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

Peter Hähner*, Celal Soyarslan, Betül Gülçimen Çakan, Swantje Bargmann

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

32 Citations (Scopus)
183 Downloads (Pure)


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 σy is commonly associated with an elastic-plastic transition force Fe via σy = αFe/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 σy which is based on the curvature of the force–displacement curve rather than a single Fe 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.

Original languageEnglish
Article number107974
JournalMaterials & Design
Publication statusPublished - 15 Nov 2019
Externally publishedYes


  • Finite element method
  • Power law hardening
  • Small Punch test
  • Yield stress determination


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