Schapery theory

There is strong interest to analytically describe the fzme-dependence of polymer creep in order to extrapolate the deformation behaviour into otherwise inaccessible time-ranges. Several empirical and thermo-dynamical models have been proposed, such as the Andrade or Findley Potential equation [47,48] or the classical linear and non-linear visco-elastic theories ([36,37,49-51]). In the linear viscoelastic range Findley [48] and Schapery [49] successfully represent the (primary) creep compliance D(t) by a potential equation ... 

R A Schapery, A theory of non-linear thermo-viscoelastidty based on irreversible thermodynamics . Proceedings 5th US National Congress Applied Mechanics, ASME, 1966, p 511. 

Fig. 60. Comparison of experimental (circles) creep and recovery behavior of a glass-reinforced phenolic resin with the predictions from the Schapery (147-149) nonlinear viscoelastic model. o Experimental Data A Predicted Recovery Data (Nonlinear Theory). After Schapery (147), with permission.

R. A. Schapery, A Theory of Nonlinear Thermoviscoelasticity Based on Irreversible Thermodynamics Proc. 5th U. S. National Congress of Applied Mechanics, ASME, New York, 1966, pp. 511-530. 

R. A. Schapery, Further Development of a Thermod3mamic Constitutive Theory Stress Formulation, Report AA ES 69-72, Purdue University, Lafayette, Ind., 1969. 

Schapery [16, 17] has used the theory of the thermodynamics of irreversible processes to produce a model that may be viewed as a further extension of Leaderman s. Schapery continued Leaderman s technique of replacing the stress by a function of stress /(a) in the superposition integral, but also replaced time by a function of time, the reduced time ip. The material is assumed to be linear viscoelastic at small strains, with a creep compliance function of the form [17]... 

A thermodynamically consistent theory for nonlinear viscoelasticity was first proposed by Schapery.(26) Jhe law can be derived from fundamental principles using the concepts of irreversible thermodynamics. A comprehensive review of the thermodynamics basis of Schap-ery s theory has been presented by Hiel et... 

In 1963 Nagdi and Murch published a paper entitled On the Mechanical Behavior of Viscoelastic-Plastic Solids just before Schapery first published his efforts on a thermodynamic approach to nonlinear viscoelasticity and prior to the development of early viscoplastity theories. Likely because both nonlinear viscoelasticity and/or viscoplasticity caught the attention of the technical community, Nagdi s work received little attention. However,... 

Schapery, R.A. (1966) A engineering theory of nonlinear viscoelasticity with applications. Int. J. Solids. Structures, 2,407. 

Earlier authors proposed theories which predict the speed of viscoelastic crack propagation, by assigning a detailed structure to the crack tip, both under unstable and subcritical or fatigue failure. We mention Knauss (1970, 1974), Knauss and Dietmann (1970), Mueller and Knauss (1971) and a review by Knauss (1973) also the work of Wnuk (1971-73b). Later, there was the work of Schapery (1974-79), McCartney (1977-79) and Golden and Graham (1984). See also Kanninen and Popelar (1985). Majidzadeh et al. (1976) discuss various models in the context of application to pavement design. McCartney (1987) is concerned with crack extension criteria for fibre-reinforced composites. 

Schapery RA. Theory of crack initiation and growth in viscoelastic media. 1. Theoretical development. Int JFract 1975 ll(l) 141-59. 

Schapery, R. A., "A Theory of Non-Linear Thermoviscoelasticity Based on Irreversible Thermodynamics," Proc. Fifth U.S. Nat. Cong, of Appl. Mech., ASME, 511-530 (1966). 

A simpler and effective approach was given by Schapery [149]. The theory has proven to describe reasonably well the non-linear viscoelastic behaviour for several polymers [150]. The constitutive equation in terms of strain is restricted to small strains by the rmderlying thermodynamic theory. For the unidirectional case is given as... 

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