Modeling the powder compaction process using the finite element method and inverse optimization

This paper focuses on studying and adapting modeling techniques using the finite element method to simulate the rigid die compaction of metal powders. First, it presents the implementation of the cap constitutive model into ABAQUS FE software using the closest point projection algorithm. Then, an inverse modeling procedure was proposed to alleviate the problems raised by the interpretation of the experimental tests and to more accurately determine the material parameters. The objective function is formed, based on the discrepancy in density data between the numerical model prediction and the experiment. Minimization of the objective function with respect to the material parameters was performed using an in-house optimization software shell built on a modified Levenberg?CMarquardt method. Thus, an integrated simulation module consisting of an inverse optimization method and a finite element method was developed for modeling the powder compaction process as a whole. The simulation and identification module developed was applied to simulate the compaction of some industrial parts. The results reveal that the maximum absolute error between densities is 2.3%. It corresponds to the precision of the experimental method.     

A densification model for mixed metal powder under cold compaction

Densification behavior of mixed copper and tool steel powder under cold compaction was investigated. By mixing the yield functions proposed by Fleck et al. and by Gurson for pure powder in terms of volume fractions of Cu powder and the fraction of contact, a new mixed yield function was employed for densification of powder composites under cold compaction. The constitutive equations were implemented into a finite element program (ABAQUS) to compare with experimental data and with results from the model of Kim et al. for densification of mixed powder under cold isostatic pressing and die compaction. Finite element calculations by using the yield functions mixed by the fraction of contact agreed better than those by volume fractions of Cu powder with experimental data.     

Densification behavior of aluminum alloy powder under cold compaction

Densification behavior of aluminum alloy (Al6061) powder was investigated under cold compaction. Experimental data were obtained under triaxial compression with various loading conditions. A special form of the Cap model was proposed from experimental data of Al6061 powder under triaxial compression. The proposed yield function and several other yield functions in the literature were implemented into a finite element program (ABAQUS) to compare with experimental data for densification behavior of Al6061 powder under cold isostatic pressing and die compaction. The agreement between finite element calculations from the proposed yield function and experimental data is very good under cold isostatic pressing and die compaction.     

Near net shape processing of a sintered alumina component: adjustment of pressing parameters through finite element simulation

Near net shape forming of alumina powder by cold die pressing and pressureless sintering was investigated. From experimental data of triaxial compression test of alumina powder, a hyperbolic cap model with a critical state line was proposed for densification of alumina powder at room temperature. For pressureless sintering, the phenomenological model for densification and viscous behavior of alumina powder proposed by Kim and co-workers was used. The constitutive models were implemented into a finite element program (ABAQUS) to simulate densification of alumina powder under cold die pressing and pressureless sintering. Finite element results were compared with experimental data for density distribution and deformation of an alumina powder compact under cold die pressing and pressureless sintering. New conditions of compaction were then proposed to reduce the distortion of the sintered part.     

Effect of friction between powder and a mandrel on densification of iron powder during cold isostatic pressing

The effects of friction between the powder and the mandrel on densification behavior of metal powder were investigated under cold isostatic pressing. The friction coefficients between the powder and the mandrels with different surface roughness were determined from the relationship between the compaction pressure and the ejection pressure of the mandrel from powder compacts. The elastoplastic constitutive equations based on the yield function of Shima and Oyane were implemented into a finite element program (ABAQUS) to simulate compaction responses of metal powders during cold isostatic pressing. Finite element results were compared with experimental data for pure iron powder under cold isostatic pressing.     

Densification behaviour of ceramic powder

A three-dimensional compaction device has been developed to carry out compaction of a ceramic powder. The details of the device, which provides compaction with various stress ratios, are described. A densification criterion for the powder is proposed; this is similar to that for the case for metal powders, but the role of the hydrostatic stress component appears to be different. Stress-strain rate relations are then derived using the concept of plastic potential; experimental results show that the normality of the strain rate vector to the surface which corresponds to the criterion almost holds.     

