Showing papers on "von Mises yield criterion published in 1991"

A linearized integration technique for incremental constitutive equations

Abstract: A numerical technique is proposed to obtain stress–strain response curves from rate-type and incremental constitutive equations during generalized loadings. The proposed method linearizes the loading constraints of laboratory experiments, links them to the constitutive relations, and forms a linear system of ordinary differential equations. It circumvents the difficulties associated with the non-uniqueness and bifurcation of boundary value problems. The method is illustrated for the elastoplastic von Mises and Roscoe and Burland models subjected to torsion, circular stress path, and undrained triaxial compression. The approach pertains to most stress–strain relationships and laboratory experiments of geomechanics. It is useful for research on material modelling, engineering practice and computational mechanics.

Non‐linear analysis of stiffened plates using super elements

Abstract: A new numerical technique for large deflection elasto-plastic analysis of stiffened plates is presented. The method uses super finite elements which are macro elements having analytical as well as the usual finite element shape functions, specially designed so that only one plate element per bay and one beam element per span are needed. The large deflection theory by von Karman and the von Mises yield criterion and associated flow rule are employed. The governing equations are derived using the principle of virtual work, integrated numerically using Gauss quadrature and solved by Newton–Raphson iteration. Numerical solutions are presented for simple beams and plates, and plates stiffened in one or two mutually perpendicular directions. Good approximations are obtained with only one-element representations of each plate bay or beam span with significant savings in computing time, costs and storage requirements as compared with using regular finite elements.

Integrated topology and boundary shape optimization of 2-D solids

Abstract: This study is concerned with the development of an integrated procedure for the computation of the optimal topology as well as the optimal boundary shape of a two-dimensional, linear elastic body. The topology is computed by regarding the body as a domain of the plane with a high density of material and the objective is to maximize the overall stiffness, subject to a constraint on the material volume of the body. This optimal topology is then used as the basis for a shape optimal design method that regards the body as given by boundary curves. For this case the objective is to minimize the maximum value of the Von Mises equivalent stress in the body, subject to an isoperimetric constraint on the area as well as a constraint on the stiffness. The solution procedures for the shape design are based on variational formulations for the problems and the results of a variational analysis are implemented via finite element discretizations. The discretization grids are generated automatically by an elliptical method for general two-dimensional domains. Computational results are presented for the design of a fillet, a beam and a portal frame.

Convergence of the Newton‐Raphson algorithm in elastic‐plastic incremental analysis

Abstract: A spatially continuous, time discrete formulation of the loading of an elastic, perfectly plastic body governed by a von Mises yield condition is presented. It is assumed that incremental changes in strain occur along minimum work paths, which is equivalent to a backward difference implicit integration algorithm or the radial return method.

A comparison of various methods for estimating the parameters in mixtures of von Mises distributions

Abstract: In this paper we compare five methods for estimating the unknown parameters in a mixture of two von Mises distributions. We propose a new method based on the characteristic function and compare it with the classical methods based on maximum likelihood and moments. Thus far these methods have been successfully applied only to linear data. Here we show that the application to circular data is reasonably straightforward and that convergence to the final estimates is fairly rapid. For various simulated known mixtures the results obtained are satisfactory. Finally, we introduce a modification of the method of moments which is considerably faster in CPU time than any of the other methods used and gives good results.

Inelastic nonuniform torsion of steel I-beams

Abstract: This paper presents a finite element model for analysing the elastic-plastic nonuniform torsion behaviour of thin-walled steel I-beams. The model uses Vlasov's warping strain model to represent warping torsion, and a mitre model for uniform torsion. The mitre model allows the representation at the tips of flanges of the transverse uniform torsion shear stresses. For elastic-plastic analysis, the incremental theory of plasticity is adopted, employing the Prandtl-Reuss flow rule and the von Mises yield criterion. The material state determination algorithm and the variable arc-length method are also employed to improve the accuracy and reliability of the solutions. The numerical integration over the cross-section is carried out by dividing it into a number of triangular areas and then applying the no-bias area-coordinate Gaussian numerical integration scheme. The numerical examples provided show that good agreement is obtained with predictions of other models of inelastic nonuniform torsion and the experimental results by using the present finite element model. It is also concluded that the present model can predict more realistic results at higher rotations than other models which ignore the transverse uniform torsion shear stresses.

