The elastic stress field in the vicinity of a 2-D crack front is given by

Derive the elastic-plastic boundary shape by using the following conditions

(1) Tresca Yield Criterion with v = 0.3 and plane strain.

(2) Von Mises Yield Criterion with v = 0.3 and plane strain.

Plot the results in non-dimensional coordinates x ₁ , x ₂ divided by

Hint: under plane strain condition, ? ₃ = v (? ₁ + ? ₂ ), where v is Poisson?s ratio and ? ₁ , ? ₂ and ? ₃ are principal stresses.

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012 22, K₁ √2лr COS where K₁ =σ√√лa. 1-sin sin cos 1+sin sin 30 30 30 2 a 11110 X24 L 2-D crack r₂ = (K₁/0₂)/n. P 012 22, K₁ √2лr COS where K₁ =σ√√лa. 1-sin sin cos 1+sin sin 30 30 30 2 a 11110 X24 L 2-D crack r₂ = (K₁/0₂)/n. P