In engineering, the damage that can be detected is usually called crack. But how to describe the small cracks which cannot be measured in the early stage of damage? Can we give a universal definition? Greatly appreciate your review.
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In inhomogeneous deformations across the specimen cross-section, crack can be easily obtained when stress concentrations exist.
To find it, you can use many detection methods such as; ultrasonic, magnetic particles, X-ray, and day penetrant.
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Gang:
How to define a crack? Your question is essentially how small can a crack be to still be considered as a crack, and more specifically what dimensions preclude the use of continuum and fracture mechanics to analyze such a crack. In general, for a continuum approach, which has the advantage of being widely applicable, a crack naturally needs to have at least one dimension larger than an atomic (or lattice) spacing.
As there are no size-scales in elasticity, in principle any sized elastic crack could be analyzed. However, from a fracture mechanics perspective, for the use of linear-elastic fracture mechanics (LEFM), its is any violation of the elastic constitutive law used that must be considered, i.e., this region of violation needs to be small enough to be ignored, e.g. the crack size (and the remaining uncracked ligament) should to be some 10 to 15 times larger than the crack-tip plastic zone.
For nonlinear elastic fracture mechanics (NLEFM) approach, the crack size (and remaining uncracked ligament) need to be at least a order of magnitude larger than the region of unloading, i.e., increment of crack advance) and the crack-tip zone of non-proportional loading. Indeed, the prevailing constitutive laws used to develop the fracture mechanics approach which is utilized will be in general determine what sized cracks (and what sized components) can be analyzed, as in the LEFM and NLEFM examples given above.
The physical definition, however, of when a crack is actually a crack is very relevant to the question of crack initiation for fatigue analysis and life prediction. Traditional total life (S/N) approaches to fatigue life estimation of course include initiation, but one doesn't generally need to know the dimensions of any crack formed as only the applies stress (or strain) and the number of cycles to failure are measured. For damage-tolerant life-prediction strategies, conversely, the crack size does become important, as conventionally the lifetime is calculated in terms of the cycles for the largest undetected crack to grow to failure. LEFM approaches work well here, e.g., by integration of the Paris law for fatigue-crack growth, but there are problems with small cracks which can display non-conservative behavior, i.e., faster growth rates (and lower fatigue thresholds) than larger cracks at the same applied stress-intensity range. For a brief classification of the relevant crack sizes here, the reader is referred to the attached reference on small fatigue cracks.
If we could perform such damage-tolerant life-prediction calculations and include crack initiation, this would dramatically enhance predicted lifetimes but, in addition to the question at hand as to when a crack is actually a crack, this is a tall order as the initiation life is invariably a marked function of the nature of the component surface, and to reliably characterize the surface condition in, for example, every turbine blade in every gas turbine, would be impossible. However, a recent study has attempted to characterize the precursor microstructural damage prior to the formation of an actual crack (Lavenstein et al., Science, 370 (2020) 190), and if this approach can ever be feasibly harnessed industrially, then maybe the question of when a crack is actually a crack may not be so important!
ROR
Any discontinuity in a solid material is taken as a crack. If the discontinuity is present on the surface, it is called surface crack. If the discontinuity exists inside the solid material, it is called internal crack. Non-destructive testing techniques which are used to detect/locate cracks, essentially detect any discontinuity in the material.
to break or to make something break so that a line appears on the surface, but without breaking into pieces.
The line which appears on surface when the material is hit by a hammer due ti its impact is also a crack (surface crack) and it may extend deep inside the material or even become a through crack leading to fracture.
A defect (looks like a crack, hole, void) or group of similarly oriented grains (difficult to detect) when loaded that causes plasticity. If a visible defect, it may exhibit "opening displacement." On repeated loading, visible defects may exhibit deformity. To detect the plasticity associated with a defect may require high resolution imaging and image comparison. Plasticity may occur due to in-plane as well as out-of-plane displacements. In high cycle fatigue, interior defects may exhibit plasticity and I know no way to detect them.
I couldn't answer nearly as well as some of the above already have. I'm more of a practical engineer, not getting too deep into the science.
In my opinion, and not going into the calculative or scientific definition, a crack can be considered to be an imperfection in a material which can lead to a part's failure to perform the desired function. So, in the context of a shiny table top, a small imperfection which can cause the table top to look bad will be considered a surface crack. However, in the context of a shaft, surface abrasions can not be considered as cracks unless they hinder the safety, integrity and functionality of the shaft.
The planer discontinuity in the order of 4 angstrom units can be considered as a crack.
Hi Gang Zhu
As you know, there are many methods to detect defects and so many types of cracks. in case of your question, for describing the size of the crack, based on the resolution and precision of the method for identifying the size of the crack, you can name the type of crack that you can't find in the previous stage, for example, micro-crack, nano-crack and so on.
For fine ceramic, I think using X-ray CT to scan structure and measuring the small cracks as pores is a feasible path. It will help us to quantitate the small cracks.
We quote Bilby and Eshelby (1968): "To discuss the crack field and its interaction with other inclusions and inhomogeneities, it seems most satisfactory to adopt the following point of view and treat a crack as an inclusion at whose boundary there is zero surface traction, or a narrow zone where the elastic constants are zero."
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