On the Quasi-Analytical Solutions of Elastic-Plastic Problems with Nonlinear Hardening

Abstract: Elastic-plastic equilibrium problems accessible to analytical treatment are mainly one-dimensional ones exhibiting spherical or cylindrical symmetry. For perfectly plastic behaviour as well as material with linear isotropic hardening, Tresca’s yield criterion and the flow rule associated to it lead to linear differential equations for stresses and displacement. (In the case of spherical symmetry the Tresca and the von Mises criterion coincide.) The image points of the plastic region may lie on different edges or sides of the Tresca prism in stress space. Correspondingly, the plastic region is composed of several parts with different mathematical forms of the yield condition (e.g. [1]). Continuity of radial stress and displacement at the borders separating these parts and the boundary conditions constitute a system of equations that is linear in the integration constants and the load parameter but nonlinear in the border radii. It can be solved without problems, in general. Solutions of this type are termed analytical. Nevertheless, they are not restricted to perfectly plastic behaviour or linear hardening but exist also in cases of special nonlinear hardening laws [2].

A finite strain, total Lagrangian finite element solution for metal extrusion problems

Abstract: A detailed formulation for finite element analysis of metal forming problems is carried out in this work. It incorporates every aspect of the analysis, including the iterative solution procedures for geometric and material non-linearities, implementation of the material model, and formulation of curved contact surfaces. The finite element formulation is based on a total Lagrangian approach which by-passes the use of the Jaumann stress rate tensor commonly used in the updated Lagrangian formulation. The yield model used is of the Von Mises type with both kinematic and isotropic hardening and is formulated in the Eulerian space. This model is then transformed to the Lagrangian reference frame. Stresses and the plastic strain components are evaluated using an elastic predictor-radial corrector algorithm with subincrementation. The curved contact boundaries are modeled using Hermite parametric curves, although other formulations such as β-splines and Besier parametric curves may also be used with slight modifications. Applicability of these formulations in solving extrusion problems is examined through several runs performed using the UNIFES program developed by the authors. It is shown how the distance between the nodes on the die interface can lead to fluctuations in the extrusion pressure and how the amplitude of these fluctuations may be reduced by mesh refinement. A detailed account of the solution procedures is also provided.

The Proportional Anisotropic Elastic Invariants

Abstract: In this paper we illustrate the six proportional invariants of an orthotropic elastic material using the elastic constants for spruce as the numerical example. The proportional elastic invariants play a role in anisotropic linear elasticity similar to the roles played by the hydrostatic stress and strain and the von Mises stress and strain in isotropic elasticity

Isotropic polycrystal yield surfaces of b.c.c. and f.c.c. metals: crystallographic and continuum mechanics approaches

Abstract: For the crystallographic approach, isotropic yield surfaces of bcc metals with the ratio of critical shear stress on {112}〈111〉 slip systems to that on {110}〈111〉 slip systems in the range of ( √ 3 2 , 2 √3 ) have been simulated with the Taylor model Isotropic yield surface fcc metals is included as a special case where {112}〈111〉 slip systems are all removed out All the yield surfaces considered are located between the Mises and Tresca criteria; and linear variations of the average size and the “shape” of the isotropic yield surface with the critical shear stress ratio were found For the continuum mechanics approach, using a series of stress transformation functions proposed in the present work, the Hill and the Hershey, Hosford and Hill (HHH) yield function shave been developed to be new yield functions expressed in 6-dimensional stress space The new yield function based on the HHH expression can include the Mises and the Tresca criteria, as well as the isotropic form of the Barlat and Lian (BL) yield function as special cases By comparison of the new yield function with the isotropic yield behaviours of both bcc and fcc metals simulated with the Taylor model, very good agreements are obtained and the parameters in the new yield function are determined in the sense of crystallographic plasticity theory

