Showing papers on "von Mises yield criterion published in 1979"

Accurate Numerical Solutions for Elastic-Plastic Models

Abstract: The accuracy of two integration algorithms is studied for the common engineering condition of a von Mises, isotropic hardening model under plane stress. Errors in stress predictions for given total strain increments are expressed with contour plots of two parameters: an angle in the pi plane and the difference between the exact and computed yield-surface radii.

Asymptotic expansions for bivariate von Mises functionals

Abstract: A Berry-Essen result and asymptotic expansions are derived for the distribution of bivariate von Mises functionals under moment and smoothness conditions. The results apply to the Cramer-von Mises ω 2 — statistic as well as to the Central Limit Theorem in Hilbert space, yielding a convergence rate O(n −1+ɛ) for every ɛ>0 on centered ellipsoids.

Biaxial cyclic deformation behaviour of steels

Abstract: — The cyclic stress-strain curves for 1% Cr-Mo-V steel and AISI 316 stainless steel were determined under biaxial loading conditions at various temperatures and strain rates. It is shown that these curves may be correlated in terms of the maximum shear stress and strain amplitudes. It is argued that, even though metals obey the von Mises yield criterion for monotonie loading, the micromechanisms of slip which produce the stabilized cyclic stress-strain behaviour are governed by the Tresca criterion.

Elastic springback in plates and beams formed by bending: The springback radius of curvature for plates formed by bending, derived based on the isotropic-hardening model, is compared with a power-law solution, the rectangular-beam solution, and experimental plate and beam data

Abstract: A plane-strain solution is presented to predict the springback of plates formed by bending. The solution assumes that the strains are small, that the material is an isotropichardening von Mises material, and either that the stress-strain diagrams for tension and compression are identical or that an average diagram can be employed. The plastic portion of each stress-strain diagram is approximated by a finite number of straight lines. Both analytical solutions and experimental evidence indicate that the much simpler plane-stress solution can be used to predict springback for both beams and plates. Experimental data confirm that the type of die has a pronounced effect on the springback for beams and plates if the material exhibits a yield point.

Axially Symmetric Radial Flow of Rigid/Linear-Hardening Materials

Abstract: A closed-form solution has been discovered for axially symmetric radial flow of rigid/linear-hardening materials. It is assumed that the materials obey the von Mises flow rule and that the flow field is in steady state. Explicit expressions for the stress components and the radial velocity are given. The applicability of the solution to wire drawing or extrusion is discussed. Some approximate formulas are derived and shown to be in good agreement, within their range of validity, with experimental results for drawing.

Crack separation energy-rates for the DBCS model under biaxial modes of loading

Abstract: A Modified version of the Dugdale-Bilby-Cottrell-Swinden (DBCS) model simulating the effect of plasticity at the tip of a crack in an infinite region was used by kfouri and rice (1978) to calculate the crack separation energy-rate GΔ corresponding to a finite crack growth step Δa during plane strain mode I crack extension. The loading consisted of a remote uniaxial tension σp applied normally to the plane of the crack. Using Rice's path-independent integral J to characterize the applied load in the crack tip region, and assuming the length R of the crack tip plastic zone to be small compared with the length of the crack, an analytical expression was derived relating the ratios (J/GΔ) and (†a/R) for small values of (†a/R). The analytical solution was incomplete in itself in that the value assumed in the plastic region of the DBCS model for the normal stress Y acting on the extending crack surfaces was the product of the yield stress in uniaxial tension σY and an unknown parameter C, the value of which depends on the effect of the local hydrostatic stresses in the case of plane strain conditions. The analytical solution was compared with a numerical solution obtained from a plane strain elastic-plastic finite element analysis on a centre-cracked plate (CCP) of material obeying the von Mises yield criterion. The value used for the yield stress was 310 MN/m2 and moderate isotropic linear hardening was applied with a tangent modulus of 4830 MN/m2. A uniaxial tension σp was applied on the two appropriate sides of the plate. The comparisons showed that the analytical and finite element solutions were mutually consistent and they enabled the value of C to be established at 1.91. In the present paper similar comparisons are made between the analytical solution and the finite element solutions for the CCP of the same material under different biaxial modes of loading. By assuming further that the form of the analytical solution does not depend on the details of the geometry and of the loading at remote boundaries, a comparison has also been made with the results of a finite element analysis on a compact tension specimen (CTS) made of the same material as the CCP. The different values of C obtained in each case are consistent with investigations by other authors on the effect of load biaxiality on crack tip plasticity.

On the elastic-viscoplastic proportional combined twist and stretch of a circular bar of rate-sensitive material

Abstract: T he elastic-plastic behaviour of a solid circular bar made of a homogeneous, isotropic and nonhardening material but of a rate-dependent type, subjected to different proportional deformation programmes of twist and stretch, is analysed. In this investigation the material is assumed to yield according to the von Mises criterion and then to follow a rate-dependent post-yield constitutive law of the Perzyna type. Four radial paths in the angte-of-twist and axial-stretch plane were investigated. For each deformation path the numerical solution of the governing system of quasi-linear partial differential equations gave the corresponding loading path and the radial variation of the stress field at selected times. This study complements that of S. A. M eguid and J.D. C ampbell (1979) which considered mainly nonproportional deformation paths. In this work residual stress profiles were also calculated, based upon instantaneous unloading after various amounts of deformation. Comparison with predictions of a rateindependent theory for a limiting state, where elastic strains are negligible, is made. Over a considerable range, the loading paths beyond the initial yield were nearly straight, at the elastic slope. The load trajectory then bends over and approaches a point on the limit-state locus. The results showed that the approximate procedure of increasing the flow stress by an empirically determined factor corresponding to a mean plastic strain-rate gave a good estimate for the limit-state stresses.

Photoplastic study of the effect of friction on the deformation and flow of rings in axial compression

Abstract: The influence of friction on the deformation, flow, and strain distribution of rings in axial compression was investigated using the method of photoplasticity. A rigid polyester resin (Laminac 4116) which exhibits plastic strain birefringence in visible light was used. Its deformation properties can be adjusted to best simulate aluminium undergoing hot deformation. Data from uniaxial tension and compression tests indicate that the polyester material may follow a modified von Mises yield criterion. Rings with geometry 6:3:2 (outside diameter:inside diameter:thickness) were compressed axially by different amounts (8 to 24%) between platens with different coefficients of friction. Results are compared with the mathematical solution for constant interface friction and with allowance for bulge formation. Three-dimensional strain distributions are determined and the position of the neutral radius (epsilon/sub theta/ = 0) through the thickness are presented. The results reveal an increase in the neutral radius where the contact area increases. The experimentally obtained strain distributions are integrated in the axial and radial directions and are compared with the external displacements that are measured on the deformed rings.

Non-linear mechanical response of various metals. V. Yield condition for isotropic hardening

Abstract: For pt.IV see ibid., vol.11, p.459 (1978). The parameters appearing in a particular incremental type constitutive equation for an isotropic incompressible strain hardening elastic-plastic solid with large deformation have been computed directly from measurements of the Swift effect by way of the thin-walled tube approximation. It is shown that these parameters, determined for thin-walled tubes of aluminium, copper in the fully annealed state, and copper and iron both in the as-received state, can be used to evaluate the particular form of the associated yield function for a wide range of the available plastic deformation. The yield function, evaluated in this way, is shown for an initial range of response to be a particular form of modified von Mises yield function. This particular form of modified von Mises yield function is used to compare the predictions at initial yield in simple compression and simple torsion with the predictions obtained from the Swift effect.

Behavior of Materials under Dynamic Combined Stresses of Torsion and Tension

Abstract: The paper is concerned with the experiment on the multi-axial stress-strain relations in time dependent materials. In order to examine the dynamic behavior of solid materials under combined stresses, a testing machine for applying the impulsive torque and tension simultaneously to the specimen has been desined. Experiments are performed with various ratios of torque to axial force by the e-quipment. During the loading process, the load ratios are kept constant, and we can obtain almost proportional loading. Equivalent strain rates are about 30 sec−1 to 50 sec−1. The dynamic yield surfaces in the (σ — τ plane are ellipse like Von Mises’s yield surface in static loading, but the radii are larger than the static one and time dependent property is found clearly in biaxial loading too. The flow lure can be expressed by the Perzyna type formula.

Thermo-Elastic-Plastic Stresses in Hollow Cylinders Due to Quenching

Abstract: : A hollow cylindrical tube rapidly quenched for the purpose of developing a high strength material structure is analyzed. The quenching creates severe thermal stresses early in the quenching cycle while later the material transformation by virtue of a volume change in the transformed material causes large transformation stresses. The transient temperature distributions and the elastic treatment of the stresses has been treated previously. The present work is an attempt to consider the thermo-elastic-plastic aspects of the problem. The von Mises' yield criterion and the Prandtl-Reuss stress strain relations are used. Results are calculated based on a new finite difference approach.

A Numerical Approach to Elastic-Plastic Plane-Strain Problems of Thick- Walled Cylinders

Abstract: : A new finite-difference approach has been developed for solving the elastic-plastic plane-strain problems of thick-walled cylinders subjected to internal or external pressure. The material is assumed to obey the von Mises' yield criterion, the Prandtl-Reuss flow theory and the isotropic hardening rule. The numerical scheme is stable for ideally-plastic as well as straining- hardening materials. The approach is simpler than others, and very accurate solutions can be obtained by reducing the grid sizes and load increments. The results for the stresses and strains in all principal directions have been computed as functions of loading history.

Long-Term Prediction of the Non-Linear Stresses Induced on a Ship Hull in Sea Waves

Abstract: A method of predicting the non-linear stresses such as the von Mises' equivalent stress on the longitudinal members of a ship in sea waves is proposed, by assuming that total normal stress and total shearing stress would be regarded as completely dependent randam variables.The application of this method is made for a large oil tanker in short-and long-term sea waves. The short-and long-term trends of the equivalent stresses on the longitudinal members are investigated in relation to heading angle.