Please check the following European standard: EN-14651. Test method for metallic fibered concrete - Measuring the flexural tensile strength (limit of proportionality (LOP), residual). Attached please find a copy of the standards.

Bending moment diagram will be the same but stress distribution at the cross section of the beam will be changed.   

Thank you sir....Is it because the bending moment depends only on the loading and the resultant reactions?

Yes. But be carefull about the statically indetermined system. Because reactions can be changed.. Because of the moment of inertia chances.. 

The bending moment diagram depend only from location of the cross section of the beam, with or without a crack.

The presence a crack, can effect only the distribution of the stresses on the cross section of the beam.

Thank you sir. The answers are very helpful....

The BM diagram will remain the same since the beam is statically determinate.

Just to emphasize -

a bending moment diagram is an integral characteristics M = \int \sigma_x z dz so it is in general to "rough" to judge about \sigma_x or in the case of a crack about the full stess tensor components \sigma_x, \sigma_z and \tau_xz or stress intensity

and once you have delamination then such an integral as A Bending Moment has a little sence (integral of a discontinous function over a "gap")

Sir from the Euler beam model we know M=EI * d2u/dx2 . So if a crack is induced the moment of inertia will change. so will moment will also change?

I  emphasize:

if the beam is statically indeterminate, the furthermore constraints introduce geometric conditions in the problem, with result to change the bending moment diagram of the beam. Therefore, the cross section, where exist the crack, will effect on the bending moment which develops thereon.

No, Moment will be the same but d2u/dx2 will change. That means deflection curve will change. This answer is giving considering your former question's condidations.. 

M=EI * d2u/dx2 is based on on that plane sections will remain plane and this is not the case when you have crack.

Since the beam is simply supported beam then the moment diagram will stay the say. Moment is based in this case on equilibrium. Changes will occur on curvature M/EI and deflection 

Thank you sir. So the changes in moment of inertia will be compensated by the d2u/dx2 term and the moment will remain unchanged.

When the crack is induced in a beam, obviously curvature d^2u/dx^2 will change that directly affects stress resultants.

Yes, the bending moment for a statically determinate problem such as this is based on statics alone and will not be influenced by the geometry.  

Yes, deflection, curvature, stresses and strain will be affected. However moment, shear force and reaction won't be changed as they are  based on equilibrium

Consider piecewise problem: the crack is closed and open. Therefore, this is nonlinearity. In expecting the appearance of power second and higher harmonics to eigenfrequencies, that's in the absence of crack, at dynamical tests.

If the beam is simply supported, we deal with the statically determinate system. It follows that a crack produces no effect on the bending moment diagram and transverse shear force diagram. What changes in the presence of a crack is slopes, deflections, and stresses.

Imagine the beam is sagging. If the crack length is in the compression half of the beam above the neutral layer, then crack will get closed due to bending. in this case there will be no change in SFD or BMD as the compression in beam will try to close the crack faces making it behave like intact solid.

If the crack is in lower half of the sagging beam, then crack faces will show the excess opening due to tension in below neutral layer fibers in the beam. Crack will reflect itself as discontinuity in the slope and deflection diagram.  This deflection can be imagined as the crack modeled as y torsional spring.