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In this paper, an anisotropic material model based on a non-associated flow rule and nonlinear mixed isotropic-kinematic hardening is developed. The quadratic Hill48 yield criterion is considered in the nonassociated model for both yield function and plastic potential to account for anisotropic behavior. The developed model is integrated based on f...
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... a second simulation, the material behavior is performed by assigning a loading program with loading history illustrated in Figure 9. The related stress-strain curves, in the notched point, are reported in Figure 10, where a comparative analysis of the isotropic hardening behavior and the mixed isotropic/kinematic hardening behavior is illustrated. Figure 11 illustrates the time evolution of the back-stress components: X xx , X yy , and X xy at notched point. ...
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... Now we switch out attention to the structural plate model from Section 2 and evaluate it for the problem of uni-axial bending at hand. Using the same Cartesian coordinate system as before, we write the elasticity law (4) for the bending moment (15), invert it and find the total curvature in the axial direction to ...
Modelling of roll forming process of sheet metal requires efficient treatment of plastic deformations of thin shells and plates. We suggest a new general approach towards constructing the governing equations of bending of an elastic-plastic Kirchhoff plate on the structural mechanics level. The generic function of the isotropic hardening law is formulated in terms of variables, which are meaningful for a material surface, namely resultant bending moments and dissipative work. This function is then identified by comparison of the exact solutions for a uni-axial or isotropic bending experiment within the structural model and with the continuum model of a through-the-thickness element. We validate the approach against both the fully three-dimensional simulations as well as the results of the traditional elastic-plastic plate analysis, the latter one featuring the continuum laws of plasticity treated in the integration points along the thickness direction. We considered benchmark problems from the literature as well as a prototype for the roll forming problem. Besides good agreement regarding the shape of plastic zones and force-deflection characteristics, experiments also demonstrate higher computational efficiency of the new stress resultant model.
... One of the characteristics of rolled sheet metal materials is that they exhibit anisotropic behavior, which affects the formability of the final part (Wali et al. 2016) and is commonly described by the Lankford coefficients (r-value) and yield stresses for defined orientations relative to the rolling direction. Hence, an accurate and appropriate anisotropic constitutive model is essential to improve the accuracy and efficiency of the manufacturing process numerical simulations. ...
... As an alternative, recent efforts (Wali et al. 2016;Cvitanic et al. 2008;Taherizadeh et al. 2009;Wang et al. 2014;Lian et al. 2018;Tang et al. 2019;Wu et al. 2020) have been made to develop numerical analysis methods based on non-associated flow rule (NAFR) formulations. The plastic flow rule is disassociated from the yield criteria by introducing a new expression for the plastic potential. ...
A numerical analysis based on associated flow rule (AFR) and non-AFR is presented and applied to anisotropic sheet metals. The models are defined in the quadratic form of the Hill’48 anisotropic function under a general three-dimensional stress condition. The anisotropic parameters for the yield function are identified using the directional planar yield stresses, bulge yield stress and shear yield stress. On the other hand, those for the plastic potential function are determined using the directional r-values. Three different models were implemented into the finite element code, through a developed user subroutine. Two models (r-values based and σ-based) related to AFR and a full expression related to the non-AFR are analyzed for the cup drawing test. Capabilities of the developed model for predicting the anisotropic behavior of sheet metal are investigated by considering cup heights and through-thickness strain distributions obtained from the simulations. Numerical results were compared with experimental data. Such comparisons and corresponding analysis demonstrate that the developed material model considering 3D conditions can improve accuracy when predicting the anisotropic behavior. Furthermore, the simple formulations are efficient and user-friendly for computational analyses and to solve common industrial sheet metal forming problems.
... This section develops the formulation of the constitutive elastoplastic equations (detailed in [22][23][24][25][26][27][28][29][30][31][32][33][34]) to model anisotropic yielding, and non-linear isotropic hardening used to simulate thin sheets manufactured by plastic deformation considered in sheet forming process, such as stamping and bending. The integration scheme used is based on the elastic prediction-plastic correction method. ...
The present paper presents numerical and experimental comparative studies between the conventional bending process (bending using punch and V-die) and bending with a rubber-pad cushion. In fact, a finite-element method is introduced to compare these two procedures used to bend AA1050-H14 Aluminum thin sheet. An elastoplastic constitutive model with quadratic yield criterion of Hill 48 and isotropic hardening behavior has been adopted in FE simulations performed using ABAQUS explicit. To model rubber material, a Mooney–Rivlin theory is used in the finite-element simulation. The purpose of this study is to see the difference between the two methods in terms of effort evolution, springback, stress distribution, thinning. Analyze the effect of the rubber material; in fact, natural rubber, and polyurethane with hardness 50, 70, and 90 shore A are investigated. This numerical study was validated by an experimental investigation that proved the efficiency of the elastic cushion to bend in a better way this thin aluminum sheet.
