§12.5 Miscellaneous Topics 525 For stress relaxation de/dt =0,and from egn.(12.26) 0=E+, i.e. =_E.di 6 n If,at t=0,o =oo,the initial stress,this equation can be integrated to yield a=aoe-i/n doe-tm (12.27) This is analogous to the strain"recovery"equation(12.25)showing that,in this case,stress relaxes from its initial value oo exponentially with time dependent upon the relaxation time t". For the creep recovery stage from a constant level of stress,do/dt =0 and eqn.(12.26) gives e=- (12.28) the basic equation of pure Newtonian flow.Generally,however,the creep behaviour of viscoelastic materials is far more complex and,once again,the model does not adequately represent both recovery and relaxation situations.More accurate model representations can only be obtained,therefore,by suitable combinations of the Voigt-Kelvin and Maxwell models (see Figs.12.12 and 12.13). 2 Fig.12.12.The "standard linear solid"model. 由 77777 Fig.12.13.Maxwell and Voigt-Kelvin models in series.$12.5 Miscellaneous Topics 525 For stress relaxation ds/dt = 0, and from eqn. (12.26) i.e. If, at t = 0, a = 00, the initial stress, this equation can be integrated to yield = ,oe-E‘/S = uoe-t/t’’ (12.27) This is analogous to the strain “recovery” equation (12.25) showing that, in this case, stress relaxes from its initial value a0 exponentially with time dependent upon the relaxation time t”. For the creep recovery stage from a constant level of stress, da/dr = 0 and eqn. (12.26) gives i=- (12.28) the basic equation of pure Newtonian flow. Generally, however, the creep behaviour of viscoelastic materials is far more complex and, once again, the model does not adequately represent both recovery and relaxation situations. More accurate model representations can only be obtained, therefore, by suitable combinations of the Voigt-Kelvin and Maxwell models (see Figs. 12.12 and 12.13). U rl Fig. 12.12. The “standard linear solid” model. Fig. 12.13. Maxwell and Voigt-Kelvin models in series