The creep compliance of a polymer is given below. A specimen of polystyrene is loaded in creep with a stress of 10MPa for 25hours and 30MPa for an additional 25hours and then unloaded. What is the creep strain after 75hours?

t (hours) J(t) MPa-1
0 1.0 x 10-3
25 1.4 x 10-3
50 1.6 x 10-3
75 1.7 x 10-3

t (hours) Stress MPa
0 10
25 30
50 0

ϵ (75hours):

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To find the creep strain after 75 hours, we need to use the given creep compliance data.

First, let's define some variables:
t1 = 25 hours (time with a stress of 10 MPa)
t2 = 25 hours (time with a stress of 30 MPa)
t3 = 75 hours (total time)

To calculate the creep strain at t1, we can use the given creep compliance data: J(t1) = 1.4 x 10^-3 MPa^-1.

Creep Compliance (J) is defined as the strain (ε) divided by the stress (σ): J = ε/σ.

Rearranging the formula, we can calculate the strain ε at t1:
ε(t1) = J(t1) x σ(t1) = (1.4 x 10^-3 MPa^-1) x (10 MPa) = 1.4 x 10^-2

Next, we need to calculate the creep strain at t2. Since the stress is different, we'll use the creep compliance value at t2, which is J(t2) = 1.6 x 10^-3 MPa^-1.
ε(t2) = J(t2) x σ(t2) = (1.6 x 10^-3 MPa^-1) x (30 MPa) = 4.8 x 10^-2.

Now, to find the total creep strain at t3 (75 hours), we need to consider the creep strains from t1 and t2:
ε(t3) = ε(t1) + ε(t2) = (1.4 x 10^-2) + (4.8 x 10^-2) = 6.2 x 10^-2.

Therefore, the creep strain at 75 hours is 6.2 x 10^-2.