PSI - Issue 33

Toru Yagi et al. / Procedia Structural Integrity 33 (2021) 1225–1234 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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the pop-in is accompanied by an audible 'click'. When pop-in occurs during CTOD test, if that pop-in is judged as a fracture, the fracture toughness of the material is determined by the point of the pop-in (e.g., the point A of the P - V g curve shown in Fig. 2). If pop-in is judged as insignificant, the fracture toughness is determined by the point of a complete fracture (the point B of the P - V g curve shown in Fig. 2).

Fig. 1 Crack surface of CTOD specimen with a pop-in

Fig. 2 P - V g curve of specimen with pop-in occurrence

1.2. Review of study for pop-in judgment criterion ASTM E399, the first fracture toughness test standard using the stress intensity factor, K IC , used the 95% secant line as shown in Fig. 3 to evaluate the pop-in that was occasionally observed during the test. This standard, which requires a small yield state, does not allow for much blunting of the P - V g curve, and in effect does not allow for pop-in with a compliance change of 5% or more. The UK also adopted the K IC test developed in the U.S. as DD3 in 1972, and at the same time compiled its own CTOD test method as DD19. The secant line method should be considered as part of the criteria for determining deviation from the plane strain condition rather than as a criterion for determining pop-in. As the CTOD test became more widely used in industry and more pop-in was observed, it became necessary to clearly specify the criteria for pop-in in the CTOD test standard.

Fig. 3 95% secant line in ASEM E399

In 1986, Willoughby (1986) describes the mechanism of a pop-in crack formation with the theory of the stress wave. In the standard three-point bending test, when a small crack suddenly originates at the tip of the fatigue crack, a stress wave which breaks down the static balance originates at the crack tip as shown in Fig. 4. The stress wave then reflects at the lower jig which is a fixed-end reflection. The reflected stress wave then approaches to the tip of the propagating crack and the specimen becomes the more relaxed condition. Willoughby considered that a running crack which is small enough to be arrested before the reflected stress wave arrives will also arrest in real structure because he considered that this relaxation leads to decrease of the crack driving force. The velocity of the stress wave is that of the longitudinal wave which is about 5000 m/s. It is known that the crack velocity of the cleavage fracture is 500 m/s – 1500 m/s based on a numerous experimental study in this field, but the crack may decelerate during the crack propagation and arrest, so he set the crack speed to 100m/s in this study for the safety side consideration. Based on this theory, the maximum crack length of un-affectedly arrested brittle crack in the standard bending specimen is 4% of ligament. This consideration became the basis of the current pop-in judgment criterion in major standards.