Showing papers on "von Mises yield criterion published in 1989"

Non- and semi-parametric maximum likelihood estimators and the von Mises method. II

Abstract: Having shown in Part I of this paper that some well-known NPMLE's are compactly differentiable functions of the empirical data, and moreover solve a compactly differentiable generalized likelihood equation, we prove an efficiency theorem which shows that such an estimator asymptotically achieves the information bound in the generalized Hajek-Le Cam convolution and asymptotic local minimax theorems.

Application of local damage models to the numerical analysis of ductile rupture

Abstract: — Two damage models were implemented into the finite element program ADINA to study the correlation between microscopical damage and macroscopical material failure. In the first model, based on the Gurson yield function the nucleation, growth and the coalescence of voids were incorporated into the constitutive relations. In the second model the void growth was determined according to the Rice and Tracey model using the von Mises yield function, and material failure was simulated by eliminating the elements where the critical void growth ratio was exceeded. The numerical results for the local and global behaviour of the specimens were compared with experiments. The generality of the damage parameters was checked by investigating several specimen geometries. Both damage models deliver qualitatively consistent results with regard to the influence of the stress triaxiality on the void growth and on the beginning of the material failure. However, the Gurson model gives a more accurate numerical simulation because the damage development and the stress drop continue after the onset of void coalescence while the critical void growth model causes less convergence problems in the simulation of large crack extension. The Jn-curve was estimated on the basis of both models.

Shape design of elastostatic structures based on local perturbation analysis

Abstract: This paper describes a non-gradient formulation for solving shape optimal design problems involving structures in plane stress or having an axially symmetric geometry. The minimization of the maximum von Mises stress value at a traction free boundary poses a non-linear optimization problem in which the design variables do not appear explicitly in the formulation. The most commonly used approach is to apply a standard non-linear programming technique. There exists in this field no universally accepted solution method. The major difficulty of shape optimization in connection with FEM is to perform an accurate and efficient sensitivity analysis. The perturbation analysis introduced here takes advantage of the character of the problem. It is based on methods from the theory of notches. The results are applied to an FE-model of the structural component. The iterative method with such a direction of search works efficiently even for a large number of design variables as shown by Schnack (1977b, 1978, 1979, 1980, 1983 and 1985). Using a dynamic programming formulation (see also Schnack and Sporl 1986), the existence of a solution for the shape optimal problem will be discussed. Examples of applications to structural components from mechanical engineering are presented to demonstrate the power of this approach.

Application to Series of Residual Wind Directions

Abstract: Part II of this monograph will now be concluded with an application of the concepts presented in chapters 6 to 9. In this chapter we shall therefore return to the analysis of the wind series (wt) which was discussed in detail in Part I. Both, a first order wrapped autoregressive and a first order von Mises model are fitted to the directional component (θt) of the residual series (ft). It is also shown that the wrapped normal approximation described in section 6.3 works well in this example. Using this approximation it is found that the von Mises model is slightly better suited for describing time series in which periods with a prevailing wind direction alternate with periods when the direction changes more rapidly.

A numerical model for the thermo‐elasto‐plastic behaviour of a material

Abstract: This paper presents a numerical model for the thermo-elasto-plastic behavior of an isotropic material The model is based on the assumption that the yielding of the material obeys von Mises distortion energy theory and the material exhibits isotropic strain hardening This unique model can be used both for isothermal and non-isothermal cases The original formulation for the non-isothermal three-dimensional case has been specialized for plane stress conditions and the equations for the computation of warping and thickness change are provided The finite element implementation of this model is also outlined

Characterization of Strain Hardening for a Simple Pressure,Sensitive Plasticity Model

Abstract: Paralleling the development of strain hardening for the pressure-independent von Mises criterion, a simple plasticity model in strain space was presented to characterize strain hardening for pressure-sensitive compressible materials. Two hardening moduli,HT andHC, which emerged from the constitutive equations and can becalculated from uniaxial stress-strain curves in tension and compression, were used to characterize the strainhardening responses forgeneral and special stress systems. The results indicated the implications and restrictions of the yield function on the hardening responses. It was also shown that strain softening, under general stress systems, can be a natural consequence of pressure-sensitive yielding. Consequently, a strain-space formulation is recommended for most (if not all) pressure-sensitive plasticity models. Preliminary application to the yielding of polymers under hydrostatic pressure gave reasonable results for polyethylene at moderate pressure and small strains; the results for polycarbonate were generally poor. Finally, the advantages and limitations of the present approach were discussed.

Control of the Von Mises Stress with Dynamic Programming

Abstract: The problem treated is the minimization of the von Mises equivalent stress in elastostatic structures subjected to manufacturing and behavioural constraints by variation of partial boundaries. This constrained non-linear problem is solved using a discrete non-gradient approach which allows a high number of design variables and works without any restrictions imposed to the geometrical shape of the design boundary. The existence of the solution for this class of problems follows from a dynamic programming formulation. Axisymmetric and three-dimensional problems are solved using this method.

Multiaxial Stress Rupture Criteria for Ferritic Steels

Abstract: Many ferritic steels become ‘creep-brittle’ after long times at high temperatures. This paper is concerned with the behaviour of such steels under multiaxial stressing, which is the type of loading that they invariably encounter in service in power and process plant applications. Various criteria have been proposed for predicting failure under multiaxial stress states. In the present investigation the applicability of these criteria to ferritic steels was initially assessed using rupture data obtained on a single cast of 2\frac{1}{4}CrMo steel tested under different stress states. The best correlation between prediction and experiment was given by relatively simple formulations containing only maximum principal stress, σ1 and von Mises’ effective stress, \(\bar \sigma \), terms. Of these formulations, the one which was considered to be most consistent with the physical processes controlling creep was then applied to the available multiaxial rupture-life data for ferritic steels. These data cover a wide range of steels tested under a variety of stress states. It was found that the rupture life, t r could be generally well expressed as: $$t_r \, = \,M\sigma _1^{ - 2.5} \bar \sigma ^{ - m + 2.5} $$ (1) where ‘M’ and ‘m’ can be obtained from uniaxial stress-rupture tests

Endochronic Plastic Behavior of Perforated Thin Plate

Abstract: In this paper an incremental form of the theory of Endochronic plasticity is employed in the FEM to investigate the elastoplastic behavior of perforated thin plate under monotonie cyclic loading histories. The material under analysis is OFHC copper and its material functions and the kernal function associated with the theory are determined by the cyclic stress-strain hysteresis loops. Since the theory uses more “real” material functions (not bilinear models in the sense of classical plasticity), and does not request pre-existing yield surfaces and their subsequent hardening rules; the computational methods are more natural and convenient. The FEM results under cyclic loading are believed more reliable. At the same time, this paper combines the Endochronic plasticity with the von Mises yield criterion to compute plastic zones in the perforated plate. For the plate with single central hole under monotonie loading, the shapes of plastic zone calculated are similar to those of Theocaris' results by using experimental results of 57s Al alloy and the von Mises criterion. Under 3 1/2 cycles of cyclic loading, since cyclic hardening is not significant, the shapes of plastic zone are not variant too much. For the plate with optimum auxiliary holes, the shapes of plastic zone are almost the same as under monotonie and cyclic loading. However under the same loading condition, except general yield, the plastic zone are smaller than those in the single hole plate. Meanwhile there are no plastic response between auxiliary holes, these results lead to smoother principal stress distribution and lower stress concentration. For residual stress and strain distribution, the results show that they are approaching to steady response as number of cycle increased; however, the plate with auxiliary holes has much slower variations than those of the single hole plate. These results will provide significant information in the fatigue design.

Lifting aerofoil calculations using von Mises variables

Abstract: A natural streamline coordinate system approach has been developed for steady two-dimensional incompressible lifting flow problems. Flow equations with appropriate boundary conditions are presented in terms of von Mises coordinates (x, ψ), where ψ is the streamfunction for the flow. The finite difference method is used to discretize the non-linear elliptic equation describing the flow. Favourable agreement with available results is obtained.

An Experimental Study of Plastic Flow at Large Finite Strain

Abstract: Experimental data from uniaxial and biaxial compression loadings of rectangular block specimens of annealed 1100 aluminum at large finite strains are presented. Special attention is focused on the plastic incompressibility and existence of von Mises equivalent stress-strain curves under complex stress states, which are two of the basic assumptions implied in plasticity theories.

A finite element solution of Steckel rolling using measured velocity boundary conditions

Abstract: A numerical solution for plane strain Steckel rolling using an experimentally determined stress-strain curve and measured roll-work interface velocities is presented. The solution is based on rate formulation of the constitutive equations for an isotropic elastic plastic work hardening material with von Mises yield condition and on an incremental finite element analysis employing constant strain increment triangles. Interfacial velocities are measured and used as prescribed boundary conditions in the numerical model of the deformation process. Some predictions are presented such as distributions of normal pressure in the contact region of the roll and drawing stress. For several reductions, the drawing force compares favorably with experimental values.

A Total Lagrangian Finite Element Analysis for Metal Forming With Application to Metal Extrusion.

Abstract: 1. IN TRO D U CTIO N ...........................................................................................................1 1.1 General R em arks................................................................................................... 1 1.2 Objectives................................................................................................................ 5 1.3 S cope......................................................................................................... 6 2. FIN ITE ELEM ENT FORM ULATION..................................................................... 9 2.1 In troduction ............................................................................................................ 9 2.2 M athematical Form ulations................................................................ 10 3. MATERIAL MODEL AND ITS IM PLEM ENTATION......................................15 3.1 In tro d u ctio n ..........................................................................................................15 3.2 Prelim inary Definitions and Relations............................................................17 3.3 Constitutive Model for Elasto-Plastic Behavior of M etals ......................23 3.4 Numerical Implementation of the M aterial M odel......................................31 3.5 A Simple Vectorization Technique ..............................................................41 3.6 Uniaxial Verification of the Material M odel.................................................44 4. SIMULATION OF CONTACT BOUNDARIES...................................................49 4.1 In tro d u ctio n ......................................................................................................... 49 4.2 Hermite Formulation of Cubic Curves..................................... 50 4.3 Motion of the Nodal Points on the Curved Boundaries ...................... 54 4.4 Use of Multiple Curves in Generating Complex B oundaries....................57 4.5 Description of the Relevant Subroutines.......................................................60

On the Initial Yield Surface of Polycrystalline Materials under Combined Tension-Torsion Stresses

Abstract: The yield criterion of a polycrystal under combined tension-torsion loadings is derived. A Monte Carlo procedure is employed to estimate the associate parameters for a randomly oriented FCC polycrystal. The results are found in good agreement with the von Mises yield criterion, but different characteristics of the yield surfaces are observed.