Jean Francois Ganghoffer

Abstract:

A novel and rational approach based on Lie analysis is proposed to investigate the mechanical behavior of materials exhibiting experimental master curves. It relies on the idea that the mechanical response of materials is associated with hidden symmetries; the general objective of this contribution is to reveal those symmetries from measurements and to construct constitutive laws from them. This approach leads to the formulation of constitutive laws from data as well as the possibility of predicting new master curves and material charts; especially, the time-temperature equivalence principle for polymers is obtained from the requirement of group invariance of the field equations. After an exposition of the general methodology, an application is done to the uniaxial creep and rupture behavior of a Chrome-Molybdene alloy (9Cr1Mo) at different temperatures and stress levels. Constitutive equations for creep and rupture master responses are identified for this alloy and validated on experimental data.