For some viscoelastic polymers that are subjected to stress relaxation tests, the stress decays with time according to where σ(t) and σ(0) represent the time-dependent and initial (i. e., time = 0) stresses, respectively, and t and τ denote elapsed time and relaxation time, respectively; τ is a time-dependent constant characteristic of the material. A specimen of some viscoelastic polymer, the stress relaxation of which obeys this equation, was suddenly pulled in tension to a measured strain of 0.69; the stress necessary to maintain this constant strain was measured as function of time. Determine Er(10) for this material (in MPa) if the initial stre

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Determine Er(10) for this material (in Mpa) If the initial stress level was 2.76 Mpa (400psi) which dropped to 1.72 Mpa(250psi) after 60s

Er(10) for the material  = 2.55 / 0.69 = 3.695 ≈ 3.70 Mpa

Explanation:

The equation of stress decay for viscoelastic polymers

   equation 1

t = elapsed time = 60s

T = relaxation time

input the given values into the equation

1.72 = 2.76 exp ( -

exp ( - 60/T ) = 1.72/2.76  therefore T = 126.87S

Considering 10s for t  

taking Ln of both sides of the equation

Ln

therefore = 370 psi

To determine the Er(10) for the material in (Mpa) we apply the relaxation modulus equation

Er(t) =

where Eo = strain level = 0.69

Er(t) = E(10)

= 2.55 Mpa

input this variables into equation

Er(10) for the material  = 2.55 / 0.69 = 3.695 ≈ 3.70 Mpa

answer:

(b)

explanation: