An aluminium alloy plate carries a remote tensile stress perpendicular to a straight…

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

An aluminium alloy plate carries a remote tensile stress σ=80 MPa\sigma = 80\,\mathrm{MPa} perpendicular to a straight edge crack of length a=5 mma = 5\,\mathrm{mm} (measured from the edge into the plate), for which the geometry factor is Y=1.12Y = 1.12. The plate is thick enough for plane strain to hold through most of its thickness, so its toughness is the plane-strain value, KIc=30 MPa m1/2K_{Ic} = 30\,\mathrm{MPa\,m^{1/2}} and yield stress σY=400 MPa\sigma_Y = 400\,\mathrm{MPa}. ((a)) Find the stress intensity factor KIK_I at the tip of the crack. ((b)) Find the critical flaw length aca_c at which the plate would fracture under this stress. ((c)) Estimate the plastic zone size rpr_p where the crack meets the plate's free surface, in plane stress, at the tip of the actual 5 mm5\,\mathrm{mm} crack and state whether small-scale yielding holds.

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