Showing papers on "von Mises yield criterion published in 1996"

A multi‐mode approach to finite, three‐dimensional, nonlinear viscoelastic behavior of polymer glasses

Abstract: In this study a phenomenological constitutive model is proposed to describe the finite, nonlinear, viscoelastic behavior of glassy polymers up to the yield point. It is assumed that the deformation behavior of a glassy polymer up to the yield point is completely determined by the linear relaxation time spectrum and that the nonlinear effect of stress is to alter the intrinsic time scale of the material. A quantitative three‐dimensional constitutive equation for polycarbonate as a model polymer was obtained by approximating the linear relaxation time spectrum by eighteen Leonov modes, all exhibiting the same stress dependence. A single Leonov mode is a Maxwell model employing a relaxation time that is dependent on an equivalent stress proportional to the Von Mises stress. Furthermore, a Leonov mode separates the (elastic) hydrostatic and (viscoelastic) deviatoric stress response and accounts for the geometrical complexities associated with simultaneous elastic and plastic deformation. Using a single set of...

Shear capacity of plate girders with trapezoidally corrugated webs

Abstract: In this paper, the shear capacity of plate girders with trapezoidally corrugated webs is numerically studied using a non-linear finite element method. Effects of large deflections are taken into account and a perfectly elastic-plastic material model obeying a von Mises yield criterion is assumed. The following geometric parameters that influence the shear capacity of such girders are investigated: (1) the overall dimension of the web panel; (2) the web thickness; (3) the corrugation depth of the web; (4) the corrugation angle; and (5) the width of the plane sub-panel of the web. More specifically, the influence of these parameters both on the ultimate shear capacity and on the remaining shear capacity in the post-buckling range, as well as on the buckling modes, are reported. Based on the numerical results, empirical formulae that were proposed earlier for the prediction of the shear capacity are examined and suggestions for an optimal design of such girders in shear are given.

Stress concentration in all-ceramic posterior fixed partial dentures.

Abstract: Two-dimensional finite-element analysis was used to study levels and distribution patterns of stress within three-unit fixed partial dentures (mandibular first premolar to first molar) constructed of different materials (Type III gold alloy, Dicor, and In-Ceram) and with different connector heights (3.0 mm versus 4.0 mm). In the computer models, 10 MPa of stress was applied centrally to the prosthesis. Resultant von Mises stresses were concentrated within the connectors; the greatest stress occurred at the axial location of the connector. Stresses were 40% to 50% lower for 4.0-mm connectors. Patterns of stress distribution were similar for premolar and molar connectors. Stress levels within In-Ceram models were lower than for the other two materials and represented a lower percentage of the ultimate strength of the material. Based on a two-dimensional finite-element analysis model, In-Ceram would appear to be the best choice for posterior fixed partial dentures.

Stress distribution around inclusions, interaction, and mechanical properties of particulate‐filled composites

Abstract: Stress analysis was carried out to determine the stress distribution around particles in particulate-filled composites. The effect of interacting stress fields was also taken into account. At large filler contents, interacting stress fields compensate for the effect of stress concentration. The solutions were introduced into the Von Mises criterion for yielding. The composition dependence of tensile yield stress was determined by using different boundary conditions and averaging techniques. An analytical expression was derived that predicts particle size and adhesion dependence of the yield stress. The analysis shows that large particles and weak interaction lead to debonding. In the case of strong adhesion, the dominating micromechanical deformation process is the shear yielding of the matrix. In such cases, particle size dependence can be explained with the effect of interfacial interactions, which lead to the formation of an interphase. The dominating deformation mechanism is determined by particle characteristics and adhesion of the components. The predictions of the analysis are in good agreement with experimental observations.

Ultimate strength of girders with trapezoidally corrugated webs under patch loading

Abstract: Ultimate strength of steel plate girders with trapezoidally corrugated webs under patch loading is studied using a non-linear finite element method. Effect of large deflection is taken into account and a von Mises material either without strain hardening (elastic-perfectly plastic), or with strainhardening obeying Ramberg-Osgood's equation, is assumed. The following factors that influence the ultimate strength are investigate (1) strainhardening models; (2) initial imperfections (local and global); (3) variation of yield stress and strain-hardening degree at the corrugation corners due to cold forming, ‘corner-effects’; (4) loading position; (S) load distribution length, and (6) variation of geometric parameters. Based upon the numerical results obtained, an empirical formula for the prediction of the ultimate strength is suggested.

