Shape Optimization of the Conventional Simple Shear Specimen

Abstract:

Shear tests of rectangular sample are widely used by the scientific community for characterizing the material behavior due to large strains obtained. However, for some hard metals, such as the dual-phase steel DP 980, premature rupture occurs in the vicinity of the grips. Due to this fact, the shape of the shear specimen is optimized in this work with the aim of maximizing the deformation achieved in the central part of the specimen without the occurrence of rupture near the grips. As the rupture occurs at the corners of the shear specimen only the boundaries are subjected to shape optimization. A representation with cubic splines is adopted for the definition of the boundaries geometry. The material is defined by Hill’s 1948 yield criterion combined with an isotropic hardening law. Two macroscopic rupture criteria are considered and an objective function approach based on the maximization of the shear strain average value is defined. For this study, a direct search optimization method is used for minimizing the objective function. The optimized geometries obtained for the different rupture criteria and different set of design variables are compared. The use of a larger number of design variables allows to obtain optimized geometries with higher average shear strain. The best specimen geometry shape allows increasing the maximum deformation of DP 980 steel to 1.05 without occurrence of rupture. In addition, the final specimen geometries show a concave shape for the boundaries which means that this kind of shape is the best one to delay the rupture in shear specimens.

• Periodical: Key Engineering Materials (Volumes 554-557)
• Pages: 2156-2164
• DOI: https://doi.org/10.4028/www.scientific.net/KEM.554-557.2156
• Online since: June 2013
• Authors: Nelson Souto, António Andrade-Campos, Sandrine Thuillier
• Keywords: Large Strain, Rupture Criterion, Shape Optimization, Shear Specimen

References

[1] Iosipescu, N.; New Accurate Procedure for Single Shear Testing of Metals, Journal of Materials 2:537-566, 1967.

[2] Miyauchi, K.; A proposal of a planar simple shear test in sheet metals, Sci. Papers RIKEN 78:27-42, 1984.

[3] G'Shell, C.; Boni, S.; Shrivastava, S.; Application of the simple shear test for determination of the plastic behaviour of solid polymers at large strains, Journal of Materials Science 18:903-918, 1983.

DOI: 10.1007/bf00745590

[4] Rauch, E. F.; G'Shell, C.; Flow localisation induced by a change in strain path in mild steel Materials Science and Engineering A 111:71-80, 1989.

DOI: 10.1016/0921-5093(89)90199-8

[5] Genevois, P.; Etude expérimental et modélisation du comportement plastique anisotrope de tôles d'acier en grandes déformations, Ph.D. Thesis, Institut National Polytecnique de Grenoble, France, 1992.

[6] Bouvier, S.; Haddadi, H.; Levée, P.; Teodosiu, C.; Simple shear tests: Experimental techniques and characterization of the plastic anisotropy of rolled sheets at large strains, Journal of Materials Processing Technology v.172:96–103, 2006.

DOI: 10.1016/j.jmatprotec.2005.09.003

[7] Thuillier, S.; Manach, P. Y.; Comparison of the Work-Hardening of Metallic Sheets using Tensile and Shear Strain Paths, International Journal of Plasticity 25:733-751, 2008.

DOI: 10.1016/j.ijplas.2008.07.002

[8] Yoon, J. W.; Barlat, F.; Grácio, J.; Rauch, E.; Anisotropic Strain Hardening Behavior in Simple Shear for Cube Textured Aluminum Alloy Sheets, International Journal of Plasticity v.21:pp.2426-2447, 2005.

DOI: 10.1016/j.ijplas.2005.03.014

[9] Dunand, M.; Mohr, D.; Optimized butterfly specimen for the fracture testing of sheet materials under combined normal and shear loading, Engineering Fracture Mechanics 78:2919–2934, 2011.

DOI: 10.1016/j.engfracmech.2011.08.008

[10] Mishra, A.; Experimental investigation and numerical prediction of forming limits in bending of metallic sheets, Ph.D. Thesis, Université de Bretagne-Sud (UBS), France, to be defended in 2013.

[11] Mishra, A.; Leguen, C.; Thuillier, S.; Marie, E.; Investigation of ductile damage in DP 980 steel sheets using mechanical tests and x-ray microtomography, Proc. of the 14th International ESAFORM Conference on Material Forming: ESAFORM 2011, (Eds.) 1353:1464-1469; AIP Conference Proceedings, 2011.

DOI: 10.1063/1.3589723

[12] Abaqus; ABAQUS/Standard - User's manual, Dassault Systémes, 2009.

[13] Rice, J. R.; Tracey, D. M.; On the ductile enlargement of voids in triaxial stress fields, Journal of the Mechanics and Physics of Solids 17:201-217, 1969.

DOI: 10.1016/0022-5096(69)90033-7

[14] Cockroft, M. G.; Latham, D. J.; Ductility and the workability of metals, Journal of the Institute of Metals 96:33-39, 1968.

[15] Coleman, T.; Branch, M. A.; Grace, A.; Optimization Toolbox - for use with Matlab, MathWorks Inc., 1999.

[16] González, J. L. M.; Parameter optimisation and adjustment by the simplex method (Nelder-Mead), Proc. of the 1st Meeting of EcosimPro Users, (Eds.) C19:1-11; UNED, 2001.

[17] Lagarias, J. C.; Reeds, J. A.; Wright, M. H.; Wright, P. E.; Convergence properties of the Nelder-Mead simplex method in low dimensions, SIAM Journal Optimization 9:112-147, 1998.

DOI: 10.1137/s1052623496303470