Aspects of the residual stress field at a notch and its effect on fatigue

Abstract: X-ray stress measurements for a 1 mm radius notch were carried out and a residual stress distribution, induced by shot peening in the notched part, was detected. It is shown that the residual stress exhibits a concentration effect at the notch, but the concentration factor is different from that of the loading stress. The residual stress concentration is related to the shape of the specimen and the strength of the material. The fatigue limits of medium carbon steel specimens were tested with rotating bending. The compressive residual stress at the notch part of a specimens tempered at high temperature relaxes rapidly under cyclic loading; the increase in the fatigue limit after shot peening shows more or less the same behaviour as that of a smooth specimen treated in the same way. In contrast, a great improvement in the notch fatigue limit is observed for a specimen tempered at low temperature with a high yield strength. A biaxial shear stress model is used to explain the residual stress relaxation; this model agrees with the experimental data and is better than the Von Mises criterion.

Advanced development of the boundary element method for elastic and inelastic thermal stress analysis

Abstract: The focus of this dissertation is on advanced development of the boundary element method for elastic and inelastic thermal stress analysis. New formulations for the treatment of body forces and nonlinear effects are derived. These formulations, which are based on particular integral theory, eliminate the need for volume integrals or extra surface integrals to account for these effects. The formulations are presented for axisymmetric, two and three dimensional analysis. Also in this dissertation, two dimensional and axisymmetric formulations for elastic and inelastic, inhomogeneous stress analysis are introduced. The derivatives account for inhomogeneities due to spatially dependent material parameters, and thermally induced inhomogeneities. The nonlinear formulation of the present work are based on an incremental initial stress approach. Two inelastic solutions algorithms are implemented: an iterative; and a variable stiffness type approach. The Von Mises yield criterion with variable hardening and the associated flow rules are adopted in these algorithms. All formulations are implemented in a general purpose, multi-region computer code with the capability of local definition of boundary conditions. Quadratic, isoparametric shape functions are used to model the geometry and field variables of the boundary (and domain) of the problem. The multi-region implementation permits a body to be modeled in substructured parts, thus dramatically reducing the cost of analysis. Furthermore, it allows a body consisting of regions of different (homogeneous) material to be studied. To test the program, results obtained for simple test cases are checked against their analytic solutions. Thereafter, a range of problems of practical interest are analyzed. In addition to displacement and traction loads, problems with body forces due to self-weight, centrifugal, and thermal loads are considered.

Evaluation of yield function including effects of third stress invariant and initial anisotropy

Abstract: By means of combining Drucker's yield function with Hill's quadratic yield function, the anisotropic yield function of the sixth degree is proposed. It is able to include the effects of the third deviatoric stress invariant and initial anisotropy. The experimental evaluation is made on thin-walled cylindrical specimens of mild steel (in the fully annealed condition and the stress-relief annealed condition after a tensile pre-strain) and 2024 aluminum alloy (in the -0 and -T6 tempered conditions). By applying proportional combined loadings of axial load, internal pressure, and torsion to the specimens, a change of yield stress with a rotation of the principal stress axes and a difference between the directions of the principal stress and principal strain increment are examined Under tension–internal pressure and tension–torsion, the yield surfaces and strain behaviour are determined. The fully annealed steel is almost isotropic for yielding although it reveals the effect of the third deviatoric str...

A Micromechanical Composite Yield Model Accounting for Residual Stresses

Abstract: An analytical micromechanical model is used to predict yielding in continuous-fiber unidirectional metal-matrix composite materials. The von Mises criterion is used to predict yielding of the composite matrix based on (1) the average stresses in the matrix, and (2) the largest of the average stresses in each of the modelled matrix subcells. Two-dimensional yield surfaces are generated under thermomechanical loading conditions for two metal matrix composites, boron/aluminum and silicon carbide/titanium. Results indicate that, depending on the material, temperature excursions typically experienced in processing may cause matrix yielding at zero far-field applied stress. The analysis shows that thermal stresses distort and shift the yield surface based upon subcell stresses. Thus the importance of micromechanics is demonstrated.

