PSI - Issue 28

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

1312

3

(4)

, b b a a E S E S 

where E b is the effective Young’s modulus before the onset of the fiber layer fracture, S b is the composite cross sectional area before the onset of the fiber layer fracture, E a is the effective Young’s modulus after the fiber layer fracture and S a is the composite cross-sectional area after the fiber layer fracture. In other words, the fracture of the epoxy/fiber layers leads to a decrease in the effective Young’s modulus of the fiber-metal laminate, since the cross section of the sample reduces. In particular, a decrease in the rectangular cross section upon removal (or fracture) of the fibrous layer is directly related to a change in the composite thickness, and the change in the effective Young’s modulus of the fiber-metal laminate can be taken into account by the formula:

a b E E 

h h

b a

(5)

,

where h b is the thickness of the fiber-metal laminate before the onset of the fiber layer fracture, ha is the thickness of the fiber-metal laminate after the onset of fiber layer fracture. The fracture time t * i of of i th fiber layer is determined from the incubation time criterion of fracture (Petrov (2007)):

i 

     i i f 

   

  s

f

t

1

*

(6)

1,

ds





i

i 



i

f

t

f



*

i is the fracture incubation time of the i th fiber layer, σ f

i is the static strength of the i th fiber layer, and α f i is a

where τ f

parameter of amplitude sensitivity of the i th fiber layer. Considering the stages of elastic and plastic deformations separately, we can write the stress-strain relations in the case of a linear strain growth as ε ( t )= ε̇ t H ( t ) (the constant strain rate). In terms of relaxation model of plasticity, the effective stress of the fiber-metal laminate is expressed in the following form:                          . ( ), ( ) ... , ( ), ( ) , ( ), ( ) , ( ), ( ) * 1 0 2 * 1 * 1 ( ) 0 1 * 1 ( ) 0 0 1 1 1 0 0 n t E t Al y t t E Al y t t t E t t t t E t t t t E t E t t n                            (7) All parameters α , τ and β i are invariant to the loading history and only depend on structural transformations in the material. Introducing the independent mechanisms controlled by α , τ and β i parameters make it possible to predict the temporal effects of irreversible deformation of materials (Selyutina and Petrov (2019)) in a wide range of the strain rates. 4. Discussion The efficiency of the relaxation model of plasticity is verified for the glass- (Sharma et al. (2019)) and carbon- (Xia et al. (2007)) fiber reinforced aluminium laminates. The fiber metal laminate, considered by Sharma et al. (2019), consists of three layers of Al 2024-T3 0.4 mm thick and two layers of unidirectional glass fiber reinforced epoxy prepreg 1.25 mm thick. The fiber metal laminate, studied by Xia et al. (2007), has three layers of LY12CZ aluminium alloy of thickness 0.25 mm and two layers of unidirectional carbon fiber reinforced epoxy prepreg of thickness 0.3 mm. Both fiber metal laminates were subjected to quasi-static and dynamic tensile loading. Based on experimental          ( ) 1 t t E n  