Limitations of the Hollomon strain-hardening equation

Conventional strength and strain-hardening parameters have been derived for idealized true-stress/true-strain curves obeying the Hollomon equation σ= K p n , 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/d p is significantly affected by n only when p <0·01; then dσ/d p 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 n σ max , nK or the 0·2% proof-stress/true-tensile-strength ratio. The magnitude of the strain hardening, given by Δσ = (σ 2 - σ 1 ), 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.