Volume 20, Issue 1 (January 1992)
Finite Element Method (FEM) Analysis of Elastic-Linear-Hardening Materials and Comparison with Measurements on Commercial Materials
The Brinell hardness HB (kgf/mm2) of elastic-linear-hardening materials with various yield stresses σY (MPa) and hardening moduli H (MPa) is analyzed by a finite element method (FEM). The well known empirical formula for the ratio of tensile strength σB to HB, σB/HB ⋟ 3.5, does not hold for materals having a large relative strain hardening modulus H/σY, where H is defined by dσ/dε in the σ-ε curve. It is shown that the dimensionless stress-strain curves (σ/σY vs. ε) of elastic-linear-hardening materials and those of various commercial materials give the crucial measurement in determining the value of σB/HB. The ratio of σB/HB remains in the range of 3.2 to 3.8 if the relative strain hardening modulus H/σY at large strains is less than ∼2.5. Correlations between the stress-strain curve and indentation shape, plastic zone size, and residual stresses are also investigated.