Numerical Studies On Ductile Fracture Of Pressure Sensitive Plastic Solids

Abstract

Experimental studies have shown that the yield strength of many important engineering materials such as polymers, ceramics and metallic glasses is dependent on hydrostatic stress. In addition, these materials may also exhibit plastic dilatancy. These deviations from the assumptions of classical plasticity theories have also been observed for some metallic alloys, although to a lesser extent compared to non-metals. In pressure independent plastic solids, it has been found that the level of crack tip constraint can affect the near-tip stress and deformation fields and hence the fracture resistance. The objective of the present work is to study the effects of pressure sensitive yielding, plastic dilatancy and constraint loss on the ductile fracture processes under mode-I conditions. Further, the three-dimensional (3D) structure of elastic-plastic near-crack front fields in a pressure independent plastic solid under mixed mode (combined modes I and II) loading is also examined. A finite element study of 3D crack tip fields in pressure sensitive plastic solids under mode-I, small scale yielding (SSY) conditions is first carried out. The material is assumed to obey a small strain, Extended Drucker-Prager (EDP)yield criterion. The roles of pressure sensitive yielding, plastic dilatancy and yield locus shape on the 3D plastic zone development and near-crack front fields are systematically investigated. It is found that while pressure sensitivity leads to a significant drop in the hydrostatic stress all along the 3D crack front, it enhances the plastic strain and crack opening displacements. However, plastic incompressibility results in elevation of both near-tip hydrostatic stress and notch opening. The implications of these observations on micro-void growth and interaction near a notch tip are studied in detail subsequently. The effects of constraint loss on void growth near a notch tip under mode-I loading in materials exhibiting pressure sensitive yielding and plastic dilatancy are investigated by performing large deformation elastic-plastic finite element analyses. To this end, two-dimensional (2D)plane strain and 3Dmodified boundary layer formulations are employed by prescribing the elastic K-T field as remote boundary conditions. The results are generated for different combinations of K (or J ) and T -stress. The material is assumed to obey a finite strain, EDP yield condition. The distributions of hydrostatic stress and plastic strain in the ligament connecting the notch and a nearby void (cylindrical or spherical) as well as the growth of the notch and the void are studied. The results show that void growth with respect to J is enhanced due to pressure sensitivity, and more so when the plastic flow is non-dilatational, which corroborates with the trends exhibited by the 3D crack tip fields. However, the evolution of ductile fracture processes like void growth, plastic strain localization and ligament length reduction with respect to J is retarded in the case of spherical voids. Further, irrespective of pressure sensitivity, loss of crack tip constraint can significantly slow down void growth. The effects of pressure sensitive yielding and plastic dilatancy on near-tip void growth and multiple void interaction mechanisms in single edge notched bend (SENB) and center cracked tension (CCT) specimens which display high and low constraint levels, respectively, are investigated next. It is observed that the latter mechanism which is favored by high initial porosity is further accelerated by pressure sensitive yielding and high constraint. The predicted resistance curves based on a simple void coalescence mechanism show enhancement in fracture resistance when constraint level is low and when pressure sensitivity is suppressed. Finally, detailed elastic-plastic finite element simulations are carried out using a boundary layer (SSY) formulation to investigate the 3D nature of near-crack front fields in a von Mises solid under mixed mode (combined modes I and II)loading. The plastic zones and radial, angular and thickness variations of the stresses are studied corresponding to different levels of remote elastic mode mixity and applied load, as measured by the plastic zone size with respect to the plate thickness. The 3D results are compared with those obtained from 2D simulations and asymptotic solutions to establish the validity of 2D plane stress and plane strain approximations near a crack front. It is found that, in general, plane stress conditions prevail at a distance from the crack front exceeding half the plate thickness, although it could be slightly smaller for mode-II predominant loading.