最小限の観測点による 永久強度の応力―ひずみ関係における高精度ベイズ推定

観測値とした場合、推定されたスケーリング係数 λ(ε) の95%信用区間は全域で極めて小さく、比例限近傍から塑性域に至る滑らかな非線形挙動が高精度に再現できることを確認した。さらに、中間ひずみ点を除外した2点観測（ε=0,0.015）について推定精度を検証した結果、永久強度の推定曲線は3点観測条件と整合的に一致し、相対誤差は全ひずみ域で概ね±4%以内に収まった。また、中間ひずみ域の推定値も3点観測で得られた信用区間内に含まれ、区間内補間に対して十分な再現性が確認された。これらの結果から、本手法は観測点数を大幅に削減しても永久強度の応力―ひずみ関係を高精度に推定できる実用的評価法であることを示した。

This study develops a Bayesian integration framework that enables high-accuracy estimation of the permanent strength stress–strain relationship using only minimal information obtained from stress relaxation tests. A nonlinear asymmetric scaling function was combined with Bayesian inference to reconstruct the permanent strength response from a small number of observation points. The method was applied to a spring-grade stainless stee（l SUS301CSP-H）exhibiting a round-house（nonlinear）ardening behavior, and evaluated for three specimen orientations（RD, DD, TD）in both the as-received and annealed onditions. When three observation points（f＝0, 0.005, 0.015）were used, the inferred scaling factor m（f） showed extremely narrow 95％ credible intervals, demonstrating that the elastic–plastic transition and subsequent hardening behavior can be accurately reproduced. Even when the intermediate strain point was removed and only two points（f＝0 and 0.015）were used, the reconstructed permanent-strength curves remained in close agreement with the three-point results. The relative error between the two-point and three-point estimations was within ±4％ across the entire strain range, and the predicted intermediate-strain values consistently fell within the credible interval obtained from the threepoint model. These results confirm that the proposed Bayesian scaling approach can accurately reconstruct the permanent strength stress–strain relationship while significantly reducing the number of required relaxation tests, offering a highly efficient framework for practical material characterization.

Bayesian inference, Permanent strength, Stress relaxation, In-plane anisotropy, Stainless spring steel sheet, Scaling model