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module module high

IndisputableMonolith.Materials.FatigueThresholdFromJCost

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This module defines the per-cycle fatigue J-cost as a function of the stress ratio together with predicates for endurance thresholds and fatigue failure regimes. Materials modelers working in cyclic loading would cite these constructions when embedding Recognition Science cost axioms into fatigue analysis. It is a definition module whose properties follow directly from the imported J-cost and constant axioms.

claimThe per-cycle fatigue cost is the map $C_f(R)$ where $R$ is the stress ratio, satisfying $C_f(R)=0$ at yield, $C_f(R)>0$ off yield, and reciprocal symmetry $C_f(R)=C_f(1/R)$. Endurance threshold and infinite-life predicates are defined from the sign of $C_f$ relative to the Berry creation threshold.

background

Recognition Science measures deviation from self-similarity via the J-cost function $J(x)=(x+x^{-1})/2-1$. The module applies this to fatigue by treating the stress ratio as the argument of J on each cycle. It imports the RS time quantum from Constants and the base J-cost axioms from the Cost module. Sibling definitions include fatigueCost, EnduranceThreshold, IsFatigueFailing, IsInfiniteLife, and the certification object FatigueThresholdCert.

proof idea

This is a definition module, no proofs.

why it matters in Recognition Science

The module supplies the J-cost foundation for fatigue analysis inside the Recognition framework. It feeds the certification of endurance thresholds and the exclusive-regime lemmas that appear among its siblings. The construction directly instantiates the general Cost axioms for cyclic materials loading.

scope and limits

depends on (2)

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declarations in this module (12)