Geometrically non-linear and elastoplastic three-dimensional shear flexible beam element of von-mises-type hardening material

Abstract: A three-dimensional elastoplastic beam element being capable of incorporating large displacement and large rotation is developed and examined. Elastoplastic constitutive equations are applied to the beam element based upon the assumption of small deformational strain leading to a material formulation which is completely objective for the application of stress update procedures. The continuum-type equations of plastic model of J2 mixed hardening are transformed into the beam equations by satisfying beam hypotheses. An effective stress update algorithm is proposed to integrate elastoplastic rate equations by means of the so-called multistep method which is a method of successive control of residuals on yield surfaces. It avoids severe divergence when the displacement increments become large which is usual for the continuation methods. Material tangent stiffness matrix is derived by using consistent elastoplastic modulus resulting from the integration algorithm and is combined with geometric tangent stiffness matrix. Different from other elements, the present element is shear flexible and can satisfy the plasticity condition in a pointwise fashion. A great number of numerical examples are analysed and compared with the literature. The proposed beam element is verified to be not only quite accurate but also very effective for the analyses of pre-buckling and large deflection collapse of spatial framed structures.

Finite Element Method for Gradient Plasticity at Large Strains

Abstract: A finite element method for gradient elasto-plastic continuum in which the yield strength of strain hardening/softening materials not only depends on the effective plastic strain but also on its Laplacian is presented. The consistent integration algorithm to update the stress and the internal state variable at integration points and the consistent compliance matrix for the gradient plasticity are formulated in the non-local sense. The methodology to derive the finite element formulation for the gradient plasticity at large strains presented in this paper is applicable to general finite element analysis; the formulation in the context of the two-dimensional four-noded mixed finite element with one integration point and mean von Mises yield criterion is particularly derived. Numerical examples are tested to demonstrate the capability and performance of the present finite element method at large strain in solving for the strain localization problem.

Family of Invariant Stress Surfaces

Abstract: A family of invariant stress surfaces with a cubic dependence on the deviatoric stress components is expressed as a linear combination of the second and third deviatoric stress invariants. The general format is described in terms of two functions of the mean stress. A simple geometric derivation demonstrates the convexity of the contours in the deviatoric plane. An explicit representation of the deviatoric contours in terms of a size and a shape parameter is given. The shape parameter effects a continuous transition from a triangle to a circle in the deviatoric plane. An explicit format in terms of the triaxial compression and tension generators is derived, and the plane stress contour is given in explicit form. Many previously proposed failure and yield criteria are obtained as special cases.

Initial stress differences between tipping and torque movements. A three-dimensional finite element analysis

Abstract: The aim of this study was to analyse the distribution of the stress on dental and periodontal structures when a simple tipping dental movement or torque movement is produced. A tridimensional computer model based on finite element techniques was used for this purpose. The model of the lower canine was constructed on the average anatomical morphology and 396 isoparametric elements were considered. The three principal stresses (maximum, minimum and intermediate) and Von Mises stress were determined at the root, alveolar bone and periodontal ligament (PDL). It was observed how the distribution of stress is not the same for the three structures studied. In all loading cases for bucco-lingually directed forces, the three principal stresses were very similar in the PDL. The dental apex and bony alveolar crest zones are the areas that suffer the greatest stress when these kind of movements are produced.

Notch fracture in γ -titanium aluminides

Abstract: The notch fracture behavior of twoγ-titanium aluminide alloys, having duplex and fully lamellar microstructures, has been investigated as a function of notch geometry and test temperature. The unnotched tensile properties and notch fracture loads are used to perform finite element analysis (FEA) to determine triaxial tensile stresses and effective plastic strains in the vicinity of notch roots. These results, together with fractographic examinations of notch failures, indicate that a crack nucleates in the triaxial tensile field when the effective von Mises stress just exceeds the uniaxial tensile yield stress. The high tensile stress component then propagates the nucleated microcrack to failure with local stress intensity reaching the toughness of the material. Thus, both plasticity and high tensile stress are required to cause notch failure.

A Model Study of Thermal Stress-Induced Voiding in Electronic Packages

Abstract: Thin film metallizations are one of the most important interconnects in large-scale integrated circuits They are covered by substrates and passivation films Large hydrostatic (mean) tension develops due to the constraint and thermal mismatch, and voiding is identified as the failure mechanism This phenomenon of rapid nucleation and growth of voids is called cavitation instability and it can lead to the failure of ductile components in electronic packages such as metallizations A micromechanics model is developed to provide the critical mean stress level that will trigger the cavitation instability It is found that this critical mean stress level the cavitation stress, not only depends on the material properties but also is very sensitive to defects in the material For example, the cavitation stress decreases drastically as the void volume fraction increases The stress-based design criterion for ductile components in electronic packages should then be: (1) Von Mises effective stress < yield stress; and (2) mean stress < cavitation stress, which is particularly important to the constrained ductile components in electronic packages such as vias and conductive adhesives An analytical expression of cavitation stress for elastic-perfectly plastic solids is obtained, and numerical results for elastic-power law hardening solids are presented

