The isochronous stress-strain curves for an epoxy material at different times are shown in Figure 8.53. This material is used as the matrix in a unidirectional E-glass-epoxy composite having a fiber volume fraction of 0.6 . Using micromechanics and the Elastic-Viscoelastic Correspondence Principle, determine the longitudinal relaxation modulus \(E_{1}(t)\) for the composite at \(t=1 \mathrm{~h}\) and \(t=10,000 \mathrm{~h}\). Note that the strain in Figure 8.53 is given in percent strain (e.g., a percent strain value of 1.5 corresponds to a strain of 0.015). Elastic properties of fibers are given in Table 1.1.

Figure 8.53:

Table 1.1:

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Stress level (MPa) 5 15 20 0.5 1.0 1 h 10 h 100 h 1.5 1,000 h 5,000 h 10,000 h 100,000 h Projected Total strain, % at indicated stress and time mm/mm or in./in. x 100 2.0 2.5 0.5 1.0 2.0 1.5 15 3.0 2.5 Stress level (103 psi)