Plasticity in Materials with Heterogeneous Microstructures
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NEW experimental and modeling techniques to analyze material behavior often include the effects of microstructural features such as grain size, grain orientations, grain boundaries, etc., using both experimental and theoretical tools.[1–9] In References 10 and 11 Hall and Petch use an empirical relation (known as the Hall–Petch relation) to relate the size dependency on yield strength and to show that a smaller (mean) grain size results in a higher yield strength. The underlying mechanism for this behavior is described as being based on the dislocation pile-up theory developed by Eshelby et al.[12] and the Hall–Petch relation is thought of as a special case of stress-gradient theory,[13–17] where interactions between dislocations and the grain boundaries occur under an inhomogeneous state of stress. Similarly, a strain-gradient theory based on different mechanisms and length scale effects is developed and related to the formation of geometrically necessary dislocations (GNDs) that accommodate the lattice curvatures during non-uniform straining.[18–29] A combination of strain-gradient and stress-gradient theory is proposed in Reference 16 and these theories are viewed as complementary to each other rather than competing. The shortcoming is that in most of these models, the mean grain size is used without considering the stochastic internal parameters of the microstructure such as
HAO LYU, Ph.D. Candidate, and DAVID P. FIELD and HUSSEIN M. ZBIB, Professors, are with the School of Mechanical and Materials Engineering, Washington State University, Pullman, WA, 99163. Contact e-mail: [email protected] ANNIE RUIMI, Associate Professor, is with the Department of Mechanical Engineering, Texas A&M University at Qatar, Doha, 23874, Qatar. Manuscript submitted May 20, 2016. METALLURGICAL AND MATERIALS TRANSACTIONS A
grain size, grain shape, grain locations and/or grain boundary properties.[30] Experiments have shown that different grain size distributions can lead to different material strengths especially if the material is heterogeneous. For instance in Reference 31 Lehto et al. study the influence of grain size distribution on the strength of welded structural steel using various grain size distributions. In Reference 32, Masumura et al. investigate the effect of grain size distributions using fine-grained specimens and in Reference 33 through 35, Rajagopalan et al. show the effect of grain size distribution in nanocrystalline metals. These studies show that the distribution of grain sizes results in heterogeneity that leads to different local interactions and behaviors. Another study by Ghosh and Raj[36] is based on a creep model of various metals where all grains are subjected to an equal strain rate and the distribution of internal stresses is based on the grain size distribution. In Reference 32, Masumura et al. propose a model that includes Hall–Petch strengthening for larger grains and Coble creep (Coble 1963) for smaller grains. In addition, the grain size is correlated to the Hall–Petch constant, the Coble constant, an
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