curves. FIGURE 8.3 学 学 学 e(tj)4 3 Strain,e(t) linear viscoelastic behavior.For example,moving So to the left-hand side scale becomes a straight line,and this provides another way to check for scales to plot creep compliance data.A power law plotted on a log-log erally conducted over several decades,it is often convenient to use log-log posite and the polymer matrix material.Since creep experiments are gen- only on the polymer matrix,and indeed that n is the same for the com- [2]that,for polymer matrix composites,the creep exponent n depends determined parameters.It has been shown experimentally by Beckwith where So is the initial elastic compliance and Si and n are empirically power law expression of the form as those shown in figure 8.3(a)can be described mathematically using a Typically,the creep compliance for linear viscoelastic creep curves such rials being discussed are linear viscoelastic. viscoelastic.In this book,it is always assumed that the viscoelastic mate- become nonlinear,and this means that the material becomes nonlinear stress level becomes high enough,the isochronous stress-strain curve will continue to behave in a linear viscoelastic manner.For example,if the limits on the ranges of stress and time within which a material will which its isochronous stress-strain curves are linear.There are always material is linear viscoelastic within the range of stresses and times for and obviously S(t)increases with time.Phenomenologically speaking,a Illustration of creep curves at constant stress and corresponding isochronous stress-strain (a)Creep curves at constant stress Time,t S(t)=So+Sut" 9 at time t=t1 (b)Isochronous stress-strain curve Strain at time Principles of Composite Material Mechanics 621re8.4. yields FIGURE 8.4 e8-A6181-7)4268.51-727426884-7g history in figure 8.5,the total strain response at any time t>ta is given by time since the application of the input stress.Thus,for the stress-time to the input stress,but the proportionality factor is a function of the elapsed mann Superposition Principle,the strain response is linearly proportional and ta respectively,as shown in figure 8.5.According to the Boltz- neous linear viscoelastic material by the stresses Ao,Aoz,and Aos at times Consider the 1-D isothermal loading of a nonaging,isotropic,homoge- temperature and aging effects will be considered in section 8.2.6. material,which is different from viscoelastic creep or relaxation.Both the elapsed time (t-t)only.Aging is a time-dependent change in the at any time t due to an input at time f=t is a function of the input and material is at a constant temperature and is "nonaging,"then the response developed by using the Boltzmann Superposition Principle [3].If the The stress-strain relationships for a linear viscoelastic maternal can be 8.2.1 Boltzmann Superposition Integrals for Creep and Relaxation versus logf with slope n and vertical axis intercept logS,as shown in which is the equation for a straight line on a log-log plot of logIS(t)-Sol of equation(8.2)and taking the log of both sides of the resulting equation Illustration of log creep compliance vs log time plot Analysis of Viscoelastic and Dynamic Behavior 思 器