PSI - Issue 28

N. Selyutina et al. / Procedia Structural Integrity 28 (2020) 1310–1314 N. Selyutina / Structural Integrity Procedia 00 (2019) 000–000

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2

applied load and the how composites experience the dynamic loads. However, the response of the composite at the onset of irreversible deformation varies depending on the structure of the composite. A model that takes into account the structural-time nature of the strain-rate effect is needed. Utilizing the structural-temporal approach, Petrov et al. (2007) suggested an incubation time-based criterion of dynamic yielding, which effectively predicted limiting loading parameters of plastic deformation and explained the instability of strain rate dependencies on the dynamic yield point. One conclusion, also reached by previous papers on this subject, is that strain-rate effect on any material yield strength cannot be considered as an intrinsic material property. These investigations eventually resulted in the relaxation theory of plasticity (Selyutina et al. (2015), Selyutina and Petrov (2019)). In this paper, the model is modified to predict regions of the deformation diagrams of glass- and carbon- reinforced fiber metal laminates as functions of metal thickness and strain rates. 2. The relaxation model of plasticity for effective compound materials In this study, we attempt to predict the deformation process of inhomogeneous fiber metal laminates using the relaxation model of plasticity (Selyutina et al. (2016)). This model was previously proposed for homogeneous materials and was applied to construct stress-strain curves in a wide range of strain rates. In this study, we continue to consider the fiber-metal laminate as a single compound material with effective mechanical properties, including Young’s modulus and yield strength. Given the uniaxial deformation behaviour of the fiber metal laminate such as the yielding of metallic layers, delamination and fiber layer failure, we expand the relaxation model of plasticity with the conditions for the fracture of some fiber-epoxy layers in a progressive manner as observed in the experiments. Let us introduce a dimensionless effective relaxation function 0< γ ( t )≤1, defined as follows



        

  s

    

     ds

t

1,

1

1,







y

t





( ) t

(1)





1









    

    

  s

  s

    

    

   

     ds

t

t

1

, 1

1.

ds













y

y

t

t









The equality γ ( t )=1 in (1) corresponds to the case of purely elastic deformation, t < t y . The time at the onset of yield t y is defined as the moment at which the equality sign in condition by (1) is attained. The gradual decrease of the effective relaxation function in the range 0< γ ( t )<1 describes a transition to the plastic deformation stage. During the plastic stage of deformation, t ≥ t y , the relaxation function γ ( t ) satisfies the condition



 

( )      y  

     ds

t

1

t s

1.

(2)

 



t



Here, we suppose that the equality (2) is retained from the onset of yield t = t y (the detailed calculation scheme for t y is given in Selyutina et al. (2016)) through the subsequent irreversible deformation process in the material (0< γ ( t )<1). We determine the true stresses in the deformed sample at t ≥ t y in the following form: ( ) ( ) ( ), t E t t    (3) where E ( t )= E γ 1- β ( t ) is the coefficient related to the uniaxial behaviour of stresses; E is Young’s modulus; β is the scalar parameter (0≤ β <1), which describes the degree of hardening of the material. The case of β =0 corresponds to the absence of hardening. At the time of fiber layer fracture, the force with which the effective material is loaded does not change, and compatibility relations are established as: