Small punch test: An approach to solve the inverse problem by deformation shape and finite element optimization

If little is known about the sample under test, ascertaining a quantitative material true stress–true strain relationship from a small punch test is not direct. Conventional inverse simulation methods have used experimental force–displacement curves that ignore the deformation shape of the punched sample. We present small punch test methodology and results that used experimental deformation shape parameters, finite element modeling, and pattern search optimization, to solve the inverse problem. The approach yielded three coefficients of a plasticity function that approximately described the true stress–true strain relationship for an annealed mild steel sample. To further highlight the importance of optical measurement and deformation shape, a finite element sensitivity analysis indicated that deformation width was just as sensitive to material properties as deformation height.