Internal stresses due to slip gradients
Our focus is on continuum modeling of the crystal lattice resistance arises from short range (thermal components) and long range (Athermal component) interaction of geometrically necessary dislocation (GNDs) in hierarchical nanostructured/miniaturized crystalline materials.
The length-dependent behaviors of the metal matrix composites (MMCs) comprising nano/ microcrystalline matrices and reinforcements are investigated using mechanism based crystal plasticity theory. Systematic computational simulations on bare polycrystalline and MMC architectures are performed in order to isolate the contributions due to grain size, inclusion size and the interaction thereof. Based on these results, an analytical model developed for the interaction hardening exhibits a Hall-Petch type dependence on these microstructural sizes that can be incorporated into homogenized approaches.
A length dependent continuum crystal plasticity theory is developed accounting for internal residual stresses that arise from two sources: (1) GND-GND elastic long range interaction (LRI) arising from the finite/non-homogeneous distribution of the GND density field and (2) the LRI between the GND density and free surfaces appear as image fields. Using some numerical examples, it has been shown that the internal stresses affect the overall strengthening and hardening under monotonic loading, which is mediated by the severity of initial imperfections which are common in miniaturized specimens in the form of tapered surfaces, fillets, fabrication induced damage, and so on. Under cyclic loading the asymmetry in the tensile and compressive strengths due to this internal stress is also strongly influenced by the degree of imperfection. A comparison of developed model with experimental results suggests that the length-scale for internal stresses, described as a correlation length-scale, should increase with decreasing specimen thickness. This observation is rationalized by associating the internal length-scale with the average slip-plane spacing, which may increase with decreasing specimen size due to paucity of dislocation sources.