A dislocation based analysis of continuum mechanical and microscopic local stresses during cyclic deformation of copper
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A relationship between continuum mechanical internal stress variables, kinetic back stress, isotropic drag stress, and microscopic local stresses in the dislocation cell interior and cell walls, is developed based upon Mughrabi's composite model of deformation of heterogeneous microstructure during cyclic deformation in cell forming metals. The experimental data on the evolution of kinematic back stress and isotropic drag stress during cyclic deformation of Cu along with TEM measurements of cell diameter and cell width are utilized to determine the evolution of mobile and immobile dislocation densities in the cell interior and cell walls, respectively, as a function of the number of cycles. The range of values obtained is in agreement with the available experimental data.
I. INTRODUCTION
Internal stresses develop when mobile dislocations resulting from plastic deformation interact with obstacles. In the continuum approach, these internal stresses are defined as kinematic back stress and isotropic drag stress and are represented by the center and radius of the yield surface. The use of kinematic back stress and isotropic drag stress in modeling cyclic plasticity was first suggested by Onat,1 and since then kinematicisotropic hardening type models have been used to model various characteristics of cyclic plasticity such as isotropic softening, the Bauschinger effect, and strength differential effect.2"4 The experiments for the continuous measurement of kinematic back stress and isotropic drag stress within the hysteresis cycle as well as from cycle-to-cycle have been recently conducted by the author.5 The technique of measurement, in brief, involves measurement of yield strength in tension, Y,, and in compression, Yc, in real time by controlled unloading and reloading of the specimen within the primary hysteresis loop [Fig. l(a)]. From the yield strength measurements one can determine kinematic back stress, a, and isotropic drag stress, «, by (Y, + Yc) a= K
=
(Y, ~ Y)
The technique has advantages over other methods of measurement since accurate a and K data within the cycle and from cycle-to-cycle can be generated from a single specimen for a given strain rate and strain amplitude. J. Mater. Res., Vol. 5, No. 10, Oct 1990
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It has been demonstrated by Mughrabi6 8 that the dominant long-range stress system in deformed cellforming materials like Cu involves back stresses in the cell interior which are balanced, for the most part, by opposing stresses in the cell walls. Interfacial dislocations are generated to ensure the compatibility of deformation between the cell walls and cell interiors. The local inhomogeneous stress distribution in the cell interior and the cell walls was investigated by using x-ray diffraction measurements.6 Also, the microstructural local stresses in the cell interior,
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