Question

2.3 Consider an infinite periodic array of equally spaced cracks along the x-axis in an infinite plate subjected to equal uniform stresses $\sigma$ along the x- and y- axes at infinity (Fig. 2.14). Verify that the Westergaard function is $\sigma \sin(\frac{\pi x}{W}) Z_4 = \left[ \sin^2(\frac{\pi x}{W}) - \sin^2(\frac{\pi a}{W}) \right]^{1/2}$ Fig. 2.14 An infinite periodic array of equally spaced cracks in an infinite plate subjected to equal uniform stresses $\sigma$ at infinity Then show that the stress intensity factor is given by $K_I = \sigma (\pi a)^{1/2} \left( \frac{W}{\pi a} \tan \frac{\pi a}{W} \right)^{1/2}$

          2.3 Consider an infinite periodic array of equally spaced cracks along the x-axis
in an infinite plate subjected to equal uniform stresses $\sigma$ along the x- and y-
axes at infinity (Fig. 2.14). Verify that the Westergaard function is
$\sigma \sin(\frac{\pi x}{W})
Z_4 = \left[ \sin^2(\frac{\pi x}{W}) - \sin^2(\frac{\pi a}{W}) \right]^{1/2}$
Fig. 2.14 An infinite periodic array of equally spaced cracks in an infinite plate subjected to equal
uniform stresses $\sigma$ at infinity
Then show that the stress intensity factor is given by
$K_I = \sigma (\pi a)^{1/2} \left( \frac{W}{\pi a} \tan \frac{\pi a}{W} \right)^{1/2}$

2.3 Consider an infinite periodic array of equally spaced cracks along the x-axis
in an infinite plate subjected to equal uniform stresses σ along the x- and y-
axes at infinity (Fig. 2.14). Verify that the Westergaard function is
σsin((π x)/(W))
Z4 = [ sin^2((π x)/(W)) - sin^2((π a)/(W)) ]^1/2
Fig. 2.14 An infinite periodic array of equally spaced cracks in an infinite plate subjected to equal
uniform stresses σ at infinity
Then show that the stress intensity factor is given by
KI = σ (π a)^1/2( (W)/(π a)tan(π a)/(W))^1/2

Added by Josep R.

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