A constant strain is applied to a polymer that can be represented by the Maxwell model, and the initial stress is 5.0 MPa. If the relaxation time is 50 s, which value is closest to the stress after 100 s?

Answer: B. About 0.68 MPa

Stress relaxation in the Maxwell model follows σ(t) = σ₀exp(−t/τ), and t/τ = 100/50 = 2.0, so σ = 5.0 × exp(−2.0) = 5.0 × 0.135 ≈ 0.68 MPa. About 1.8 MPa uses exp(−1), the stress at t = τ. About 4.3 MPa is 5.0 × (1 − exp(−2)), confusing relaxation with an expression that grows over time, like creep in the Voigt model. The relaxation time is the ratio of viscosity to modulus, τ = η/E, and it shortens as temperature rises. The loss of clamping force in plastic gaskets and plastic parts in bolted joints is due to this stress relaxation.