Showing papers on "von Mises yield criterion published in 1968"

The plastic yield behaviour of polymethylmethacrylate

Abstract: The yield behaviour of an amorphous glassy polymer has been investigated under a system of combined stress in an attempt to define a criterion for yield. Sheets of polymethylmethacrylate were compressed in plane strain and the compressive yield stress was determined as a function of the tension applied in the plane of the sheet. The compressive yield stress was found to decrease with applied tension more rapidly than would be expected if the shear yield stress of the material were independent of pressure. The results have been analysed in terms of a Coulomb yield criterion where the shear yield stress is expressed as a constant plus a friction term proportional to the pressure on the shear plane. Birefringent shear zones were observed in the deformed region after the load was removed and these zones were inclined at 52.9° to the plane of the sheet. It was found that if the stresses at yield were expressed as nominal stresses then the inclination of the shear planes predicted by the yield stress data coincided with the observed inclination. It also appears that it may be possible to define a fracture criterion in terms of the applied stress system.

The yield behaviour of oriented polyethylene terephthalate

Abstract: Oriented sheets of polyethylene terephthalate have been deformed in tension and simple shear, with the primary variable as the angle between the tensile stress or the shear stress and the initial draw direction. In tension, deformation bands were observed in all cases, as has been reported previously (Brown and Ward 1968 a), and a clear yiold point was observed in all cases. The stress–strain curves for simple shear on the other hand showed very appreciable changes with the direction of the shear stress, and deformation bands were observed only in certain cases. These qualitative features are consistent with the principles proposed in the previous paper, on the basis of the tensile behaviour. An attempt is made to obtain a yield criterion which is consistent with both the tensile and shear data. It was found that neither a critical resolved shear stress criterion nor this modified by a normal stress term was adequate to explain the tensile yield data. However, a modification of the von Mises yiel...

Mechanical anisotropy of oriented polymers

Abstract: Measurements of tensile and shear yield stress have been made on strips cut at various angles to the draw direction from films of drawn amorphous poly(ethylene terephthalate). The data were well fitted by a criterion of the von Mises type but with modifications to allow for the anisotropy of the samples and also for a built-in compressive stress in the draw direction. In the tensile experiments a sharp neck is usually formed at an angle to the tensile direction and this angle is predicted with good accuracy by an application of the theory of plastic potential.

A Theoretical and Experimental Study of Projectile Impact on Clamped Circular Plates

Abstract: A method for the analysis of the plastic deformation of a circular plate subject to projectile impact is presented based on the assumption that the material is rigid viscoplastic, obeying a von Mises yield condition and associated flow rule. The predictions of the analysis are com­pared with the results of experiments in which projectiles of different masses are fired at various velocities at clamped plates of mild steel. The plates used in the experiments are such that substantial plastic strains can develop, while the maximum displacements are of the same order as the thickness. The analytical method presented predicts the behaviour of the plates to within the accuracy of the tests. The material constants which fit the results are in accord with those obtained from different tests.

Theoretical Analysis for the Redrawing of Cylindrical Cups through Conical Dies without Pressure Sleeves

Abstract: A theory for the redrawing of cylindrical cups through conical dies is presented. In the absence of a pressure sleeve a zone of unconstrained drawing exists prior to the conical zone and the principle of minimum energy is used to establish the extent of the zone and the associated deformation and stresses. A linearization of the von Mises yield criterion for plane stress problems is adopted and use of the flow rule associated with this criterion allows the variation of thickness across an element to be taken into account in the solution of the stress equilibrium equation; the strains can also be determined without resorting to numerical integration. Because the deformation during redrawing takes place in a series of discrete steps, work-hardening can be conveniently included in the analysis. Bending and unbending contribute significantly to the process work and a more detailed examination of the mechanism is justified. The present theory allows the effects of friction, die angle and die intersection radiu...

Finite element analysis of inelastic structures

Abstract: Differential stress-strain relationships are used to generate a system of simultaneous firstorder differential force-displacement equations which are integrated numerically to obtain the stresses, strains, and displacements in inelastic structures. For the biaxially stressed element, the concept of isotropic hardening and a generalized stress are used to evaluate an effective modulus and Poisson's ratio, which vary continuously from their initial values during elastic straining action to their asymptotic values during intense plastic straining action. The surface of plasticity for this element closely approximates the von Mises surface when the generalized stress is set equal to the von Mises stress and the strain distribution is essentially identical to that obtained by the Prandtl-Reuss incremental flow theory. The analysis of the MIT shear lag structure is presented to demonstrate the applicability of the method to systems of practical size and interest. Nomenclature A = equilibrium matrix B = compatibility matrix C = stress-strain matrix C = differential stress matrix E = Young's modulus Et = tangent modulus Es = secant modulus K — stiffness matrix K = differential stiffness matrix P = applied load parameter u = element nodal displacements X = element nodal forces X = load constant n = Poisson's ratio fjLt = tangent Poisson's. ratio Us = secant Poisson's ratio e = strain a- = normal stress