A Note on Residual Stress, Lattice Orientation and Dislocation Density in Crystalline Solids

Steigmann, David J.; Ogden, Ray W.

doi:10.1007/s10659-012-9378-1

Cited by 4 publications

(4 citation statements)

References 10 publications

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“…The initial value of plastic deformation is taken to be the uniform two-dimensional rotation associated with a lattice inclined at angle θ to the horizontal. This initial condition is associated with a state of vanishing residual stress [32].…”

Section: 2 Examplesmentioning

confidence: 99%

A model for elastic–viscoplastic deformations of crystalline solids based on material symmetry: Theory and plane-strain simulations

Edmiston¹,

Steigmann²,

Johnson³

et al. 2013

International Journal of Engineering Science

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: A model for the elastic-viscoplastic response of metallic single crystals is developed on the basis of the modern finite-deformation theory of plasticity combined with considerations of material symmetry. This is proposed as an alternative to conventional crystal plasticity theory, based on a decomposition of the plastic deformation rate into a superposition of slips on active slip systems. A simple special case of the general theory, modeling evolving geometrically necessary dislocations and their effect on hardening, is developed and used as the basis of numerical experiments.

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Section: 2 Examplesmentioning

confidence: 99%

A model for elastic–viscoplastic deformations of crystalline solids based on material symmetry: Theory and plane-strain simulations

Edmiston¹,

Steigmann²,

Johnson³

et al. 2013

International Journal of Engineering Science

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“…25 In this case, we see an increase in the residual strain field with the increase in temperature because as fewer dislocations contribute to the residual strain, they cancel each other out to a lesser extent-ultimately reaching higher magnitudes. 26 The optical furnace in this work enabled the current experiment to probe a large region of sample that is evenly heated with limited thermal gradients. Further studies with this optical furnace may be able to give further insight into the evolution of the microstructure and dislocation density with the increase in temperature in a host of samples.…”

Section: Usage During a Dfxm Experimentsmentioning

confidence: 99%

Radiation furnace for synchrotron dark-field x-ray microscopy experiments

Yildirim

Vitoux

Dresselhaus-Marais

et al. 2020

Review of Scientific Instruments

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“…In particular, H is, almost everywhere, a skew-symmetric matrix. Since (H ε u ε ) 13…”

Section: Compactness Lemmasmentioning

confidence: 99%

“…The theory of linear elasticity with residual stress goes back to Cauchy (1829), but for a long time the attention of researchers was almost exclusively given to the so-called linear theory of elasticity. In recent years, instead, the theory with residual stress has been studied and used quite extensively, see [2,6,16,17,19,20,22,23,24,25,28,29,30] and references therein.…”

Section: Introductionmentioning

confidence: 99%