Strain gradient plasticity in glassy polymers

Plasticity in material is primarily a function of strain. Thus, no length scale enters the constitutive law and no size effect is predicted. However, recent observed plasticity phenomena displayed size dependence. Size dependence can be included in the constitutive law by postulating that yield stress depends upon both strain and strain gradient. For metal, dislocation-based and phenomenological strain gradient plasticity laws have been developed on the basis of torsion as well as indentation evidence. In the dislocation approach, the accumulation of both randomly stored and geometrically necessary dislocations gives rise to deformation flow resistance. In the phenomenological approach, a non-linear generalization of the Cosserat couple stress theory is introduced to represent the roles of strain hardening and strain gradient hardening. For glassy polymer, microstructural studies of the deformation processes have shown some similar characteristics to those in crystalline materials such as slips and kink bands. This suggests that deformation processes in polymers might potentially affected by strain gradient. The aim of the present research is to develop a strain gradient plasticity law for glassy polymers. In order to develop a strain gradient plasticity law for glassy polymers, existing approaches and methodologies for strain gradient plasticity of crystalline metal have been firstly reviewed. A strain gradient plasticity law based on Argon's molecular kinking yielding theory is proposed for glassy polymers. In this law, stress is a function of both strain and strain gradient with a strain gradient plasticity modulus M which is temperature and molecular dependence. In order to determine the validity of the proposed relation, the effects of strain gradient on plastic deformation in thermosetting epoxy resin and polycarbonate thermoplastic were investigated using nanoindentation and atomic froce microscopy while the molecular dependence is investigated using epoxy with varied cross-link density. Similar to the case for metals, both epoxy and polycarbonate exhibited elevated hardening as a result of strain gradient imposed during indentation. Comparison of indentation hardnesses of epoxy and polycarbonate with strain gradient plasticity law gave good agreement. This suggests that strain gradient plasticity in glassy polymers is determined by molecular kinking mechanisms. The influence of the molecular structure, specifically the experimental investigation of the effect of cross-link density, revealed that both the characteristic length L and the strain gradient modulus are directly dependent on cross-link density. Highly cross-linked epoxies are more sensitive to strain gradient. The physical rationale behind the dependence and the relation between strain gradient plasticity and conventional plasticity in glassy polymer are discussed with respect to these findings