The fracture of a solid almost always occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displacement develops in this case perpendicular to the surface of displacement, it is called a normal tensile crack or simply a crack; if a displacement develops tangentially to the surface of displacement, it is called a shear crack, slip band, or dislocation. - Definition from "Mechanics of Brittle Fracture" 

Thanks David, I didn't know this source and it looks like a definition typical from fracture mechanics, we could develop something in the sense of defining a crack through the singularity in the displacement field (it looks to me that your definition goes in that way. I think my definition is more mechanistic. Do you believe it is wrong?

Cláudio -

A more physical description of a crack might involve the intermolecular forces between two surfaces. In the Dugdale model, there is a critical surface displacement at which the two surfaces no longer feel the force from each other. We might imagine a crack as a displacement between opposing surfaces that exceeds the effective range of the forces.

-Jon

A crack in a structural member introduces local flexibility that would affect vibration response of the structure.

We can use this definition from Bilby and  Eshelby (1968): We can treat a crack as an inclusion at whose boundary there is zero surface traction, or a narrow zone where the elastic constants are zero.

The material is assumed to be under load.

Hi,  I'm very pleased with the discussion, I believe we can define cracks in multiple ways. My definition was more "engineering-like" (my student wanted a definition which would prevent calling a forging fold a crack). Most of the other definitions come from the effect of a crack in the displacement/force field of the otherwise continuous body. I remembered we have the book of Kerson Broberg (Cracks and Fracture, Academic Press, 1999), my favorite author, in the library, I quote:

"A crack may be defined as a material separation by opening or sliding, with the separation distance substantially smaller than the separation extent - the crack length" then, later he completes "the separation distance is often comparable to certain micro-structural length dimension..." calling the Barenblatt-Dugdale critical distance inside the definition.

Maybe some FEM expert would define a crack a "discontinuity in the displacement field with a cohesive zone at the tip".  The problem with the "critical distance" would be that, in order to decide whether a discontinuity is or is not a crack, we would need to know this critical distance, I still believe my definition is more "operational" . in this sense. 

Another problem is with cracks which have propagated through the whole body section. Is is still a crack, or not.? It seems to me that the Bilby Eshelby definition would still consider this a crack, but the definition by Broborg would not (the separation distance would be unbound, so it would be, in principle, larger than the separation length.

What do you think?

I think it depends on which scale you are talking. Micro or Macro?

It's kinda link porosity, which can have different formation mechanism in micro or macro scales.

Ehsan, I think we can produce definitions for both scales. Maybe they should be different for each scale. Porosity should not be considered a crack, but in ductile fracture we have cracks which evolve from adjoining voids (as in the standard Gurson model), so, you see, this definition should be flexible enough to to allow one case  to be called a crack and not the other. So, you see, this is not about semantics.

Dear Claudio, I think your definition is clear and simple,  so, as a definition, it's very good. If we include the atomic scale, we would have to discuss the Quantum Mechanics and then it would be a mechanism discussion.  We can say, for example,  that a crack starts as a perturbation in frequency distribution  of the atoms vibration (Debye).

I think that due their ambiguous shape and characteristics , a crack needs two kinds of definition: a engineering (macro) and another in atomic scale.

And about the "pre-crack" terminology? Newman and another researchers have used this concept (Fatigue Crack Growth Thresholds, Endurance Limits, and Design, STP 1372, ASTM). I am always very curious about it.

One could argue that no definition in needed, everybody (even children) know what is a crack, but I agree with you, the definition must be adapted for the particular context. I was thinking about this, according to my definition, Irwin's crack would not be a crack, since it is introduced as a discontinuity in a semi-infinite x axis (so it has no point of origin and does not grow, it is just a mathematical object), but in engineering we need something more substantial than a mathematical abstraction, for example, in a badly performed weld, if the molten zone detaches from the base metal (maybe because it didn't melt the base metal), this should not be called a crack.

I think your definition is a good one for use in the field of fracture mechanics. However, it is too specific for other purposes. My computer's dictionary defines a crack as:

"a line on the surface of something along which it has split without breaking apart" 

but even that is too specific. It does not allow for cracks inside bulk materials. Here is my try at a "scientific" definition specific to solid materials: 

Crack: A place in or on a solid material where there is an absence of solid material, and the linear magnitude of either one or two dimensions of this absence (its length and/or width) greatly exceed the linear magnitude of its third dimension. 

The problem is of course that one has to define "greatly exceed."

My only worry with my definition is about the last part. A crack which grew so much that it indeed split the body in two parts is still a crack or we should not use this name for this? It seems to me that the two definitions you gave prevent using the name crack for this situation, but we could argue that a crack is still a crack infinitesimally before breaking the solid in two parts, but not immediately after? It seems to me that continuity would require that the crack continues being a crack even after the total fracture.

I think a crack ceases to be a crack after a solid material specimen has split into two parts at the place where the crack previously existed. I guess I would call the result the two "crack failure surfaces." 

A crack is a crack is a crack

of which Griffith found not a lack

even if oilmen call it a frack

a crack is a crack is a crack

@CH.H. Scholz: Best (actually only) poem I have ever seen on RG. A fracking good poem in my opinion. 

Briefly, crack is a surface inside a solid, where the interaction of its parts is manifested only in compression, as if the body has been dissected within the surface.

This question is directly related to the preparing of the fracture mechanics specimen of thin material in lab. Is it enough just to cut by a knife? If not, how to perform a sharp crack?

Sharon, this has a deep significance for polymer fracture mechanics, we have some results which indicate this depends on the polymer. This situation is in the edge of the definition I mentioned.

A crack consists of two surfaces within a solid body, between which atomic bonds do not exist, and where the surfaces are bounded by their intersections with the surface of the body or by a line along which atomic bonds exist. The surfaces are called fracture surfaces or crack faces, and the line is called the crack front.

