Biaxial loading of continuously graded thermoviscoplastic materials. (English) Zbl 1163.74009
Summary: We study biaxial loading of a sheet made of a continuously graded thermoviscoplastic material. The material phases are supposed to exhibit thermal softening, strain-rate sensitivity and strain hardening, continuously varying along all directions. First, we formulate the plane stress problem for a non-homogeneous material and study the behavior of temperature, strain and strain rate related to inhomogeneities of thermomechanical parameters and geometrical defects. Next we present the “effective” instability analysis of D. Dudzinski and A. Molinari [Int. J. Solids Struct. 27, No. 5, 601–628 (1991; Zbl 0734.73032)], adapted to the non-homogeneous case, to define the critical conditions and select the localization modes, by studying the overall strains for which a certain level of instability growth is developed. Finally, we present the numerical simulation of the full nonlinear dynamical problem. Several aspects of the deformation process and the related role of non-homogeneities are analyzed: onset of strain and temperature localization, ductility, contours of temperature increase as detectors of instability, interplay with initial defects, multiple necking, decrease of thinning-rate, and finally the variation of multiple necking due to boundary conditions.
MSC:
| 74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |
| 74F05 | Thermal effects in solid mechanics |
| 74E05 | Inhomogeneity in solid mechanics |
| 74H10 | Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics |
| 74S05 | Finite element methods applied to problems in solid mechanics |
Keywords:
dynamic plane stress analysis; non-homogeneous materials; strain/temperature localization; instabilityCitations:
Zbl 0734.73032Software:
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