The governing parameter method for implicit integration of viscoplastic constitutive relations for isotropic and orthotropic metals

Abstract: A general algorithm of implicit stress integration in viscoplasticity, based on the governing parameter method (GPM) is briefly presented. It is assumed that the associative viscoplastic constitutive relations are governed by the Perzyna formulation with a generalization suggested by Simo and Hughes. The algorithm is first applied to isotropic metals obeying the von Mises yield condition with mixed hardening and then, to orthotropic metals with a generalized Hill's yield condition including a mixed hardening assumption. Derivation of consistent tangent moduli is presented for both viscoplastic material models. The proposed computational procedures are efficient, since they reduce the problem of stress integration to the solution of one nonlinear equation, can use large time steps and are applicable to 2-D, 3-D, shell and beam structures. The tangent elastic viscoplastic matrix provides high convergence rate in the overall equilibrium iterations. Numerical examples illustrate the main characteristics of the developed computational procedures.

A General Orthotropic von Mises Plasticity Material Model With Mixed Hardening: Model Definition and Implicit Stress Integration Procedure

Abstract: A general orthotropic von Mises plasticity model, with an extension of the Hill’s yield criterion to include mixed hardening, is introduced in the paper. Material constants and equivalent stress-equivalent plastic strain curves are defined in a way to suggest their experimental determination. The model represents a special case of a general anisotropic metal plasticity model proposed by the authors. An implicit stress integration procedure, representing an application of the governing parameter method (GPM) introduced by the first author, is presented. The GPM is briefly described, and the computational procedure, together with calculation of the consistent tangent moduli, are given in some detail for a general three-dimensional deformation, with direction of application to plane stress/shell conditions. Numerical examples illustrate applicability of the model and effectiveness of the computational algorithm.

Effect of interlayer on maximum contact stresses of hard coating under sliding contact

Abstract: In order to prevent surface damage or spalling of a coating with an interlayer under sliding contact, the understanding of the effect of the interlayer on the maximum contact stresses (maximum tensile stress, maximum shearing stress, maximum von Mises stress) is necessary, Because the damage or the spalling of coating initiates usually from the positions of these maximum stresses. Therefore, in this paper, the sliding contact problem of a hard coating with an interlayer was analyzed using the finite element method. The results show the effect of four typical elastic moduli of the interlayer, i.e., E inter = 2 E topp , ( E top + E base )/2, E base and E inter = E base /2 (here E inter is the elastic modulus of interlayer, E top is the elastic modulus of the hard coating and E base is the elastic modulus of the base) on these maximum stresses. In the case of maximum tensile stress on the surface, E inter = 2E top is most useful for decreasing the stress as compared to other interlayers, while in the case of maximum shearing stress on the interface between the coating and the substrate, E inter = E base /2 is most useful for decreasing the stress. In the case of maximum von Mises stress, E inter = 2 E top shows the largest effect of interlayer on the stress. In addition, the effect of the coating thickness and the friction coefficient on these maximum stresses are also presented in the paper.

Multiaxial Plasticity and Fatigue Life Prediction in Coiled Tubing

Abstract: Coiled tubing is being used increasingly in the oil well drilling and servicing industry. Continuous steel tubing of structural dimensions (up to 89 mm or 3.5 in. in diameter) is wound onto a large-diameter reel for repeated deployment into and out of a well bore. The bending strain range associated with each wrap-unwrap cycle can exceed 3% with lives well below 100 cycles. During constant internal pressure fatigue testing, tubing has been observed to grow in diameter by as much as 30%. This paper describes an analytical model to predict the fatigue behavior of coiled tubing subjected to variable pressure service conditions. The approach utilizes standard low-cycle fatigue data but requires additional experimental results from constant pressure fatigue testing. The algorithm is based on estimates of biaxial ratcheting from an incremental plasticity model using a hybrid associated flow rule, a modified kinematic hardening rule with multiple von Mises yield surfaces, and a specialized limit surface concept. An empirical damage parameter was formulated based on constant pressure fatigue data using mean and fluctuating von Mises equivalent strain components occurring throughout the life of a section of tubing. This parameter is used with the Palmgren-Miner definition of cumulative damage to track damage that is accumulating nonlinearly under constant or variable pressure histories. Modifications to standard incremental plasticity components and implementation assumptions used to apply the model are presented and discussed. The predictive capability of the model is demonstrated relative to data generated under constant and variable pressure histories.

