<p>Gvirtzman et al. (Nature 637(8045):369–374, 2025) have made recently very interesting experiments showing how small shear cracks nucleate and then evolve at the interface between two rectangular blocks. They find essentially an approximate geometrical factor for confined cracks in plates in the condition for nucleation (threshold shear stress <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\tau _{thresh}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mrow> <mi mathvariant="italic">thresh</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>) in a classical Griffith crack condition for quasi-static nucleation. However, they seem to suggest that slowly creeping patches approach the interface width and accelerate only when a topological transition takes place in which they become 1D through cracks. We observe that this second implication is due to the fact that the measured threshold shear stress <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\tau _{thresh}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mrow> <mi mathvariant="italic">thresh</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> is very close to the cohesive strength <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\tau _{coh}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mrow> <mi mathvariant="italic">coh</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> in previously reported experiments by the same group in PMMA solids (about 1&#xa0;MPa), which suggests the width of the specimen they have used may be rather special. The general model they have derived is entirely consistent with classical fracture mechanics, which doesn’t require cracks to accelerate at this topological change. Including the cohesive strength <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\tau _{coh}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>τ</mi> <mrow> <mi mathvariant="italic">coh</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> crack nucleation in the model, and how cracks should behave when they are very small with respect to the plate width <i>W</i>, we provide a possible diagram of nucleation of cracks, depending on their shape and dimension, showing that we should take care when using their new formula, because deviations may be large if cracks are small—a full 3D numerical solution is to be preferred which is not difficult to obtain today.</p>

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A comment on a dynamic crack nucleation criterion

  • X. M. Liang,
  • M. Ciavarella

摘要

Gvirtzman et al. (Nature 637(8045):369–374, 2025) have made recently very interesting experiments showing how small shear cracks nucleate and then evolve at the interface between two rectangular blocks. They find essentially an approximate geometrical factor for confined cracks in plates in the condition for nucleation (threshold shear stress \(\tau _{thresh}\) τ thresh ) in a classical Griffith crack condition for quasi-static nucleation. However, they seem to suggest that slowly creeping patches approach the interface width and accelerate only when a topological transition takes place in which they become 1D through cracks. We observe that this second implication is due to the fact that the measured threshold shear stress \(\tau _{thresh}\) τ thresh is very close to the cohesive strength \(\tau _{coh}\) τ coh in previously reported experiments by the same group in PMMA solids (about 1 MPa), which suggests the width of the specimen they have used may be rather special. The general model they have derived is entirely consistent with classical fracture mechanics, which doesn’t require cracks to accelerate at this topological change. Including the cohesive strength \(\tau _{coh}\) τ coh crack nucleation in the model, and how cracks should behave when they are very small with respect to the plate width W, we provide a possible diagram of nucleation of cracks, depending on their shape and dimension, showing that we should take care when using their new formula, because deviations may be large if cracks are small—a full 3D numerical solution is to be preferred which is not difficult to obtain today.