PSI - Issue 33

Sergey Smirnov et al. / Procedia Structural Integrity 33 (2021) 259–264 Author name / Structural Integrity Procedia 00 (2019) 000–000

261

3

Therefore, it is possible to speak about the repeatability of the experimental data and about the applicability of Arcan specimens.

Table 1 – Experimental data and processing results α, (0) P max , (N) ν, %

σ n , (MPa)

σ s , (MPa)

W n , (kJ/m

3 )

s , (kJ/m

3 )

W

90

675 720 812 970

2.9

0

4.50 4.43 3.82 2.47

0

5.67 5.51 4.11 1.72

67.5

14.0

1.84 3.82 5.97 7.52

0.35 1.53 3.72 5.89

45

5.7 7.8 4.6

22,5

0

1127

0

0

Suppose the stress state at the epoxy/substrate interface is homogeneous; therefore, to evaluate it, we use the average values of normal σ n and shear σ s stresses,

P

P

(1)

,

max

max





s 



n

cos( ) 

sin( ) 

S

S

where P max is the tensile load corresponding to the moment of adhesive joint failure, or failure load; S is the area of adhesion. The loading diagrams are linear dependences; consequently, failure occurs within elastic deformation of the polymer coating. The formulation of the local failure criterion uses the assumption that the strain energy density in a selected microvolume including the joint is the driving force for the delamination of the adhesive joint under a force action. For this purpose, a microvolume simultaneously belonging to the glue and the substrate is conventionally selected on the joint, which is inside and along which slippage and delamination are prohibited. The microvolume is balanced at a given time, and on its opposite faces there are equal stresses σ ij in a local coordinate system ( x ', y ', z '). The z '-axis is directed along the normal to the joint, and the x '- and y '-axes lie in its plane. The stresses σ ij are calculated from solving a problem on the determination of the stress-strain state. The effective values of the components of elastic strain ε ij in the microvolume can be found from the physical equations

1 3 ij      ij    

2

,

G

 

 

ij

ij

3 k    is hydrostatic stress,

2(1 ) G E    is the shear modulus, ν is Poisson’s ratio, ε = ε ii is volumetric

where

(1 2 ) k   

strain, is the bulk modulus, δ ij is the Kronecker symbol ( δ = 1 when i = j , δ = 0 when i ≠ j ). The values of the strain energy density components W n and W s in the selected microvolume are calculated as E

2 E   , n

2  

2 (2) The following formulas can be used to find the effective values of the normal elastic modulus � , the shear modulus ̅ and Poisson’s ratio ν� for the selected microvolume under a plane stress state in the first approximation (Daniel et al. (2006), Hsieh et al. (2005)): n W 2 s s W G