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Currently working on: Crack Closure

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Crack closure is a phenomenon in fatigue loading, during which crack remains in a closed position even though some external tensile force is acting on the material until the applied force reaches a critical value. Crack closure can arise from many sources including plastic deformation or phase transformation during crack propagation, corrosion of crack surfaces, presence of fluids in the crack, or roughness at cracked surfaces.

Crack closure effect (example of R=0). Stress intensity factor, K, is calculated from the external applied force P, and the crack tip opening displacement, CTOD, varies with time during a sinusoidal cycle of K. Nominal stress intensity factor range, ΔK, is calculated from K_max and K_min. However, crack closure occurs when K < K_cl even though under positive K,allowing us to define an effective stress intensity range, ΔK_eff from K_max and K_cl, which is less than the nominal applied ΔK.

During cyclic loading, a crack will open and close: the crack tip opening displacement, CTOD, will vary cyclically in phase with the applied force. Obviously, if the loading cycle includes a period of negative  force (i.e. R < 0) , then during this period CTOD will be equal to zero as the crack faces are pressed together. It turns out, however, that CTOD can also be zero at other times, even when the applied force is positive. In this case, the stress intensity factor, K, can not reach its minimum anymore. Thus the amplitude of the stress intensity factor, ΔK, is reduced relative to the case in which no closure occurs, reducing the crack growth rate. As R increases to above approximately 0.7 the crack faces do not contact even at the minimum of the load and closure does not occur.

$\Delta K=K_{max}-K_{min}$

$\Delta K_{eff}=K_{max}-K_{cl}$

$\Delta K_{eff}\leq \Delta K$

Where ΔK is the stress intensity factor range, K_max is the maximum stress intensity factor, K_min is the minimum stress intensity factor, ΔK_eff is the effective stress intensity factor range, and K_cl is the stress intensity factor when the first fracture surface contact takes place.

The phenomenon of crack closure was first discovered by Elber in 1970. He observed and confirmed that a contact between the fracture surfaces could take place even during cyclic tensile loading. The crack closure effect helps explain a wide range of fatigue data, and is especially important in the understanding of the effect of R ratio (less closure at higher R ratio) and short cracks (less closure than long cracks for the same cyclic stress intensity).

Plasticity-induced crack closure

The phenomenon of plasticity-induced crack closure is associated with the development of residual material on the flanks of an advancing fatigue crack. To understand the mechanisms of this phenomenon, two cases need to be distinguished: plane stress and plane strain.

Under plane stress conditions, the piece of material in the plastic zone is elongated, which is mainly balanced by an out-of-the-plane flow of the material. Hence, the plasticity-induced crack closure under plane stress conditions can be expressed as a consequence of the stretched material behind the crack tip, which can be considered as a wedge that is inserted in the crack and reduces the cyclic plastic deformation at the crack tip and hence the fatigue crack growth rate.

Under plane strain conditions and constant load amplitudes, there is no plastic wedge at large distances behind the crack tip. However, the material in the plastic wake is plastically deformed. It is plastically sheared; this shearing induces a rotation of the original piece of material, and as a consequence, a local wedge is formed in the vicinity of the crack tip.

Phase-transformation-induced crack closure

Deformation-induced martensitic transformation in the stress field of the crack tip is another possible reason to cause crack closure. It was first studied by Pineau and Pelloux and Hornbogen in metastale austenitic stainless steels. These steels transform from the austenitic to the martensitic lattice structure under sufficiently high deformation, which leads to an increase of the material volume ahead of the crack tip. Therefore, compression stresses are likely to arise as the crack surfaces contact each other. This transformation-induced closure is strongly influenced by the size and geometry of the test specimen and of the fatigue crack.

Oxide-induced crack closure

This occurs where rapid corrosion occurs during crack propagation. It is caused when the base material at the fracture surface is exposed to gaseous and aqueous atmospheres and becomes oxidized. Although the oxidized layer is normally very thin, under continuous and repetitive deformation, the contaminated layer and the base material experience repetitive breaking, exposing even more of the base material, and thus produce even more oxides. The oxidized volume grows and is typically larger than the volume of the base material around the crack surfaces. As such, the volume of the oxides can be interpreted as a wedge inserted into the crack, reducing the effect stress intensity range. Experiments have shown that oxide-induced crack closure occurs at both room and elevated temperature, and the oxide build-up is more noticeable at low R-ratios and low (near-threshold) crack growth rates.

Roughness-induced crack closure

Misfit of fracture surfaces in roughness-induced crack closure

This concept explains the crack closure phenomena in mode II type of loading, which is due to the misfit of the rough fracture surfaces of the crack’s upper and lower parts. Due to the anisotropy and heterogeneity in the micro structure, out-of-plane deformation occurs locally when Mode II loading is applied, and thus microscopic roughness of fatigue fracture surfaces is present. As a result, these mismatch wedges come into contact during the fatigue loading process, resulting in crack closure. The misfit in the fracture surfaces also takes place in the far field of the crack, which can be explained by the asymmetric displacement and rotation of material.

Roughness induced crack closure is justifiable or valid when the roughness of the surface is of same order as the crack opening displacement. It is influenced by a lot of factors including grain size, loading history, material mechanical properties, load ratio, type of the specimen and so on.