A steel pressure-vessel plate carries a remote tensile stress and contains a central…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Bending, Ringing, Breaking and Flowing, Ch Fracture: stress concentration, cracks and toughness

Problem

A steel pressure-vessel plate carries a remote tensile stress

\sigma = 150\,\mathrm{MPa}

and contains a central through crack of full length

8\,\mathrm{mm}

(half-length

a = 4\,\mathrm{mm}

), for which the geometry factor is

Y = 1

. The plate is thick enough for plane strain to hold through most of its thickness, so its toughness is the plane-strain value,

K_{Ic} = 60\,\mathrm{MPa\,m^{1/2}}

and yield stress

\sigma_Y = 600\,\mathrm{MPa}

. ((a)) Find the stress intensity factor

K_I

for the crack. ((b)) Find the critical half-length

a_c

at which the plate fails at this stress. ((c)) Estimate the plastic zone size

r_p

where the actual crack meets the plate's free surface, in plane stress, and state whether small-scale yielding holds.

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