Theory of Time-Temperature-Stress Equivalent Principle Based on Schapery Equation and Its Application on Granite

  • Yuanguang ZHU Institute of Rock and Soil Mechanics
  • Quansheng LIU Wuhan University
  • Bin LIU Institute of Rock and Soil Mechanics
  • Jingdong JIANG Wuhan University
Keywords: time-temperature-stress, shift factor, nonlinear creep, granite


The time-temperature-stress equivalent (TTSE) principle refers to the phenomenon that the time-dependent mechanical properties of materials rely on the variations of temperature and stress level. Thus, it is reasonable to predict the long time material mechanical properties based on their relationships with rising temperatures and stress levels. According to the single-integral nonlinear constitutive equation proposed by Schapery, a general expression of the TTSE principle for nonlinear viscoelastic creep property is deduced. The specific expression for time-temperature-stress shift factor is presented by assuming quadratic polynomial form of the Doolittle formula for the viscosity as a function of free volume. Creep curves of granite at different temperatures and stress levels are introduced, and the validation of applying time-temperature-stress principle to predict the long time creep property of granite is provided. The master curves are generated through vertical shift modification and horizontal shift equivalence of all creep curves, and corresponding coefficients in the shift equations are determined by curve fittings. The results indicate the modified time-temperature-stress equivalent relation is appropriate to predict the long time creep property of granite.