Quantitative description of damage evolution in ductile fracture of tantalum
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I. INTRODUCTION
IT has been well established that ductile fracture in metals subjected to tensile plastic deformation occurs by the nucleation, growth, and coalescence of voids in either quasistatic or dynamic conditions.[1–4] Nucleation of voids occurs at the sites of second-phase particles, or inclusions, when the plastic deformation in the matrix increases the particle-matrix interface stress to a point where the particles either break or debond from the matrix.[5,6] Voids may also nucleate at grain boundaries, shear bands, or at substructure heterogeneities such as dislocation pileups, when dynamic loads are applied.[7,8] There is also some evidence for nucleation by vacancy coalescence under conditions of high strain rates and stress triaxiality where the mechanism is similar to that which occurs in creep-rupture tests.[3] Under dynamic loading conditions, void growth occurs primarily by slip while coalescence occurs by the direct joining of voids. Remote linking occurs when the strain field that surrounds each void begins to interact with that of its nearest neighbor and localized plastic zones are created between voids.[3] Several mathematical models exist that attempt to describe dynamic ductile fracture. Seaman et al.[9] developed a model that included nucleation and growth of ductile voids as functions of stress and stress duration. Johnson[10] proposed a simplified void-growth model in which an equation for voidgrowth rate was obtained in terms of the applied mean stress. This model, however, ignored void nucleation. Later, Johnson and Addessio[11] proposed a model of void growth under tensile plasticity based on the Gurson yield-surface criterion.[12] Needleman and Tvergaard[13] analyzed numerically the ductile crack-growth rate in a material containing second-phase particles. This model, which is also based on the Gurson yield-surface criterion, considers nucleation and J.M. RIVAS, Postdoctoral Research Associate, and A.K. ZUREK, W.R. THISSELL, D.L. TONKS, and R.S. HIXSON, Technical Staff Members, are with the Los Alamos National Laboratory, Los Alamos, NM 87545. This article is based on a presentation given in the symposium entitled “Dynamic Behavior of Materials - Part II,” held during the 1998 Fall TMS/ ASM Meeting and Materials Week, October 11–15, 1998, in Rosemont, Illinois, under the auspices of the TMS Mechanical Metallurgy and the ASM Flow and Fracture Committees. METALLURGICAL AND MATERIALS TRANSACTIONS A
growth of new voids to evaluate the increment of void volume fraction. For a discussion of some of these modeling efforts, see the recent work by Thomason.[14] More comprehensive numerical models of dynamic ductile fracture, however, require quantitative microstructural information to adequately describe the ductile-fracture process. To study damage accumulation in dynamic ductile fracture, spallation experiments constitute an optimum experimental configuration. Spallation is defined as a dynamic, uniaxial strain-fracture condition. Spallation in a material is due to the tensile stresses g
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