A Novel Flow Model of Strain Hardening and Softening for Use in Tensile Testing of a Cylindrical Specimen at Room Temperature

We develop a new flow model based on the Swift method, which is both versatile and accurate when used to describe flow stress in terms of strain hardening and damage softening. A practical issue associated with flow stress at room temperature is discussed in terms of tensile testing of a cylindrical specimen; we deal with both material identification and finite element predictions. The flow model has four major components, namely the stress before, at, and after the necking point and around fracture point. The Swift model has the drawback that not all major points of stress can be covered simultaneously. A term of strain to the third or fourth power (the “second strain hardening exponent”), multiplied and thus controlled by a second strain hardening parameter, can be neglected at small strains. Any effect of the second strain hardening exponent on the identification of the necking point is thus negligible. We use this term to enhance the flexibility and accuracy of our new flow model, which naturally couples flow stress with damage using the same hardening constant as a function of damage. The hardening constant becomes negative when damage exceeds a critical value that causes a drastic drop in flow stress.

Non-orthogonal elastoplastic constitutive model for sand with dilatancy

A non-orthogonal elastoplastic constitutive model for sand with dilatancy is presented in the characteristic stress space. Dilatancy of sand is represented by the direction of plastic flow, which can be directly determined by applying the non-orthogonal plastic flow rule to an improved elliptic yield function. A new hardening parameter is developed to describe the contractive and dilative volume change during the shear process, which is co-ordinated with the non-orthogonal plastic flow direction. The combination of the non-orthogonal plastic flow rule and the proposed hardening parameter renders the proposed model with the ability to reasonably describe the stress-strain relationship of sand with dilatancy. The model performance is evaluated by comparing with the experimental data of sand under triaxial stress conditions.

The Hardening in Alloys and Composites and Its Examination with a Diffraction and Self-Consistent Model

The paper presents the results of diffraction stress measurement in Al/SiC composite and in 2124T6 aluminum alloy during the in situ tensile test. The main aim of the work is to observe the stress values for different stages of tensile test for the composite after applying two types of thermal treatment and for the alloy used as a matrix in this composite, to identify the type of hardening process. The experimental results were compared against the calculations results obtained from the self-consistent model developed by Baczmański [1] - [3] to gain the information about the micromechanical properties (critical resolved shear stress τcr and hardening parameter H) of the examined materials. This comparison allowed researchers to determine the role of reinforcement in the composite as well as the impact of the heat treatment on the hardening of the material.

Determination of the yield function and its derivatives of the Barcelona Expansive model

The main purpose of this paper is to determine the yield function F of the Barcelona Expansive Model and its partial derivatives with respect to the stress vector σ, the suction s and the hardening parameter χ. These results are important by the fact that they are used to solve the elastoplastic problem of unsaturated expansive soils.

Stochastic homogenization of plasticity equations

In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule function are given through a dynamical system on a probability space. A parameter ε > 0 denotes the typical length scale of oscillations. We derive effective equations that describe the behavior of solutions in the limit ε → 0. The homogenization procedure is based on the fact that stochastic coefficients “allow averaging”: For one representative volume element, a strain evolution \hbox{$[0,T]\ni t\mapsto \xi(t) \in \symM$} induces a stress evolution \hbox{$[0,T]\ni t\mapsto \Sigma(\xi)(t) \in \symM$}. Once the hysteretic evolution law Σ is justified for averages, we obtain that the macroscopic limit equation is given by −∇·Σ(∇su) = f.

Thermo-Mechanical Cyclic Plastic Behavior of 304 Stainless Steel at Large Temperature Ranges

Thermo-mechanical cyclic experiments on 304 stainless steel were performed at several temperature ranges which had maximum temperatures ranging from 350°C to 1000°C and a minimum temperature of 150 °C. Related isothermal cyclic experiments were also performed. Temperature-history dependent cyclic hardening significantly occurred under thermo-mechanical cyclic loading with maximum temperatures around 600°C, whereas almost no cyclic hardening was observed when the maximum temperature was 1000°C. The observed thermo-mechanical cyclic plastic behavior in the saturated state of cyclic hardening was then simulated using a cyclic viscoplastic constitutive model, leading to the following findings. It was difficult to predict the saturated thermo-mechanical cyclic behavior using only the isothermal cyclic experimental data. The saturated thermo-mechanical cyclic behavior was simulated well by introducing a cyclic hardening parameter depending on the maximum temperature. This means that the cyclic hardening parameter should not change with temperature but depend on the maximum temperature in the saturated state of cyclic hardening under thermo-mechanical cyclic loading.

Blast Alleviation of Cellular Sacrificial Cladding: A Nonlinear Plastic Shock Model

The anti-blast behavior of cellular sacrificial cladding is investigated based on a continuum-based nonlinear plastic shock model. A rate-independent, rigid–plastic hardening (R-PH) model with two material parameters, namely the initial crushing stress and the strain hardening parameter, is employed to idealize the cellular material. The governing equation of the motion of cover plate is obtained and solved numerically with a fourth-order Runge–Kutta scheme. A comparison of the crushing percentage contours of sacrificial cladding based on the R-PH model and the rigid–perfectly plastic–locking (R-PP-L) model is carried out. Results transpire that the R-PP-L model is not accurate enough to evaluate the energy absorption. Dimensional analysis is employed to study the critical length of cellular sacrificial cladding and an empirical expression is determined by the controlling valuable method. An asymptotic solution is also obtained by applying the regular perturbation theory. Finally, the design criteria of cellular sacrificial cladding based on the R-PH shock model is verified by a cell-based finite element model.

Comparison of Three Methods for Material Hardening Parameter Identification under Cyclic Tension-Compression Loadings: Roll Levelling Case Study

The roll levelling is a forming process used to remove the residual stresses and imperfections of metal strips by means of plastic deformations. The process is especially important to avoid final geometrical errors when coils are cold formed or when thick plates are cut by laser. In the last years, and due to the appearance of high strength materials such as Ultra High Strength Steels, machine design engineers are demanding a reliable tool for the dimensioning of the levelling facilities. In response to this demand, Finite Element Analysis is becoming an important technique able to lead engineers towards facilities optimization through a deeper understanding of the process.In this scenario, the accuracy and quality of the simulation results are highly dependent on the accuracy of the implemented material model. During roll levelling process, the sheet metal is subjected to cyclic tensile-compressive deformations, therefore a proper constitutive. model which considers the phenomena that occurs during cyclic loadings, such as the Bauschinger effec, work hardeningt and the transient behaviour, is needed. The prediction of all these phenomena which affect the final shape of the product are linked to the hardening rule.In the present paper, the roll levelling simulation of a DP1000 steel is performed using a combined isotropic-kinematic hardening formulation introduced by Chaboche and Lemaitre since its simplicity and its ability to predict the Bauschinger effect. The model has been fitted to the experimental curves obtained from a cyclic tension-compression test, which has been performed by means of a special tool developed to avoid the buckling of the specimen during compressive loadings. The model has been fitted using three different material hardening parameter identification methodologies which have been compared.