Project ForgeMatch the following criteria of material failure, under biaxial stresses σ1 and σ2 and yield stress σy, with their corresponding graphic representations in σ1-σ2 space: P: Maximum-normal-stress criterion, Q: Maximum-distortion-energy criterion, R: Maximum-shear-stress criterion. L: a hexagonal (cut-corner) envelope, M: a square envelope bounded independently at ±σy on each axis, N: an ellipse.
- AP-M, Q-L, R-N
- BP-N, Q-M, R-L
- P-M, Q-N, R-L
- DP-N, Q-L, R-M
Explanation
Maximum-normal-stress theory bounds |σ1| and |σ2| independently, giving a SQUARE envelope (P-M). Maximum-shear-stress (Tresca) theory gives a HEXAGONAL envelope in 2D principal-stress space (R-L). Maximum-distortion-energy (von Mises) theory gives an ELLIPTICAL envelope (Q-N).
Source: GATE ME 2011 (2011)
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