Basic Equations for Mechanics and Kinematics of a Specimen-Machine System in Tensile Test of a Crystal

Abstract

Basic equations (BE) in the title are derived, whose main characteristics are as follows. (I) Plastic deformation of a single-crystal specimen is due to slip on Nslip systems, where Nis an arbitrary positive integer. (2) The major part of the BE is a set of simultaneous differential equations. By the BE, the tensile stress, the resolved shear stresses, the unloaded specimen length, and crystal orientation factors are related to controlled or measured variables mentioned below and also to deformation-state variables such as slip strain rates on the N active slip systems. (3) The BE are derived for two kinds of tensile test; 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 crystal is decomposed into the product of its plastic and elastic parts. The decomposition is uniquely defined by using base vectors of material coordinates and those of lattice coordinates. (5) The single-crystal test-piece consists of the cylindrical central part (specimen) and the end parts; theformer is assumed to be stressed uniformly and undergo homogeneous elastic plastic deformation, while the latter and the testing machine are assumed to deform elastically. The BE include Young's modulus and Poisson's ratio of the specimen and a combined modulus of the end part-machine system. (6) The BE are necessary for computer simulation of tensile tests of single crystals. Methods for comparison between the results of simulation and those of experiment are discussed in connection with the slip strain and the resolved shear stress on the primary slip system.