Ο ρόλος των υλικών ανομοιογενειών στη θερμοϊξωπλαστική διάτμηση

Abstract

The role of materials non-homogeneities in the emergence and evolution of nonuniformities in thermoviscoplastic shearing, is examined. The thermomechanical parameters (strain hardening, strain rate sensitivity and thermal softening), as well as all the material parameters, are supposed to depend explicitly on the space variable. By considering both the isothermal and anisothermal cases, is proved that at regions, where the thermomechanical parameters vary considerably with respect to the position, the strain gradient is monotonically increasing in the course of deformation, independently of the relation between strain hardening, strain rate sensitivity and thermal softening. Thus, even stable (in the sense that the “blow up” of the strain is excluded) solutions may result in catastrophic deformation. This conclusion suggests that new non-uniformity measures, based on the control of the strain gradient, are more suitable to give stability conditions for non-homogeneous materials. Numerical solutions concerning the interplay between material non-homogeneities, initial defects and boundary conditions, are given. The influence of either one may overcome that of the others, in the formation of shearing zones. The results are in complete agreement with the analytical behavior of the models. Moreover, in the case of a multicomponent material of periodic structure, results similar to those of CHARALAMBAKIS & MURAT ([1989] and [1990]) were found, showing that the strain gradient “oscillates”, while the stress converges strongly, due to its compensated nature, as the thickness of the layers becomes very small. Finally, some numerical homogenization results are presented. The “homogenized” parameters can be approximated by the mean values of the parameters of the non-homogeneous material. However, the behavior of the “homogenized” material cannot reveal the destabilizing effect of the amplification of strain gradient due exclusively to the material nonhomogeneities.