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<p>Stair-like wavy cracking commonly arises in brittle laminated materials due to the interplay between heterogeneous mechanical properties of layered structures and external boundary conditions. Based on the energy release rate (ERR) criterion and the straight-crack equivalence assumption, we derive an explicit solution for the continual kinking conditions under which crack propagation in brittle laminates through repeated kinking (stair cracking) governed by three parameterized factors. The theoretical solution yields phase diagrams mapping three fracture modes determined by (1) the ratio between the critical fracture toughness when cracking along the interface (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({G}_{\text{dc}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mtext>dc</mtext> </msub> </math></EquationSource> </InlineEquation>) and that during traversing fracture (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({G}_{\text{mc}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>G</mi> <mtext>mc</mtext> </msub> </math></EquationSource> </InlineEquation>), (2) the angle between the initial crack and interfaces, and (3) the stress ratios of boundary conditions. Such an efficient engineering approach, with ERR playing the central role, achieves high accuracy in predicting crack path patterns, as validated through finite-element simulations.</p>

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Energy release rate governed stair cracking in brittle laminates and shale fracking

  • 期刊论文

  • 发表日期：

    2026年2月28日

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  • Xiaguang Zeng,
  • Yujie Wei

摘要

Stair-like wavy cracking commonly arises in brittle laminated materials due to the interplay between heterogeneous mechanical properties of layered structures and external boundary conditions. Based on the energy release rate (ERR) criterion and the straight-crack equivalence assumption, we derive an explicit solution for the continual kinking conditions under which crack propagation in brittle laminates through repeated kinking (stair cracking) governed by three parameterized factors. The theoretical solution yields phase diagrams mapping three fracture modes determined by (1) the ratio between the critical fracture toughness when cracking along the interface ( \({G}_{\text{dc}}\) G dc ) and that during traversing fracture ( \({G}_{\text{mc}}\) G mc ), (2) the angle between the initial crack and interfaces, and (3) the stress ratios of boundary conditions. Such an efficient engineering approach, with ERR playing the central role, achieves high accuracy in predicting crack path patterns, as validated through finite-element simulations.