Assessment of hollow spheroid models for ductile failure prediction by limit analysis and conic programming

作者：Pastor E; Kondo D^*

来源：European Journal of Mechanics - A: Solids , 2013, 38: 100-114.

DOI：10.1016/j.euromechsol.2012.08.002

• Gurson-type models
• Oblate and prolate voids
• Micromechanics
• Limit analysis
• Upper and lower bounds
• Conic programming

Several extensions of the Gurson model have been proposed such as to account for void shape effects (e.g. Gologanu, M., Leblond, J., 1993. Approximate models for ductile metals containing non-spherical voids - case of axisymmetric prolate ellipsoidal cavities. journal of the Mechanics and Physics of Solids 41 (11), 1723-1754; Gologanu, M., Leblond, J., Perrin, G., Devaux, J., 1994. Approximate models for ductile metals containing non-spherical voids case of axisymmetric oblate ellipsoidal cavities. Journal of Engineering Materials and Technology 116, 290-297; Gologanu, M., Leblond, J., Perrin, G., Devaux, J., 1997. Recent extensions of Gurson's model for porous ductile metals. In: Suquet, P. (Ed.), Continuum Micromechanics, Springer Verlag; Garajeu, M., Suquet, P., 1997. Effective properties of porous ideally plastic or viscoplastic materials containing rigid particles. Journal of the Mechanics and Physics of Solids 45, 873-902 and more recently by Monchiet, V., Charkaluk, E., Kondo, D., 2007. An improvement of Gurson-type models of porous materials by using Eshelby-like trial velocity fields. Comptes Rendus Mecanique 335, 32-41). The main goal of this study is to assess the latter models by establishing relevant numerical LA-type lower and upper bounds to the exact solutions for 3D stress and strain conditions. Numerical limit analysis techniques are extended to the case of spheroid cavities under various 3D loading conditions. First numerical tests for the hollow sphere (Gurson) model were performed to verify the computational efficiency of the new codes. A second series of tests, performed for uniform strain rate boundary conditions and axisymmetric loadings, allowed to assess the criteria proposed by Gologanu et al. in the case of prolate voids as well as oblate ones. It is shown that the 1997-Gologanu et al. criterion appears to be very accurate for the above boundary conditions. For the assessment of a recent criterion derived by Monchiet et al. (2007), we performed other computations corresponding to uniform stress boundary conditions for both oblate and prolate cavities. It is shown that the Monchiet et al. (2007) criterion appears to be an estimate which may be improved. However, this criterion is very accurate when compared to the numerical results with strain rate boundary conditions. Finally a first attempt with 3D-loadings seems to confirm the above conclusions.

• 出版日期2013-4