Description of yield surface evolution using a convected plasticity model

The convected plasticity model proposed by Wu, 2003a, Wu, 2003b, Wu, 2005, Wu, 2007, making use of convected coordinate system, is applied to discuss the evolution of yield surface. It is shown that this constitutive model is capable of describing all experimentally observed features of subsequent yield surface: isotropic hardening, kinematic hardening, distortion, and rotation of yield surface. The rotation of yield surface in 3D stress space has not been much discussed in the literature, but recent experiments at National Taiwan University (Sung et al., 2011) have shown that it is an important property of subsequent yield surface. In particular, the rotation of subsequent yield surface is pre-strain path dependent. It does not rotate, when the pre-strain is tensile; but the yield surface rotates about the axial stress axis when the pre-strain is torsional.     

On a mechanical analogy in the ideal plasticity theory

The Cauchy problem of propagation of plastic state zones in a boundless medium from the boundary of a convex surface, along which normal pressure and shear forces act, is considered. In the case of complete plasticity, the Tresca system of quasi-static equations of ideal plasticity, which describes the stress-strain state of the medium, is known to be hyperbolic and to be similar to a system that describes a steady-state flow of an ideal incompressible fluid. This system is numerically solved with the use of a difference scheme applied for hyperbolic systems of conservation laws. Results of numerical calculations are presented. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 74–80, July–August, 2008.     

Reproduction of solutions of bidimensional ideal plasticity

The symmetries of a system of differential equations allowed the transformation of its solutions to a solution of this system. New analytical exact solutions of a system of two-dimensional ideal plasticity equations were constructed from two well-known solutions, that for a circular cavity stressed by normal pressure, and Prandtl's solution for a block compressed between perfectly rough plates, for the case where the thickness of the block was rather small. A mechanical sense of new solutions was discussed.     

Extremal properties of endochronic plasticity,part II: Extremal path of the constitutive equation with a yield surface and application

Extremal paths for endochronic constitutive equations without using a yield surface and the corresponding principle of minimum potential work were obtained in Part I of this article. In this paper, the extremal properties of endochronic constitutive equation with a yield surface and the corresponding method for deformation bound analysis are proposed. An example is presented that demonstrates that the application of endochronic constitutive models to simplified analysis is not significantly different from classical models due to the derived extremal properties. The adopted constitutive model involves both nonlinear isotropic and kinematic hardening, which may provide more accurate results in simplified and bounding analysis.     

Stress space and strain space formulation of the elasto-plastic constitutive relations for singular yield surface

This paper gives the stress space and the strain space formulations of the elastoplastic constitutive relations at a singular point on a yield surface, discusses the parallelism of the two space formulations and points out that the strain space formulation has a wider range of applicability.     

On relations for general two-dimensional ideal plasticity problems under the full plasticity condition

Relations for two-dimensional ideal plasticity problems under the full plasticity condition are determined with material anisotropy, inhomogeneity, and compressibility properties taken into account. These properties are determined by the direction cosines of the principal stress, the coordinates of points in space, and the mean stress.For the yield strength we take a function of the form k = k(σ, n ₁, n ₂, n ₃, x, y, z). The desired relations are determined for the general plane ideal plasticity problem. The relations thus obtained are generalized to the cases of axisymmetric and spherical plasticity problems.     

An effective computational algorithm for rate-independent crystal plasticity based on a single crystal yield surface with an application to tube hydroforming

Up to now, several computational methods have been proposed for crystal plasticity models. The main objective of these computational methods has been to overcome the problem with the non-uniqueness of active slip systems during the plastic deformation of a single crystal. Crystal plasticity models based on a single crystal yield function have been proposed as alternative algorithms to overcome this problem. But the problem with these models is that they use a highly non-linear yield function for the crystal, which makes them computationally expensive. In this paper, a computational method is proposed that would modify a single crystal yield function in order to make it computationally efficient. Also to better capture experimental data, a new parameter is introduced into the single crystal yield function to make it more flexible. For verification, this crystal plasticity model was directly applied for the simulation of hydroforming of an extruded aluminum tube under complex strain paths. It was found that the current model is considerably faster than the previous crystal plasticity model based on a power-law type single crystal yield surface. Due to its computational efficiency, the current crystal plasticity model can also be used to calculate the anisotropy coefficients of phenomenological yield functions.     

A general cyclic plasticity model taking into account yield surface distortion for multiaxial ratchetting

Most of the theoretical studies devoted to multiaxial ratchetting are focused on the location of the macroscopic yield domain in order to predict the correct direction of plastic strain rate, since normality of the plastic strain rate to the yield surface is usually assumed. To the authors' knowledge, the shape of subsequent yield surfaces was always kept constant in these models for simplicity reasons but unlike experimental observations. In a previous paper [J. Eng. Mater. Technol. 124(4) (2002) 402], the authors have explained the need to take into account yield surface distortion in macroscopic modeling and have therefore proposed such a constitutive model but only for biaxial loadings. In the present paper, the generalization of this distortional model is proposed for any loading paths. The model is then identified and validated on a large data base obtained firstly with an efficient polycrystalline model that can predict multiaxial ratchetting as well as yield surface distortion, and secondly with the experimental results of complex tests realized on a type 316L stainless steel.     

Localization in elasto-plastic materials: Influence of the plasticity yield surface in biaxial loading conditions

The influence of the plasticity yield surface on the development of instabilities in plane plates in biaxial loading is analyzed in order to understand and simulate the localization pattern observed in an expanding hemisphere experiment. First, a criterion for the activation of slip bands is formulated in the form of a critical hardening coefficient: it is particularized to the Von Mises and Tresca surfaces. In the Von Mises case, the criterion gives a strongly negative hardening coefficient in biaxial loading conditions different from the ones of plane strain. In the Tresca case, the criterion is fulfilled for a perfectly plastic material in uniaxial and biaxial loading; besides, in equi-biaxial loading, two possible orientations for slip bands are exhibited; this can be understood, with a few approximations, by the existence of a vertex point on the Tresca yield surface which give additive degrees of freedom for the direction of the plastic strain rate. Second, the development of localization in the loading conditions met in an expanding hemisphere experiment is simulated using both plasticity yield surfaces; whereas the Von Mises simulation does not localize, the Tresca simulation exhibits a pattern composed of a network of shear bands of different orientations; this pattern is not far from the pattern observed experimentally.     

General yield conditions in a plasticity analysis of soil-wheel interaction

Plasticity theory and a general representation of the Mohr failure criterion are applied to the problem of soil-wheel interaction. Load, drawbar pull (or drag), and torque are computed for a rigid wheel being driven on Jones Beach sand. Analytical results obtained from solutions using a conventional Mohr-Coulomb linear failure envelope are compared to those obtained from a non-linear solution. Conclusions are drawn from the comparison that attest the importance of considering the nonlinearity of failure envelopes in certain cases for accuracy of soil-wheel interaction prediction. Preliminary experimental results show reasonable agreement with predicted values of wheel performance parameters.     

Mechanism-based multi-surface plasticity model for ideal truss lattice materials

The mechanical behavior of ideal truss lattice materials is controlled by the so-called direct action mechanism at the microscale which involves the uniform stretching and compressing of individual truss members. Standard homogenization techniques have been employed to develop a general micromechanics-based finite-strain constitutive model for truss lattice materials. Furthermore, a specialized small-strain plasticity model has been derived. Both models have been implemented in a finite-element program and used to simulate the anisotropic plastic behavior of the octet-truss lattice material in various applications including cyclic uniaxial loading, pure shear, and three-point bending. The constitutive model predictions agree well with the results obtained from discrete finite element models. Regarding the plasticity of the octet-truss lattice material, it has been found that the elastic domain is constrained by twelve pairwise parallel hyperplanes in the six-dimensional stress space. Moreover, the mechanism-based small-strain formulation reveals that the direction of plastic flow is normal to the pressure-dependent macroscopic yield surfaces.     

A class of exact solutions of the ideal plasticity equations

A class of exact solutions is formulated for the ideal plasticity equations in the case of plane deformation. The solutions describe the plastic state of various wedges, notched half-planes, and domains in the form of funnels produced by detonation, the plastic state of domains having a horn configuration, etc. Many of the solutions have natural boundaries comprising envelopes of slip lines. The equations for the boundaries, slip lines, and stresses are presented in explicit form.     

Polar plasticity of thin-walled composites made of ideal fibre-reinforced material

The present study investigates the influence that polar material response has on the plastic behaviour of thin-walled structures made of ideal fibre-reinforced materials (Spencer, 1972); or, equivalently, on the response of thin-walled fibrous composites within the first branch of the matrix dominated form (MDM) of the bimodal theory of plasticity (Soldatos, 2011, Dvorak and Bahei-El-Din, 1987). The plasticity studies mentioned above assume that fibres are infinitely thin and, therefore, perfectly flexible. They possess no bending stiffness and, hence, their negligible bending resistance cannot influence the developed stress state, which is accordingly described by a symmetric stress tensor. In contrast, the present study considers that if fibres resistant in bending are embedded in a material at high volume concentrations, their flexure produces couple-stress and, as a result of this kind of polar material behaviour, the stress tensor becomes non-symmetric. Under plane stress conditions that dominate behaviour of thin-walled structures, the stress-space and, therefore, conditions of plastic yield and relevant yield surfaces are thus four-dimensional. However, shapes and properties of initial yield surfaces relevant to the f₁-branch of MDM are studied comprehensively by considering their projection on particular planes of such a four-dimensional stress-space. It then becomes easier understood that, in the regime of polar material response, a thin-walled structure made of ideal fibre-reinforced material deforms plastically when suitable combinations of shear stress values are reached simultaneously, rather than when only one of two unequal shear stress components reaches some maximum absolute value. Thus, polar material plasticity dismisses the conventional concept of material yield stress in shear and replaces it with a pair of two independent yield moduli. Existence of the latter is perceived as a theoretical justification of the expectation that, due to the presence of fibres, two rather than one shear yield parameters of the composite should be present and accountable for. The non-zero values of those parameters are shown to exert paramount influence on the form of the yield surface of the ideal fibre-reinforced material of interest.