Limitations of the Hollomon strain-hardening equation

Abstract

Conventional strength and strain-hardening parameters have been derived for idealized true-stress/true-strain curves obeying the Hollomon equation σ=Kϵpn, where K and n have values typical of real metals. All stress parameters are proportional to the constant K. The true tensile strength is almost independent of n, but the stress at 0·2% plastic strain is strongly dependent on n. The strain-hardening rate dσ/dϵp is significantly affected by n only when ϵp<0·01; then dσ/dϵp increases with increasing n when n<0·2 and decreases with increasing n when n>0·2. The strain-hardening rate is not easily related to the parameters nσmax, nK or the 0·2% proof-stress/true-tensile-strength ratio. The magnitude of the strain hardening, given by Δσ = (σϵ2 - σϵ1), also has a maximum between n=0·1 and 0·3. With these results, assumptions and conclusions in the published literature are discussed and some are shown to be incorrect. It is concluded that for maximum strength and strain hardening in materials obeying the Hollomon equation, large values of K and n values between 0·1 and 0·3 are required.

07.29: A unified methodology for the modelling of steel behaviour: An application‐oriented methodology

“…Goggins [5] found that this feature significantly affects the initial yield strength of specimens, but did not significantly affect the post-yielding behaviour. The two parameters ( K and n ) of the Hollomon model [3] found from tests of the 40x40x2.5SHS specimens in this study are almost similar to those given in the literature to describe steel behaviour (for example, [15,16]). However, these parameters are found to be significantly smaller for the other specimens (50x25x2.5, 20x20x2.0), as they had displayed significantly less hardening behaviour in the physical tests.…”

Description of full-range strain hardening behavior of steels

“…The deficiency of this formula is that it cannot characterize many materials in the full range exhibiting various distinct strain hardening stages, which have been observed in various types of steels (Quach et al 2008 ; Rasmussen 2003 ; Abdella 2006 ; Bowen and Partridge 2002 ; Gardner and Nethercot 2004a , b ) and other metals (Monteiro and Reed-Hill 1973 ; Markandeya et al 2006 ). Therefore, many other types of formulas have been proposed (Ludwigson 1971 ; Voce 1948 ; Chinh et al 2004 ).…”

Work hardening in selective laser melted Al‐12Si alloy

“…The work hardening exponent (n-the power index in the Hollomon equation) for both the SLM and cast samples were calculated from Figure 2B and 2D. 15 It has been observed that the work hardening exponent (n) for the SLM sample is 0.26, and for the cast sample is approximately 0.32. In general, the values of n lies between 0.2 and 0.5 for most of the metals.…”