PSI - Issue 50

Danila D. Vlasov et al. / Procedia Structural Integrity 50 (2023) 299–306 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

301

3

Fig. 3. Calculation scheme of the joint.

Consider a package of unit width with length dx (Fig. 3, b). The equilibrium equations of the upper (index 1) and lower (index 2) elements of the joint are written in the form:

1 dN N N dx dx dx dN N N dx dx dx             1 1 2 2 2 xz xz

0

(1)

0

From where, after simplification, we can get:

dN dx dN

0

dx

1

xz   

(2)

0

dx

2

xz   

dx

Due to the occurrence (according to the hypothesis) in the adhesive layer only shear stresses, the shear strain in it is denoted as follows:

(

)

u u 

; xz 

G

1

2









(3)



By further differentiating the expression (3):

(

)

1      2

d dx



(4)

And substituting in it the strain of a unit cell of unit width: