Abstract
It is generally observed that the existence of geometrical discontinuity like notches in materials will lead to strength weakening, as a resultant of local stress concentration. By comparing the influence of notches to the strength of three typical materials, aluminum alloys with intermediate tensile ductility, metallic glasses with no tensile ductility, and brittle ceramics, we observed strengthening in aluminum alloys and metallic glasses: Tensile strength of the net section in circumferentially notched cylinders increases with the constraint quantified by the ratio of notch depth over notch root radius; in contrast, the ceramic exhibit notch weakening. The strengthening in the former two is due to resultant deformation transition: Shear failure occurs in intact samples while samples with deep notches break in normal mode fracture. No such deformation transition was observed in the ceramic, and stress concentration leads to its notch weakening. The experimental results are confirmed by theoretical analyses and numerical simulation. The results reported here suggest that the conventional criterion to use brittleness and/or ductility to differentiate notch strengthening or weakening is not physically sound. Notch strengthening or weakening relies on the existence of failure mode transition and materials exhibiting shear failure while subjected to tension will notch strengthen.
Highlights
From the stress-displacement curves (Fig. 2a) and the peak strength as a function of the constraint (a/ρ) shown in Fig. 2b, we see significant strengthen enhancement when a/ρ increases: The yielding strength of an Al T6061 bar is about 390 MPa, in contrast to the yield strength of 680 MPa in the circumferentially notched bar with a/ρ = 23
By exploring the mechanical response of three distinct materials – Al T6061, bulk metallic glasses (BMG) Vitreloy 1, and ceramic Al2O3, we obtain the following three conclusions: (1) Al T6061 and BMGs exhibit notch-strengthening with increasing constraints, and the normal stress eventually reaches cohesive strength of the materials and leads to mode I fracture
(2) Notch strengthening in Al T6061 and BMGs is a resultant of deformation transition from shear failure to mode I fracture
Summary
From the stress-displacement curves (Fig. 2a) and the peak strength as a function of the constraint (a/ρ) shown, we see significant strengthen enhancement when a/ρ increases: The yielding strength of an Al T6061 bar is about 390 MPa, in contrast to the yield strength of 680 MPa in the circumferentially notched bar with a/ρ = 23. Ductile metals like Al T6061 exhibit pressure-independent behavior if they fail in shear. In such circumstance, the strength reflects the shear. If we consider the notch as a crack, Griffith strength theory[7] predicts that the failures stress σ y of a cracked sample follows σ y = cKC (πa)−1/2 for KC being the fracture toughness and c being a geometrical factor. When bars with circumferential notches are subjected to uniaxial tension, we have
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