Ali Halouani

Efficient pseudo-inverse approach for damage prediction in cold forging process simulation

This article presents an efficient pseudo-inverse approach for the damage prediction in cold forging process simulation. Pseudo-inverse approach combines the advantages of the fast inverse approach and accurate incremental approaches. Some intermediate configurations are created geometrically and corrected mechanically to well describe the deformation path. The formulation of an axi-symmetrical element based on pseudo-inverse approach is presented. A strain-based damage model is introduced in the flow theory of plasticity. A direct scalar integration algorithm of plasticity-damage is developed, leading to a fast and robust algorithm for large strain increments. The cold forging processes of two axi-symmetrical parts are simulated to validate pseudo-inverse approach by the incremental approach ABAQUS/Explicit. Pseudo-inverse approach gives very good results, but uses much less CPU time.

Optimization of Forging Preforms by Using Pseudo Inverse Approach

A simplified method called “Pseudo Inverse Approach” (PIA) has been developed for axi-symmetrical cold forging modelling. The approach is based on the knowledge of the final part shape. Some intermediate configurations are introduced and corrected by using a free surface method to consider the deformation paths without classical contact treatment. A new direct algorithm of plasticity is developed using the notion of equivalent stress and the tensile curve, which leads to a very fast and robust plastic integration procedure. Numerical tests have shown that the Pseudo Inverse Approach is very fast compared to the incremental approach. In this paper, the PIA will be used in an optimization loop for the preliminary preform design in multi-stage forging processes. The optimization problem is to minimize the effective strain variation in the final part and the maximum forging force during the forging process. The numerical results of the optimization method using the PIA are compared to those using the classical incremental approaches to show the efficiency and limitations of the PIA.

Simulation of Axi-Symmetrical Forging Process by “Inverse Approach”

The simplified method called Inverse Approach (I.A.) has been developed by Batoz, Guo et al.[1] for the sheet forming modelling. They are less accurate but much faster than classical incremental approaches. The main aim of the present work is to study the feasibility of the I.A. for the axi-symmetric forging process modelling. In contrast to the classical incremental methods, the I.A. exploits the known shape of the final part and executes the calculation from the final part to the initial billet. Two assumptions are used in this study: the assumption of proportional loading for cold forging gives an integrated constitutive law without considering the strain path and the viscoplasticity, the assumption of contact between the part and tools allows to replace the tool actions by nodal forces without contact treatment. The comparison with Abaqus shows that the I.A. can obtain a good strain distribution and it will be a good tool for the preliminary preform design.

Optimization of cold forging perform tools using Pseudo Inverse Approach

Abstract A new fast method called “Pseudo Inverse Approach” (PIA) for the multi-stage axi-symmetrical cold forging modelling is presented. The approach is based on the knowledge of the final part shape. Some intermediate configurations are introduced and corrected by using a free surface method to consider the deformation paths without contact treatment. A new direct algorithm of plasticity is developed using the notion of equivalent stress and the tensile curve, leading to a very efficient and robust plastic integration procedure. Numerical tests show that the Pseudo Inverse Approach is very fast compared with the incremental approach. The PIA is used in an optimization procedure for the preliminary preform tool design in multi-stage cold forging processes. This optimization problem aims to minimize the equivalent plastic strain and the punch force during the forging process. The preform tool shapes are represented by B-Spline curves. The vertical positions of the control points of B-Spline are taken as design variables. The evolution of the objective functions shows the importance of the tool preform shape optimization for the forging quality and energy saving. The forging results obtained by using the PIA are compared with those obtained by the classical incremental approaches to show the efficiency and accuracy of the PIA.

Numerical modeling of axi‐symmetrical cold forging process by “Pseudo Inverse Approach”

The incremental approach is widely used for the forging process modeling, it gives good strain and stress estimation, but it is time consuming. A fast Inverse Approach (IA) has been developed for the axi‐symmetric cold forging modeling [1–2]. This approach exploits maximum the knowledge of the final part’s shape and the assumptions of proportional loading and simplified tool actions make the IA simulation very fast. The IA is proved very useful for the tool design and optimization because of its rapidity and good strain estimation. However, the assumptions mentioned above cannot provide good stress estimation because of neglecting the loading history. A new approach called “Pseudo Inverse Approach” (PIA) was proposed by Batoz, Guo et al.. [3] for the sheet forming modeling, which keeps the IA’s advantages but gives good stress estimation by taking into consideration the loading history. Our aim is to adapt the PIA for the cold forging modeling in this paper. The main developments in PIA are resumed as fol...

Fast Plastic Integration Algorithm for Damage Prediction in Forming Process Simulations

The iterative Return Mapping Algorithm (RMA) is widely used for the plastic integration owing to its accuracy and efficiency, but it is CPU time consuming and may cause divergence problems in case of large strain increments. This paper presents a fast plastic integration method called Direct Scalar Algorithm (DSA) for the damage prediction in forming process simulations. A simplified three-dimensional (3D) strain-based damage model is coupled with the plasticity and implemented into the DSA which does not need iterative solution to make the plastic integration very fast and robust even for very large strain increments. The basic idea is to transform the constitutive equations in terms of the unknown stress vectors into a scalar equation in terms of the equivalent stresses which can be determined by using the experimental tensile curve; thus, the plastic multiplier ∆λ can be directly calculated. The DSA is as accurate as RMA but much faster for the plastic integration.

Fast Plastic Integration Algorithms for Forming Process Simulations

This paper presents a fast plastic integration algorithm and compares it with other algorithms for forming process simulations. The iterative Return Mapping Algorithm (RMA) is widely used owing to its accuracy and efficiency, but it is still time consuming and may cause divergence problems. Another algorithm based on the Incremental Deformation Theory (IDT) was proposed, using the deformation theory of plasticity by piecewise; it is very fast but could not well consider the loading history, leading to notable errors. The new Direct Scalar Algorithm (DSA) based on the flow theory of plasticity is proposed in this paper. The basic idea is to transform the constitutive equations in terms of the unknown stress vectors into a scalar equation in terms of the equivalent stresses which can be determined by using the experimental tensile curve; thus, the plastic multiplier λ can be directly calculated without iterative solution. The DSA is a fast and robust plastic integration algorithm. The comparison of the results obtained by using the three algorithms shows the accuracy and efficiency of the DSA.

A Pseudo Inverse Approach with Kinematically Admissible Intermediate Configurations for the Axi-Symmetrical Cold Forging Modelling

A simplified method called “Pseudo Inverse Approach” (PIA) has been developed for the axi-symmetrical cold forging modeling in this paper. The traditional “Inverse Approach” (IA) based on the assumptions of the proportional loading and simplified tool actions may quickly give a fairly good strain distribution, but poor stress estimation. Meanwhile the PIA proposed in this paper not only keeps the advantages of the Inverse Approach but also gives good stress estimation by taking into account the loading history. To fulfill this aim, some kinematically admissible intermediate configurations represented by the free surface are used to consider the deformation paths without classical contact treatment. A new direct algorithm of plasticity integration has been used by using the notion of equivalent stress and the tensile curve, leading to a very fast and robust plastic integration procedure. An axi-symmetrical forging has been taken as an example to validate the PIA.