As pointed out by Sajith and Brian, the state of stress near the surface will be plane stress and as you go towards the centre of the specimen, it will become plain strain. The state of stress basically dictates the extent of constraint that the crack tip will experience. That is the reason why you get a curved crack front, often called "thumb nail" fracture. As Brian explained if you take a sufficiently thick specimen, you will find the extent of curvature substantially reduced, because majority of the specimen (across thickness direction) will now experience plain strain state of stress and the region  under plane stress is negligibly small.

Your second question on prediction of crack front: The answer is theoretically yes. You may have to model the specimen (may be FE platform), apply load as you would do during experiments, evaluate the crack tip stress fields at various locations of the crack tip and monitor the resultant displacement vectors.

Answer to you second question is in the first para. If you have substantial curved crack front then you are dealing with predominantly plane stress situation and hence the fracture toughness that you get depends upon the specimen thickness you have chosen. If your crack front is more or less flat then you are imposing predominantly plain strain condition. Plain strain fracture toughness is thickness independent and hence the property of the material.

Hi,

I think it is related to the plane of maximum shear stress

Each point along the crack front grows according to the KI at that point and will have jumped whenever local crack tip KI exceeds fracture toughness KIC to a larger depth till again KI for the new crack depth falls below KIC for this new larger crack. 

Hi,

That is because the portion close to the surfaces are under plane stress condition where as plane strain condition prevails at center. Therefore the stress intensity factor at the center are larger and the crack propagates faster in the center of the sample leading to the curved shape of the crack front.

Hi,

As noted by Sajith, one major issue is the variation of plane stress to plain strain conditions along the crack front.  The crack will grow at different rates depending upon those conditions.  Often times, the wider the specimen, the more uniform plain strain type conditions exist and the less curvature will be observed.  It is the ratio of the two areas which exacerbate the curvature.  Edge grooves can increase the constraint on the surface and help to keep the crack front straight, if they can be accommodated by your material.

As pointed out by Sajith and Brian, the state of stress near the surface will be plane stress and as you go towards the centre of the specimen, it will become plain strain. The state of stress basically dictates the extent of constraint that the crack tip will experience. That is the reason why you get a curved crack front, often called "thumb nail" fracture. As Brian explained if you take a sufficiently thick specimen, you will find the extent of curvature substantially reduced, because majority of the specimen (across thickness direction) will now experience plain strain state of stress and the region  under plane stress is negligibly small.

Your second question on prediction of crack front: The answer is theoretically yes. You may have to model the specimen (may be FE platform), apply load as you would do during experiments, evaluate the crack tip stress fields at various locations of the crack tip and monitor the resultant displacement vectors.

Answer to you second question is in the first para. If you have substantial curved crack front then you are dealing with predominantly plane stress situation and hence the fracture toughness that you get depends upon the specimen thickness you have chosen. If your crack front is more or less flat then you are imposing predominantly plain strain condition. Plain strain fracture toughness is thickness independent and hence the property of the material.

Thank you very much for you all. It helped me a lot. 

Thanks guys !

Best regards

M.

Can one get crack front shape from equations? -- Yes, and here's one very recent paper on t he matter: "Numerical prediction of crack front shape during fatigue propagation considering plasticity-induced crack closure", doi:10.1016/j.ijfatigue.2016.03.018, where, I'm sure, you can find more relevant bibliography on the matter. Google can help you, too.

PS: surprisingly, another paper with nearly the same title published almost simultaneously with the formerly cited one: "Numerical Modeling of the Surface Fatigue Crack Propagation Including the Closure Effect", DOI:

10.1080/15502287.2015.1125402

Elfriede Bankwitz

Good Evening. In addition to the discussed physical aspects, and the important paper of Bouchaud et al., we should have in our mind one simple effect - from the geological point of view. The loss of cohesion starts at one point and propagates radially, forming a curvature of the crack front around a growing fracture plane (exquisite examples in nature, see the attached pictures). Ringlike features (e.g. arrest lines) on the crack surface mark the temporary crack front during propagation. All these characteristics can be formed in natural rocks (granites, sediments etc) as in a table of chocolate -- independent of the dimension or type of the material.

Regards Elfriede Bankwitz