Finite-element stress analysis of double-lap adhesive joints

Abstract: Stress distributions in double-lap adhesive joints have been analyzed by using an elastoplastic finite-element method to predict the joint strength. The effects of yield stress, Young's moduli of the adherends, and the overlap length on the interface stress distributions have been examined. In addition, the joint strength was estimated by taking into account the crack growth that occurs at the interface, using von Mises' criterion. Experiments were carried out for the joint strength. The analytical results are in fairly good agreement with the experimental results for the joint strength. It was found that the joint strength increased as Young's moduli and the yield stresses of the adherends and the overlap length increased. However, it was also seen that the joint strength did not increase when overlap length-to-thickness ratio, l2/t1, was more than 10.3.

Updated Stress Concentration Factors for Filleted Shafts in Bending and Tension

Abstract: Published elastic stress concentration factors are shown to underestimate stresses in the root of a shoulder filleted shaft in bending by as much as 21 percent, and in tension by as much as forty percent. For this geometry, published charts represent only approximated stress concentration factor values, based on known solutions for similar geometries. In this study, detailed finite element analyses were performed over a wide range of filleted shaft geometries to define three useful relations for bending and tension loading: (I) revised elastic stress concentration factors, (2) revised elastic von Mises equivalent stress concentration factors and (3) the maximum stress location in the fillet. Updated results are presented in the familiar graphical form and empirical relations are fit through the curves which are suitable for use in numerical design algorithms. It is demonstrated that the first two relations reveal the full multiaxial elastic state of stress and strain at the maximum stress location. Understanding the influence of geometry on the maximum stress location can be helpful for experimental strain determination or monitoring fatigue crack nucleation. The finite element results are validated against values published in the literature for several geometries and with limited experimental data.

Fatigue Failure Criterion of Adhesively-Bonded Joints Under Combined Stress Conditions

Abstract: A study was conducted to investigate fatigue failure criteria for adhesively-bonded joints under combined stress conditions. Two types of adhesively-bonded joint specimens were used: the scarf joint and the butterfly-type butt joint. Both types of joints have considerably uniform combined stress distributions in the adhesive layer. Furthermore, the stress distributions of these joints were analyzed by a finite element method. The results showed that the maximum principal, the von Mises equivalent and the maximum shear stresses in the uniform stress region of the adhesive layer at the endurance limit are correlated with the principal stress ratio.

Effect of FE idealisation, load conditions and interface assumptions on the stress distribution and fatigue notch factor in the human femur with an endoprosthesis

Abstract: The load transferred through the hip joint is one of the major forces occurring in the human body. After the replacement of this joint in THR arthroplasty, the load is transferred through the implant to the femoral bone. Loosening of the fixation of the implant and the fatigue failure of prosthetic stems create problems for both patient and surgeon. Both problems can be reduced by the use of Finite Element (FE) analysis to predict stresses and fatigue lifes but the results are sensitive to assumptions regarding the loading conditions and the idealisation of the components. Consequently the stress distributions and resulting fatigue notch factors in the human femur with an endoprosthesis have been determined for different assumptions regarding the form of the idealisation, the load conditions, and the interface conditions. The FE results show that a realistic loading condition without a tension banding force always produces the highest fatigue notch factor and von Mises stresses. An equivalent 2D plane stress model obtained by varying the thickness is likely to give more realistic stresses because it predicts more realistic strains than other 2D approximations. The full bonded interface is a satisfactory approximation for the real interface conditions because it predicts stress distributions of the correct form without excessive stress concentration.

Exact Stress Integration for Von Mises Elasto-Plastic Model with Constant Hardening Modulus

Abstract: Exact integration for the elasto-plastic von Mises Yield Criterion is presented for general stress space. Truncated series solution is obtained under a constant strain rate assumption. On the other hand, a trial and error definite integral solution is obtained under the assumption of constant stress rate. Either could be suitable for the numerical implementation of the model on vector computers and speeding of finite element calculations.

A spherical basis function neural network for approximating acoustic scatter

Abstract: This paper describes a neural network for approximation problems on the sphere. The von Mises basis function is introduced, whose response depends on polar rather than Cartesian input coordinates. The architecture of the von Mises basis function (VMBF) neural network is presented along with the corresponding gradient descent learning rules. The VMBF neural network is used to solve a specific benchmark spherical problem of approximating a known function, the reflection factor of a plane wave scattering at a rigid sphere.