Showing papers on "von Mises yield criterion published in 1972"

The plastic flow of isotropic polymers

Abstract: This paper describes a study of the plastic stress-strain behaviour of a number of polymeric materials deformed under different states of stress. Tests were carried out on samples of polymethyl methacrylate, polystyrene, polyethylene terephthalate, polyvinyl chloride, epoxy resin, and high density polyethylene. The extent to which plasticity theory can be used to describe the observed behaviour has been considered and it is concluded that in spite of their viscoelastic behaviour and the large elastic strains prior to yield plasticity theory can be applied provided that stresses are expressed as true stresses at yield. The most appropriate yield criterion for PMMA is a von Mises criterion modified so that the yield stress varies linearly with the hydrostatic component of the stress tensor. For PS a modified Tresca criterion is more appropriate. The inclination of the bands of local shear deformation that form in these materials is not at 45° to the directions of principal stress. In most cases this apparent deviation appears to be entirely due to elastic recovery on unloading, but for polystyrene there is an extra deviation probably due to the occurrence of small plastic volume changes during yield.

On R. Von Mises' Condition for the Domain of Attraction of $\exp(-e^{-x})^1$

Abstract: There exist well-known necessary and sufficient conditions for a distribution function to belong to the domain of attraction of the double exponential distribution $\Lambda$. For practical purposes a simple sufficient condition due to von Mises is very useful. It is shown that each distribution function $F$ in the domain of attraction of $\Lambda$ is tail equivalent to some distribution function satisfying von Mises' condition.

The flow and fracture of unidirectional

Abstract: A yielding criterion, based upon calculated internal stress distributions, was developed for composite materials under various externally applied biaxial tension loadings. The stress distributions were computed using the finite element technique; the criterion showed that the yield strength of the composite is significantly higher than the transverse uniaxial yield strength for a wide range of biaxial loadings. Limited amounts of preliminary data were generated (using the hydraulic bulge test to develop biaxial stress loadings) to validate the analytical yielding criterion. The data obtained showed better agreement with the new yielding criterion than they did with the existing Hill Criterion.

Evaluation of finite-plasticity theories for nonproportionate loading of torsion-tension members

Abstract: Based on the assumption that the material was isotropic and even, and satisfied the condition of isotropic hardening for a von Mises material, finite-incremental and total-strain theories were derived for solid circularsection torsion-tension members subjected to nonproportionate loading. Torsion-tension members made of SAE 1045 steel and aluminum alloy 7075-T6 were subjected to proportionate and nonproportionate loading. During the nonproportionate loading, either the axial loal P or torque T was held constant while the other was increased. Excellent agreement was found between the incremental theory and experimental data indicating that the assumption of isotropic hardening is valid for this type of loading. For some of the nonproportionate loading paths, incremental and total-strain theories gave nearly identical results.

On plasticity, elastic relaxation phenomena, and a stress-strain relation which characterizes Schofield-Scott Blair media

Abstract: A generalization is given of the author's theory for plasticity phenomena. The theory includes the possibility of both stress and strain relaxation in the preplastic range. Methods of non-equilibrium thermodynamics are used. The plasticity phenomenon is explained by introducing a physical assumption concerning the phenomenological coefficients. A yield function is proposed which includes the Bauschinger effect and strain hardening. If the free energy f has the form f=f(1)+f(2), where f(1) is a function of the temperature and the elastic strains and f(2) is a function of the temperature and the inelastic strains, and if cross effects between the plastic flow and elastic relaxation phenomena may be neglected, the proposed yield function is such that the derivative with respect to time of the deviator of the plastic strain tensor is given by \(\eta \left( {{{\partial \Phi } \mathord{\left/ {\vphantom {{\partial \Phi } {\partial _{\tau \alpha \beta } }}} \right. \kern- ulldelimiterspace} {\partial _{\tau \alpha \beta } }}} \right)\), where Φ is the yield function, ταβ is the mechanical stress tensor, and η is a coefficient which vanishes in the preplastic range. If the equations of state may be linearized the proposed yield function reduces to a function which is analogous to a yield function proposed by Freudenthal. If the plastic flow phenomenon is not associated with changes in the microscopic structure of the medium the proposed yield function reduces to the Von Mises function. It follows from the theory that in a first approximation elastic relaxation phenomena in the preplastic range may be described by the equation for Poynting-Thomson media (standard linear solids). An equation which characterizes Schofield-Scott Blair media is also derived from the developed theory.

The ductile fracture of anisotropic materials - A theoretical and experimental evaluation of the Dugdale model applied to anisotropic materials

Abstract: A theoretical solution is obtained which adapts the Dugdale model to anisotropic materials. The effect of anisotropy is shown to modify each isotropic field equation by amultiplicative constant which is a function of the anisotropic-material constants. A limit on the validity of a Dugdale-type solution is found using a von Mises' yield criterion which implies that the crack and plastic zone will extend along a direction other than the crack line. As long as the material is within pirescribed limits, the Dugdale finiteness condition is shown to be affected by material anisotropy only in the calculation of a yield stress. Experimental results on crack-opening displacements are presented which indicate that a large degree of anisotropy is necessary to cause significant deviations from isotropic theory. Results are presented which indicate that anisotropy does affect the direction of crack propagation.