... Mechanical properties of AA6022-T43 (Wali et al. 2016) ...
In this paper, elasto-plastic model based on non-associated flow rule is implemented in Abaqus/Explicit software via VUMAT subroutine to study the influence of some process parameters: cone wall angle, tool diameter, and sheet thickness, on the formability, plastic deformation and thinning during single point incremental forming (SPIF) process. The present work presents useful guidance to show the effect of these three parameters in improving the quality of manufactured products and in obtaining a better formability during SPIF process.
... Experimental results for the uniaxial tensile test of specimen of the aluminum AA1050-H14 are applied to identify the hardening parameters. The Voce law is well suited to reproduce isotropic hardening [25][26][27][28][29][30][31]. Using the least-squares method, the experimental tensile stress-strain curve of the specimen along the rolling direction can be fitted by the Voce equation as: Table 1 shows mechanical properties of aluminum alloy (AA1050-H14) sheet. ...
The purpose of this manuscript is to carry out an experimental and numerical investigation of bulging process of aluminum AA1050-H14 sheet metal in free expansion when using a flexible punch. Three types of rubber with different hardness are used
as flexible punch. First, a mechanical characterization and identification of aluminum sheet metal and polyurethane rubber parameters is achieved for validation purpose. Then, an experimental study of flexible bulging process is performed to analyze
the effect of rubber type and hardness on forming capability. The obtained results show that the polyurethane with hardness of 70
Shore A is considered as the most suitable punch for the bulging operation when comparing with silicone and natural rubber.
Finally, a comparison between bulging with flexible and rigid punches is conducted using the finite element code ABAQUS/ Explicit. The developed simulations predict efficiently the realistic thickness distribution along the bulged part.
... The integration is conducted using the implicit Euler method (Backward Euler method), the strain-driven integration algorithm allows to have the stress history from the strain history. Using this integration method, an algorithmic tangent modulus is employed to maintain the quadratic rate of asymptotic convergence of the Newton approach used to determine the plastic multiplier as detailed in the works of [39][40][41][42][43][44][45]. ...
A geometrically nonlinear analysis of elastoplastic ceramic/metal functionally graded material (FGM) shells is investigated in this paper based on the first-order shear deformation theory. The elastoplastic behavior of the ceramic particle-reinforced metal matrix FGM shell is assumed to follow Ludwik hardening law. The elastoplastic material properties are assumed to vary smoothly through the thickness of the shells. The Mori–Tanaka model and self-consistent formulas of Suquet are employed to locally evaluate effective elastoplastic parameters of the ceramic/metal FGM composite. The homogenization formulation and numerical algorithms are implemented into ABAQUS/Standard via a user material subroutine (UMAT) developed to study the FG shells in large displacements and rotations. With the aim of demonstrating the accuracy of the present method, current numerical results are compared to experimental and numerical ones considering geometrically nonlinear elastoplastic FGMs and show very good agreement. The overall robustness of the new developed solution taking into account both geometric and material nonlinearities is demonstrated through several non-trivial benchmark problems taken from the literature. The effect of the constituent distribution on the deflections is analyzed.
... A non-associated flow rule with mixed nonlinear kinematic hardening was developed to predict both anisotropic and cyclic characteristics [30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. Taherizadeh et al. [40] based on their previous work [41] adapted an associated formulation to develop a non-associated constitutive model with mixed isotropic-kinematic hardening for finite element simulation of sheet metal forming. ...
... They obtained five nonlinear equations according to the plane stress condition: one tensor equation and two scalar equations. Later, Wali et al. [44] proposed to improve description and to reduce the number of constitutive equations using a simple integration algorithm of a non-associated anisotropic plasticity, with generalized quadratic function for yield criteria and plastic potential and nonlinear isotropic/ kinematic hardening. Two equations are solved by using the Newton-Raphson iterative scheme and zero tensor equation. ...
... Two equations are solved by using the Newton-Raphson iterative scheme and zero tensor equation. In this framework, the present investigation is an extension of Wali et al.'s [44] work to numerical simulation of incremental sheet metal engineering. The model is implemented to UMAT and VUMAT subroutines to simulate different sheet metal forming processes taking into account the prediction of both anisotropy and hardening behaviors. ...
This paper focuses on numerical simulation of single point incremental forming (SPIF) process. Via a user-defined material (VUMAT) subroutine is employed to implement a non-associated mixed isotropic–kinematic hardening material model. The accuracy of the proposed non-associated flow rule model to predict the material behavior and the anisotropy in sheet metal forming simulations is examined by comparing numerical results with experimental measurements. The suggested model shows good agreement with experimental results compared to the associated Hill_R and Hill_S models. The proposed non-associated flow rule demonstrates a good efficiency to simulate the springback after sheet metal forming and to predict the thickness variation during incremental sheet metal forming process. The present non-associated model can improve the prediction of both anisotropic and hardening behaviors of material used in numerically controlled sheet metal forming technology.
... Belhassen et al. (2016),Wali et al. (2015Wali et al. ( , 2016,Mars et al. (2016), Ben Said et al. (2017 andAutay et al. (2017). ...
... Belhassen et al. (2016),Wali et al. (2015Wali et al. ( , 2016,Mars et al. (2016), Ben Said et al. (2017 andAutay et al. (2017). ...
In this paper, an extended finite element method is proposed to analyze both geometric and material non-linear behavior of general Functionally Graded Material (FGM) plate-shell type structures. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the elastoplastic behavior of the ceramic particle-reinforced metalmatrix FGM plates-shells. The standard quadrilateral 4-nodes shell element with three rotational and three translational degrees of freedom per node, S4, is extended in the present study, to deal with elasto-plastic analysis of geometrically non-linear FGM plate-shell structures. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plate-shell type structures. The nonlinear approach is based on Mori-Tanaka model to underline micromechanics and locally determine the effective FGM properties and self-consistent method of Suquet for the homogenization of the stress-field. The elasto-plastic behavior of the ceramic/metal FGM is assumed to follow Ludwik hardening law. An incremental formulation of the elastoplastic constitutive relation is developed to predict the tangent operator. In order to to highlight the effectiveness and the accuracy of the present finite element procedure, numerical examples of geometrically non-linear elastoplastic functionally graded plates and shells are presented. The effects of the geometrical parameters and the volume fraction index on nonlinear responses are performed.
... En mise en forme des tôles métalliques, un modèle de plasticité associée est celui le plus utilisé dans la littérature, puisqu'il nécessite la définition d'un seul potentiel plastique. Cependant, une loi de plasticité non-associée permet une meilleure description du comportement plastique de certains matériaux métalliques (e.g., Badreddine et al., 2010 ;Bigoni et Hueckel, 1991 ;Cvitanić et al., 2008 ;Mohr et al., 2010 ;Qian et al., 2017 ;Safaei 23 et al., 2014 ;Stoughton, 2002 ;Stoughton et Yoon, 2009 ;Taherizadeh et al., 2010Taherizadeh et al., , 2015Wali et al., 2016). ...
L’objectif de ce sujet de thèse est de prédire l’apparition des instabilités plastiques (striction diffuse et striction localisée) dans les matériaux métalliques. Ces matériaux sont décrits par des modèles de comportement élasto-plastique couplés à l’endommagement. L'approche de Lemaitre, reliant l'endommagement à la déformation plastique équivalente et au taux de restitution de la densité d'énergie élastique, est adoptée. Parmi les différents critères et indicateurs qui sont considérés pour la prédiction des instabilités matériau, la théorie de bifurcation et les critères de type force maximum sont tout particulièrement analysés et comparés. Un objectif important de cette étude consiste à déterminer les mécanismes déstabilisants clés associés à cette modélisation du comportement, ainsi que l’impact des différents aspects physiques et des paramètres matériau sur l’apparition de la striction. Les développements résultants sont appliqués à une sélection représentative de matériaux métalliques afin prédire leurs limites de formabilités. Cette approche combinant des lois de comportement et critères de striction peut être utilisée comme outil théorique et numérique d’aide à la conception de nouveaux matériaux à ductilité améliorée
... The numerical treatment of the proposed algorithm is implemented in ABAQUS using user interface material subroutines UMAT. More details on the formulation and numerical implementation of the present model can be found in Wali et al. [27] and Wali et al. [30]. ...
Based on experimental test results, flax fiber reinforced polymer composites are characterized by nonlinear visco-elastoplastic behavior. The aim of this work is to model the quasi-unidirectional flax fiber reinforced composite behavior through a three dimensional formulation with orthotropic elasticity and orthotropic plasticity using Hill criterion. The isotropic hardening and Johnson Cook parameters are identified from unidirectional tensile tests at different strain rates. The adjustment of Hill's yield criterion is developed based on yield stresses obtained in tensile tests at different directions. The numerical integration of the constitutive equations is implemented in a user-defined material, UMAT subroutines for the commercial finite element code ABAQUS. Once model parameters are identified using tensile tests, the model needs to be validated by confronting it with other experimental results. That is why experimental and numerical three-point bending tests are carried out in order to validate the proposed model with tests that have not served for the identification. Finally, a numerical parametric study on low velocity impact of a flax/epoxy composite circular plate is investigated.
