Determining tensile yield stresses from Small Punch tests: A numerical-based scheme

The Small Punch (SP) test serves the screening of mechanical material properties and their degradation in a virtually non-invasive way. It requires robust frameworks for the derivation of mechanical properties and microstructure–mechanical property correlation. The tensile yield stress σ_y is commonly associated with an elastic-plastic transition force F_e via σ_y = αF_e/h² with h denoting the SP disc thickness and a dimensionless coefficient α considered constant. Here it is shown that α cannot be taken as a constant. Instead a new self-consistent data reduction scheme is proposed for the determination of σ_y which is based on the curvature of the force–displacement curve rather than a single F_e force level. The scheme derives from finite element simulations of a wide range of strength coefficients C and hardening exponents n of power law flow σ = Cϵⁿ. To a good approximation the scheme depends only on the hardening exponent n, which depends on the curvature, whereas C and the elastic modulus barely matter. The method is validated by comparing the yield stress predictions with the actually implemented yield stresses in the simulations, using various types of hardening rules, as well as experimental data. The uncertainty of yield stress determination by SP tests is thereby largely reduced as compared to the traditional scheme.