Both monotonic and cyclic loading are considered for homogeneous and bimaterial systems. The new criterion determining the angle of crack propagation in mixed mode loading conditions is proposed. As a rational consequence of the above treatment, the minimum value of the strain-energy density is replaced by the minimum value of the radius of the elastic-plastic boundary in the role of the decisive quantity defining the direction of crack propagation. It was shown that the introduction of a core region with variable radius affects the expected angle of propagation and, in the case of the S-criterion, results in values of this angle indepedent from Poisson's ratio.
Thus, the value of r depends explicitly, not only on the material properties of the plate, but also on the angular direction around the crack-tip. In the present paper the Mises elastic-plastic boundary is introduced to define the core region, instead of the respective circle. The exact value of r is not defined quantitatively. When applying any of the fracture criteria to predict crack propagation, the evaluation of the stresses needed is performed at a constant distance r from the crack-tip The circle with radius r is called the core region.
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