Effect of load redistribution in transient plastic flow
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THE plastic deformation of crystalline solids can be fundamentally understood as the interaction of four concurrent interdependent phenomena:[1,2] 1. The thermally activated and stress-dependent release of dislocations from obstacles 2. The hardening of the material by increasing dislocation density and/or decreasing subgrain size 3. The concurrent softening of the material by coarsening of dislocation structures and strengthening phases; this is important at high homologous temperature 4. The stress redistribution that takes place as regions of the material with different local strengths deform in accord with strain compatibility and stress equilibrium In this paper, we will focus on this last element and consider how load redistribution from the coupled deformation of ‘‘hard’’ and ‘‘soft’’ regions of a material microstructure affects its deformation. We attempt to do this in a unified way with respect to creep and constant strain rate deformation. In either case, the basic result is the same: soft parts of the microstructure deform first, shedding load to harder regions. This may eventually cause them to deform. Strain transients that extend to many times the elastic strain can easily result from this process, even in the absence of any traditional strain hardening. Here we will study this process analytically and confine our discussion to materials that show no hardening due to structural changes such as increasing dislocation density. This exercise in many respects follows a previous analysis where a cellular automaton method was used to look at the transient deformation of heterogeneous material.[3] One of the findings from that study is shown in Figure 1. Basically, the study showed that over a wide range of conditions, when a material of heterogeneous strength is subjected to creep, the softest WEI GAN, Project Engineer, and PEIHUI ZHANG, Applications Engineer, are with Edison Welding Institute, 1250 Arthur E. Adams Drive, Columbus, OH 43221-3585. ROBERT H. WAGONER and GLENN S. DAEHN, Professors, are with the Department of Materials Science and Engineering, The Ohio State University, 2041 College Road, Columbus, OH 43210-1124. Contact e-mail: [email protected] Manuscript submitted August 27, 2005. METALLURGICAL AND MATERIALS TRANSACTIONS A
obstacles will first deform, giving linear creep. As harder obstacles carry load, a complex transient is seen. This can robustly produce logarithmic or power-law creep. Eventually, if the material does not show real hardening, stress will redistribute and another linear, steady-state–like regime is found. One must examine many orders of magnitude in time and strain to see this behavior experimentally, but many examples do exist in the literature;[4–9] one is shown in Figure 2.[10] As discussed elsewhere,[3] this general form depicted in Figures 1 and 2 can robustly show the standard forms of creep transient behavior (logarithmic, Andrade, power-law, and so forth). The purpose of the cellular automaton modeling was to provide an approximate and rapid way to satisfy equil
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