Towards Measurement And Simulation Of Elasto-Plastic Deformation

Abstract

The stretch forming process is frequently used in the automotive industry (outer pan- els, inner panels, stiffeners etc.), the packaging industry and household appliances sector, to manufacture complicated shapes and curvatures. However it requires accurate prediction of tool geometries and manufacturing parameters to avoid the currently used trial and error approach. Metal forming is also associated with cer- tain defects like local thinning, wrinkling, tearing etc. Avoiding such defects and prediction of spring back presumably requires a thorough understanding of the de- formation mechanics and material behavior beyond the elastic range. In the stretch forming operation, material essentially passes through the elastic, yield point and plastic states. Elastic behavior can be explained based on classical theory of elasticity wherein linear trend of infinitesimal deformation is expressed by generalized Hooke’s law. In the plastic range, the theory is based on certain exper- imental observations of the macroscopic behavior of metals in the uniform state of combined stresses. Experimentally observed results are idealized into mathematical formulation to describe the complex behavior of metals under combined state of stress. These formulations are based on some assumptions like material behavior is time independent, strain rate effects could be neglected, hysteresis loop and Bauschinger effects which arise from the non-uniformity of the microscopic scale could be disregarded etc. The thermal effects are neglected and material is assumed to be isotropic. Supposedly because of these assumptions existing theory of plastic- ity does not accurately predict the phenomenon of stretch forming occurring during plastic deformation. Theories are being developed like that of Rao and Shrinivasa [2002], which consider stresses during deformation as resistance due to shape change, volume change, rate of shape change and rate of volume change. Such theories need variation of material parameters like bulk modulus (K), shear modulus (G), bulk viscosity (µ’) and shear viscosity (µ) as deformation progreses. Therefore uni-axial tension exper- iments have been conducted to find out the strains at the corresponding loads. Mild steel and aluminum have been chosen for the experiments. Chemical and physical properties of the materials are chosen such that they are very similar to those used in the automotive industry for stretch forming. A procedure is developed using uni-axial tension test results to calculate the material parameters for the entire range of material deformation. For mild steel, bulk modulus and shear modulus decrease and become almost zero as the material deforms from elastic to transition region. After transition zone, both moduli increase and then decrease as material deforms in the strain-hardening region. For aluminum both bulk and shear moduli decrease non-linearly as material deforms from elastic to plastic region. The behavior of bulk modulus and shear modulus are consistent with the stress-strain behavior of the materials. For mild steel as well as aluminum, the bulk and shear viscosities are positive in the elastic region and in the large deformation region the values are small compared to elastic region. We can separate the various stresses, hydrostatic, deviatoric and viscous stresses, associated with (µ) and (µ’) and contribution of each to the total stresses can be obtained. It is observed that contribution from the viscous stresses is as high as 5 % when the material is subjected to large strain rate tests. The strain rate in stretch forming operation may be different from the strain rate at which the material parameters are calculated. Knowing the material para- meters at one strain rate, the stress-strain curves at different strain rates can be predicted. The repeatability of computation of the material parameters and contributions from the viscous and non-viscous stresses for large deformation has been ascertained by using different test samples. The material parameters obtained from one set of samples have been applied to different samples and experimental versus predicted stresses have been found to match fairly well. A lot more work needs to be done to reach the goal of accurately predicting the behavior during stretch forming. Test data on different materials need to be generated and the new theories need to be validated for compression as well as loading and unloading cases.