Theoretical study of void closure in nonlinear plastic materials

Void closing from a spherical shape to a crack is investigated quantitatively in the present study. The constitutive relation of the void-free matrix is assumed to obey the Norton power law. A representative volume element (RVE) which includes matrix and void is employed and a Rayleigh-Ritz procedure is developed to study the deformation-rates of a spherical void and a penny-shaped crack. Based on an approximate interpolation scheme,an analytical model for void closure in nonlinear plastic materials is established. It is found that the local plastic flows of the matrix material are the main mechanism of void deformation. It is also shown that the relative void volume during the deformation depends on the Norton exponent,on the far-field stress triaxiality,as well as on the far-field effective strain. The predictions of void closure using the present model are compared with the corresponding results in the literature,showing good agreement.The model for void closure provides a novel way for process design and optimization in terms of elimination of voids in billets because the model for void closure can easily be applied in the CAE analysis.