J.F.W. Bishop

Bio: J.F.W. Bishop is an academic researcher from University of Bristol. The author has contributed to research in topics: von Mises yield criterion & Hardening (metallurgy). The author has an hindex of 2, co-authored 2 publications receiving 1889 citations.

XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses.

Abstract: Summary A general relationship between stress and plastic strain in a polycrystalline aggregate is derived for any metal in which individual crystals deform by slipping over preferred planes under a critical shear stress. Full account is taken of the non-uniform distortion due to mutual constraints between the grains of an aggregate. It is shown that a plastic potential exists which is identical with the yield function. Upper and lower bounds are obtained for an approximate calculation of this function for any applied system of combined stresses.

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.

The Elastic Behaviour of a Crystalline Aggregate

Abstract: The connection between the elastic behaviour of an aggregate and a single crystal is considered, with special reference to the theories of Voigt, Reuss, and Huber and Schmid. The elastic limit under various stress systems is also considered, in particular, it is shown that the tensile elastic limit of a face-centred aggregate cannot exceed two-thirds of the stress at which pronounced plastic distortion occurs.

Mechanical properties of solid polymers

Abstract: A concise, self-contained introduction to solid polymers, the mechanics of their behavior and molecular and structural interpretations. This updated edition provides extended coverage of recent developments in rubber elasticity, relaxation transitions, non-linear viscoelastic behavior, anisotropic mechanical behavior, yield behavior of polymers, breaking phenomena, and other fields.

Influence of voids on shear band instabilities under plane strain conditions

Abstract: The effect of microscopic voids on the failure mechanism of a ductile material is investigated by considering an elastic-plastic medium containing a boubly periodic array of circular cylindrical voids. For this voided material under uniaxial or biaxial plane strain tension the state of stresses and deformations is determined numerically. Bifurcation away from the fundamental state of deformation is analysed with special interest in a repetitive pattern that represents the state of deformation inside a shear band. Both in the fundamental state and in the bifurcation analysis the interaction between voids and the details of the stress distribution around voids are fully accounted for. Comparison is made with the shear band instabilities predicted by a continuum model of a ductile porous medium. Based on the numerical results an adjustment is suggested for the approximate yield condition in this model of dilatant, pressure sensitive plastic behaviour.

A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals : application to zirconium alloys

Abstract: We present in this work a visco-plastic self-consistent (VPSC) anisotropic approach for modeling the plastic deformation of polycrystals, together with a thorough discussion of the assumptions involved and the range of application of such approach. We use the VPSC model for predicting texture development during rolling and axisymmetric deformation of Zirconium alloys, and to calculate the yield locus and the Lankford coefficient of rolled Zircaloy sheet. We compare our results with experimental data and find that they are in good agreement with the available experimental evidence. We also compare the VPSC predictions with the ones of a Full Constraints approach and observe that they differ both quantitatively and qualitatively: according with the predictions of the VPSC scheme, deformation is accommodated mostly by the soft systems, the twinning activity is much lower, and fewer systems are active, in average, per grain. These results are a consequence of having accounted for the grain interaction with its surroundings, which is a crucial aspect when modeling plastically anisotropic materials.