Tensile Response of Materials 国上清充通大学 SANCEAI JUO TO阳UY Problem with engineering stress and strain Consider the following sequence of deformations: Lo e1-2=1 e13=0 2 2L0 [e1-2+e2-3]=h e2-3=-h From stage1→3，no strain Decomposition into 1>2 &2>3 gives a net strain of 2. Institute of Forming Technology Equipment 16
Tensile Response of Materials Institute of Forming Technology & Equipment Problem with engineering stress and strain 16 Consider the following sequence of deformations: L0 2L0 L0 e1→2 = 1 e2→3 = ½ e1→3 = 0 1 2 3 [e1→2 + e2→3] = ½ From stage 1 → 3 , no strain Decomposition into 1 → 2 & 2 → 3 gives a net strain of ½
Tensile Response of Materials 上清充通大学 SANCEAI JUO TO阳UY True stress and strain ▣ The definitions of true stress and true strain P A J L Lo A;>instantaneous area Same sequence of deformations considered before: 1 Lo 81-2=Ln(2) 81-3=0 2 2L0 [81-2+82-3]=0 e2-3=-Ln(2) True strains are additive,engineering strains are not. Institute of Forming Technology Equipment 17
Tensile Response of Materials Institute of Forming Technology & Equipment True stress and strain 17 Ai P 0 ln 0 L L L dL L L The definitions of true stress and true strain Ai → instantaneous area Same sequence of deformations considered before: L0 2L0 L0 1→2 = Ln(2) 2→3 = Ln(2) 1→3 = 0 1 2 3 [ 1→2 + 2→3] = 0 True strains are additive, engineering strains are not