Reconciling fracture toughness parameter contradictions in thin ductile metal sheets

Abstract

A B S T R A C T The well-known trade-off between strength and fracture toughness in bulk specimens is often used to explain the low fracture toughness of very thin ductile face-centred cubic metal specimens, but this interpretation contradicts the relative length scales of thickness-dependent strength and thickness-dependent fracture toughness. This study uses the concept of similitude to demonstrate that linear elastic fracture mechanics analysis of 25.4 μm thick annealed aluminium is invalid, although the resulting fracture toughness measurements fit well with the existing literature and idea of a strength/fracture toughness trade-off. Similarly, an elastic plastic fracture mechanics analysis is sensitive to out-of-plane deformation that cannot be practically eliminated or corrected for with a model. However, a plastic collapse analysis using a critical net section stress criterion is demonstrably valid by the concept of similitude, is insensitive to out of plane deformation, and agrees with the evidence of extensive plasticity in the fracture surfaces.Keywords ductile tearing; fracture mechanics; fracture toughness; plastic collapse; stable crack growth; thin sheet. N O M E N C L A T U R Ea = crack length in SE(T) specimen or half crack length in M(T) specimen Atot = total work applied to specimen A tot ¼ ∫ Δ 0 Pd Δ b = uncracked ligament length B, B 0 , B * = thickness, minimum thickness for plane strain, critical thickness J, J max = J-integral, maximum valid J measurement for a given specimen goemetry K = stress intensity factor K Ic , K R = fracture toughness in mode I loading, propagation toughness in K-R analysis L À = mean lineal intercept grain size LEFM, EPFM = linear elastic fracture mechanics, elastic-plastic fracture mechanics M(T) = middle crack tension specimen geometry P = force applied to specimen R = load ratio σ min /σ max used in fatigue precracking SE(T) = single edge crack tension specimen geometry t = traction acting normal to J-integral path Γ u = displacement vector at a point along path Γ w = width of SE(T) or half width of M(T) specimens W = strain energy density x, y = in-sheet coordinate axes perpendicular and parallel to tensile stress, respectively Y = geometric correction factor used in computation of K ¼ σ Y ffiffiffiffiffiffi π a p Correspondence: C. L. Muhlstein.

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