Constitutive relations, plastics mechanical behavior

The dependence of mechanical behavior on constitution in Zr02-Ni system results from the variation of microstructure and its distribution. In the regions rich in Ni or PSZ, the mechanical performance is controlled by continuous matrix component and displays elasto-plastic or linear elastic characteristics, respectively. The non-linear elastic behavior at 60 vol% PSZ is related to the connectivity transition of matrix component. 

If this deformation field does not fulfill the geometrical compatibility, a strain tensor related to stress is generated. The constitutive equation, which represents the mechanical behavior of the material, relates this strain tensor and the stress tensor. Due to the memory effect of wood, this tensor has to be divided into two parts (1) an elastic strain, connected to the actual stress tensor and (2) a memory strain, which includes all the strain due to the history of that point (e can deal with plasticity, creep, mechanosorption, etc.). 

As a general rale, visco-plastic material behavior is specified for FEM simulation of chip removal. Thermo-mechanically coupled calculations are used. For describing material behavior, the use of the Johnson-Cook equation (Eq. 4) is preferred. Another semiempiiical model presented by Zerilli and Armstrong considers micro-mechanical effects in relation to the thermal activation behavior of face-centered (fee) and body-centered cubic (bcc) structures of the workpiece material. Other constitutive material laws are formulated by Oxley, Clifton Hensel-Spittel, and El-Magd, respectively, whereas the stress s is determined by different linear or exponential procedures within the equation terms. 

---