Observation of Deformation and Lattice Rotation in a Cu Bicrystal
- PDF / 763,522 Bytes
- 8 Pages / 593.972 x 792 pts Page_size
- 37 Downloads / 209 Views
INTRODUCTION
CRYSTALLINE metals plastically deform by dislocation motion along given slip systems that are a function of the Bravais lattice and atomic motif of the crystal. As such, plastic deformation is inherently anisotropic, and deformation behavior within a single crystallite is a function of the local structure and orientation of the crystallite. The classic works of Taylor[1] and others describe such phenomena, and numerous models have been developed that are based on the premise established by Taylor (cf. References 2–6). These models ignore any nonlocal effects that might be presented by a sudden change in crystal structure or in orientation of the lattice, such as are encountered by dislocations at phase boundaries, grain boundaries, and dislocation cell walls (or subgrain boundaries). Finiteelement models have incorporated crystal plasticity formulations with compatibility constraints of the mesh at boundaries but often contain no additional consideration for the presence of internal interfaces. A few models have been developed based on the general theory of crystal plasticity that include grain boundary effects in some manner, either explicitly or implicitly, in the models, and many observations of the importance of grain boundary structure effects on deformation have been made.[7–14] The models that include grain boundary structure generally treat the boundary as a separate layer that has a specific constitutive behavior based on the structure of the boundary. Strain gradient plasticity models have also been developed that inherently include crystallite boundary effects as positions of potentially DAVID P. FIELD, Professor, is with the School of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164-2920. Contact e-mail: dfi[email protected] A. ALANKAR, formerly Graduate Student, School of Mechanical and Materials Engineering, Washington State University, is Research Associate with the Department of Microstructure Physics and Metal Forming, Max-PlanckInstitut fu¨r Eisenforschung GmbH, 40237 Du¨sseldorf, Germany. Manuscript submitted December 11, 2009. Article published online December 9, 2010 676—VOLUME 42A, MARCH 2011
high strain gradients, but generally these models lack the inclusion of anisotropy or effects of boundary character in the formulation.[15,16] Livingston and Chalmers[17] proposed the idea of a slip-transfer criterion that defines when two neighboring grains are oriented favorably for dislocations to pass from one grain to the next on a specific slip system whose orientation is similar to that of the moving dislocation. Shen et al.[18] developed a slip transmission criterion that incorporates an explicit dependence on the interface normal orientation as well as the geometry of the slip planes in each crystallite. This criterion suggests that the extent of slip interaction between neighboring grains will be governed according to the following relation: ½1 Mij ¼ li lj bi bj In this equation, l is a unit vector defining the line of intersection between the grain
