Chin Liu strain rate sensitivity index–strain equation of superplasticity and influence of specimen geometry

Abstract

The influence of specimen geometry on the strain rate sensitivity index–strain (m–δ) relationship has been determined for a Zn–5Al (wt-%) eutectic alloy at a strain rate ɛ of 0·025 min⁻¹ and a temperature of 250°C. It was found that all the m–δ curves were of the type m_L=m_max>m₀ and > m_F for δ₀ < δ_L < δ_F, where m_L is the strain rate sensitivity corresponding to the ‘limit strain’ δ_L; δ₀ (=0) is the initial strain; and δ_F is the total elongation at fracture. Tests were performed for five values of specimen width/length w₀/l₀ between 0·15 and 0·39. With increase in w₀/l₀, it was observed that the m–σ curves shifted to higher positions; the values of total elongation at fracture δ_F and strain rate sensitivity index at zero strain (δ₀) m₀ and at the limit strain (δ_L) m_L increased; and the strain rate sensitivity index at fracture strain (δ_F) m_F varied little. Consistent with these findings, increasing the thickness of the specimen from 1 to 2 mm at constant w₀/l₀ caused a shift in the m–σ curve to the right and increased the value of δ_F and also the limit strain at maximum value of m. From the m–δ data obtained, a modification to the Chin Liu equation is proposed to take into account specimen geometry δ_F=(C_3,F^{(m₀′− m_L′)/(w₀/l₀)}ɛ^{m_F−1[ (m₀′(w₀/l₀)]}−1)100%, where C is the slope of the m-δ curve; (m₀′(w₀/l₀)=m₀, m₀′>m₀ and (m_L′(w₀/l₀)=m_L, m_L′>m₀ for w₀/l₀ between 0·15 and 0·39. When w₀/l₀=1(or w₀=l₀), the notch effect is eliminated and the total elongation at fracture will take its maximum value.

MST/1034