The three fracture modes (classical classification)
In fracture mechanics, cracks are classified into three fundamental modes:
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Mode I → Opening (tensile)
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Mode II → Sliding (in-plane shear)
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Mode III → Tearing (anti-plane shear)
Key classification: in-plane vs anti-plane
In-plane modes (Modes I & II)
These involve motion within the crack plane
🔸 Mode I (Opening mode)
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Displacement normal to the crack surface , but still within the 2D plane
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Think: crack faces pull apart
🔸 Mode II (Sliding mode)
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Displacement parallel to the crack front
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Shear motion within the plane
👉 Both are in-plane because:
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Motion is fully described by (u_x, u_y)
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No out-of-plane component
Anti-plane mode (Mode III)
🔸 Mode III (Tearing mode)
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Displacement is perpendicular to the plane
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Crack surfaces slide out of the page
👉 This is anti-plane because:
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Motion is entirely in (z)-direction
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Decoupled scalar problem (SH wave)
Clean summary table
| Fracture Mode | Physical Meaning | Plane Category | Displacement |
|---|---|---|---|
| Mode I | Opening (tension) | in-plane | (u_x, u_y) |
| Mode II | Sliding (shear) | In-plane | (u_x, u_y) |
| Mode III | Tearing (shear) | Anti-plane | (u_z) |
Why this classification matters (deep insight)
This is not just naming---it reflects fundamental physics:
🔸 In-plane (Modes I & II)
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Governed by coupled Navier equations
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Generates:
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P waves (compression)
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SV waves (in-plane shear)
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More complex:
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dilation + shear coupling
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important for real earthquakes
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🔸 Anti-plane (Mode III)
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Governed by scalar wave equation
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Generates:
- SH waves only
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Much simpler:
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no volumetric strain
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no coupling
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