Cavity growth and constitutive softening in ductile solids

A model of the cavity growth and constitutive softening occurring in porous solids undergoing plastic deformation has been developed using the finite element method. The model considered an infinite solid containing a three-dimensional periodic array of initially spherical cavities. Both dilatational (volume-changing) and extensional (shape-changing) cavity growth were predicted, for a number of stress states and applied deformation cases. Constitutive softening was also predicted and was seen as a loss in material load-carrying capacity, relative to a fully-dense material, due to the presence of porosity. The model presented in this thesis represents an improvement over previous models of cavity growth since it incorporates the combined effects of a finite or non-zero void volume fraction, material workhardening and cavity shape change during deformation.

The principal factors governing the cavity growth rate were shown to be stress triaxiality and material workhardening. Increased void volume fraction did not significantly affect the dilatational growth rate (eg. r/r, where r is the cavity radius). Increased stress triaxiality and void volume fraction had a marked effect on the extensional cavity growth, causing the cavities to "flatten" rather than elongate during axial extension of the porous solid. Constitutive softening was primarily a function of stress triaxiality and void volume fraction.

The numerical results were used to assess previous analytical models of cavity growth and constitutive softening seen in the technical literature. One principal result from this work was the "calibration" of the well-known Gurson yield function to provide predictions of dilatational growth rate and constitutive softening in accordance with the results from the current model of the infinite periodic array of cavities. This calibrated form of the Gurson yield function is recommended for use in modeling the stable cavity growth phase of ductile fracture.

Experimental assessment of the predictions of cavity growth and constitutive behaviour were undertaken based on tensile tests of uniaxial and notched specimens of free-cutting brass. This material contains a globular lead phase which has a low strength relative to the brass matrix and was assumed to act as a dispersion of pre-existing cavities.

The cavity growth predictions using the calibrated Gurson model demonstrated reasonable agreement with experiment. The predicted specimen constitutive behaviour from the Gurson-based predictions was superior to that obtained using a conventional Von Mises plasticity model.