2025 Volume 64 Issue 1 Pages 156-163
Permanent strength is a material property independent of temperature and time, making it particularly useful for evaluating the elastic limit and mechanical strength of spring materials. However, conventional methods rely on long–duration stress relaxation tests, imposing significant time constraints and limiting practical applications. This study presents a Bayesian nonlinear scaling model to estimate the permanent strength–strain relationship with minimal experimental data and enhanced accuracy. To validate its effectiveness, the method was applied to ultra–thin phosphor bronze (JIS C5210–H, t=0.25 mm), and its stress–strain behavior was analyzed. The proposed model integrates Bayesian inference with a nonlinear logistic scaling function, enabling systematic estimation of permanent strength while quantifying uncertainty. This approach allows for a unified evaluation across different conditions and material types. The results demonstrate that the model provides high–precision estimations of permanent strength, confirming its applicability to ultra–thin sheet materials and broader structural applications. Furthermore, this method effectively estimates the elastic limit and yield strength of spring materials, where the 0.01% proof stress at an extremely low strain rate (ε=1×10-6/s) proves particularly useful as a design parameter.
