PSI - Issue 18

Alexey N. Fedorenko et al. / Procedia Structural Integrity 18 (2019) 432–442 A.N. Fedorenko, B.N. Fedulov, E. V. Lomakin / Structural Integrity Procedia 00 (2019) 000–000

441

10

  

  1 , n

(14)

QS S

A B    

where A , B and n are the constants that are supposed to be determined in order to satisfy Eq.(4). Dynamic multiplier   Dyn S   for the experimental set of Fig. 10 is chosen in the form close to Miller (1976) due to better test correlation:       0 1 sinh ln / , N Dyn S C              (15)   1 Dyn S    . Eventually, with all introduced assumptions, the problem is reduced to a solution of the following ordinary differential equation with the variation of a set of material’s constants: where C , N , 0   are material constants and in case of 0      the function













N









n

(16)

1  

1 sinh ln / C   

,

A B

12 G vt

0      









with a set of constants A , B , C , N ,

0   , n determined to match experimental curves of Fig. 10 as listed in Table 3.

Fig.10. Experimental and predicted shear stress versus strain diagrams

Table 3. Constants defined for experimental curves of Fig.10.

0  

A (MPa)

B(MPa)

n

C

N

G 12 (MPa)

75

76

1.5

0.06

0.00002

1.5

7500

7. Conclusion The failure prediction approach based on the degradation parameters for laminated composite materials is presented. Experimental verification for proposed model is performed based on widely used WWFE data to biaxial loading. The predicted results demonstrated satisfactory agreement with experiment. Another verification problem of composite specimen with the presence of concentrator was modelled and compared with experimental data. For this problem, constitutive equations taking into account nonlinearity of the shear stress–strain relations were used. The predicted loading diagram and spatial damage distribution correlate well with experiment. The mathematical model for materials with dependence of elastic properties on the type of loading was proposed. The constitutive relation to shear response with damage rate dependency supplements the developed model.