Effect of Pressure-Dependency of the Yield Criterion on the Strain Rate Intensity Factor

In the case of several rigid plastic models, the equivalent strain rate (quadratic invariant of the strain rate tensor) approaches infinity in the vicinity of maximum friction surfaces. The strain rate intensity factor is the coefficient of the leading singular term in a series expansion of the equivalent strain rate in the vicinity of such surfaces. This coefficient controls the magnitude of the equivalent strain rate in a narrow material layer near maximum friction surfaces. On the other hand, the equivalent strain rate is involved in many conventional equations describing the evolution of parameters characterizing material properties. Experimental data show that a narrow layer in which material properties are quite different from those in the bulk often appears in the vicinity of surfaces with high friction in metal forming processes. This experimental fact is in qualitative agreement with the aforementioned evolution equations involving the equivalent strain rate. However, when the maximum friction law is adopted, direct use of such equations is impossible since the equivalent strain rate in singular. A possible way to overcome this difficulty is to develop a new type of evolution equations involving the strain rate intensity factor instead of the equivalent strain rate. This approach is somewhat similar to the conventional approach in the mechanics of cracks when fracture criteria from the strength of materials are replaced with criteria based on the stress intensity factor in the vicinity of crack tips. The development of the new approach requires a special experimental program to establish relations between the magnitude of the strain rate intensity factor and the evolution of material properties in a narrow material layer near surfaces with high friction as well as a theoretical method to deal with singular solutions for rigid plastic solids. Since no numerical method has been yet developed to determine the strain rate intensity factor, the present chapter focuses on analytical and semi-analytical solutions from which the dependence of the strain rate intensity factor on process and material parameters are found. In particular, the effect of pressure-dependency of the yield criterion on the strain rate intensity factor is emphasized using the double shearing model.