Crack Growth Resistance Curve

For convenience in experimentation, the limitation on deviation from linearity may be expressed more conveniently in terms of the reciprocal slope of a secant line that connects the maximum load point Pp at pop-in and the origin. With reference to Eqn. (4.19) 

For the recommended range of values of Uo/W of 0.45 to 0.55, a value for H/50 of 0.05 has been adopted for the testing of single-edge-cracked specimens. This is embodied in the so-called hve percent slope offset method for establishing the pop-in load in ASTM Method E-399 for Plane Strain Fracture Toughness [2]. 

The question of how large a pop-in indication should be required can only be answered empirically. Ideally, the crack advance at pop-in should include sufficient material to be representative of the fracture property of the entire specimen. At this juncture, the consensus is that the increment of growth should be at least equal to the formally dehned plane strain plastic zone correction factor (see Eqns. (4.14) to (4.16)). This limit may be related to the load-displacement record in a manner similar to that discussed previously. 

In addition to these limitations, E-399 stipulates a maximum load level Pmax beyond the pop-in load to ensure validity namely, Pmax/F), 1.1. It should be recognized that this requirement, along with those discussed earlier, presumes that the specimen dimensions could be tailored to the expected fracture toughness of the material to be evaluated. In reality, judgment must be used in the interpretation and utilization of data. Depending on apphcations, adjustments in specimen sizes may be essential to meet code requirements, and commitment to specimen design should only be made after preliminary evaluations. 

Some commonly used specimens and stress intensity factor solutions are given in ASTM Method E-399 on fracture toughness testing [2]. Stress intensity factor solutions for other geometries are given in handbooks by Sih et al. [4] and Tada et al. 

---

G.E. Hale, A Testing Protocol for conducting J-crack Growth Resistance Curve Tests on Plastics, ESIS Draft Protocol, May 1994. 

Figure 7. Crack growth resistance curve of two initial crack lengths...

The single specimen technique was used to determine the value of the energy J versus crack growth Aa. The crack growth resistance curve is derived from experimental data, according to a power law J = b (Aa) (where b and c are constants). 

Macheret, J. and Bucci, R.J. (1993) A crack Growth Resistance Curve Approach to Fiber/Metal Laminate Fracture Toughness Evaluation , Eng. Frac. Mech. Vol.45, N0.6, pp.729-739. 

Fracture Behavior and Crack Growth Resistance Curve... 

Figure 2.11. Crack growth resistance curve for an ideally brittle material.

Figure 2.16. Crack growth resistance curves associated with Types 1 and 2 load-displacement response in Region C (Fig. 2.15) (a) for Type 1 response associated with thicker materials (b) Type 2 response for thinner materials.

Figure 4.18 shows the crack growth resistance curve as a function of crack length (i.e., the sum of the starting crack length and the individual crack growth increments) that had been constructed from the data (i.e., the local peaks and valleys in the load-displacement trace) in Fig. 4.17. The increase in crack-driving forces (in terms of G) at two stress levels are shown as dashed line. At the lower stress level, the trend line shows the inadequacy of the driving force to continue crack growth...

Figure 4.18. Crack growth resistance curve constructed from the load-displacement data in Fig. 4.14, showing the relationship between increasing stress, crack growth, and the evolntion of crack growth resistance and fractnre tonghness [8].

Fig. 2. /-integral crack growth resistance curves for Fe-49Ni at room temperature, 76 K, and 4 K. 

The concept of crack growth resistance curves (1 -curves) for determining critical stress intensity factors (Kc) is relatively new. A proposed standard method for -curve determination has been developed [ ]. The mechanics of i -curve testing with a crack-line-wedge-loaded (CLWL) specimen and the detailed pro-... 

Fig. 4. Crack growth resistance curves for cryogenic steels at -170°C (duplicate tests). Aaeffective effective crack length.

Figure 14.16 Crack growth resistance curves in partially stable zirconia (Mg-PSZ). The first two digits of the nomenclature show the average grain size, in microns. From Ref. [16].

Influence of Crack Growth Resistance Curve Upon Failure by Fracture 621... 

European Structural Integrity Society (ESIS) Testing Committee protocol for conducting J-crack growth resistance curve tests on plastics, in D. R. Moore, B. R. K. Blackman, P. Davies, A. Pavan, P. Reed, J. G. Williams, eds., Experimental Methods in the Application of Fracture Mechanics Principles to the Testing of Polymers, Adhesives and Composites, Elsevier, London, 2000, p. 140. 

Fig. 5.12. Plot of the crack-growth resistance Kir and the stress a versus the crack length a for the case of increasing Kir during crack propagation. In both figures, the same crack-growth resistance curve Kir(Ao) is plotted (after [104]) (2/2)...

If the crack-growth resistance curve Kir o) is known, this criterion together with the condition Ki(a,a) = Kui(a) allows to calculate the beginning of unstable crack propagation. 

---