Stress-strain relation estimation method and spring-back prediction method, and method for manufacturing press formed part

A stress-strain relation estimation method for estimating a relation between a stress and a strain of a metal sheet by using a Yoshida-Uemori material model representing a Bauschinger effect of the metal sheet, the stress-strain relation estimation method comprising:

• a uniaxial tensile stress-strain curve acquisition step of experimentally acquiring a stress-strain curve under a uniaxial tensile stress of the metal sheet by a uniaxial tensile test using the metal sheet as a test piece;
• a cyclic stress-strain curve acquisition step of experimentally acquiring a stress-strain curve under a tension-compression cyclic stress of the metal sheet by a tension-compression cyclic loading test using the metal sheet as a test piece;
• an experimental value of mechanical property value calculation step of calculating an experimental value of a mechanical property value of the metal sheet from the stress-strain curve under the uniaxial tensile stress of the metal sheet experimentally acquired by the uniaxial tensile test, the mechanical property value being a yield stress, a tensile strength, a uniform elongation, and a stress in a high strain range equal to or higher than the uniform elongation;
• a conversion parameter definition step of defining a conversion parameter obtained by combining and converting at least two parameters among parameters for use in the Yoshida-Uemori material model;
• a constraint condition setting step of setting a constraint condition that limits a possible range of the conversion parameter using the calculated experimental value of the mechanical property value;
• an objective function setting step of calculating a residual between the stress-strain curve under the uniaxial tensile stress experimentally acquired and a stress-strain curve under the uniaxial tensile stress calculated by the Yoshida-Uemori material model, a residual between the stress-strain curve under the tension-compression cyclic stress experimentally acquired and a stress-strain curve under the tension-compression cyclic stress calculated by the Yoshida-Uemori material model, and a residual between the experimental value of the mechanical property value of the metal sheet and a calculated value of the mechanical property value calculated by the Yoshida-Uemori material model, and setting a weighted residual square sum obtained by multiplying each calculated residual by an individual weighting factor as an objective function;
• and
• a parameter decision step of deciding the conversion parameter and other parameter of the Yoshida-Uemori material model so as to minimize the objective function under the constraint condition.