Showing papers on "von Mises yield criterion published in 1977"

On the correlation of indentation experiments

Abstract: The relationship between indentation pressure produced by cones, pyramids and spheres, and the mechanical properties of elastic-plastic materials is considered, based on previous work which uses the expansion of a cavity in an elastic-plastic material. According to the earlier model, there are three zones: a hydrostatic 'core' of which the indenter is embedded; a hemispherical shell, where plastic flow is taking place; and beyond this the elastic hinterland. An improved correlation with experimental results is obtained if it is assumed that the hemispherical core is a region in which the stresses are changing from purely hydrostatic to values which satisfy the Von Mises yield criterion. A further improvement results if a correction is made for the lack of geometric similarity of the strain field in indentations by spheres.

A Characterization of the Von Mises Distribution

Abstract: The von Mises, or circular normal density on the unit circle is the hitting density of a two-dimensional Brownian motion starting at the origin, with constant drift velocity and direction. The concentration and location parameters of the density have a natural relation to the drift parameters.

Path dependence of the J-integral and the role of J as a parameter characterizing the near-tip field

Abstract: The J-integral has significant path dependence immediately adjacent to a blunted crack tip under small-scale yielding conditions in an elastic-plastic material subject to mode I loads and plane-strain conditions. Since the J-integral, evaluated on a contour remote from the crack tip, can be used as the one fracture-mechanics parameter required to represent the intensity of the load when small-scale yielding conditions exist, J retains its role as a parameter characterizing the crack-tip stress fields, at least for materials modelled by the von Mises flow theory. Some results obtained using both the finite-element method and the slip-line theory are suggestive of a situation in which an outer field parameterized by a path-independent value of J controls the deformation in an inner or crack-tip field in which J is path dependent. The outer field is basically the solution to the crack problem when large deformation effects involved in the blunting are ignored. Thus, the conventional small-strain approaches in which the crack-tip deformation is represented by a singularity have been successful in characterizing such features as the crack-tip opening displacement in terms of a value of the J-integral on a remote contour. An interesting deduction concerns a nonlinear elastic material with characteristics in monotonic stressing similar to an elastic-plastic material. Since J is path independent everywhere in such a material, the stress and strain fields near the crack tip in such a material must differ greatly from those arising in the elastic-plastic materials studied so far. This result is of significance because it is believed that such nonlinear elastic constitutive laws can represent the limited strain-path independence suggested by models for plastic flow of polycrystalline aggregates based on crystalline slip within grains.

Optical response and yield behavior of a polyester model material

Abstract: A mixture of flexible and rigid polyester resins is one of the materials that has been used in the past to model elasto-plastic prototype behavior. As a result of recent curtailments in plastic production, one of the constituents of the mixture is no longer available. A different flexible resin of the same family is available, however, and has been shown in this program to be suitable for optical-model studies involving deformations into the plastic range of material response. In this paper, complete mechanical and optical properties for the new model material are presented for both uniaxial tensile and compressive loadings. Results from a series of thin-walled cylinder tests under internal-pressure loadings are also presented which provide some information on the optical and yield characteristics of the polyester model material under a biaxial state of stress. Results of the study indicate that stress-strain curves for the material can be modified significantly by changing the mixture ratio or the test temperature. Optical data from the study indicate that the fringe order in the material is a function of the instantaneous principal-strain difference. Data from the uniaxial tension and compression tests, together with limited data from the cylinder tests, indicate that the polyester material may follow a modified von Mises yield criterion which accommodates differences in tensile and compressive yield strengths of a material.

Inelastic Finite Element Analysis Using Tresca Yield Condition

Abstract: A derivation of elastic-plastic stress rate-strain rate relations for strain-hardening materials in plane stress condition is presented in this paper for materials that obey Tresca yield condition. The development is similar to that for von Mises yield condition but differs significantly due to the special considerations necessary in dealing with the corners of the yield surface. These relationships are employed to obtain an elastic-plastic solution for a notched plate of strain-hardening material subjected to a monotonically increasing tensile load. The results are compared to those previously available in the literature. It is shown that the stress-strain relations developed for Tresca yield condition can be used as easily as those of von Mises yield condition which have commonly been employed. The resulting solution is more conservative and leads to safe results.

Note on Conditions for Weak Convergence of Von Mises' Differentiable Statistical Functions

Abstract: In establishing weak convergence of von Mises' differentiable statistical functions to a normal distribution usually square integrability conditions with respect to the underlying kernel function are assumed. It is shown that these conditions can be weakened by assuming integrability of the von Mises' functional itself. In addition it is pointed out that in nontrivial cases the conditions of square integrability of the kernel do not hold whereas weak convergence of the von Mises' functional can still be proved.

Strain gradients in plasticity

Abstract: An analytical model of a plastically deforming solid is assumed to be a material where the second spatial gradients of strain are included in the constitutive equations. These constitutive equations are combined, in a one dimensional shearing problem, with the second law of thermodynamics and condition of thermodynamic stability. The results are that a phase change occurs when the von Mises yield condition is reached because the material is also thermodynamically unstable. The second law of thermo-dynamics forces the deformations that occur to be nonhomogeneous on a small scale. Therefore the model is in agreement with experimental data. This type model therefore can be used to unify the continuum theories of plasticity with those with a more “physical” basis because deformations occur at two different scales.

Asymmetric two-dimensional jet efflux from a channel

Abstract: Irrotational flow of two-dimensional jets from a channel is treated without direct use of a logarithmic hodograph plane. An analytical approach is introduced for solving the general problem of two jets issuing from a channel with three end plates. Numerical values of the contraction coefficient and the angle of jet deflection are obtained for the special case where the two jets are located symmetrically and all the end plates are in line. Limiting cases of the resulting single-jet problem are the symmetric and asymmetric configurations solved by von Mises (1917). Results for the asymmetric case improve upon the theoretical values reported by von Mises and compare favorably with existing experimental data.

A probabilistic approach to polycrystalline plasticity part II: applications

Abstract: Using our constitutive theory for polycrystalline plasticity, we have calculated characteristic yield conditions for several sample materials in which the dependence of the dislocation velocity on stress is given by an empirical power function. The shape of the yield surfaces for these materials varies resembling that of von Mises when the stress exponent is small and that of Tresca when the exponent is large. Additional examples illustrate the ability of the proposed theory to model such phenomena as the development of anisotropy during plastic deformation, material hardening and softening, the occurrence of upper and lower yield points, and a Bauschinger effect.