A steel ship deck plate is 30 mm thick and 12 m wide. It is loaded with a nominal uniaxial tensile stress of 50 MPa. It is operated below its ductile-to-brittle transition temperature with KI c equal to 28.3 MPa. If a 65-mm-long central transverse crack is present,

Question

A steel ship deck plate is 30 mm thick and 12 m wide. It is loaded with a nominal uniaxial tensile stress of 50 MPa. It is operated below its ductile-to-brittle transition temperature with [latex]K_{Ic}[/latex] equal to 28.3 MPa. If a 65-mm-long central transverse crack is present, estimate the tensile stress at which catastrophic failure will occur. Compare this stress with the yield strength of 240 MPa for this steel.

Accepted Answer

For Fig. 5–25, with d = b, 2a = 65 mm and 2b = 12 m, so that d/b = 1 and a/d = 65/12([latex]10^{3}[/latex]) = 0.00542. Since a/d is so small, β = 1, so that

[latex]K_{I} = σ\sqrt {πa} = 50 \sqrt {π(32.5 × 10^{−3})} = 16.0 MPa \sqrt {m}[/latex]

From Eq. (5–38),

[latex]n =\frac {K_{Ic}}{K_{I}}[/latex] (5–38)

[latex]n =\frac {K_{Ic}}{K_{I}}=\frac {28.3}{16.0} = 1.77[/latex]

The stress at which catastrophic failure occurs is

[latex]σ_{c}=\frac {K_{Ic}}{K_{I}} σ=\frac {28.3}{16.0}(50)=88.4 MPa[/latex]

The yield strength is 240 MPa, and catastrophic failure occurs at 88.4/240 = 0.37, or at 37 percent of yield. The factor of safety in this circumstance is [latex]K_{Ic}/K_{I}[/latex] = 28.3/16 = 1.77 and not 240/50 = 4.8.

Question 5.6: A steel ship deck plate is 30 mm thick and 12 m wide. It is ...

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