Prediction of stress–strain diagram from forming load in stretch forming

The objective of this research is to propose a prediction method of a stress–strain diagram based on a stroke-load diagram in stretch forming. In the proposed method, a set of characteristics in a stress–strain diagram and the same number of characteristics in a stroke-load diagram are chosen. A square matrix of influence coefficient is calculated on a master material using finite element analysis so that each element of the matrix is a partial differential of a stroke-load characteristic by a stress–strain characteristic. In the actual process of stretch forming, the differences of characteristics in a stroke-load diagram are measured between the target and master materials. Based on the differences of characteristics of stroke-load, the characteristics of a stress–strain diagram for the target material are calculated using the inverse matrix of the influence coefficient. In the present paper, the essential concept is introduced, and the error of prediction is estimated numerically, followed by experimental verification.

► We propose a prediction method of a stress–strain diagram based on a stroke-load diagram in stretch forming.
► A set of characteristics pj in a stress–strain diagram and characteristics fi in a stroke-load diagram are chosen.
► A square matrix of influence coefficient ∂fi/∂pj is calculated on a master material.
► The differences of characteristics ▵fi of stroke-load between master and target materials are measured.
► The stress–strain diagrams for the target material are calculated using the inverse matrix of the influence coefficient.