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Showing papers on "von Mises yield criterion published in 1973"


Journal ArticleDOI
TL;DR: In this paper, a modified von Mises criterion, τ = τ 0 − μP, was used to describe the yielding behavior of a cross-linked epoxy resin under a biaxial stress system, indicating that flow of the material is pressure sensitive.
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.

538 citations


Journal ArticleDOI
TL;DR: In this article, a yield criterion based on the von Mises criterion was proposed, which accommodates differences in tensile and compressive yield strengths and accounts for any dependence of yielding on the hydrostatic component of the applied stress state.
Abstract: A yield criterion, not previously compared with the actual macroscopic behaviour of polymers, is herein compared with the pressure-modified octahedral shear stress criterion earlier suggested by others. This new relation, which is a version of the von Mises criterion, accommodates differences in tensile and compressive yield strengths and accounts for any dependence of yielding on the hydrostatic component of the applied stress state.

434 citations


Journal ArticleDOI
TL;DR: In this article, the critical tensile strain for the formation of a craze in polystyrene was investigated under conditions of biaxial stress with one principal stress compressive, and the results were consistent with the suggestion of Sternstein and Ongchin that for crazes to form the hydrostatic component of the stress tensor must be tensile.
Abstract: The critical stress for craze formation in four different grades of polystyrene has been investigated under conditions of biaxial stress with one principal stress compressive. The results are consistent with the suggestion of Sternstein and Ongchin (1969) that for crazes to form the hydrostatic component of the stress tensor must be tensile. It has further been shown that a convenient way to express the criterion for the formation of crazes is in terms of a critical tensile strain, ∊c, which is a function of the hydrostatic component of the stress tensor. This critical-strain criterion can readily be applied to predict the onset of crazing under a general triaxial state of stress, and it may be possible to interpret the variation of the two parameters in the criterion in terms of two distinct critical processes in the formation of a craze, one process pressure-dependent the other not.

116 citations


Journal ArticleDOI
TL;DR: In this paper, a Groves-and-Kelly calculation showed that the combination of pyramidal slip on {11¯02} and basal slip on (0001){112¯0} will allow homogeneous deformation of Al2O3 polycrystals.
Abstract: Crystallographic notation for Al2O3 is reviewed, with particular reference to the correct basis to be used in describing slip systems. A Groves-and-Kelly calculation showed that the combination of pyramidal slip on {11¯02} and basal slip on (0001){112¯0} will allow homogeneous deformation of Al2O3 polycrystals. Furthermore, operation of either the {101¯1} or the {011¯2} slip system will also satisfy the Von Mises criterion, since each system is capable of 5 independent deformation modes. Electron microscopy of an Al2O3 polycrystal deformed ≅5% at 1150°C under a hydrostatic confining pressure confirmed that pyramidal slip had occurred.

107 citations


Journal ArticleDOI
TL;DR: In this article, the authors compared a pressure modified von Mises criterion with a predicted yield locus based on a pressure-modified von-Mises criterion for high density polyethylene.

60 citations


Journal ArticleDOI
TL;DR: In this article, the bifurcation stress for a simply-supported elastic-plastic plate in uniaxial compression is calculated for the case when the stress is at a vertex of the yield surface which is locally similar to that of Tresca.
Abstract: The bifurcation stress is calculated for a simply-supported elastic-plastic plate in uniaxial compression, in the case when the stress is at a vertex of the yield surface which is locally similar to that of Tresca. The effect of coupled hardening between yield-surface facets which meet at the vertex is included. It is found that the bifurcation stress may be substantially lower than that associated with the von Mises yield surface. The latter is known to give results too high to be reconciled with experiment. Reductions of order 10–30 per cent are shown to be unexceptional, even with the retention of an elastic value for the shear modulus.

43 citations


Journal ArticleDOI
TL;DR: In this article, the influence of biaxial loading on plastic zone size and crack opening displacement has been examined, and the theoretical predictions are supported by a limited amount of experimental data.

38 citations


Journal ArticleDOI
TL;DR: In this paper, the results of three finite element stress analysis programs are compared for the problem of the elasto-plastic bending of a notched beam under plane strain conditions.
Abstract: The results of three finite element stress analysis programs are compared for the problem of the elasto–plastic bending of a notched beam under plane strain conditions. Both Tresca and von Mises yield criteria are considered and the numerical results are compared with an available analytical solution based on slip-line field theory. The general conclusion is drawn that finite element methods can be used with confidence in elasto–plastic stress analysis.

