PSI - Issue 50

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

302

4

; 1 N N h Eh   





(5)

Using relations (2), we obtain first- and second-order differential equations containing the required shear stresses τ xz and longitudinal coordinate x .

1 G dx Eh   G dx Eh    1 xz d 2 2 2 xz d





N N 

(6)

1

2



0





(7)

xz

The solution of equation (7) is found in the form:

2

G

( ) Cshkx Cchkx k  ( );

(8)







1

2

xz

Eh



From where we get the distribution of shear stresses along the length of the adhesive joint. For the initial illustrative data: N =100 N, E =70*10 9 Pa, G =15*10 9 Pa, and at dimensions: h =5 mm, δ =0.2 mm, l =10 mm the stress distribution is shown in Fig. 4.

2          l   

ch k x

Nk





(9)

xz

2       kl

2

sh

Fig. 4. Shear stress distribution along the length of the adhesive joint.

From (9) and Fig. 4 it is obvious that the maximum shear stresses occur at the edges of the joint at x =0 and x = l . In this case, the value of the shear stresses can be determined by the equation (10):