I think that the exact definition of a crack depends on what you want to do. What you want to study or understand. If it is mathematical you may need a mathematical definition. My Ph D thesis was about "Lipschitz crack domarns". This is a bounded domain in two dimensions where the boundary can locally be described by a Lipschitz continuous funktion that contains a Lipshitz curve, the crack, whith one end on the boundary of the domarn and one end in the interiör.

With this definition is was possible to characterize the solvability of the Dirichlet probelm for the Laplace equation with L^p-data on the boundary of the Lipschitz crack domain.

I think also that the definition depends of your objectifs.

Cracks, crack initiation, crack growth process induce different domage levels on materials and structures

Hakan, is there a physical basis to constraining the 2D crack to Lipschitz-continuous shapes?

It does'nt depends on material.

crack = tensional fracture = fracture in wich the movement is mainly perpendicular to the walls

normally are the first to form in fault evolution, but also are formed during the development of the faults 

I am not that wise to answer this but I would like to answer.

To define something is to put the subject in boundaries, which gives the subject a uniqueness by distinguishing it from similar and non-similar features, I guess.

Whereas, crack is a broad domain. A micro-crack is also a crack and a notch is as well. A hole of any shape or a gap is a crack. But  a hole filled with something is not a crack as long as it does not delaminates, because mechanical continuity will be there, so a grain boundary is not a crack. An inclusion in a steel matrix is also not a crack.

Having said that, I would define a crack as hole in or on the surface of a solid[ I wont say discontinuity, as that would be a vague term liable to be confused with stacking faults or interfaces] which has a surface associated with it and a ligament susceptible to crack growth stably or catastrophically. 

In general, definition of a word consists of specialized vocabulary used in a particular profession or technical field and understood by the people. Thus, definition based on specialized vocabulary can only be understood by the people in that field but not the people outside the field. This is what I noticed in many definitions for crack given above such as in Fracture Mechanics or Metallurgy and Materials Science. To simplify, a crack for people in science and technology can be defined as "the line of intersection of a separated surface in a solid with the outside surface having a small gap with respect to the width and the depth creating a two dimensional character". If the audience is technical people with some knowledge of fracture mechanics , then the gap may be replaced by crack opening displacement (COD), or the crack origin etc.

If an opening tends to expand in any direction unexpectedly way, this may said to be a crack. If it does not, it is as it before.

I believe the correct definition of a crack depends on the material scale you consider.

If we consider continuum mechanics, the concept of a crack should be defined with respect to the initial configuration, as the other physical quantities are defined (not to be confused with the difference between Lagrangian and Eulerian coordinate systems). Given that n is the dimension of the manifold (i.e. the continuum, n=1,2,3), the crack is a N-1 submanifold (point, line or surface) that modifies the geometric connection of the continuum in its initial configuration. More physically, if a 3D continuum has no discontinuities in the initial configuration, the appearance of a crack is the appearance of a geometric discontinuity (an internal surface) at some point of the deformation history. From the change in the geometric (or metric) connection of the continuum stems the change in the elastic fields (we can be viewed as discontinuities only if we refer to an uncracked initial configuration). Two interesting observations can be made. First, the concept of a crack runs contrary to one of the basic assumptions of continuum mechanics, i.e. that the geometric connection of the continuum remains unchanged during the deformation history. Second, theories like Linear Elastic Fracture Mechanics, that deal only with initial flaws and do not evaluate crack propagation, are not actually considering cracks but extremely peculiar geometries (for example, a plate with an internal cut and sharp corners).

If we move to discrete mechanics (molecular dynamics), onset of a crack corresponds, at first sight, with bond breaking. However, let us consider a themoset polymer. Polymer chains in such material are linked together by chemical bonds in all 3 directions. But they are also intertwined with themselves and with the other chains (mechanical locking). Thus, separation of chains and consequent crack onset implies not only bond breaking but also frictional dissipation and dissolution of mechanical interlocking configurations. Thus, we could say that cracking at the microscopic level entails separating molecules up to a point where they will not link together again without external work.

And this leads to the third consideration I want to make. Crack onset and propagation imply dissipation of energy into heat and/or sound and consequent increase of entropy. These two are fundamental in distinguishing cracks as physical phenomena and not mere geometric features.

Thus, a definition of crack could be:

given a N-dimensional continuum, a crack is a N-1 geometric object that modifies the initial geometric (metric) connection of the continuum. At the microscopic level, this corresponds to the separation of atoms and molecules to the point where they will not form any link (chemical, mechanical, electrostatic,...) without external work supplied to the system. The appearance of a crack is distinguished by dissipation of energy into heat and/or sound and increase of entropy.

Your definition of crack seems to be two dimensional: it's a surface where the body is not connected. Not a pore or a nail hole. That agree's with my intuition.

I think the definition depends on what you want to study. If you are interested in the mathematics of it you want to know about mathematical properties. I did work in the 80-ies about Lipschitz cracks in two dimensions, so the crack was a Lipschitz curve. It has limited derivative, but not differentiable in all points. One can similarly talk about Lipchitz surfaces. One can expect other communities to have develop other definitions of cracks with they have worked with for some time, depending on their traditions and what they try to study.

There is a similar question related to the issue here: how are cracks different from voids. In material science and engineering we are sometimes concerned with failure mechanisms e.g. through formation of a crack (due to fracture of an inclusion or a second phase particle) or formation of a micro void (at grain boundaries, triple junctions or other interfaces). In my opinion, cracks forms by breaking of bonds and this does not change the density of the specimen while formation of a void is associated with a decrease in density. Thus, crack formation due to particle fracture should be an elastic process which with subsequent plastic deformation may grow into a void.