29 citations


01 Oct 1973
TL;DR: In this paper, the authors evaluated four hardening rules of the incremental theory of plasticity to determine which of the rules are better suited for use in finite element or finite difference structural analysis computer programs.
Abstract: : The report presents an evaluation of four hardening rules of the incremental theory of plasticity to determine which of the rules are better suited for use in finite element or finite difference structural analysis computer programs. The hardening rules considered are isotropic hardening, the Prager-Ziegler kinematic hardening rule, the Mroz model, and the mechanical sublayer model. Comparisons of experimental data with hardening rule predictions (from a total incremental plasticity formulation using the von Mises yield condition and associated flow rule) for simple loading paths are first considered. Next the computer storage requirements associated with each hardening rule are investigated. Finally, the two most promising hardening rules are incorporated into an existing dynamic, shell of revolution finite element computer code and the cases of an impulsively loaded circular ring and circular plate are examined. Conclusions regarding the areas of applicability of each hardening rule are then presented. (Author)

19 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examined the yield criteria for anisotropic laminated media and showed that the criterion of Tsai and Wu is a direct extension of Von Mises' criterion.
Abstract: This study examines the yield criteria for anisotropic laminated media. It will be shown that for laminated media with isotropic layers, the criterion of Tsai and Wu is a direct extension of Von Mises'. Also presented here is a set of equations governing the relative positions of the yield ellipses. Furthermore, a general expression for the yield condition of a laminated medium composed of generally anisotropic layers is obtained.

15 citations


Journal ArticleDOI
TL;DR: In this article, the authors present a discussion of the yielding behavior of particulate media during shearing, based on the results of a laboratory investigation of the stress-strain properties of samples of glas...
Abstract: This paper presents a discussion of the yielding behavior of particulate media during shearing, based on the results of a laboratory investigation of the stress–strain properties of samples of glas...

Journal ArticleDOI
TL;DR: In this paper, a macroscopic theory of isotropic plastic flow under multiaxial stress states is developed from considerations of thermally activated dislocation motion on discrete randomly-oriented slip planes.

Journal ArticleDOI
TL;DR: In this paper, a yield criterion in planestress state is derived based on isotropic representation of a scalar valued function depending upon symmetric 2×2 stress and strain matrices.
Abstract: A yield criterion in planestress state is derived here based on isotropic representation of a scalar valued function depending upon symmetric 2×2 stress and strain matrices. The material has been assumed to be incompressible. In particular, for tension-torsion loading the yield surface is nonsymmetric with respect to the torsional stress axis. Due to the non-symmetry, the yield condition describes the second-order effect relating to axial-strain accumulation in cyclic torsion, and at the same time it has got a very simple form compared to other yield conditions describing this effect.

Journal ArticleDOI
TL;DR: In this article, the von Mises yield criterion and its associated flow rule are used to compute stresses and strains associated with geometric and material discontinuities in large elastic-plastic plates under conditions of plane strain.
Abstract: The finite element method has been used to compute stresses and strains associated with geometric and material discontinuities in large elastic-plastic plates under conditions of plane strain. The plate material is assumed to obey the von Mises yield criterion and its associated flow rule. Numerical results are discussed in connection with a tentative criterion of fatigue crack initiation.

01 Sep 1973
TL;DR: In this article, a method of analyzing nonlinear static and dynamic responses of deformable solids has been developed based on an incremental variational formulation using the Lagrangian mode of description.
Abstract: : A method of analyzing nonlinear static and dynamic responses of deformable solids has been developed based on an incremental variational formulation using the Lagrangian mode of description. The material nonlinearity due to plasticity or viscoplasticity as well as the geometric nonlinearity due to large displacements are considered. The equations of motion are obtained in a linearized incremental form using the principle of virtual work and solved using step-by-step numerical integration procedures. Equilibrium check is made at the end of each step and the residual forces are added to the next increment for improved accuracy over the pure incremental method. For elastic-plastic solutions the flow theory of plasticity is used along with the von Mises yield condition for isotropically hardening materials. The viscoplastic constitutive theory is also in the form of an associated flow law and capable of considering strain rate sensitive behavior. The viscoplastic strains are taken into account using an initial strain formulation. The discretization of the structure is achieved by the use of degenerate isoparametric finite elements and the computer codes that have been developed are capable of analyzing large axisymmetric deformations of shells of revolution. (Modified author abstract)

