Master Curve Representation

As shown in Eq 3, the sigmoidal function in combination with the Williams – Landel-Ferry (WLF) equation may be used to construct master curves. Shifting to an arbitrary temperature (in case of this investigation 5 °C) is done by solving for the shifting factors with the parameters of the sigmoidal function by least – squares method.

The different parameters of Eq 3, as determined from non-linear represen­tation analysis with the curve-fitting toolbox of Matlab (MathWorks Knarrar – nasgatan 7, Kista Entre, Box SE-16421Kista, SWEDEN), are indicated in Table

2. R-square is the square of the correlation between the response values and the predicted response values. The master curve constructed from Eq 3 is shown in Fig. 5(a) and will be used in ABAQUS to define the thermorheologically simple behavior of the MA

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Time, s

Measured creep compliance, 1/GPa

log (D) at 5, °C

log (D) at 15, °C

log (D) at 25, °C

1

3.70 • 10-02

8.14 • 10-01

6.92 • 100

2

1.34 • 10-01

7.13 • 10-01

1.53 • 1001

5

2.59 • 10-01

1.57 • 100

2.35 • 1001

10

4.26 • 10-01

2.19 • 100

3.73 • 1001

20

7.72 • 10-01

3.79 • 100

6.07 • 1001

50

1.33 • 100

6.17 • 100

8.46 • 1001

100

2.01 • 100

1.97 • 1001

9.79 • 1001

200

2.91 • 100

3.22 • 1001

1.21 • 1002

500

4.68 • 100

5.78 • 1001

1.85 • 1002

1000

6.50-10°

8.60T001

2.58T002

TABLE 1—Creep compliance from IDT.

where D = creep compliance,1/GPa; T = time of loading, s; Tref = reference tem­perature, K; T = temperature, K; bj = minimum value of D; b2 = span between maximum and minimum value of D; aj and a2 = parameters describing the shape of the sigmoidal function; cj and c2 = WLF constants.