Elastic-plastic transition in stochastic heterogeneous materials:Size effect and triaxiality

The transition from elastic to fully plastic deformation under monotonic loading is studied in heterogeneous materials with stochastic microstructure. The yield stress is defined on the local scale as a random field of specified mean, variance and correlation length, while all other elastic-plastic material parameters are deterministic and constant over the problem domain. The elastic-plastic transition is gradual and the range of strains over which it takes place depends on the yield stress variance (the contrast) and on strain hardening. The plastic heterogeneity leads to fluctuations in the hydrostatic stress and triaxiality fields. Large local triaxiality values result during the transition, particularly for materials with high contrast and low strain hardening. This is expected to favor void nucleation and growth with implications for the subsequent plastic deformation. Reducing the model size in one direction leads to a size effect which becomes pronounced once the respective dimension decreases below ∼10 correlation lengths of the input yield stress field. The elastic-plastic transition is broader and the level of triaxiality is reduced in the thinner samples. Therefore, the effect of heterogeneity is reduced in samples of smaller dimensions. This represents a potential mechanism for the experimentally observed increased ductility of bulk brittle polymers when put in thin fiber form, and for the 3D to 2D crazing transition in thin polymeric films.