A Method of Numerical Analysis of Plastic Flow in Plane Strain and Its Application to the Compression of a Ductile Material Between Rough Plates, Journal of Applied Mechanics, 18(1), 1951, 46–52.
[13] Alexandrov, S., Chung, K.-H., Chung, K., Effect of Plastic Anisotropy of Weld on Limit Load of Undermatched Middle Cracked Tension Specimens, Fatigue & Fracture of Engineering Materials & Structures, 30, 2007, 333–341, doi:10.1111/j.1460-2695.2007.01110.x.
[14] Alexandrov, S., Lyamina, E., Pirumov, A., Nguyen, D.K., A Limit Load Solution for Anisotropic Welded Cracked Plates in Pure Bending, Symmetry, 12, 2020, 1764, doi:10.3390/sym12111764.
[15] Lyamina, E., Kalenova, N., Nguyen, D.K., Influence of Plastic Anisotropy on the Limit Load of an Overmatched Cracked Tension Specimen, Symmetry, 12, 2020, 1079, doi:10.3390/sym12071079.
[16] Aranđelovic, M., Sedmak, S., Jovicic, R., Perkovic, S., Burzic, Z., Radu, D., Radakovic, Z., Numerical and Experimental Investigations of Fracture Behaviour of Welded Joints with Multiple Defects, Materials, 14, 2021, 4832, doi:10.3390/ma14174832.
[17] Alexandrov, S.E., Goldstein, R.V., Tchikanova, N.N., Upper Bound Limit Load Solutions for a Round Welded Bar with an Internal Axisymmetric Crack, Fatigue & Fracture of Engineering Materials & Structures, 22, 1999, 775–780, doi:10.1046/j.1460-2695.1999.t01-1-00208.x.
[18] Hill, R., New Horizons in the Mechanics of Solids, Journal of the Mechanics and Physics of Solids, 5, 1956, 66–74, doi:10.1016/0022-5096(56)90009-6.
[19] Alexandrov, S., Lyamina, E., Jeng, Y.-R., Application of the Upper Bound Theorem for Metal Forming Processes Considering an Arbitrary Isotropic Pressure-Independent Yield Criterion with No Strength Differential Effect, International Journal of Advanced Manufacturing Technology, 126, 2023, 3311-3321 doi:10.1007/s00170-023-11312-5.
[20] Hosford, W.F., A Generalized Isotropic Yield Criterion, Journal of Applied Mechanics, 39, 1972, 607–609, doi:10.1115/1.3422732.
[21] Alexandrov, S., Richmond, O., Singular Plastic Flow Fields near Surfaces of Maximum Friction Stress, International Journal of Non-Linear Mechanics, 36, 2001, 1–11, doi:10.1016/S0020-7462(99)00075-X.
[22] Alexandrov, S., Richmond, O., On Estimating the Tensile Strength of an Adhesive Plastic Layer of Arbitrary Simply Connected Contour, International Journal of Solids and Structures, 37, 2000, 669–686, doi:10.1016/S0020-7683(99)00023-2.
[23] Kudo, H., Some Analytical and Experimental Studies of Axi-Symmetric Cold Forging and Extrusion—I, International Journal of Mechanical Sciences, 2, 1960, 102–127, doi:10.1016/0020-7403(60)90016-3.
Journal of Applied and Computational Mechanics

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