Residual Strength

Residual Strength (structures/damage-tolerance/residual-strength)

Use when the task is the residual strength of a cracked structure for a damage tolerance assessment: residual strength from fracture toughness, critical crack length, and the margin against the limit load.

Domain quick reference

• Residual strength is the highest stress a cracked structure carries before fracture; FAR 25.571 damage tolerance practice requires it to stay above the limit load at the assumed damage size.
• The mode I stress intensity factor K = beta * sigma * sqrt(pi * a) scales the crack-tip stress field; beta is the geometry factor (1.0 for a central through-crack in a wide plate).
• Fracture occurs when K reaches the material fracture toughness Kc; the crack length at which the applied stress drives K to Kc is the critical crack length.
• Residual strength falls with the inverse square root of the crack length, so a short crack barely reduces strength while a long crack drops it sharply.
• Units convention (single, consistent in the logic module): sigma in MPa, crack lengths in meters, K and Kc in MPa*sqrt(m).

Workflow

1. Establish the material fracture toughness Kc, the geometry factor beta, and the current crack length; compute the residual strength with residual_strength.
2. Get the applied stress level; find the critical crack length with critical_crack_length.
3. Compare residual strength with the limit load using residual_margin; a margin below 1.0 means the cracked structure fails the limit load requirement.
4. Check the applied stress directly against Kc with crack_ok.
5. Feed the critical crack length and margin into the inspection interval and repair decision.

Pitfalls

• Mixing units in K = beta * sigma * sqrt(pi * a): passing sigma in Pa with Kc in MPasqrt(m) shifts the result by 1e6. Keep sigma in MPa, crack lengths in meters, and K and Kc in MPasqrt(m).
• Using the total crack length 2a instead of the half-length a for the through-crack formula.
• Comparing K with Kc at a stale crack size: the critical crack length changes with the applied stress level.
• Treating the margin as a fixed property: it falls as the crack grows, so re-evaluate it at each assumed inspection size.
• Omitting the geometry factor beta, or applying the infinite-plate value to a finite panel or an edge crack.

Behavior contract (gate 3)

The residual strength, critical crack length, and margin logic is exercised by the gate 3 contract test: scripts/test_residual_strength_logic.py against scripts/residual_strength_logic.py (stdlib unittest, offline). Run: python3 scripts/test_residual_strength_logic.py

Compliance

• Standards referenced, not reproduced: FAR-25 is US government work (public domain); residual strength methodology is common fracture-mechanics knowledge, summary-only per standards-map.yaml.
• compliance: STANDARDS-REF, gated: false.