Calculation of a constitutive potential for isostatic powder compaction

A macroscopic constitutive potential has been developed for the deformation of a powder compact of cylindrical particles during pressure sintering. The derivation is based on finite-element simulations of the densification process that proceeds under the synergistic action of power-law creep deformation in the particles, evolution of the nonlinearly developing contact area between the particles, and interparticle and pore free-surface diffusional mass transport. Solution to this initial/boundary-value problem as deformation proceeds with time provides all necessary information for the calculation of the constitutive potential. The associated constitutive law predicts the densification rate of the powder compact at a given temperature and pressure in terms of material parameters, such as creep constants and diffusion coefficients, and reflects the role played in the densification process by various micromechanical features at the microscale such as the pore surface curvature. The model predictions are compared with the existing analytical models for plane strain densification and experimental data from sintering of copper wires by grain boundary and curvature-driven pore surface diffusion.     

Experimental based finite element simulation of cold isostatic pressing of metal powders

The present work addresses the various ingredients required for reliable finite element simulations of cold isostatic pressing (CIP) of metal powders. A plastic constitutive model for finite deformation is presented and implemented into an explicit finite element (FE) code. The FE implementation is verified so that numerical errors (both temporal and spatial errors) are kept under control. Thereafter, uniaxial die compaction experiments are performed required for determining the material parameters in the constitutive model. Subsequently they are applied for the simulation of a “complex” CIP process. The experimental observations of the complex CIP process were used to validate the overall method by comparing the FE results (final dimensions and average relative density) to the experimental observations. The numerical results (final dimensions and relative density) are in good agreement with the experimental observations.     

Constitutive parameter estimation of a viscoelastic model with internal variables

The present work is aimed at estimating the constitutive parameters of viscoelastic materials. The constitutive equation addressed takes internal dissipation into account by means of internal variables. The identification method is built on an optimization problem where the minimum of an error function is sought. The error function is based on the difference between the experimental response and the model one and on the parameter constraints as well. The constitutive parameters are estimated by means of a modified Levenberg–Marquardt algorithm. The viscoelastic material characterization was assessed through an experimental set-up consisted of a sandwich beam with a viscoelastic core.     

Model for compaction of metal powders

A new yield criterion for metal powder compaction based on continuum mechanics has been proposed. It includes three parameters to characterize the geometric hardening of powder compact and strain hardening of incompressible metal matrix. The elasto-plastic finite element method to describe compaction of metal powders has been formulated using the new yield criterion. The values of parameters in the yield criterion could be determined through cold isostatic pressing (CIP). The finite-element method was used to simulate compaction behaviour of copper powders of different shape and mean particle size.     

Densification of mixed metal powder at high temperature

Densification behaviors of mixed metal powder under high temperature were investigated. Experimental data of mixed copper and tool steel powder with various volume fractions of Cu powder were obtained under hot isostatic pressing and hot pressing. By mixing the creep potentials of McMeeking and co-workers and of Abouaf and co-workers originally for pure powder, the mixed creep potentials with various volume fractions of Cu powder were employed in the constitutive models. The constitutive equations were implemented into a finite element program (ABAQUS) to compare with experimental data for densification of mixed powder under hot isostatic pressing and hot pressing. Finite element calculations by using the creep potentials of Abouaf and co-workers agreed reasonably well with experimental data, however, those by the model of McMeeking and co-workers underestimate experimental data as observed in the case of pure metal powders.     