Strain-history effect on isotropic and anisotropic plastic behavior

Abstract: An experimental investigation was performed to evaluate the effect of strain history on an initially isotropic material. A hot-rolled 2.5-in.-diam bar of SAE 1045 steel provided all the test specimens. Axial and circumferential compression data indicated that the steel was isotropic. Additional tension and torsion data indicated that the steel was an isotropic-hardening von Mises material; this was also confirmed by proportionate loading of thin-walled cylinders such that the ratio of axial to circumferential stresses was either 0, 1/2, 1, 2 or ∞. Two additional sets of cylinders were preloaded either in simple axial tension or as closed-ended cylinders to an effective plastic strain of 0.006 before they were proportionately loaded. The preloading had a pronounced effect on yield surfaces for reloading if the effective plastic strain on reloading was only slightly greater than that for the preloading. The effect of preloading on the yield surfaces was small when the effective plastic strain was three to four times that for the preloading. Hill's anisotropic theory was used to predict stress-strain relations for several of the reloaded cylinders. Good agreement was obtained between theory and experiment.

Tresca-type plastic materials in the theory of hypoelasticity. I. Mechanical constitutive equations and simple shear deformation

Abstract: The mechanical constitutive equation of the Tresca-type plastic material is defined as a special case of the constitutive equation of the hypoelastic material. The singularity condition of the equation gives the Tresca yield criterion and the associated flow rule. The material defined corresponds with the Prandtl-Reuss material, which is characterized by the von Mises yield criterion and the St. Venant-Levy flow rule. The simple shear deformation of the Tresca type plastic material is analysed theoretically. The hypoelastic yield occurs and the shear stress has a maximum value at a finite angle of shear. After that state the shear stress decreases monotonically to zero value, while the maximum difference of the principal stresses gradually approaches a constant value. For the case equivalent to real materials the stress in the state of hypoelastic yield satisfies substantially the Tresca yield criterion.

On the Geometrically Similar Expansion of a Hole in a Thin Infinite Plate

Abstract: The problem is considered of expanding a central cylindrical hole from zero radius in a thin infinite plate of conical profile such that, initially, thickness is proportional to radius, chosen so that geometrical similarity is maintained. A previously incorrect theory is modified by using a matrix formulation of the equations suitable for iterative solution on the digital computer, and the predicted profile of the plate is compared with that found from an experiment performed on a finite mild steel plate of conical profile. The Prandtl-Reuss relations for the large deformation elastic-plastic flow of a work-hardening material obeying the Maxwell (von Mises) yield criterion are used. Apart from the intrinsic interest of obtaining a complete solution to a problem of this type, the solution will be used to provide a valid model against which to test solutions obtained by finite element methods for large deformation elastic-plastic analysis.

Elastic-Plastic Analysis of Cylindrical Shells

Abstract: The behavior of cylindrical shells under a progressively increasing load is studied. For this purpose a mathematical model is used to replace the continuum. The model consists of rigid bars joined together by deformable nodes. The material is assumed elastic-perfectly plastic. The Prandtl-Reuss incremental theory of plasticity together with the von Mises yield condition are adopted. Two examples of cylindrical shells with different boundary conditions are presented. The deflections, forces, and moments in the shells are found for each load level till the ultimate load is reached. The load deflection characteristic and the progression of yield zones in the shells are found. The method can be extended to represent reinforced concrete behavior of shell roofs.

Plastic Analysis of Anisotropic Disks and Plates

Abstract: The method of limit analysis is used to estimate the collapse loads of rotating disks and laterally loaded circular plates. The material is transversely anisotropic and is assumed to obey either the Tresca or von Mises yield criterion. Analyses indicate that the effect of transverse anisotropy on the collapse loads depends upon the case under consideration. While transverse anisotropy substantially increases the collapse load in the case of solid disks and circular plates under lateral pressure, it has no effect on the collapse load of a circular plate under shear loading. The collapse loads in the case of annular disks and annular plates under lateral pressure may increase or remain constant after an initial increase with respect to transverse anisotropy. This effect depends on the assumed yield criterion. Some similarities in the analysis of the disk and the circular plate exist. Typical results of the analyses are presented.

Symmetric Buckling of Inelastic Spherical Shells

Abstract: A numerical method for determining the buckling loads and stresses for elastic-plastic spherical shells subjected to uniform external pressure is presented. No restriction is placed on shallowness in the analysis. The incremental theory of plasticity and the von Mises yield criterion are used in formulating the problem. The governing differential equations are formulated in terms of displacements and are solved with the aid of finite differences, an incremental-iterative technique, and a high speed digital computer. Buckling loads are taken as the first maximum of a load-average deflection curve. Numerical results are presented for a clamped spherical shell. Buckling loads are compared to the elastic complete sphere value and the limit analysis load. The relationship of the radius-thickness ratio to buckling stress is presented.

