PSI - Issue 5

C P Okeke et al. / Procedia Structural Integrity 5 (2017) 600–607 C P Okeke et al / Structural Integrity Procedia 00 (2017) 000 – 000

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influence of one to the other is not consistence. For the same model parameter, there is no relationship between C 10 and C 01 for PBT-GF30 material. These materials behaviors in 2 parameter model give a good understanding why Mooney-Rivlin 2 parameter stresses for both materials exhibit linear behavior. The model parameter C 10 represents the linear elastic behavior, while the change in C 01 means a shift from linear to non-linear behavior [6]. In the 3 parameter Mooney-Rivlin model, all the parameters for PMMA materials have a strong correlation with each other. As the C 10 is increasing, C 01 and C 11 are decreasing at almost the same rate; hence they have strong negative relationship, while C 11 and C 01 are positively correlated and one has a strong influence to the other. For PBT-GF30 material again there is a good correction between the parameters, however the relationship between C 01 and C 11 is not strong. In the 5-parameter model, there is a linear relationship between C 11 and C 20 , only C 01 and C 20 show a weak relationship for PMMA material. For PBT-GF30 material there are linear relationships between C 10 and C 01 and between C 11 and C 20 . All the parameters have a strong relationship between each other for PBT-GF30 material.

Table 2: Model parameter correlation

PMMA

PBT-GF30

C 10

C 10

Mooney R - 2 Par

C 01

-0.883 0.047

-0.622 0.263

R

P-value

C 01

C 10

C 01

C 10

C 01

-0.995 0.000 -0.982 0.003 -0.992 0.001 -0.889 0.044 0.891 0.043 -0.943 0.016 C 10

-0.895 0.040 -0.994 0.001 -1.000 0.000 -0.934 0.020 0.935 0.020 -0.962 0.009 C 10

Mooney R - 3 Par

C 11

0.990 0.001

0.840 0.075

C 01

C 11

C 20

C 01

C 11

C 20

C 01

C 11

0.827 0.084 -0.830 0.082 0.895 0.040

0.929 0.023 -0.930 0.022 0.958 0.010

Mooney R - 5 Par

C 20

-1.000 0.000 0.991 0.001

-1.000 0.000 0.996 0.000

C 02

-0.991 0.001

-0.997 0.000

μ r1

μ r1

α r1

-0.859 0.062

-0.971 0.006

Ogden - 1st Order

μ r1

α r1

μ r2

μ r1

α r1

μ r2

α r1

-0.732 0.159 0.987 0.002 0.810 0.097

-0.994 0.001 0.984 0.003 0.999 0.000

μ r2

-0.612 0.272 -0.255 0.679

-0.969 0.006 -0.997 0.000

Ogden - 2nd Order

α r2

0.883 0.047

0.984 0.002

In the 1 st order Ogden model, the relationship between μ r1 and α r1 is less significance for PMMA, however, for PBT-GF30 both parameters have a strong relationship in opposite direction. In the 2 nd order of Ogden model, α r1 parameter doesn’t have a correlation with o ther parameters for PMMA, μ r1 has a strong positive relationship with μ r2 and α r2 respectively, and μ r2 also shows a fai rly strong relationship with α r1 . All the parameters for 2 nd Ogden model are strongly related for PBT-GF30 material.

8. Conclusions