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An endochronic constitutive model for cold powder compaction processes is developed. Although the concept of yield surface has not been explicitly assumed in the endochronic theory, it is demonstrated that the cone-cap yield surface can be derived as a special case of the proposed endochronic model. The plastic flow rule and the dilatancy condition of the model are derived and a procedure for calibration of the material parameters of the constitutive model is proposed. Since large deformations are observed in powder compaction processes, the endochronic constitutive model based on large strain plasticity is presented and an integration scheme for the rate constitutive equations is... 

In this paper, an endochronic constitutive model is developed for cold powder compaction processes. As large deformations are observed in powder forming processes, the endochronic constitutive model based on large strain plasticity is presented and an integration scheme for the rate constitutive equations is established. Although the concept of yield surface has not been explicitly assumed in the endochronic theory, it is demonstrated that the cone-cap yield surface can be derived as a special case of the proposed endochronic model. The plastic flow rule and the dilatancy condition of the model are derived and a procedure for calibration of material parameters of the constitutive model is... 

In this paper, an h-adaptive analysis for the mixed finite element solution of powder forming problems is presented involving localization due to material instability. A remeshing strategy is employed to compute the distribution of required element size using the estimated error distribution. Once the new element size and its alignment have been indicated, an automated procedure is used to construct the mesh according to a predetermined size and elongation distribution. The numerical results were obtained for a multi-level component to indicate the failure surfaces and evaluate the ultimate capacity of material. © 2003 Elsevier Science B.V. All rights reserved  

In this paper, an endochronic plasticity model is developed based on a large strain plasticity to describe the behavior of powder material in cold compaction process. The elastic response is stated in terms of hypoelastic model and endochronic plasticity constitutive equations are stated in unrotated frame of reference. A trivially incrementally objective integration scheme for rate constitutive equations is established. Algorithmic modulus consistent with numerical integration algorithm of constitutive equations is extracted. Finally, the numerical schemes are examined for efficacy in the modeling of a plain bush and a rotational-flanged powder compaction component. It is shown how the... 

In this paper, a density-dependent endochronic plasticity is presented for modelling the isothermal deformation behaviour of metal powder at low homologous temperature. As large deformation is observed in powder compaction process, a hypoelastic-plastic formulation is developed in the context of finite deformation plasticity. Constitutive equations are stated in unrotated frame of reference that greatly simplifies endochronic constitutive relation for finite plasticity. The material parameters in the constitutive model are calibrated for a tip shape component by fitting the model to reproduce data from true triaxial compression experiments. Numerical algorithm for accurate and stable... 

In this paper, an integrated software environment is demonstrated for computational simulation of powder forming processes. The powder compaction software, PCS_SUT, is designed in both popularity and functionality with the development of user-friendly pre- and post-processing software. Pre-processing software is used to create the model, generate an appropriate finite element grid, apply the appropriate boundary conditions, and view the total model. Post-processing provides visualization of the computed results. In PCS_SUT, a numerical model is developed based on a Lagrangian finite element formulation for large deformations, a cap plasticity theory for non-linear behaviour of material, and... 

As product complexity increases and economic constraints result in a demand for greater efficiency, industry must invest in new innovative ways to assist design and manufacture. As a first step in the long-term development of such a system, a computer software environment has been developed for pre- and post-processing for unstructured grid-based computational simulation. This paper describes the powder compaction software (PCS_SUT), which is designed for pre- and post-processing for computational simulation of the compaction of powder. Pre-processing software is used to create the model, generate an appropriate finite element grid, apply the appropriate boundary conditions, and view the... 

In this paper, a combined experimental and numerical investigation is described for powder compaction processes. It utilises material properties derived from experimental work as input for inelastic analysis of a finite element model. Numerical modelling of the powder compaction process is performed using a large-displacement finite element method. Powder material parameters, such as cohesion, internal friction angle and Young's modulus, were experimentally established as functions of relative density. These non-linear functions are incorporated into the inelastic analysis of the finite element model in order to establish model input parameters during different stages of compaction. Finally,... 

In this paper, the coupled thermo–mechanical simulation of hot isostatic pressing (HIPing) is presented for metal powders during densification process. The densification of powder is assumed to occur due to plastic hardening of metal particles. The constitutive model developed is used to describe the nonlinear behavior of metal powder. The numerical modeling of hot powder compaction simulation is performed based on the large deformation formulation, powder plasticity behavior, and frictional contact algorithm. A Lagrangian finite element formulation is employed for the large powder deformations. A modified cap plasticity model considering temperature effects is used in numerical simulation... 

The compaction forming of metal powder is a process involving large deformations, large strain, non-linear material behavior and friction. Consequently, the numerical analysis of such a highly non-linear process is a formidable computational problem. In this paper, an ALE technique is presented based on a generalized cap plasticity model in simulation of powder forming processes. In ALE formulation, the reference configuration is used for describing the motion, instead of material configuration in Lagrangian, and spatial configuration in Eulerian formulation. This formulation introduces some convective terms in the finite element equations and consists of two phases. Each time step is... 

In this paper, the 3D analysis of metal powder during the cold compaction process is simulated by the finite element method based on deformation theories. Since the compaction process involves a very large reduction in volume, a large displacement finite element method is applied for the spatial discretization. During compaction, powders exhibit strain or work hardening, the volume reduces and the material becomes harder. In this study, a quasi-nonlinear analysis is carried out during the FE modelling of powder forming process. The material parameters are experimentally established as functions of relative density. These nonlinear functions are incorporated into the inelastic analysis of... 

In this paper, a double-surface plasticity model, based on a combination of a convex yield surface consisting of a failure envelope, such as a Mohr-Coulomb yield surface and, a hardening cap model, is developed for the nonlinear behaviour of powder materials in the concept of a generalized plasticity formulation for the description of cyclic loading. This model reflects the yielding, frictional and densification characteristics of powder along with strain and geometrical hardening which occur during the compaction process. The solution yields details on the powder displacement from which it is possible to establish the stress state in the powder and the densification is derived from... 

In this paper, a computational algorithm is presented in three-dimensional dynamic modeling of powder compaction processes. The contact node-to-surface algorithm is employed to impose the contact constraints in large deformation frictional contact, and the contact frictional slip is modified by the Coulomb friction law to simulate the frictional behavior between the rigid punch and the work-piece. The 3D nonlinear contact friction algorithm is employed together with a double-surface cap plasticity model within the framework of large FE deformation in order to predict the non-uniform relative density distribution during the dynamic simulation of powder die-pressing. Finally, the performance... 

In this paper, the large deformation frictional contact of powder forming process is modeled based on a new computational algorithm by imposing the contact constraints and modifying the contact properties of frictional slip. A simple and efficient numerical algorithm is presented for imposing the contact constraints and frictional contact properties based on the node-to-surface contact technique to simulate the large deformation contact problem in the compaction process of powder. The Coulomb friction law is used to simulate the friction between the rigid punch and the workpiece by the use of penalty approach. A double-surface cap plasticity model is employed together with the nonlinear... 

In this paper, a three-invariant cap plasticity with a kinematic hardening rule is presented for powder materials. A general form is developed for the cap plasticity which can be compared with some common double-surface plasticity models proposed for powders in literature. The constitutive elasto-plastic matrix and its components are derived based on the definition of yield surface, hardening parameter and non-linear elastic behavior, as function of relative density of powder. The procedure for determination of powder parameters is described. Finally, the applicability of the proposed model is demonstrated in numerical simulation of triaxial and confining pressure tests. © 2006 Elsevier B.V.... 

In this paper, an application of Arbitrary Lagrangian-Eulerian (ALE) method is presented in plasticity behavior of pressure-sensitive material, with special reference to large deformation analysis of powder compaction process. In ALE technique, the reference configuration is used for describing the motion, instead of material configuration in Lagrangian, and spatial configuration in Eulerian formulation. The convective term is used to reflect the relative motion between the mesh and the material. Each time-step is divided into the Lagrangian phase and Eulerian phase. The convection term is neglected in the material phase, which is identical to a time-step in a standard Lagrangian analysis.... 

In this paper, the influence of powder-tool friction on the mechanical properties of the final product is investigated in pressing metal powders. A computational algorithm is presented for simulation of frictional contact in the compaction process of powder. The large deformation finite element (FE) formulation is characterized by the use of penalty approach in which a plasticity theory of friction is incorporated to simulate sliding resistance at the powder-tool interface. The constitutive relations for friction are derived from a Coulomb friction law. A double-surface cap plasticity model is employed together with the nonlinear contact friction behavior in numerical simulation of powder... 

In this paper, a new computational technique is presented based on the extended arbitrary Lagrangian-Eulerian finite element model (X-ALE-FEM) in plasticity forming of powder compaction. An arbitrary Lagrangian-Eulerian (ALE) technique is employed to capture the advantages of both Lagrangian and Eulerian methods and alleviate the drawbacks of the mesh distortion in Lagrangian formulation. In order to remove the limitation of the mesh conforming to the boundary conditions in this process, the extended finite element method (X-FEM) is implemented by incorporating discontinuous fields through a partition of unity method. The implementation of X-FEM technique in the framework of ALE model is...