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

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Fig. 8. The stress–strain diagrams under conditions of compression of the composite at the angles 0°, 22.5°and 45° to the direction of the warp of the cloth for longitudinal strain and for transverse strain

Fig. 9. The stress–strain diagrams for the conditions of shear with tension/compression directions 0°/90°, 22.5°/112.5° and 45°/ 135° for longitudinal strain and for transverse strain 6. Strain rate dependency Strain rate effect can be considered as a dependence of first ply failure (FPF) criterion on damage parameters 1  and 2  and their evolution during loading. Considering simplified FPF as maximum stress criterion Eq. (4), we can assume that the set of damage parameters or Xt , Xc , Yt , Yc and S depend on 1  and 2  . Only shear behavior is considered in this section since it is mostly susceptible to strain rate dependency. Thus let us introduce a relation   , S S     , where index 2 for 2  is omitted for briefness hereafter. During active process of damage accumulation stress components lay on FPF surface, which leads to the equation   12 , S      . Assuming linear shear elastic dependency one can derive following relation:   12 , S G vt      , (12) where v is strain rate (s -1 ) and t – time (s). Eq.(12) is a first order ordinary differential equation and can be solved numerically. In analogy with high strain rate plasticity, one can propose a decomposition of strength function:     , QS Dyn S S S      (13)

  QS S  is a quasi-static part of the material strength, and

  Dyn S   is a dynamic multiplier, which can change

where

  0 Dyn S    . Functions

0    and

the strength under conditions of high strain rate. In case of quasi-static loading

  QS S  and   Dyn S   should be determined to provide matching experimental curves with shear loading. Experimental results to high strain rate by Hsiao et al (1998) are presented in Fig. 10. Similar to Johnson–Cook hardening law, the function   QS S  can be determined by approximation of quasi-static curve using following form: