PSI - Issue 54

Rahul Iyer Kumar et al. / Procedia Structural Integrity 54 (2024) 164–171 Iyer Kumar, De Waele / Structural Integrity Procedia 00 (2023) 000–000

167

4

quasi-static tests on identical DCB specimens is determined and used as reference for the maximum load F max that is applied to the specimen during the fatigue test. Initially, F max = 30%( F crit ) avg was chosen as the load for the first loading block and subsequently increased to 40% , 45%and 50% of ( F crit ) avg . Experiments were performed on a servo-hydraulic testing machine with a load cell capacity of 5 kN. A load ratio R = 0 . 1 and a frequency of 4 Hz are selected for the fatigue tests, these values are chosen so as to be consistent with the previous work done as part of the QUALIFY project (Jaiswal et al., 2020; Iyer Kumar et al., 2021, 2022). During each test, besides recording the load and actuator displacements, digital image correlation (DIC) and a strip of “millimeter paper” attached to the steel part of the DCB specimen are used for measuring strain fields and crack length respectively.

2.3. Data reduction method

The crack driving force for steady-state crack growth under mode I loading is given by Eqn. 3, where P is the load applied, C is the specimen compliance, B is the specimen width and d a is the instantaneous crack length extension, where the crack front is assumed to be straight.

P 2 2 B

d C d a

G I =

(3)

Standard ASTM D6115 suggests using the Modified Beam Theory (MBT), Compliance Calibration method (CC) and Modified Compliance Calibration method (CMM) to compute the cyclic SERR; however, this standard is appli cable to fibre-reinforced polymer matrix composite specimens. In our case, a DCB specimen bonded with a ductile adhesive and having a thick bondline, the model proposed by Kanninen (1973) and modified by Penado (1993) is used to determine the SERR. Lopes Fernandes et al. (2019) has used this model for statically loaded DCB specimens with thick adhesive bondline. The Kanninen-Penado model considers a beam which is free at one end and supported by an elastic foundation at the other representing the unbonded and bonded regions respectively; the DCB specimen is symmetric about the centerline of the adhesive layer as shown in Fig. 3.

Fig. 3: A schematic representation of a DCB specimen modelled according to the Kanninen-Penado model (Heide-Jørgensen and Budzik, 2017; Lopes Fernandes et al., 2019)

The strain energy release rate under mode I loading condition is given by

4 k

P 2 BEI λ 2

( λ 2 a 2

G I =

(4)

+ 2 λ a + 1) where λ =

4 EI

where P is the load on the specimen, a is the crack length, E is the elastic modulus of the adherend, I is the moment of inertia of the beam and k = E ad B t is the sti ff ness of the foundation which depends on Young’s modulus E ad of the adhesive, half-thickness of the bondline t , and width of the specimen. λ − 1 is known as the process zone length which is di ff erent to the fracture process zone. The process zone is interpreted as a distance from the crack tip over which a positive peel stress is distributed (Heide-Jørgensen and Budzik, 2017).