Prediction Of Distribution Of Microstructural Parameters In Metallic Materials Described By Differential Equations With Recrystallization Term

Continuous development of the transport industry is associated with the search for new construction materials that combine high strength with good plastic properties. Intensive research during the last few decades has shown that there is still a huge potential for improvement of properties of various metallic materials. New grades called advanced high strength steels (AHSS) with multiphase structures have been developed and widely used mainly in the automotive industry. These microstructures are characterized by large gradients of properties, which cause poor local formability. It is expected that materials with a more heterogeneous microstructure will have superior formability. More detailed models of the microstructure evolution are needed to answer this question. A hypothesis was made that application of the models based on internal variables allows for predictions of gradients of final product properties. The objectives of the present paper were two-fold. The first was to investigate the possibility of the analytical and numerical solutions of the evolution equation for the internal variable and evaluation of these solutions. We propose two numerical methods which give us an accurate approximation of the solution with relatively low computational cost at the same time. Implementation of the developed solutions in the finite element (FE) code and performing multiscale simulation of the evolution of internal variables during thermomechanical processing was the second objective of this paper. This solution supplied information about the distribution of the dislocation density in the volume of the material. Case studies for selected metal forming processes recapitulate the paper.