PSI - Issue 23

Tomáš Vojtek et al. / Procedia Structural Integrity 23 (2019) 481–486 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

482

2

distinguish between these two mechanisms in order to find the relationship between the material microstructure and its mechanical properties. Mechanisms of crack closure are not fully understood yet, especially in the near-threshold regime, where the roughness-induced crack closure (RICC) and the oxide-induced crack closure (OICC) mechanisms become significant due to very small crack tip opening displacement. At threshold loading, crack closure is a large constituent of resistance to fatigue crack propagation (Suresh (1998)), often even higher than the effective threshold. At the same time, threshold is a very important parameter for residual fatigue life estimations ( Pokorný (2015)) in the damage-tolerance approach, since the crack propagates in the short crack regime and in the near-threshold regime during majority of the component lifetime. There are indication that the short crack growth can also be described in terms of the effective stress intensity factor (SIF) range Δ K and a gradual crack closure build-up with the increasing crack length using the cyclic resistance curve approach, see e.g. Zerbst (2015). Separation of the intrinsic and extrinsic components is usually done by crack closure measurement or prediction of crack closure using available models, e.g. the model of plasticity-induced crack closure (PICC) by Newman (1981). In principle the most relevant method should be the separation of the effective curve d a /d N - Δ K eff from the applied curve d a /d N - Δ K , since the backwards re-composition gives directly and exactly the material behaviour under applied loading and stress ratio R. Moreover such obtained crack tip shielding is the sum of all components, both known and unknown, and one does not need to rely on precision of any models. On the contrary, the separated extrinsic component serves as data for calibration of the available models. The disadvantage of this method is that the effective curve has to be measured which is not always possible due to high mean stress or lack of specimens. The decomposition can be done at threshold even when the effective curve is not available, since the effective threshold is a well predictable parameter (Liaw (1983)) for many alloys. 2. Quantification of crack closure The SIF range is Δ K = K max – K min and the effective SIF range is defined as Δ K eff = K max – K cl for K cl > K min . Therefore, K max = Δ K eff + K cl . For the stress ratio R = K min / K max we obtain

 K K    1 max

(1)

 R

K

 R K K      cl 1

.

(2)

eff

Although K cl is called crack closure, the value obtained using Eq. (2) is the sum of all crack tip shielding effects. The only components that are known and can be present in the investigated material are PICC, RICC and OICC. ? OICC RICC PICC cl     K K K K (3) If other components are present, they cannot be taken into account simply because they are not known. For studying of the crack closure effects it is convenient to express K cl normalized to K max , which is denoted R cl , see e.g. McClung (1991), as a function of K max . (4) R cl also equals to the limiting stress ratio R , above which Δ K = Δ K eff . Substituting the Newman ’ s crack closure function f for PICC: max K R K K K    OICC RICC PICC cl

RICC K K

OICC

PICC R    cl f

.

(5)

K

max