The use of thick-walled hollow cylinder creep tests for evaluating flow criteria for rock salt

Abstract: Finite element simulations of two laboratory creep tests on thick-walled hollow cylinders of rock salt are evaluated to determine if such bench-scale experiments can be used to establish applicability of either von Mises or Tresca stress measures and associated flow conditions. In the tests, the cylinders were loaded axially and pressurized both internally and externally to produce stress fields similar to those found around underground excavations in rock salt. Several different loading stages were used in each test. The simulations show that for each of two creep models studied, quite different deformations of the cylinders are predicted with the Mises and Tresca flow criteria, especially if friction between the cylinders and axial loading platens is ignored. When friction is included in the simulations, the differences in deformation are changed but are sill clearly distinguishable. 10 refs., 10 figs.

The application of an anisotropic yield function of the sixth degree to orthotropic material

Abstract: By combining Drucker's yield function with Hill's quadratic yield function, an anisotropic yield function of the sixth degree is proposed. The effects of the third deviatoric stress invariant and initial anisotropy are also included. Experimental evaluation is made on 1050 aluminium tubes under multiaxial stress states. The tubes in the as-received condition are subjected to progressive reductions in the hot extruding and cold drawing processes. They are annealed by heating at 200 °C for 1 h. By applying proportionally combined loadings of axial load, internal pressure, and torsion to the specimens, a change of yield stress with a rotation of the principal stress axes and a difference between the directions of the principal stress and principal strain increment are examined. In the tension-internal pressure stress field, it is found that this aluminum tube exhibits orthotropic anisotropy of high strength in the tangential direction. The yield surface in the tension-torsion stress field lies outsid...

Micromechanical analysis of nonlinear thermal deformation of filamentary metal matrix composites

Abstract: A micromechanical model was developed to predict the thermomechanical deformation of unidirectional filamentary metal matrix composites. The composite is represented by two concentric cylinders, the inner one simulating the fiber and the outer one the matrix. Both elastic and elastic-plastic analyses were performed. In the model the fiber was assumed to be linear-elastic and the matrix a work-hardening elastoplastic material. The elastoplastic analysis was based on the deformation theory of plasticity in conjunction with the von Mises yield criterion. The matrix cylinder in the model was divided into a number (N) of concentric layers with each layer having different values of tangent modulus and Poisson's ratio depending on the amount of plastic deformation. An elastic analysis of a composite cylinder with (N+1) layers was then performed and served as a subroutine for a computer program.

Large deflection elastic-plastic analysis of cylindrical shells using the finite strip method

Abstract: The finite strip method is extended to the non-linear, static analysis of cylindrical shells Large deflection effects are incorporated via first-order non-linearities in the strain-displacement relations, and material non-linearities are included via the von Mises yield criteria and associated flow rule Numerical results are presented for various example problems including the diaphragm supported cylindrical shell-roof problem, an axisymmetric cylindrical shell loaded by radial pressure, the cylindrical shell-roof problem with clamped curved ends and a pressure loaded cylindrical panel clamped all round The results are compared with known results from analytical and/or finite element analyses The results indicate that a single bending mode in the strip direction is sufficient in most cases to yield engineering accuracy for preliminary design purposes

Edge stresses in bonded armor system for divertor plate

Abstract: To safely manage the high heat loads expected in the next fusion devices, efforts have been focused on the development of the actively cooled divertor plate which consists of graphite armor tiles bonded to copper structural members. Residual stresses in the interface region were evaluated for the graphite/copper bonded system. Eigenvalue analysis was performed to investigate the favorable free-edge geometry for the interface. Results for a joint having half-plane free-edge geometry indicated no stress singularity for theta /sub 1/ approximately 120 degrees , where theta /sub 1/ is the angle between the traction free surface of the graphite and the bonding interface. Thermal stresses in a joint having a conical bonding interface with inner and outer free edges were also examined for a sequence consisting of cooling from the brazing temperature and service with a pulsed heat load of 10 MW/m/sup 2/-5 s. The normal stress on the bonding interface calculated for graphite was tensile only in the neighborhood of the interface edges. This normal stress decreased but the high stress region expanded during heat loading. The Von Mises stress in the interface edge region decreased without apparent increase in plastic strain at two different times in the thermal cycle. >