Numerical simulation of grain-size effects on creep crack growth by means of grain elements

The effect of grain size on creep crack growth is investigated by means of a numerical technique in which the actual crack growth process is simulated in a discrete manner by grain elements and grain boundary elements. The grain elements account for the creep deformation of individual grains, while grain boundary cavitation and sliding are accounted for by grain boundary elements between the grains. This grain-element technique allows for an independent study of multiple grain size effects: a (direct) size effect related to the specimen size/grain size ratio or an (indirect) effect related to the effect of grain size on nucleation rate and creep resistance. Preliminary numerical results are presented concerning the direct effect of grain size, which predict that the crack growth rate and brittleness increase with grain size.

Microstructural modelling of creep crack growth from a blunted crack

The effect of crack tip blunting on the initial stages of creep crack growth is investigated by means of a planar microstructural model in which grains are represented discretely. The actual linking-up process of discrete microcracks with the macroscopic crack is simulated, with full account of the underlying physical mechanisms such as the nucleation, growth and coalescence of grain boundary cavities accompanied by grain boundary sliding. Results are presented for C*-controlled mode I crack growth under small-scale damage conditions. Particular attention is focused on creep constrained vs. unconstrained growth. Also the effect of grain boundary shear stresses on linking-up is investigated through shear-modified nucleation and growth models. The computations show a general trend that while an initially sharp crack tends to propagate away from the original crack plane, crack tip blunting reduces the crack growth direction. Under unconstrained conditions this can be partly rationalized by the strain rate and facet stress distribution corresponding to steady-state creep.

Plasticity size effects in tension and compression of single crystals

The effect of size and loading conditions on the tension and compression stress–strain response of micron-sized planar crystals is investigated using discrete dislocation plasticity. The crystals are taken to have a single active slip system and both small-strain and finite-strain analyses are carried out. When rotation of the tensile axis is constrained, the build-up of geometrically necessary dislocations results in a weak size dependence but a strong Bauschinger effect. On the other hand, when rotation of the tensile axis is unconstrained, there is a strong size dependence, with the flow strength increasing with decreasing specimen size, and a negligible Bauschinger effect. Below a certain specimen size, the flow strength of the crystals is set by the nucleation strength of the initially present Frank–Read sources. The main features of the size dependence are the same for the small-strain and finite-strain analyses. However, the predicted hardening rates differ and the finite-strain analyses give rise to some tension–compression asymmetry.

Discrete dislocation simulations and size dependent hardening in single slip

Plastic deformation in two-dimensional monophase and composite materials is studied using a discrete dislocation dynamics method. In this method, dislocations are represented by line defects in a linear elastic medium, and their interactions with boundaries or second-phase elastic particles are incorporated through a complementary finite element solution. The formulation includes a set of simple constitutive rules to model the lattice resistance to dislocation glide, as well as the generation, annihilation and pinning of dislocations at point obstacles. The focus is on the predicted strain hardening of these materials when only a single slip system is active. When the particle morphology is such as to require geometrically necessary dislocations, hardening in the composite materials exhibits a distinct size effect. This size effect is weaker than that predicted by simple analytical estimates based on geometrically necessary dislocations.