Journal ArticleDOI
01 May 1973
TL;DR: In this article, an extended Newton method combined with the method of finite differences is shown to be a powerful means to the steady-state creep analysis of shells of revolution under the von Mises type and the power creep law.
Abstract: The extended Newton method combined with the method of finite-differences is shown to be a powerful means to the steady-state creep analysis of shells of revolution. The creep theory of von Mises type and the power creep law are assumed. As numerical examples, a simply-supported circular cylindrical shell with open ends and a clamped spherical shell, subjected to internal pressure respectively, are analysed. The results of calculation of the cylindrical shell, in particular, are compared with those of semi-infinite sandwich shell obtained by Rabotnov.

Journal ArticleDOI
TL;DR: In this article, the von Mises yield criterion is used to study circular plates including the effect of transverse shear, and appropriate relations among the generalized strain-rate variables and the normal velocity are developed.

Journal ArticleDOI
TL;DR: In this paper, a multiparameter yield surface is proposed to predict the failure of ductile materials under both tensile and torsion test experiments, as well as the hydrostatic compression test.
Abstract: Introduction T basic hypothesis in the theory of plasticity is that there exists a scalar function of stresses which characterizes the yielding of materials. This scalar function, also called the yield function,/(crfj.) generates a closed surface in the stress space by a relation /(o^) = 0. When a material is subjected to increasing forces and torques, it describes a path in the stress space. When this path intersects the yield surface /(afj-) = 0, the material yields and becomes plastic. All the classical failure theories, e.g., those of Tresca, Von Mises, and Reuss, give conflicting predictions of the yield stresses of metals even for such simple cases of pure torsion or elongation. The reason for the conflicts in these theories is that these theories essentially form one-parameter yield surfaces. So fitting these criteria on tensile tests alone make these incompatible with the torsion test data, and vice versa. These theories also do not predict the failure under hydrostatic compression. Detailed references on these theories can be obtained in Ref. 1. The proposed theory, on the other hand, forms a multiparameter yield surface. Here a start is made from the basic yield point data from both tensile and torsion test experiments, as well as the hydrostatic compression test. Thus the present theory can predict yielding under hydrostatic pressure while posing no conflict between theory and, at least, the basic tension and torsion experiments. The formulation is flexible enough to satisfy a large number of the available experimental data on the yield point and subsequent flow for ductile materials, and includes both ideally plastic and strain-hardening solids. The yield surface generated is invariant with respect to rotation of coordinate axes, a necessary requirement for all such criteria.

Journal ArticleDOI
TL;DR: In this paper, a derivation of finite element equations of and solution to the viscoelastoplastic response of an isotropic axisymmetric shell is presented.
Abstract: A derivation of finite element equations of and solution to the viscoelastoplastic response of an isotropic axisymmetric shell are presented herein. The generalized Maxwell model is incorporated into the von Mises isotropic yield function. This permits a derivation of the incremental stress as a function of elastic, viscous, and plastic strains. With this relationship inserted into the incremental equation of motion, a direct numerical integration scheme is then used to solve for incremental responses. The plastic tangent stiffness matrix is updated at each incremental time step. Numerical results are presented for a circular plate to verify correctness of the program and subsequently for a spherical cap subjected to uniformly distributed transverse impulsive load of infinite duration.

Journal ArticleDOI
TL;DR: In this paper, the effect of transverse shear on collapse loads is examined in the case of shallow spherical shells and the results indicate that the lower bound approach gives acceptable results when extremely shallow shells are considered.

Journal ArticleDOI
TL;DR: In this article, the authors derived finite-strain theories for solid circular torsion members for the conditions that the inelastic deformations are either time independent or time dependent.
Abstract: Based on the assumption that the material satisfies the condition of isotropic hardening for either a von Mises or a Tresca material, finite-strain theories are derived for solid circular torsion members for the conditions that the inelastic deformations are either time independent or time dependent. In the latter case, both creep and relaxation theories are derived. At room temperature the theories are evaluated for each of eight metals using finite-strain data from tension, compression and torsion members. Of the six metals that are found to satisfy the condition required for the isotropic-hardening model, two are von Mises, one is Tresca, and the other three are between von Mises and Tresca. At elevated temperatures, the theories are evaluated for each of five of the latter six metals, using data from tension and torsion members. Material properties obtained from the tension specimens are used to predict creep and relaxation curves for the torsion members. Contrary to the results at room temperature, creep curves for the torsion members do not all fall within the region bounded by von Mises and Tresca theories. In the case of relaxation, either excellent agreement is obtained between the von Mises strain-hardening theory and experimental data or the theory is conservative.

Journal ArticleDOI
TL;DR: In this article, the generalized Maxwell model is incorporated into the von Mises' anisotropic yield function, which permits a derivation of the incremental stress as functions of elastic, viscous, and plastic strains.

Journal ArticleDOI
TL;DR: In this article, the effect of pressure on the instability strain for simple sheet metal forming processes is calculated assuming a rigid-plastic, isotropic, incompressible material obeying the von Mises yield criterion and associated flow rule.

Journal ArticleDOI
TL;DR: In this paper, the incremental stress-strain relations have been formulated for nonisothermal kinematic hardening materials in which the yield surface is assumed to change its size with temperature.
Abstract: The incremental stress-strain relations have been formulated for nonisothermal kinematic hardening materials in which the yield surface is assumed to change its size with temperature. By following Prager’s assumption, the yield surface undergoes a translation in the direction of the plastic strain increment during the plastic flow. As pointed out by Shield and Ziegler, the yield surface with Prager’s hardening rule, in general, does not satisfy the invariance requirement with respect to a reduction in dimensions in the stress space. Nevertheless, if the von Mises criterion is adopted, such a discrepancy would not arise. If, however, other types of criterion are used, such as Tresca criterion, Ziegler’s modification must be incorporated.

Journal ArticleDOI
TL;DR: In this article, the von Mises theory and Tresca theory were compared with test data obtained from torsion-tension members and three different kinds of steels were tested; they are hotrolled mild steel, annealed mild steel and hot-rolled SAE 1017 steel.
Abstract: Finite-incremental Tresca and von Mises theories are developed for solid circular-section torsion-tension members subjected to proportionate and nonproportionate loading. The materials are assumed to be isotropic and even. Two Tresca theories and a von Mises theory are compared with test data obtained from torsion-tension members. Three different kinds of steels were tested; they are hot-rolled mild steel, annealed mild steel, and hot-rolled SAE 1017 steel. The fully plastic values of axial load and torque predicted by the Tresca theories agree with the experimental results; however, the deformations, in the strain-hardening region, predicted by both of the Tresca theories were greater than observed. The von Mises theory is nonconservative in predicting the fully plastic loads of torsion members and torsion-tension members and in predicting the deformations of torsion members in the strain-hardening region, but gives good correlation between predicted and experimental deformations for the torsion-tension members in the strain-hardening region.


Journal ArticleDOI
TL;DR: In this paper, a correspondence between principal stress space (σ) and base invariants of the stress tensor and the stress deviator (D) is established, and it is shown that the invariant spaces (σ and D) are convenient for analyzing the strength criteria of isotropic materials.
Abstract: In addition to principal stress space (σ) the spaces of the base invariants of the stress tensor (II) and the stress deviator (D) are considered A correspondence is established between these spaces The limit surfaces of revolution (of Balandin, Mirolyubov, etc) are expressed in two-dimensional (II) space in the form of parabolas, and the Mises surface in the form of a straight line in (D) space It is shown that the invariant spaces (II) and (D) are convenient for analyzing the strength criteria of isotropic materials

Journal ArticleDOI
TL;DR: In this paper, the effect of transverse shear on the yield condition and the collapse load of variable-thickness circular plates is examined for the von Mises yield condition, where the plates are loaded with a uniform transverse pressure and are hinge supported at the edge.
Abstract: Limit loads of variable-thickness circular plates are given for the von Mises yield condition. The plates are loaded with a uniform transverse pressure and are hinge supported at the edge. The effect of transverse shear on the yield condition and the collapse load is examined. It is shown that the inclusion of transverse shear in the analysis leads to restrictions on the edge thickness of the plates.