Three-stage Method for Identifying the Dynamic Model Parameters of Stranded Wire Helical Springs

The dynamic behavior of the stranded wire helical spring is described by a modified Bouc-Wen model while the model parameters must be identified using an identification method and experimental data. Existing identification methods usually relies either solely nonlinear iterative algorithms or manually trial and error. Therefore, the identification process can be rather time consuming and effort taking. As a result, these methods are not ideal for engineering applications. To come up with a more practical method, a three-stage identification method is proposed. Periodic loading and identification simulations are carried out to verify the effectiveness of the proposed method. Noises are added to the simulated data to test the performance of the proposed method when dealing with noise contaminated data. The simulation results indicate that the proposed method is able to give satisfying results when the noise levels are set to be 0.01, 0.03, 0.05 and 0.07. In addition, the proposed method is also applied to experimental data and compared with an existing method. The experimental data is acquired through a periodic loading test. The experiment results suggest that the proposed method features better accuracy compared with the existing method. An effective approach is proposed for identifying the model parameters of the stranded wire helical spring.     

Determining coefficients of friction in compaction of refractory metal powders

Knowing the coefficients of friction in tool compaction of powders of metals and alloys allows one to rationally design technological equipment for manufacturing powder semifinished products experiencing minimal warping under vacuum or hydrogen sintering. This is of particular significance when consumable electrodes are produced from powders of refractory metals being compacted as rather long fillets that are curved in sintering if any irregularities in the density in the cross section and in the fillet bulk are present. Both well-known and new methods are analyzed for finding the coefficients of friction in powder compaction, in particular in cylindrical containers. Stable and valid measurement results are shown to be unachievable. A new method for experimental determination of the coefficients of friction under powder compaction is described. It consists in comparing the force parameters of one- and two-sided compaction. This method allows finding the coefficient of side pressure and contact friction (on the cylindrical surface of the container) during the formation of briquettes of TsM-2A alloy with different concentrations of plasticizer and solvent. A positive effect of a plasticizer and negative one of a solvent on the coefficient of friction is stated.     

基于粉末本构模型和多体力学仿真的模架集成式粉末成形设备的设计

研制出一种新型的低成本、小体积、高精度的专用模架集成式粉末成形设备。以MSC.Marc与MSC.Adams软件相结合提出基于数值模拟的1 MN压机设计方法,即根据粉末压制试验构建末材料流动应力本构模型;通过该模型在MSC.Marc软件数值计算出所设计压机压制过程的模冲载荷;在分析模架集成式粉末成形设备各个模板在压制工过程运动特点的基础上,建立多体运动学数学方程;将所得模冲载荷作为边界条件加载到对模架集成式粉末成形设备在压制过程的模拟仿真;并在MSC.Adams软件中分析各个模板在压制过程中力学状态,从中分析该设备在实际工况下的可靠性。研制出电液比例阀和光栅尺相结合的控制系统,实现对缸同时驱动,解决不同模板之间的动作协调的问题,所研制试验样机实现零件轴向压制精度为±0.02 mm。实际压制过程所得各模冲载荷与模拟结果相一致,从而验证粉末成形设备设计所采用的本构模型是准确的,基于数值模拟进行粉末成形设备设计的方法的正确性。     

Numerical derivation of constitutive models for unbonded flexible risers

In this paper a new constitutive model for flexible risers is proposed and a procedure for the identification of the related input parameters is developed using a multi-scale approach. The constitutive model is formulated in the framework of an Euler-Bernoulli beam model, with the addition of suitable pressure terms to the generalized stresses to account for the internal and external pressures, and therefore can be efficiently used for large-scale analyses. The developed non-linear relationship between generalized stresses and strains in the beam is based on the analogy between frictional slipping between different layers of a flexible riser and frictional slipping between micro-planes of a continuum medium in non-associative elasto-plasticity. Hence, a linear elastic relationship is used for the initial response in which no-slip occurs; an onset-slip function is introduced to define the ‘no-slip’ domain, i.e. the set of generalized stresses for which no slip occurs; a non-associative rule with linear kinematic hardening is used to model the full-slip phase. The results of several numerical simulations for a riser of small-length, obtained with a very detailed (small-scale) non-linear finite-element model, are used to identify the parameters of the constitutive law, bridging in this way the small scale of the detailed finite-element simulations with the large scale of the beam model. The effectiveness of the proposed method is validated by the satisfactory agreement between the results of various detailed finite-element simulations for a short riser, subject to internal and external uniform pressure and uniform cyclic bending loading, with those given by the proposed constitutive law.     

