The elastic stress field in the vicinity of a 2-D

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, σ 3 = v (σ 1 + σ 2 ), where v is Poisson’s ratio and σ 1 , σ 2 and σ 3 are principal stresses.


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