Paul C. Okonkwo

Deformation and frictional heating in relation to wear in sheet metal stamping

Various analytical rules of mixture are commonly used to take into account heterogeneous features of a material and to derive global properties. But, with such models, one may not be able to fulfil the requirements for separating appropriately the different lengthscales. This might be the case for some issues such as strain localisation, surface effect, or topological distributions. At an intermediate lengthscale, which we refer to as the mesoscopic scale, one can still apply continuum mechanics. So why not perform calculations using the finite element method on volumes of material to obtain the response of Representative Elementary Volumes (R.E.V.). The construction of digital microstructures for such calculations is performed in two steps. First, a series of R.E.V.s with statistics of features of real materials should be defined. Then, finite element meshes should be produced for these R.E.V.s and updated when calculations involve large strains. Powerful automatic three-dimensional mesh generators and remeshing techniques prove necessary for this latter task. This strategy is applied to create digital R.E.V.s which match statistical features of forgings. Measurements provide micromechanical parameters of each subvolume. As an example of calculations, numerical simulations provide the anisotropic fatigue properties of forgings.