von Mises yield criterion

About: von Mises yield criterion is a research topic. Over the lifetime, 4374 publications have been published within this topic receiving 82642 citations. The topic is also known as: Von Mises stress.

CXXVIII. A theoretical derivation of the plastic properties of a polycrystalline face-centred metal

Abstract: Summary In continuation of a previous paper (Bishop and Hill 1951) it is conjectured that the work done in plastically deforming a polycrystal is approximately equal to that which would be done if the grains were free to deform equally. In conjunction with the principle of maximum plastic work, this enables the yield function of an aggregate to be calculated. This is done for an isotropic aggregate of face-centred cubic crystals, following a determination of the stresses needed to produce multi-slip. The theoretical yield criterion lies between those of Tresca and von Mises, in good agreement with observaton for copper and aluminum. It is shown further that the work-hardening of an aggregate would be a function only of the total plastic work if the grains hardened equally ; the departure from this functional relation is expressed explicitly in terms of the non-uniform hardening.

A general anisotropic yield criterion using bounds and a transformation weighting tensor

Abstract: A gspeneral Expression for the yield surface of polycrystalline materials is developed. The proposed yield surface can describe both isotropic and anisotropic materials. The isotropic surface can be reduced to either the Tresca or von Mises surface if appropriate, or can be used to capture the yield behavior of materials (e.g. aluminum) which do not fall into either category. Anisotropy can be described by introducing a set of irreducible tensorial state variables. The introduced linear transformation is capable of describing different anisotropic states, including the most general anisotropy (triclinic) as opposed to existing criteria which describe only orthotropic materials. Also, it can successfully describe the variation of the plastic strain ratio (R-ratio), where polycrystalline plasticity models usually fail. A method for obtaining the material constants using only uniaxial test data is described and utilized for the special case of orthotropic anisotropy. Finally, the use of tensorial state variables together with the introduced mathematical formulation make the proposed yield function a very convenient tool for numerical implementation in finite element analysis.

Effect of rubber particle size on deformation mechanisms in glassy epoxy

Abstract: When tested in tension, a cross-linked epoxy resin can be made to exhibit shear yielding. A modified von Mises criterion, τ = τ0 − μP describes the yielding behavior of the same resin under a biaxial stress system, indicating that the flow of the material is pressure sensitive. Butadien-acrylonitrile elastomer particles suspended in the cross-linked epoxy matrix induce large local deformations when the composite material is stressed. Particles a few hundred Angstroms in diameter cause the glassy matrix to exhibit shear banding, and the macroscopic failure envelope of such a system follows a modified von Mises criterion similar to that of the matrix resin. It was found that the coefficient of internal friction, τ, and the activation energy for yielding are approximately the same for the two cases. With larger particles (5-15,000 A diam) the failure mode changes as shown by the macroscopic yield envelope and the associated activation energy. Electron micrographs of the fracture surfaces show microcavitation, similar to crazing around each particle; the deformed glassy polymer around each particle retracts upon heating the matrix above its Tg. The fracture surface work value of the unmodified matrix is 1.75 × 105 ergs/cm2. With 10 pph small particles, the value increases to 3.32 × 105 and with 10 pph of large particles, to 15.48 × 105 ergs/cm2.