PSI - Issue 13

Evgeny Lomakin et al. / Procedia Structural Integrity 13 (2018) 664–669 Evgeny Lomakin and Boris Fedulov / Structural Integrity Procedia 00 (2018) 000–000

666

3

3 2

1 0    Φ

2

 B Q  ,









,

12

where

1 2

2

'

2

'

'

2

 

 

 















 

 

  

 

A

A

A

, A Q

Φ

[

2

],

1

1111

11 2222

22

1122

11 22 1212

12

where prime ‘ – denotes d d  .

In spite of complex form of equation, in case of proportional loading stress state parameter becomes constant, and all equations remain nonlinearity only due to shear parameter Q . Moreover, for uniaxial tension and uniaxial compression loadings, where =±1/3, first two equations become similar to classical one with zero nonlinear components. This gives possibility for relatively easy validation of required parameters of the model. 5. Example and test correlation Let us consider, as an example, the simplest approach with linear dependence of compliance coefficients on parameter   0 1111 11 11 , A a c       0 2222 22 22 , A a c       0 1122 12 12 , A a c     and the case where coefficient for pure shear compliance has no influence of tri-axiality:     , Γ . B Q Q   The last component can be found as   12 12 12 Γ /     from pure in-plane shear test, while the coefficients �� � , �� � и �� , �� can be determined from uniaxial tests. Next pictures show the possibility of this model by the correlation between the results of tests of fiberglass fabric and polyether matrix composite under tension, compression and shear tests and theoretical dependencies. Predicted diagrams in Fig.1-3 were obtained by the use of input data for coefficients provided in Table 1 and the dependency for shear function   12 12 12 Γ /     shown in Fig. 4.

Fig. 1. Tension test correlation for fiberglass fabric 1,2 –predicted loading diagrams