Mechanical Properties
The mechanical properties for the compound material are generally computed using linear weighting by the phase fractions. The exception is in the case where phase plasticity is modeled, where other types of weighting schemes can be used for the initial yield strength of the compound material.
Elasticity
The elastic behavior of the compound material is assumed to be isotropic and defined by a linear weighting of the Young’s moduli and Poisson’s ratios of the phases. This is reasonable because the elastic properties for the different phases are similar at a given temperature.
Plasticity
It is not obvious what weighting scheme should be used to define an effective initial yield strength because the initial yield strengths of the phases will differ. The following weighting scheme is used:
The simplest model for the initial yield strength of the compound material uses a linear weighting
This scheme is reasonable when the initial yield strengths are similar. However, it is well known that the yield strength of some metallurgical phases can differ significantly. Most notably, martensite is typically an order of magnitude harder than austenite, and a linear mixture rule is unsuitable. Geijselaers (Ref. 8) developed a weighting scheme that is suitable in this situation. In this model, it is assumed that the hardest phase is considerably harder than the softest phase. Assuming that the hard phase is m and the soft phase is γ, the Geijselaers weighting scheme is given by
with
The hardening function for the compound material is defined using the linear weighting
(3-35)
where is the equivalent plastic strain of the phase.
Equivalent Plastic Strains
In Equation 3-35, the hardening function for each individual phase depends on equivalent plastic strain. If we denote the equivalent plastic strain of the compound material , we must define how the equivalent of each phase evolves with this strain. The simplest assumption is to use the evolution equation
which is to say that the equivalent plastic strain of phase i follows that of the compound material. If phase transformation and mechanical straining occur simultaneously, the equivalent plastic strain of the diminishing source phase of the phase transformation can be taken to follow that of the compound material, and this is the behavior in the phase transformation physics interfaces. However, for a phase which is increasing in fraction during plastic straining, this assumption is questionable. Leblond (Ref. 7) derived an evolution equation for the equivalent plastic strain, which is suitable for the forming destination phase. The evolution equations for the source and destination phases are
where the plasticity memory coefficient was introduced to model that some plastic straining present in the source phase at the instant of transformation will be carried over to the forming destination phase. A zero plasticity memory coefficient means that no plastic straining will be remembered.