Kozo Osakada

Finite element method for rigid-plastic analysis of metal forming—Formulation for finite deformation

Abstract For the finite element analysis of metal forming processes, a method based on the equilibrium of nodal forces is proposed by assuming the deforming metal to be a slightly compressible rigid-plastic material. As an extension of the method, a formulation for finite deformation is derived on the basis of the equilibrium of nodal forces at the end of incremental deformation. The effects of work-hardening and shape change of element during incremental deformation are incorporated. This formulation is more accurate than that of the simple extension of infinitesimal deformation when dealing with non-steady problems, and is particularly effective for the processes in which the mode of deformation is sensitively changed by the distribution of flow stress and variation of shape. The effectiveness of the method is demonstrated by the examples of a tension test on an axi-symmetric specimen and of the plane-strain compression of blocks.

Simulation of plane-strain rolling by the rigid-plastic finite element method

Abstract The rigid-plastic finite element method for a slightly compressible material is applied to steady and non-steady state strip rolling. Solutions for some technical problems using a finite element analysis for rolling process are given. Stress and strain distributions in steady state plane-strain strip rolling under the condition of a constant coefficient of friction are calculated for work-hardening and non-hardening materials. The calculated distribution of roll pressure exhibits a peak at the entry which does not appear in the analysis by the slab method. Non-steady state deformation of the front and tail ends is also analysed. The calculated end shapes are in good agreement with the experimental ones for aluminium strip.

Simulation of three-dimensional deformation in rolling by the finite-element method

Abstract A method for simulating three-dimensional deformation in plate rolling and edge rolling is established on the basis of the rigid-plastic finite-element method. For the simulation with small number of elements, simplified elements which represent three-dimensional deformation in rolling with grooveless rolls are developed. Solutions for some problems associated with simulation of steady-state rolling of work-hardening plates are given. The three-dimensional behaviour of deforming plate in single-pass plate rolling and multi-pass edge rolling is simulated by assuming a constant coefficient of friction between the rolls and the plate. The computed shapes of the plates and loads are found to be in good agreement with the experimental ones carried out with aluminium plates.

A study on radial flow field for extrusion through conical dies

Abstract A generalized expression for the radial flow field for extrusion through a conical die is suggested. The upper bound to the extrusion pressure for a rigid-perfectly plastic material is obtained. Other energy methods which include solutions for work-hardening and composite billets are also obtained for the generalized radial flow field. The results are used to analyse the hydrostatic extrusion of Al, Cu and Al-Cu composite billets. The extrusion pressure and hardness distribution of the product were measured in experiments and they are compared with theoretical results.

Simulation of severe plastic deformation by finite element method with spatially fixed elements

Abstract A method for simulating large plastic deformation in metal forming processes is proposed. To avoid the difficulties arising from the distortion of elements in the rigid-plastic finite element method, the elements are defined with reference to an unchanging spatial grid rather than the workpiece, so that the elements are not changed by the deformation of material. The monitoring points embedded in the deforming material provide the information of the distortion of grid attached to the material and of distribution of flow stress. The sharp change of flow direction at the corner of tool is treated by the element with a singular point. Axi-symmetric backward extrusion of cans is simulated as an example of a process with severe deformation. The computed grid distortion, distribution of equivalent strain and working load are in good agreement with the experimental ones measured in extrusion of aluminium cans.

A Fundamental Study on Dieless Drawing

A new metal forming process termed dieless drawin. which uses no die or container has been developed. The metal bar is fixed at one end, and locally heated to a high temperature by an induction coil. It is then pulled, at the other end, with a constant velocity V1, while the induction coil is moved in the opposite, or same, direction at a constant velocity V2.

A mechanism of lubricant trapping in slow speed compression

Abstract A mechanism for the trapping of liquid lubricant in compressive metal forming is suggested. The basis of this mechanism is the interaction of elastic deformation of the tool and the hydrodynamic behaviour of the lubricant. A computer simulation of the process of slow speed compression of a cylindrical rigid-plastic billet between semi-infinite elastic tools with films of lubricant illustrates the validity of the proposed mechanism. From the result of the simulation together with dimensional analysis, the thickness of the trapped lubricant film is determined as a function of the lubricant viscosity, the elastic constant of the tool, the speed of compression and the radius of the billet.

A note on the types of slip-line field for wedge indentation determined by computer

Abstract A computer program is briefly described which calculates critical depths, loads and coefficients of friction and plots the admissible slip-line fields for the process of one-sided wedge indentation of a block of material of finite thickness at the surface indentation-penetration transition. Also some of the results of the program are described.

The flow stress of carbon steel in warm metalworking

Abstract For predicting the load in the warm metalworking of carbon steel, it is necessary to obtain the flow-stress data of the material under the specified conditions. Although quite a few experimental results of flow stress have been reported, they are not always effectively utilized. This is because (i) the combinations of the related factors are too many, and (ii) the amount of data at medium strain rate — of the order of 10/s — is not large, although metalworking is usually carried out in this strain-rate range. In this report, stress—strain curves of seven carbon steels with carbon contents of from 0.033 to 0.63% are obtained at temperatures of from 0 to 700°C using a mechanical press (strain rate of about 10/s). Two models of flow stress of carbon steel are proposed, considering strain, strain rate, initial temperature and carbon content as variables. The constants in the models are estimated by the non-linear regression method using 56 stress—strain curves obtained in the present experiments and 128 curves collected from the literature. The maximum pressure in forward extrusion is calculated using the proposed model of flow stress and the upper bound method. The calculated results show fairly good agreement with experimental results reported in the literature, except for large extrusion ratios.

Cold and warm hydrostatic extrusion of fine wire

Abstract Hydrostatic extrusion of fine copper wire of about 0.1 mm diameter was carried out at temperatures of up to 400°C to clarify and solve the problems in the industrial application of this process. It was found that because of viscous drag, the extrusion pressure increases with extrusion speed, especially when the wire is supplied from a rotating bobbin. For industrial use, lubricants of very low viscosity, such as kerosene, are needed to reduce this effect, even for a free-standing coiled billet. Because the coefficient of friction is very high in fine-wire extrusion, the extrusion pressure is high in comparison with that for rod extrusion. For small die angles, the extrusion pressure is high due to high friction, so that a comparatively large die angle is recommended. The extrusion pressure decreases gradually as the temperature rises; however, the extent of reduction in the extrusion pressure is not as great as that in the flow stress, since the coefficient of friction increases with temperature. Tungsten carbide dies give higher coefficients of friction than diamond dies, and tend to cause stick-slip motion of the billets at elevated temperatures. It is shown that boundary and extreme pressure additives are effective in decreasing the coefficient of friction at both room temperature and elevated temperatures.