Microscopic approach of powder compaction using finite element method

An approach for simulating microscopic densification behaviour of powder particles in compaction using a finite element method is proposed. In this method, the contacts between powder particles during the compaction are detected, and plastic deformation of the particles is calculated by the finite element method for a porous metal. The finite element mesh is generated by connecting the centres of the particles in contact. It is assumed that the finite elements are porous metals having an average relative density calculated from the volumes of the powder and pore inside the element. The elements are classified into the triangular and quadrilateral ones used in the conventional finite element methods and a linear one for the simple compression. The accuracy of the stiffness for plastic deformation of the particles is improved by applying the finite element method. The calculated plastic deformation of powder particles in plane-strain compaction is compared with that for a model experiment using aluminium rods.     

The compaction of powder metallurgy bars using high voltage electrical discharges

A new compaction process for the production of high density powder metallurgy (P/M) bars is suggested using a high voltage electrical discharge followed by rotary swaging. This paper gives practical details concerning the production of P/M bars from iron powder by electrical discharge, and endeavours to describe the mechanism of density increase. Experimental results for determining the effect of various parameters are presented.     

Biomechanical behaviour of heel pad tissue: experimental testing, constitutive formulation, and numerical modelling

This paper deals with the constitutive formulation of heel pad tissue and presents a procedure for identifying constitutive parameters using experimental data, with the aim of developing a computational approach for investigating the actual biomechanical response. The preliminary definition of constitutive parameters was developed using a visco-hyperelastic formulation, considering experimental data from in vitro compression tests on specimens of fat pad tissue and data from in vivo tests to identify the actual trend of tissue stiffness. The discrepancy between model results and experimental data was evaluated on the basis of a specific cost function, adopting a stochastic/deterministic procedure. The parameter evaluation was upgraded by considering experimental tests performed on the fat pad tissues of a cadaveric foot using in situ indentation tests at 0.01 and 350 mm/s strain rates. The constitutive formulation was implemented in a numerical model. The comparison of data from in situ tests and numerical results led to an optimal domain of parameters based on an admissible discrepancy criterion. Numerical results evaluated for different sets of parameters inside the domain are reported and compared with experimental data for a reliability evaluation of the proposed procedure.     

Identification of material parameters in constitutive model for sheet metals from cyclic bending tests

This paper deals with the identification of material parameters in a constitutive model for sheet metals using the bending moment versus curvature diagrams obtained by cyclic bending tests. The model can describe the cyclic strain hardening by the isotropic hardening and the Bauschinger effect by the kinematic hardening. An optimization technique based on the iterative multipoint approximation concept was used for the identification of the material parameters. This paper describes the experimentation, the fundamentals and the technique of the identification problem, and the verification of this approach.     

Prediction of history-dependent forming limits by applying different hardening models

The loading history-dependent forming limits have been computed for sheet metals undergoing various combinations of plane-stress loading conditions. The analysis method is essentially an extension of Marciniak and Kucźynski's inhomogeneous model, except that the roles of isotropic and Prager-Ziegler kinematic hardening have been examined in detail while the flow theory of plasticity is applied. A suitable modification of the constitutive equations for the kinematic hardening model converts the rate form of the constitutive equations into the finite-increment form which satisfies the yield criterion precisely. Representative combinations of strain history consisted of an initial proportional straining to either a fixed strain state or different levels of strain state followed by continued loading under different conditions of strain ratios. Comparison of computed forming limits with available experimental data shows that the ultimate choice of either an isotropic or a kinematic hardening model is dependent on a specific combination of strain history and the material properties.