Tests for samples from von mises populations

Abstract: This chapter presents a few tests from von Mises populations, including tests that are analogues of the standard normal theory tests, that is, the test of preassigned mean direction and of preassigned concentration parameter; tests of equality of two mean directions and of equality of two concentration parameters; and tests of homogeneity. These tests are modified when the data is either multimodal or axial. The chapter discusses the optimum properties of these tests and illustrates them with the help of appropriate examples. All the tests depend on the sample mean direction or on the resultant length or on both. The chapter also discusses the Rayleigh test and invariant tests. The Neyman–Pearson approach, the Fisher ancillary principle, and the tests for the concentration parameter are also reviewed in the chapter.

A Numerical Approach to Finite Elastic-Plastic Deflections of Circular Plates

Abstract: An elastic-plastic analysis of large deflection of axisymmetrically loaded circular plates is presented in this paper. Under the Kirchhoff-Love hypothesis, the incremental theory of plasticity together with the von Mises yield condition and the associated flow rule is adopted, and isotropic workhardening materials as well as elastic-perfectly plastic materials are treated. This is not an inherent limitation of the method. A numerical procedure with the finite difference approximation and the iteration technique is employed for the solution of the derived incremental basic equations of a two-point boundary value problem. Several results for various kinds of boundary condition and some values of plate thickness are given including the solutions of residual stress and strain for the first cycle of a loading-unloading process.

Yielding of Fiber Reinforced Tresca Material

Abstract: A plane stress theory of plastic failure of a composite material is formulated by considering how the plastic failure surface of the matrix is altered by the addition of an array of parallel fibers. The matrix is assumed to obey the classical Tresca maximum shear stress yield criterion. The fibers are assumed to be infinitesimally thin and perfectly rigid. The fiber-matrix bond is such that a principal effect of the fibers is to restrict the plastic flow of the matrix in such a way that no extentional plastic strain increments in the direction of the fibers may occur. The limit stresses of a unidirectionally reinforced sheet are discussed and compared to results if the composite has a matrix which obeys the von Mises yield criterion. The limit stresses of laminates depend upon the bond between the laminae. Upper and lower bounds are obtained for two-ply laminate yield stresses.

Stress analysis and design of silicon solar cell arrays and related material properties.

Abstract: A systematic approach is presented for the design of solar cell arrays to eliminate mechanical failures that might arise in components of the arrays in a thermal environment. A prerequisite to the approach is the characterization of material properties at different temperatures. Significant data is obtained for the thermal behavior of the silicon solar cell material and adhesives. Upon determining the mechanical and thermal material properties of the components of the solar cell array, utilizing a finite element idealization for predicting the stress fields in the components, and employing the von Mises failure criterion, potential failure areas in various design configurations in a given thermal environment are identified. Guide lines and means to optimize a given design are illustrated by two examples.

The Yield Behaviour of Rigid Polymers

Abstract: : The yield behavior of solid polymers has been examined, with especial reference to that of the glassy amorphous polymers. Considering polymethyl methacrylate to be a typical glassy amorphous polymer, the effects of strain rate and temperature on the yield stress have been determined by taking stress- strain curves in simple plane strain compression. The variation of the plane strain compressive yield stress with applied tension and compression has also been determined for polymethyl methacrylate and several other polymers. It was shown that the hydrostatic component of stress had a significant effect on the yield behavior of the polymers studied. This has been considered in terms of the Tresca and von Mises yield criteria modified for pressure dependence.

Thermal elastoplastic structural analysis of non-metallic thermal protection systems

Abstract: An incremental theory and numerical procedure to analyze a three-dimensional thermoelastoplastic structure subjected to high temperature, surface heat flux, and volume heat supply as well as mechanical loadings are presented. Heat conduction equations and equilibrium equations are derived by assuming a specific form of incremental free energy, entropy, stresses and heat flux together with the first and second laws of thermodynamics, von Mises yield criteria and Prandtl-Reuss flow rule. The finite element discretization using the linear isotropic three-dimensional element for the space domain and a difference operator corresponding to a linear variation of temperature within a small time increment for the time domain lead to systematic solutions of temperature distribution and displacement and stress fields. Various boundary conditions such as insulated surfaces and convection through uninsulated surface can be easily treated. To demonstrate effectiveness of the present formulation a number of example problems are presented.

Effect of the third stress invariant on the characteristic curves of a material

Abstract: The effect of the third invariant of the stress tensor (deviator) on the stress-strain intensity curve and the Lode diagram is investigated.

Viscoelastoplastic response of axisymmetric shells under impulsive loadings

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.