Multi-scale material modelling

Material behaviour is often governed by mechanisms that span multiple scales. A typical example is macroscopic fracturing in metallic materials, which depends sensitively on properties that pertain to the micro and atomic scales. These phenomena can be captured through 'explicit' multi-scale approaches, where simulations are conducted at two or more scales are interlinked, or via 'implicit' approaches where the equations describing continuum behaviour are enriched to account for multi-scale mechanisms. For example, continuum theories can be enriched to link scales in fracture mechanics and properly characterise material behaviour at the small scales involved in crack tip deformation.

Of utmost importance to fracture processes that take place within microns ahead of the crack is the role of plastic strain gradients in elevating crack tip stresses. Non-homogeneous plastic deformation requires extra storage of geometrically necessary dislocations (GNDs) to accommodate lattice curvature. As shown by discrete dislocation simulations, the resulting increased dislocation density promotes local strain hardening and leads to high crack tip stresses that are much larger than those predicted by conventional plasticity. Crack tip gradient hardening can be captured at the continuum level by using strain gradient plasticity theory. We develop suitable numerical frameworks to characterise crack tip stresses under small and large strains, as well as modelling crack growth resistance. Moreover, our theoretical and numerical analyses reveal the existence of an elastic core at the crack tip, reminiscent of dislocation free-zones, where the stresses exhibit the linear elastic singularity. We have shown that the high crack tip stresses predicted by strain gradient plasticity provide a rational basis to understand: (1) brittle fracture in the presence of plasticity (quasi-cleavage), as observed in many material systems, such as metal-ceramic interfaces or ferritic steels at low temperatures; and (2) the brittle fracture of otherwise ductile steels that have been exposed to embrittlement species.

Another interesting research question is: how much do kinematic hardening effects affect crack growth in static/monotonic fracture? Unlike fatigue analysis, isotropic hardening has been the de facto choice for modelling crack growth resistance under static loading. Contrarily, we show that kinematic/anisotropic plastic hardening effects, so far neglected, play a fundamental role under monotonic loading due to non-proportional straining as the crack advances. Our numerical results show that fracture toughness values can easily duplicate when these kinematic hardening effects are accounted for. The results could have important implications for R-curve based damage assessment.

A recent talk on this topic is given below: