A Novel Approach to Describe the Time–Temperature Conversion among Relaxation Curves of Viscoelastic Materials

Time and temperature, besides pressure in a lesser extent, represent the most significant variables influencing the rheological behavior of viscoelastic materials. These magnitudes are each other related through the well-known Time–Temperature Superposition (TTS) principle, which allows the master curve referred to relaxation (or creep) behavior to be derived as a material characteristic. In this work, a novel conversion law to interrelate relaxation curves at different temperatures is proposed by assuming they to be represented by statistical cumulative distribution functions of the normal or Gumbel family. The first alternative responds to physical considerations while the latter implies the fulfillment of extreme value conditions. Both distributions are used to illustrate the suitability of the model when applied to reliable derivation of the master curve of Polyvinil–Butyral (PVB) from data of experimental programs. The new approach allows not only the TTS shift factors to be estimated by a unique step, but the whole family of viscoelastic master curves to be determined for the material at any temperature. This represents a significant advance in the characterization of viscoelastic materials and, consequently, in the application of the TTS principle to practical design of viscoelastic components.

[1]  M. Muñiz‐Calvente,et al.  Study of the time-temperature-dependent behaviour of PVB: Application to laminated glass elements , 2017 .

[2]  F. Kozin,et al.  Effect of Length on Fatigue Life of Cables , 1987 .

[3]  J. S. Lai,et al.  Creep and Relaxation of Nonlinear Viscoelastic Materials , 2011 .

[4]  A. Fernández‐Canteli,et al.  A Unified Statistical Methodology for Modeling Fatigue Damage , 2010 .

[5]  Toyoichi Tanaka.  Experimental Methods in Polymer Science: Modern Methods in Polymer Research and Technology , 1999 .

[6]  Nicholas W. Tschoegl,et al.  The Phenomenological Theory of Linear Viscoelastic Behavior: An Introduction , 1989 .

[7]  E. Buckingham.  The Principle of Similitude , 1915, Nature.

[8]  R. Landel,et al.  The Temperature Dependence of Relaxation Mechanisms in Amorphous Polymers and Other Glass-Forming Liquids , 1955 .

[9]  N. Tschoegl.  The Phenomenological Theory of Linear Viscoelastic Behavior , 1989 .

[10]  J. Ferry.  Viscoelastic properties of polymers , 1961 .

[11]  N. G. Mccrum,et al.  On the measurement of the activation energies for creep and stress relaxation , 1964, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[12]  B. Zupančič,et al.  The closed form t-T-P shifting (CFS) algorithm , 2011 .

[13]  Alfonso Fernández-Canteli,et al.  Probabilistic failure analysis for real glass components under general loading conditions , 2019 .

[14]  Fracture strength prediction of float glass: The Coaxial Double Ring test method , 2019, Construction and Building Materials.

[15]  Linear viscoelastic materials with environmental dependent properties , 1971 .

[16]  Alfonso Fernández-Canteli,et al.  STATISTICAL MODELS FOR ANALYSIS OF FATIGUE LIFE OF LONG ELEMENTS , 1990 .

[17]  J. D. T. Oliveira,et al.  The Asymptotic Theory of Extreme Order Statistics , 1979 .

[18]  J. S. Lai,et al.  Creep and Relaxation of Nonlinear Viscoelastic Materials: With an Introduction to Linear Viscoelasticity , 2012 .

[19]  Enrique Castillo,et al.  Functional equations and modelling in science and engineering , 1992 .

[20]  E. Castillo.  Extreme value and related models with applications in engineering and science , 2005 .

[21]  W. Knauss.  The sensitivity of the time-temperature shift process to thermal variations—A note , 2008 .

[22]  Ali S. Hadi,et al.  Extreme Value and Related Models with Applications in Engineering and Science , 2004 .

[23]  J. Angus.  Extreme Value Theory in Engineering , 1990 .

[24]  Terri L. Moore,et al.  Regression Analysis by Example , 2001, Technometrics.

[25]  B. Gross.  Time-Temperature Superposition Principle in Relaxation Theory , 1969 .

[26]  J. Aczél,et al.  On scientific laws without dimensional constants , 1986 .