New interpretation about deviation of glide strains: In situ measurement by synchrotron radiation of lattice rotation in a copper single crystal

Abstract

When a face-centered-cubic single crystal is elongated uniaxially, the characteristics of deformation behavior such as amount of glide strain, operative slip systems, and the moving path of tensile axis could be theoretically predicted [1, 2]. Although there have been many deformation experiments on single crystals, experimental results have shown the general invalidity of this classical theory [3–5]. Especially Price and Kelly [3] reported that the glide strain calculated from the orientation change, assuming single slip, was always less than the glide strain measured directly from the length change of the sample. It has been commonly believed that the difference of glide strains is dependent only on the activation of secondary slip systems [6, 7]. But the difference of glide strains is too large to explain by secondary slip systems. There is still controversy about the phenomena. Constitutive relations for inelastic deformation are formulated by many researchers [8–10]. It is generally agreed that the inelastic deformation of metals is accomplished through the motion of crystal dislocations. But the equation derived by Bowen and Christian [2] do not consider the crystal dislocations. The accumulations of dislocations can give serious error in the calculation of glide strains. In this study, we revise the equations derived by Bowen and Christian [2] in order to explain the difference of glide strains. When a face-centered-cubic single crystal is elongated uniaxially, the length of sample and the angle φ has the relation that a represented in Equation 1 [2].