PSI - Issue 22

W. Zhang et al. / Procedia Structural Integrity 22 (2019) 251–258 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

255

5

level the same, the maximum cohesive strength decreases as the loading time increases. As shown from the test results, when the applied load level is 10N and the duration is 20h and 40h respectively, the maximum cohesive strength in the curve is 38N and 33N. This shows that the cumulative effect of load has a significant effect on degradation of the sealing. Within a fixed duration of time, the load acting on the sealing area will result in the decrease of cohesive energy. 3. Theoretical analysis 3.1. CZM’s definition and calculation The CZM is a mathematical model based on elastic-plastic fracture mechanics, which defines a virtual crack to describe the dynamical stress field between virtual interface. In this study, we use the exponential CZM to simulate the virtual cracking process of the cohesive zone, i.e. the overflow adhesive area in specimen. The constitutive relation of the cohesive zone is defined by the traction and the separation at the interface. In the CZM with monodirectional cracking, the relationship is given by: max = exp 1 c c              (1)  (N) indicates cohesive strength,  (mm) indicates displacement, max  indicates the maximum cohesion, c  indicates a critical displacement where the cohesion decreases as the separation increases. In the experiments, after the displacement reaches the critical point, the separation increases with smaller load. Figure 10 shows the relation curve between τ and . Therefore, the area integral of the relation curve is the fracture energy of the interface. Parameter c G is used to indicate the fracture energy: max = c c G e   (2) equation (1) can also be expressed as: = exp c c c c G              (3) Because the maximum bond strength is defined as the critical failure point, only the fitting before the critical point is compared, situation after the critical failure point does not meet the physical condition of CZM. Based on the average value of test results, max  is 44.97N and c  is 2.08mm. Therefore, the fracture energy c G calculated according to equation (3) is 254.26 N  mm=0.25426 J. The sealing cohesive strength CZM expression for specimens in this paper is as follow: = 254.26 exp = ( ) 2.08 2.08 2.08 f            (4) Figure 11 shows the exponential CZM obtained from the fitting curve in Figure 7. The overall trend and failure point of the two curves are consistent. This paper will use this strength-displacement CZM curve to characterize the cohesive failure process of the sealing area.

adhesive strength-displacement curve

0.05

0.045

0.04

0.035

0.03

0.025

τ/kN

0.02

0.015

Model Test

0.01

0.005

0

0

0.5

1

1.5

2

2.5

3

λ/mm

Fig. 10. Cohesion-displacement curve

Fig. 11. Comparison of model curve and test result.