The following nomenclature is used in this Chapter: a allotriomorphic ferrite aa acicular ferrite a w Widmanstatten ferrite ~ delta-ferrite !:i.0' increment in yield stress I austenite € true strain € true average strain €~ true plastic strain in softer phase of a dual-phase steel €~I true plastic strain in harder phase of a dual-phase steel €UTS true strain at ultimate tensile stress €y true s...

We show the existence of globally stable quasistatic evolutions for a rateindependent material model with elastoplasticity and incomplete damage, in small strain assumptions. The main feature of our model is that the scalar internal variable which describes the damage affects both the elastic tensor and the plastic yield surface. It is also possible to require that the history of plastic strain...

A mechanism-based theory of strain gradient (MSG) plasticity has been proposed in Part I of this paper. The theory is based on a multiscale framework linking the microscale notion of statistically stored and geometrically necessary dislocations to the mesoscale notion of plastic strain and strain gradient. This theory is motivated by our recent analysis of indentation experiments which strongly...

The study of polycrystals of shape-memory alloys and rigid-perfectly plastic materials gives rise to problems of nonlinear homogenization involving degenerate energies. This paper presents a characterization of the stress and strain fields in a class of problems in plane strain, and uses it to study examples including checkerboards and hexagonal microstructures. Consequences for shape-memory al...

This paper presents a micromechanics-based elastoplastic damage model for quasi-brittle rocks in compression stress state. The plastic strain is considered to be related to frictional sliding along microcracks and inherently coupled with damage evolution. By following a homogenization procedure, we first determine the free energy for the matrix-cracks system. The thermodynamic force associated ...

Abstract—A model to predict the plastic zone size for material under plane stress condition has been developed and verified experimentally. The developed model is a function of crack size, crack angle and material property (dislocation density). Simulation and validation results show that the model developed show good agreement with experimental results. Samples of low carbon steel (0.035%C) wi...

We discuss a new solution algorithm for solving elastoplastic problems with hardening. The one time-step elastoplastic problem can be formulated as a convex minimization problem with a continuous but non-smooth functional dependening on unknown displacement smoothly and on the plastic strain non-smoothly. It is shown that the functional structure allows the application of the Moreau-Yosida Theo...

For very shallow indentations in W, Al, Au, and Fe-3wt%Si single crystals, hardness decreased with increasing depth irrespective of increasing or decreasing strain gradients. As such, strain gradient theory appears insufficient to explain the indentation size effect (ISE) at depths less than several hundred nanometers. Present research links the ISE to a ratio between the energy of newly create...

In the present research, the relationship between the strain increment and Lode parameter was obtained by using Lode parameter and Levy-Mises equation. The quantitative relation between different strain increments was presented and the relationship between plastic deformation types and Lode parameter was demonstrated. The relations between plastic deformation types and stress states were reveal...

Many studies monitoring the formation of martensite during the tensile deformation of austenite report data which are, in principle, affected by both the applied stress and the resulting plastic strain. It is not clear in these circumstances whether the transformation is stress induced (i.e. the stress provides a mechanical driving force) or whether the generation of defects during deformation ...