単結晶の引張試験における試験片-試験機系の力学と運動学とを記述する基礎式

Abstract

Basic equations (BE) in the title are derived, whose main characteristics are as follows. (1) Plastic deformation of the single-crystal specimens is due to slip on N slip systems, where N is an arbitrary positive integer. (2) The major part of the BE is composed of simultaneous differential equations. By the BE, the tensile stress, the resolved shear stresses (RSS), the unloaded specimen length, and crystal-orientation factors are related to controlled or measured variables mentioned below, and to deformation-state variables such as the slip strain rates on the N active slip systems. (3) The BE are derived for two types of tensile tests; one is the test in which the extension rate (crosshead speed) is controlled and the load is measured, while the other is the test in which the load is controlled and the crystal specimen length is measured. (4) In the derivation of the BE, the deformation gradient tensor of the crystals is decomposed into plastic and elastic parts. The decomposition can be uniquely defined using base vectors of material coordinates and those of lattice coordinates. (5) The single-crystal test-pieces consist of the central parts (specimens) and the end parts; the former are assumed to be stressed uniformly and undergo homogeneous elastic plastic deformation, while the latter and the testing machines are assumed to deform elastically. The BE include Young’s modulus and Poisson’s ratio of the specimens and a combined modulus of the end part-machine system. (6) The BE are necessary for computer simulations of tensile tests of single crystals. Methods for comparing the computed results with experimental ones in respect of RSS-slip strain behavior on the primary slip systems are discussed.