Stress Fracture as Sub-Yield Bone Fatigue, and Fracture Healing as Remodeling Re-Cross

Stress fracture is bone fatigue BELOW the single-event yield. T4's Wolff threshold (spinodal 0.5324) is the load that flips bone in one step; bone also has a lower fatigue ENDURANCE LIMIT, and cyclic load above it accumulates microdamage until the bone contact network fails — the runner's stress fracture — even though no single cycle reaches yield. Sub-endurance load is protected. And the fracture HEALS: load re-crosses the switch to the dense basin [V].

A Paris/Basquin law on the bone contact number, thresholded at the fatigue endurance limit (below the T3 yield), removes contacts only for supra-endurance cyclic load. Sub-endurance loading is protected indefinitely (the S-N plateau); supra-endurance, sub-yield loading fractures after enough cycles, faster at higher load. Crucially bone HEALS — from a fractured low-density state, physiologic load drives density back from 0.00 to 1.00 (callus = T3 re-cross), unlike cartilage/OA. Shape + healing [V]; endurance-limit + damage-law form [L]; absolute cycles-to-fracture [O].

Two thresholds, not one

T4 (Wolff) established a single-event YIELD threshold: a load above the spinodal flips bone to the dense basin in one step. But bone, like any load-bearing solid, also has a lower FATIGUE ENDURANCE LIMIT. Between the endurance limit and the yield threshold lies the stress-fracture regime: each individual cycle is sub-yield and ‘safe’, yet repeated loading accumulates microdamage in the contact network until it fails. This is the classic stress fracture of runners and military recruits — injury from repetition, not from a single overload.

Sub-yield, but it still breaks

Applying the same Paris/Basquin damage law used for OA to the bone contact number, with the damage threshold at the endurance limit, the regimes separate:

Sub-endurance loading (rest, easy activity) is protected indefinitely. Supra-endurance loading, though still sub-yield, accumulates damage; at the running load the contact number declines progressively with cycle count:

Higher loads fracture in fewer cycles — an S-N (Wöhler) curve. This is distinct from T4: the bone never sees a yield-level single event.

And it heals (unlike cartilage)

Bone repairs itself, and the same T3 switch explains it: from a fractured, low-density state, physiologic loading re-crosses the R19 switch to the dense basin (density rises from 0.00 to 1.00) — the callus and remodelling of fracture healing. This is a meaningful contrast with cartilage: OA (§12) unjams irreversibly because cartilage cannot remodel back, while bone fractures heal because it can. The same substrate captures both the failure and the repair.

What is NOT claimed

The SHAPE (endurance plateau, accelerating supra-endurance failure, S-N ordering) and the load-driven healing re-cross are the result; the endurance-limit concept and the damage-law form are cited [L]. The absolute number of cycles to fracture is not fixed by the substrate and stays [O].

Analgesic lever map (cross-reference)

Stress-fracture pain is an L2-coupled case: offloading below the bone endurance limit lowers the nociceptive crossing rate and halts the microdamage at once, letting the documented healing re-cross proceed. See §25 the three-lever threshold logic for the inherited technique (concept DOI 10.5281/zenodo.20733420), and §26 L2 convergence for the worked lever sweeps. The analgesic axis adds no new physics: pain is a threshold-crossing rate on the same R19 barrier this chapter already uses.