Quantitative Atomic Force Microscopy Characterization and Crystal Plasticity Finite Element Modeling of Heterogeneous De
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INTRODUCTION
WHILE titanium and its alloys have been widely used in structural applications for several decades, the heterogeneous deformation that is characteristic of hexagonal a-titanium is still not well understood. Heterogeneous deformation usually results from two factors. One is that grains with ‘‘soft’’ crystal orientations (those grains with high Schmid factors for prismatic slip—in Ti, those grains having their c-axis nearly perpendicular to the applied uniaxial stress) are much more easily deformed than other grains, leading to large strain differences between soft and hard grains.[1] Second, constraint of one grain exerted by neighboring grains during deformation leads to spatial heterogeneity and associated strain gradients within a given grain.[2,3] The crystal plasticity finite element (CPFE) method is often used to simulate the plastic deformation processes that occur in three-dimensional microstructures, where these two kinds of heterogeneity coexist.[4–6] Nevertheless, unlike CPFE simulations of cubic metals[7,8] that show reasonable agreement with experiments, CPFE studies of hexagonal metals have not been adequately compared with experimental results. Quantitative experimental characterization is needed to assess the accuracy of CPFE simulations and to serve as the basis for further improvements in accurately simulating deformation
Y. YANG and L. WANG, Graduate Students, and T.R. BIELER and M.A. CRIMP, Professors, are with the Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, MI 48824. Contact e-mail: [email protected] P. EISENLOHR, Project Director CMC, is with the Max-PlanckInstitut fu¨r Eisenforschung, 40237 Du¨sseldorf, Germany. Manuscript submitted February 1, 2010. Article published online December 1, 2010 636—VOLUME 42A, MARCH 2011
processes that occur in real microstructures of hexagonal materials. Four dislocation slip systems have been reported for a-titanium. f1010gh1210i prismatic slip is the primary slip system because of its lowest critical resolve shear 210i stress,[9–11] but three other slip systems, f0001gh1 basal slip, f1010gh1210i pyramidal hai slip, and f1010gh2113i pyramidal hc + ai slip, can be activated provided the resolved shear stress is high enough. In addition to slip, there are also four twinning systems in a-titanium[12] that can contribute to deformation. When the maximum principal stress direction is close to the crystal c-axis orientation, either hc + ai slip, tensile (extension) twinning modes (T1 and T2), or compressive (contraction) twinning modes (C1 and C2) have high Schmid factors, and their operation often contributes to the crystal shape change. Among these four twinning systems, f1012gh1011i (T1 extension) twinning is most commonly observed at room temperature.[12] Atomic force microscopy (AFM) is an effective tool for characterizing fine-scale topography induced by different deformation processes. Since the 1990s,[13] AFM has been used to study surface relief produced during fatigue damage evolutio
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