A New Inverse Explicit Flow Curve Determination Method for Compression Tests

Abstract

Flow curves characterize plastic flow in materials and their accurate description is necessary to reproduce any forming process in simulations. For flow curve determination, laboratory uniaxial compression or tensile tests are conducted to record force-displacement during deformation. Flow stress is then calculated as the ratio of force to cross-sectional area. However, this assumption is invalid when the stress state during testing changes to non-uniaxial stress states, e.g. necking in tensile or bulging in compression tests. Alternatively, inverse methods deploy simulation models replicating experiments along with flow curves represented as an analytical equation. The parameters in this equation are then optimized by minimizing the error in simulation and experiments. An a priori guess of the analytical equation is difficult especially when the material behavior is complex e.g. Lüder or DRX flow curves, though. In this paper, a piecewise inverse method without using an analytical equation is therefore introduced and validated with flow curves for aluminum and copper under compression tests. The method determines flow curves points as tabular data at different displacement steps and hence it is easier to represent complex flow curves. Two different methods, a heuristic and an iterative one, are discussed. To minimize the error between simulated and experimental forces, the heuristic method uses an adaptive equation estimating flow stress using predetermined points and experimental force, whereas in the iterative approach the flow curve is adjusted iteratively to minimize the error. The results show that the heuristic method has a limited applicability e.g. for low friction tests, whereas the iterative method can estimate flow curves for generalized deformation conditions. Overall, the flow curves determined with the new method yield an error of less than 2% in the force estimation with simulated compression tests. The presented method hence determines accurate flow curves for forming simulations under multiaxial stress states without the necessity of analytical equations.