Coherency Strain and a New Yield Criterion
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Coherency Strain and a New Yield Criterion N.B. Jayaweera, J.R. Downes, D.J. Dunstan, A.J. Bushby,1 P. Kidd and A. Kelly2 Department of Physics, Queen Mary, University of London, London E1 4NS, UK. 1 Department of Materials, Queen Mary, University of London, London E1 4NS, UK. 2 Department of Materials Science and Metallurgy, University of Cambridge, Pembroke St., Cambridge CB2 3QZ, UK. ABSTRACT We have studied the onset of plasticity in coherently-strained semiconductor superlattices, using nano-indentation with spherical indenter tips to observe the full stress-strain curve. The yield pressure is reduced by as much as a factor of two by the presence of the coherency strain. By varying the thicknesses and strains of the superlattice layers, we provide a proof that yield commences over a finite volume. It is properties averaged or summed over this volume which determine the yield pressure. We show that the relevant yield criterion for our experimental data is the rate of change of elastic strain energy with plastic relaxation, integrated over a volume of the order of a micron across. This result is expected to be valid for other systems with highly inhomogenous strain fields, and hence to be applicable to modelling of point contact, and to the design and understanding of structural materials which have coherently-strained microstructure. INTRODUCTION The classic yield criteria are those of Tresca and von Mises. They are scalar functions of the stress tensor at a point, such that if the value exceeds a critical value, plastic yield will occur. Pointwise criteria are satisfactory for homogeneous stress, since the same scalar value will be reached simultaneously at all points within the material. However, it has long been realised that inhomogenous stress fields are not adequately treated by pointwise criteria, since for physical reasons plastic yield must initiate throughout some finite volume. Thus, in 1931, Cook [1] suggested that the yield point should be higher in cases of inhomogeneous stress. For a discussion, see Kelly [2]. For want of a satisfactory yield criterion for inhomogeneous stress, finite-element modelling of point contact fails rather badly, with serious implications for our understanding of phenomena such as wear and single-point machining. Semiconductor strained layer structures represent a very powerful tool for investigations of yield in the presence of inhomogeneous stress. Strains up to 1% and more can readily be incorporated into layers of thicknesses of a few tens of nanometres, and multilayer structures can be grown with total thicknesses of a few microns. These structures are epitaxial single crystals with atomically flat interfaces. The coherency strain is introduced by small changes in composition, in an alloy system in which other physical properties change little. So departures from bulk behaviour can be attributed unambiguously to effects of the inhomogeneous stress field alone. EXPERIMENTAL DETAILS Superlattices of InGaAs bilayers, repeated to obtain a total thickness of 2.5 µm were g
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