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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7

Fig. 6. Loading diagrams for open hole compression problem

5. Nonlinear anisotropic elasticity with susceptibility to stress state conditions The typical experimental results on loading of fabric/epoxy composites to tension/compression with different (“off axis”) warp orientation to load direction, presented by Smith and Pascoe (1977), are shown on Fig. 7-Fig. 9. Due to the obvious nonlinearity of these diagrams, one can find problematic an accurate failure prediction in combined stress state without model of nonlinear elasticity. A possible approach of anisotropic nonlinear elasticity is proposed by Lomakin and Fedulov (2015). It is based on introduction of triaxiality parameter  for the stress state characterization: 0 / ,     where 1 / 3 ii    is the hydrostatic stress component, 0 3 / 2 ij ij S S   is von Mises equivalent stress, ij ij ij S     is stress deviator components. For the developing of the nonlinear shear material model the parameter that represents the degree of shear loading or deformation should be formulated. This role could be taken by a parameter ij ij Q D   , where coefficients D ij have the following representation in coordinate system coincident with the orientation of anisotropy axes:

0 1/ 2 0 1/ 2 0 0 0 0 0

   

    

(7)

ij D

 

Elastic potential can be expressed in the form dependent on stress triaxiality and shear parameter Q as shown below:

1





(8)

, ij kl A Q     

2 ijkl

The constitutive equations obtained on the basis of potential Eq.(8) in case of plane stress conditions with the limited range for the triaxiality parameter 3 / 2 3 / 2     can be represented in following form: