Wu Shichun

FEM simulation of the deformation field during the laser forming of sheet metal

Abstract A laser beam can be used as a flexible sheet metal forming tool. Its mechanism is the forming caused by thermal stresses resulting from the irradiation of laser beam scanning. Because of the complexity of this process, numerical simulation becomes necessary for its analysis. In this paper, the deformation field during the laser bending of sheet metal is studied using the 3D thermoelastoplastic finite element method. Considering the coexistence of the temperature and stress arising and dropping during the laser forming, a handling technique for the transitional zone between the elastic zone and plastic zone is adopted. In order to increase the accuracy of calculation, the reduced integration method is applied in the calculation. The results show that: (i) the laser bending process may be divided into two stages: in the first stage, a small counter-bending away from the laser source appears, and in the second stage, a bending angle facing the laser source is just formed finally; (ii) the counter-bending angle away from the laser source in a narrow sheet is greater than that in a wide sheet, i.e. the wider the sheet, the smaller the counter-bending angle; (iii) in the zone being passed through by the laser beam and its neighbouring zone, the stresses change severely with time and place. The form of the displacement field and its change obtained from the FEM simulation calculation is identical with the observed results from experiments, and the calculated bending-angle also agrees well with the experimental data.

An experimental study of laser bending for sheet metals

Abstract In this paper, changes in the bending angle with process parameters have been studied for the laser bending of sheet metals. These parameters may be divided into three kinds: laser energy parameters; material parameters; and sheet geometric parameters. The laser energy parameters include laser power, path feed-rate, beam spot diameter and feed number. The tests show that the bending angle is, generally, in direct proportion to the laser power and feed number, and in inverse proportion to the path feed-rate and beam spot diameter. The material parameters mainly relate to a thermal-effect index, which can be shown as R = α th / ρc p , i.e. the coefficient of thermal expansion divided by the factor of the density multiplied by the specific heat. The bending angle increases with increase in the index R . There is no significant influence of the strength at room temperature on the bending angle. Among the sheet geometric parameters only, there is greater influence of the sheet thickness on the bending angle, which decreases sharply with increase in the sheet thickness.

Acquiring the constitutive relationship for a thermal viscoplastic material using an artificial neural network

Abstract In conventional constitutive theories, a kind of mathematical model is formulated to represent the plastic behavior of a material. Once the model is set, the behavior of the material can only be expressed approximately by adjusting the parameters in the model. Under conditions of high strain rate and high temperature, to secure more accurate results the model has to be more complicated in mathematical formulation, but then problems related to material parameter identification, numerical stability, etc., arise. An artificial neural network may simulate a biological nervous system and is referred to as parallel distributed processing. It cannot only make decisions based on incomplete and disorderly information, but can also generalize rules from those cases on which it was trained and apply these rules to new stimuli. In back-propagation neural networks, the information contained in the input is recoded into an internal representation by hidden units that perform the mapping from input to output. It has been proven mathematically that a three-layer network can map any function to any required accuracy. A neural network can directly map the behavior for a thermal viscoplastic material. Using a neural network, it is not necessary to postulate a mathematical model and identify its parameters. In this paper, a four-layer back-propagation neural network is built to acquire the constitutive relationship of 12Cr2Ni4A. Temperature, effective strain, and effective strain rate are used as the input vectors of the neural network, the output of the neural network being the flow stress. After the network has been trained with experimental data, it can correctly reproduce the flow stress in the sampled data. Furthermore, when the network is presented with non-sampled data, it also can predict well. The results acquired from the neural network are very encouraging.

Preform design in axisymmetric forging by a new FEM-UBET method

This paper presents a preform design method which combines the FEM-based forward simulation and the UBET-based reverse simulation techniques. The procedure is introduced briefly. The billet designed using the new technique may achieve a final forging with minimum flash. A gear blank forging is used as an example to demonstrate the preform design. The successful application of the method is shown.

A kinetic equation for damage during superplastic deformation

In this paper a kinetic equation for the isotropic damage during superplastic deformation is proposed, based on the thermodynamic theory of irreversible processes with internal state variables and the normality criterion. The damage variable D during superplastic deformation is non-linear with the equivalent plastic strain ξP, and it is shown that D is affected strongly by the triaxiality stress ratio (σm/σeq). Furthermore, in order to demonstrate the efficiency to the proposed equation, superplastic deformation experiments were performed on aluminum alloy LY12CZ and brass H62 without any pre-treatment. The comparision with the experimental results is presented on the influence of the triaxiality stress ratio on the equivalent strain to rupture: good correlation is found between the theoretical and experimental results. Therefore, this equation for damage may reflect successfully superplastic damage behaviour during superplastic deformation processes.

A kinetic equation for ductile damage at large plastic strain

Abstract In accordance with the viewpoint of continuous damage mechanics, a kinetic equation for the isotropic ductile plastic damage variable, based on the feature of void-type plastic damage and on thermodynamics, is derived. The damage variable is linear with equivalent strain and it is shown that it is affected remarkably by the triaxiality stress ratio. The kinetic equation of the damage variable in this paper may reflect not only the influence of a positive triaxiality ratio but also the influence of a negative triaxiality ratio. A comparison with the results of some experiments is presented on the influence of the triaxiality stress ratio on the strain to rupture: good correlation is found between the theoretical and experimental results.

Measurements of the changes in microstructure during superplastic deformation

Abstract In this paper, changes in the volume fraction of cavities, in the fractal dimension of cavities, in the grain size and aspect ratio (the ratio of the major axis to the minor axis) of grains and in the dislocation density during superplastic deformation have been measured quantitatively. The experimental results show that the volume fraction of the cavities, the fractal dimension of the cavities and the dislocation density increase with increase in the degree of deformation. At the early stage of deformation, the increase in the volume fraction of the cavities varies slightly with the increase in strain, but beyond a particular strain, the volume fraction of the cavities increases sharply. The stress state has a considerable influence on the growth rate of the volume fraction of the cavities: at the same strain, the volume fraction of the cavities under the plane equi-tensile stress state is greater than that under uniaxial tension. However, the volume fraction of the cavities at fracture under the plane equi-tensile stress state is smaller than that under the uniaxial tensile-stress state. The grain size after superplastic deformation increases generally, but grain fining after superplastic deformation is also discovered sometimes, due depending upon the type or commercial state of the metal: of course, it is related to the stress state in addition. The aspect ratio of the grains tends to the increase with the increase of strain, but it increases only slowly.

Coupled thermo-mechanical analysis of the high-speed hot-forging process

Abstract In hot forging, the effect of temperature on the process is great. The temperature variation has a strong effect on both the die and the workpiece: in the high-speed hot-forging process in particular there exists a significant increase in the billet temperature, which can induce microstructural modifications that alter the flow resistance of the material and other mechanical properties, as well as affecting shortcomings. In this paper, a numerical simulation technique has been employed to study the thermal behavior of the high-speed forging of an AISI1045 disk. Useful information on the temperature distribution in the entire die—workpiece domain can be provided. The influences of the forming speed and the die temperature are also investigated. It is found that die-chilling and some forging parameters have a key effect on the forging process and even on the final product shape. Through the optimization of the forging parameters, an optimum forming processing can be selected before the component is put into production.

Warm forging of stainless steels

Abstract The warm forging of stainless steels 1 Cr18Ni9Ti, Cr17Ni2, 2Cr13, 4Cr13 and Cr1 2Mn5Ni4Mo3Al has been studied. There are two problems to be overcome in the warm forging of stainless steels: the high resistance of these metals to deformation, and the pronounced tendency for metallic particles to adhere to the tools. The key factors leading to success are: the selection of the proper preheat temperature, the choice of the correct lubricant, and the determination of the best lubricating process. In this paper, suitable warm forging temperatures are established for the steels under examination, and, by determination of the coefficient of friction of different lubricants and examination of their effectiveness in practice, a preferred lubricant and lubricating process are recommended.

Numerical computation of cavity damage and failure during the superplastic deformation of sheet metals

Abstract Superplastic deformation is considered as a thermo-viscoplastic flow. The deformation and failure of superplastic sheet metals are a result of a combination and interaction process between tensile instability and internal cavity evolution, which are controlled by the rheological parameters (i.e., the strain-rate sensitivity index m, the strain-hardening exponent n, and the visco-plastic anisotropy parameter) and the cavity growth rate of the materials. Based on Gursons constitutive relationship for porous ductile materials, with some modifications, and Hills normal anisotropic (plane isotropy) yield criterion being quadratic in the stress components, a thermo-viscoplastic anisotropic damage-instability model is proposed. It includes strain hardening, strain-rate hardening, the anisotropy parameter and the internal cavity volume fraction. The superplastic sheet metals are modelled using this thermo-viscoplastic damage-instability constitutive relationship that accounts for strength degradationresulting from the growth of cavities. The current stress components and their ratio ( α = σ 2 σ 1 ), the stress triaxiality ratio ( σ m σ ), and the cavity volume fraction (f) during superplastic deformation of sheet metals for any strain path between uniaxial tension and biaxial equitension, are studied numerically. Finally, taking the occurence of localized instability ( d e 2 = 0 ) or the cavity volume fraction reaching the critical value (fc) as a fracture criterion, the limit strain and the maximum uniform strain are predicted. The rheological parameters (m, n, r), the initial cavity volume fraction and other material constants used in the calculations are determined experimently. Comparisons of the calculations with experimental results indicate that the thermo-viscoplastic damage-instability model can provide good estimations of the cavity volume fraction, the strength reduction induced by cavity growth, the deformation and instability behaviour, and the limit strain under various strain histories.