27.2 STRESS STRAIN CURVES
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While necking, the cross section at one point decreases, thus increasing the stress. In turn this continues rapidly until fracture.
The strain hardening of some materials occurs as they are stretched, the Young's modulus value increases.
Each material will have it's own stress-strain curve and these are determined experimentally, and found in abundance in handbooks.
If a material is brittle, it does not deform much and simply breaks. Or simply the ultimate and rupture strengths are the same.
Ductile materials deform quite a bit before the ultimate stress, necking typically occurs before rupture.
Creep is an effect that can lead to permanently elongated specimens,