Void Growth in Elastic-Plastic Materials

Abstract

Three-dimensional finite element computations have been done to study the growth of initially spherical voids in periodic cubic arrays. The numerical method is based on finite strain theory and the computations account for the interaction between neighboring voids. The void arrays are subjected to macroscopically uniform fields of uniaxial tension, pure shear, and high triaxial stress. The macroscopic stress-strain behavior and the change in void volume were obtained for two initial void volume fractions. The calculations show that void shape, void interaction, and loss of load carrying capacity depend strongly on the triaxiality of the stress field. The results of the finite element computation were compared with several dilatant plasticity continuum models for porous materials. None of the models agrees completely with the finite element calculations. Agreement of the finite element results with any particular constitutive model depended on the level of macroscopic strain and the triaxiality of the remote uniform stress field.

On the mechanism of void growth and the effect of straining mode in ductile materials

“…The boundaries are so controlled as to yield uniform tensile displacement along the x-direction but uniform compression on the y-direction. The two overall stresses along the boundaries are kept to have the same absolute values but opposite in sign as that done by Hom and McMeeking (1989) in their three dimensional void model. The initial void areal proportion is taken as 6.5%, same as the initial void volume fraction used by Hom and McMeeking (1989).…”

“…The two overall stresses along the boundaries are kept to have the same absolute values but opposite in sign as that done by Hom and McMeeking (1989) in their three dimensional void model. The initial void areal proportion is taken as 6.5%, same as the initial void volume fraction used by Hom and McMeeking (1989). The overall true stress±strain curve is shown in the Appendix which is very near to the three dimensional ®nite-element predictions given by Hom and McMeeking (1989).…”

“…The initial void areal proportion is taken as 6.5%, same as the initial void volume fraction used by Hom and McMeeking (1989). The overall true stress±strain curve is shown in the Appendix which is very near to the three dimensional ®nite-element predictions given by Hom and McMeeking (1989). The distribution of the local equivalent strain in the cell are quite similar to those given by Hom and McMeeking at the middle cross-section of their cell model before the overall axial straining is too large (i.e.…”

“…The reasons can be attributed to (a) the in¯uence of strain softening or secondary void damage in the matrix material around primary void (Li and Howard, 1983;Li et al, 1989;Brocks et al, 1995); (b) plastic¯ow localization due to non-uniform void distribution (Ohno and Hutchinson, 1984;Becker, 1987;Magnusen et al, 1988;Becker and Smelser, 1994); (c) the eect of void shape on void growth and ductility (Li, 1985a;Becker et al, 1989;Yee and Mear, 1996); (d) voiding instability in elastic±plastic solids (Koplik and Needleman, 1988;Huang et al, 1991); (e) the three dimensional eects (Hom and McMeeking, 1989;Worswick and Pick, 1990) and others such as, the eects of void cluster size (Benson, 1995) and the matrix compressibility on void growth (Briottet et al, 1996). Tvergaard (1981) and Needleman and Tvergaard (1984) tried to modify Gurson's model by adding more parameters so as to bring shear band bifurcation predictions of the Gurson constitutive relation into closer agreement with corresponding results of full numerical analysis and to take into account the eects of rapid void coalescence at failure.…”

Anisotropic ductile fracture of Al 2024 alloys

“…In order to quantify the effect of initial porosity, stress triaxiality, void shape, and void distribution on void growth and coalescence, a unit cell approach is commonly used [10,[24][25][26][27][28][29][30]. The continuum is imagined as a periodic array of RVEs, which are assumed to be statistically representative for the microstructure.…”