Keywords: cone-cap plasticity, isotropic hardening, powder compaction, FE model.

The knowledge of the behaviour of powder material undergoing cold compaction is necessary for predicting the final shape and the density distribution within the parts, and for preventing the failures that can occur during the subsequent sintering. Such components vary from simple bush families, which are appropriate for bearing applications, through to complex multilevel parts, which are used in automatic transmission systems. The powder compaction process transforms the loose powder into a compacted sample by increasing density. Design of a compaction process consists, essentially, of determining the sequence and relative displacements of die and punches in order to achieve this goal. The design process, which has to be done for any new type of piece to be manufactured, could be effectively improved by using a simulation tool, able to predict the mechanical response of the compact along the process.

The constitutive modelling of powder is clearly a keystone of successful quantitative solution possibilities. Without a reasonable constitutive model, which can reproduce powder behaviour under loading conditions, the computations are worthless. The process of powder compaction consists of vertical compaction of fine powders through the movement of a set of punches. The process transforms the loose powder to compacted component with the volume reduction of 80-90 percents. Thus, an efficient and reliable plasticity model will play an important role in powder compaction simulation.

The numerical simulation of the compaction process is central to an understanding of the mechanics of powder behaviour and when it is coupled with experimental inputs the simulation can be considered as an alternative tool to achieve a more economic enterprise. A successful numerical simulation needs a reliable constitutive model that allows us to predict the behaviour of the powder and a computational framework to make use of it. A number of constitutive models have been proposed for the cold compaction of powders over the past three decades, including: microscopic models, flow formulations and solid mechanics models. The geological and frictional material models are employed to capture the major features of the response of initially loose metal powders to complex deformation processing histories encountered in the manufacture of engineering components by powder metallurgy techniques. In particular a two-mechanism-model, such as Drucker-Prager or Mohr-Coulomb and elliptical cap models, which are widely used for geological materials and exhibit pressure dependent behaviour can be useful for modelling the response of powder materials. These double-surface plasticity models consist of two yield surfaces; a distortion surface and a consolidation or cap surface, which has an elliptical shape. The distortion surface controls the ultimate shear strength of material and the cap surface captures the hardening behaviour of material under compression. Such models, which are belonging to Cone-Cap plasticity model family, were widely used with success in cold powder forming process simulations [1,2,3]

In the analysis of powder forming problems, the non-linear behaviour of powder is adequately described by double-surface plasticity model. However, it suffers from a serious deficiency when the stress-point reaches in the intersection of these two different yield functions. In the flow theory of plasticity, the transition from an elastic state to an elasto-plastic state appears more or less abruptly. For powder material it is very difficult to define the location of yield surface and special treatment should be made to avoid numerical difficulties in the intersection of these two surfaces.

In the present paper, to solve the mentioned difficulty, a general and simple single yield surface Cone-Cap plasticity is presented for description of powder behaviour. Since the most important characteristic in powder forming problems is the powder relative density, this parameter is taken as the hardening parameter so that the model is particularly developed based on the nonlinear functions of powder relative density. The constitutive elasto-plastic matrix and its components are extracted in full detail. The 2D and 3D shapes of proposed yield surface are illustrated in meridian plane and principal stress space respectively. The procedure for determination of powder parameters is described and the model parameters are derived for Iron powder based on some laboratory triaxial test data. And finally the applicability of the model is demonstrated in some numerical examples.

1

Lewis RW, Khoei AR., "A plasticity model for metal powder forming processes", Int. J. Plasticity, 17, 1659-1692, 2001. doi:10.1016/S0749-6419(00)00096-6

2

Khoei AR, Bakhshiani A. and Mofid M., "An endochronic plasticity model for finite strain deformation of powder forming processes", Finite Elem. Anal. Des., 40, 187-211, 2003. doi:10.1016/S0168-874X(02)00223-8

3

Gu C., Kim M. and Anand L., "Constitutive equations for metal powders: application to powder forming processes", Int. J. Plas., 17: 147-209, 2001. doi:10.1016/S0749-6419(00)00029-2

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