The influence of matrix yield stress gradient on the growth and coalescence of spheroidal voids

In a mass of engineering materials and structures, graded variations in yield stress is inherent. To investigate the macro-mechanical response and meso-mechanism of damage by void growth and coalescence in the materials with graded yield stress, detailed finite element computations of a representative cylindrical cell containing a spherical void are performed. By comparison with the responses of a homogeneous material cell model, significant effects of the matrix yield stress gradient (YSG) on the void growth and coalescence are revealed: (1) The evolution of voids in the homogeneous matrix materials has no close relations with the matrix yield stress level, however, the YSG distribution in matrix can lead to faster void growth rate and lower void coalescence strain. (2) In the homogeneous materials, the critical shapes of voids are independent on the yield stress of matrix materials, but the graded distribution of yield stress in the matrix materials, which leads to higher local plastic strain in the softer matrix layer, have an important influence on the critical void shapes. (3) The critical void volume fraction fc is insensitive to the yield stress of the homogeneous matrix, however the YSG in matrix materials has a stronger effect on fc, especially when the stress triaxiality level is lower. (4) Higher strain energy stored in the softer material layer encircling voids is internal driving force to faster void growth. The ratio of strain energy stored in the softer matrix layer surrounding voids to the whole energy provided by outside environment can give better description to the meso-mechanism of void evolution