Simulation of bulk metal forming processes using one-step finite element approach based on deformation theory of plasticity

The bulk metal forming processes were simulated by using a one-step finite element(FE)approach based on deformation theory of plasticity,which enables rapid prediction of final workpiece configurations and stress/strain distributions.This approach was implemented to minimize the approximated plastic potential energy derived from the total plastic work and the equivalent external work in static equilibrium,for incompressibly rigid-plastic materials,by FE calculation based on the extremum work principle.The one-step forward simulations of compression and rolling processes were presented as examples,and the results were compared with those obtained by classical incremental FE simulation to verify the feasibility and validity of the proposed method.

ANALYSIS OF ROLLING BY ELASTO-PLASTIC FINITE DEFORMATION CONTACT BOUNDARY ELEMENT METHOD

A multinonlinear boundary element method is established dealing with elasto plastic finite deformation contact problem, and it is employed to analysis rolling process. With rollers as elastic bodies, workpieces as elastio plastic bodies, rolling problem can be viewed as a frictional elasto plastic contact problem. With fewer assumptions in the simulation of the rolling process, a novel and accurate method is proposed for analysis of rolling problems.

On Numerical Modelling of Industrial Powder Compaction Processes for Large Deformation of Endochronic Plasticity at Finite Strains

Compaction processes are one the most important par ts of powder forming technology. The main applications are focused on pieces for a utomotive, aeronautic, electric and electronic industries. The main goals of the compaction processes are to obtain a compact with the geometrical requirements, without cracks, and with a uniform distribution of density. Design of such proc esses consist, essentially, in determine the sequence and relative displacements of die and punches in order to achieve such goals. A.B. Khoei presented a gener al framework for the finite element simulation of powder forming processes based on the following aspects; a large displacement formulation, centred on a total and updated Lagrangian formulation; an adaptive finite element strategy based on error estimates and automatic remeshing techniques; a cap model based on a hard ening rule in modelling of the highly non-linear behaviour of material; and the use of an efficient contact algorithm in the context of an interface element fo rmulation. In these references, the non-linear behaviour of powder was adequately desc ribed by the cap plasticity model. However, it suffers from a serious deficiency when the stress-point reaches a yield surface. In the flow theory of plasticit y, 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 locati on of yield surface, because there is no distinct transition from elastic to ela stic-plastic behaviour. Results of experimental test on some hard met al powder show that the plastic effects were begun immediately upon loading. In such mater ials the domain of the yield surface would collapse to a point, so making the di rection of plastic increment indeterminate, because all directions are normal to a point. Thus, the classical plasticity theory cannot deal with such materials and an advanced constitutive theory is necessary. In the present paper, the constitutive equations of powder materials will be discussed via an endochronic theory of plasticity. This theory provides a unifi ed point of view to describe the elastic-plastic behaviour of material since it places no requirement for a yield surface and a ’loading function’ to disting uish between loading an unloading. Endochronic theory of plasticity has been app lied to a number of metallic materials, concrete and sand, but to the knowledge of authors, no numerical scheme of the model has been applied to powder material . In the present paper, a new approach is developed based on an endochronic rate independent, density-dependent plasticity model for describing the isothermal deformation behavior of metal powder at low homologous temperature. Although the concept of yield surface has not been explicitly assumed in endochronic theory, it is shown that the cone-cap plasticity yield surface (Fig.1), which is the m ost commonly used plasticity models for describing the behavior of powder materi al can be easily derived as a special case of the proposed endochronic theory. Fig.1 Trace of cone-cap yield function on the meridian pl ane for different relative density As large deformation is observed in powder compaction process, a hypoelastic-pl astic formulation is developed in the context of finite deformation plasticity. Constitutive equations are stated in unrotated frame of reference that greatly s implifies endochronic constitutive relation in finite plasticity. Constitutive e quations of the endochronic theory and their numerical integration are establish ed and procedures for determining material parameters of the model are demonstra ted. Finally, the numerical schemes are examined for efficiency in the model ling of a tip shaped component, as shown in Fig.2. Fig.2 A shaped tip component. a) Geometry, boundary conditio n and finite element mesh; b) density distribution at final stage of

Numerical Analysis of Finite Deformation of Overbroken Rock Mass in Gob Area Based on Euler Model of Control Volume

The overbroken rock mass of gob areas is made up of broken and accumulated rock blocks compressed to some extent by the overlying strata. The beating pressure of the gob can directly affect the safety of mining fields, formarion of road retained along the next goaf and seepage of water and methane through the gob. In this paper, the software RFPA＇2000 is used to construct numerical models. Especially the Euler method of control volume is proposed to solve the simulation difficulty arising from plastically finite deformations. The results show that three characteristic regions occurred in the gob area： （1） a naturally accumulated region, 0-10 m away from unbroken surrounding rock walls, where the beating pressure is nearly zero; （2） an overcompacted region, 10-20 m away from unbroken walls, where the beating pressure results in the maximum value of the gob area; （3） a stable compaction region, more than 20 m away from unbroken walls and occupying absolutely most of the gob area, where the beating pressures show basically no differences. Such a characteristic can exolain the easy-seeoaged “O”-ring phenomena around mining fields very well.

A Modified Symmetric and Antisymmetric Decomposition-Based Three-Dimensional Numerical Manifold Method for Finite Elastic-Plastic Deformations

There are relatively few studies on large rotation or deformation by means of the three-dimensional(3D)numerical manifold method(NMM).A new modified symmetric and antisymmetric decomposition(MSAD)theory is developed and implemented into the 3D NMM,eliminating the false-volume expansion and false-rotation strain/stress problems.The Jaumann rate is used to measure the material rotation,and the geometric stiffness built on the Jaumann rate is deduced.The incremental formulas of the MSAD-based 3D NMM and a practical guide on the implementation of the MSAD theory are given in detail and exemplified.The new theory and formulas can be applied to analyze both large rotation and large deformation problems.Based on the hypoelasto-plasticity theory and the unified strength theory,the unified yield criterion with associated flow rule is implemented into the MSAD-based 3D NMM.Several typical examples are studied,showing the advantage and potential of the new MSAD theory and the MSAD-based 3D NMM.