You are right, that's because plane strain conditions are dominant in the center of the sample whereas  plane stress conditions are prevalent close to the surface of the sample. As the stress intensity required for crack propagation under plane strain conditions is smaller than under plane stress conditions a crack propagates faster in the center of a sample leading to the curved shape of the crack front. Hope this helps!

Could you please tell us what is the shape of the crack in planes perpendicular to the direction of fracture propagation? If the crack front is wavy in planes perpendicular to the direction of fracture propagation, a reason for the curved shape of the crack path may be due to dislocations generation from the tip of the crack in three dimensions. In the case of a loaded crack in an homogeneous solid, we know works by Samuels and Roberts (1989) and George and Michot (1993): most of the dislocations are generated on planes cutting the crack front at one point. Also the works of Ohr and Chang (1981, 1982, 1983, 1985) gave some crucial informations on the behaviour of dislocations ahead of the crack-tip, in particular the existence of a dislocation-free zone between the crack and the generated dislocations. These lead to a model of elastic-plastic crack with an oscillatory front (see our contribution: Significance of the deviations of the crack front into the plane perpendicular to the crack propagation direction- I. Crack-front dislocation generation ). This treatment can be improved to deal with a curved shape of the crack front, in planes parallel to the direction of fracture propagation, by incorporating the more general analysis: An analysis of a non-planar crack under general loading using continuously distributed sinusoidal edge and screw dislocations. Please see these contributions in Research Gate. 

References:

Ohr, S.M. (1985). An electron microscope study of crack tip deformation and its impact on the dislocation theory of fracture. Materials Science and Engineering 72, 1-35.

Samuels, J. and Roberts, S.G. (1989). The brittle-ductile transition in silicon. I. Experiments. Proceedings, Royal Society London A421, 1-23.

George, A. and Michot, G. (1993). Dislocation loops at crack tips: nucleation and growth- an experimental study in silicon. Materials Science and Engineering A164, 118-134.

Bernd answered your question

To Agmar: Could you please tell us what is the shape of the crack in planes perpendicular to the direction of fracture propagation? Is the shape wavy? Also, if it is wavy, what is the wavelength?

Please let me add that I understand that we are dealing with fracture mechanisms pertaining to large specimens where surface effects are not relevant. In general the shape of the propagating crack, in ductile materials, is influenced by dislocations. 

Some additional evidences of the effect of dislocations on the fractured surfaces may be found in Hull et al. (1965) and in Henshall et al. (1977): fractured surfaces are rough when viewed along the crack propagation direction; this roughness (i.e., deviation of the crack front from straight line) increases with increasing amount of plasticity.

Hull, D., Beardmore, P. and Valintine, A.P. (1965). Crack propagation in single crystals of tungsten. Philosophical Magazine 12, 1021–1041.

Henshall, J.L., Rowcliffe, D.J. and Edington, J.W. (1977). Fracture toughness of single-crystal silicon carbide. Journal of the Americal Ceramic Society 60, 373–375.

If you analyze a mode I fatigue crack in a plate with a straight crack front normal to the surface in 3D, you actually get a slightly higher delta K in the center of the crack front.  If you model the crack front evolution in a fracture simulation code like Franc3D, it will thus grow faster in the center at first, and quickly assume a slightly curved crack front as you have described.

 In the case of ductile material of plain stress, fracture surface is also wavy in micron level such as SEM observation of low magnification.  By more accurate expression, in other words, fracture surface of ups and downs is observed as compared to brittle one such as normal glass. If you find out distribution of difference between maximum tensile stress and maximum equivalent stress by using such as FEM calculation for typical mode I, essence of zigzaｇ morphology formation is decided by dependence whether with or without dislocation like theory. But fracture morphology such as paper, i have never seen discription of dislocation theory. Although both dislocation and crack is usually called as defect, I think quiet different approach as fundamental model of physics. In the case of physical model including only 2 set, my theory of function junction. In the case of phenomenon including too many, it is useful to use such as artificial neural network.

This is the true color of " Multi Physics".

  In the first line above sentence, I took mistake. false; plane stress, ture; plane strain.