Aggregate strength are taken care by testing under crushing strength and impact value. Different codes provides limiting values of these two test and if any source of aggregate is not as per these recommendations then it should be rejected.

But considering fracture,I think the voids are the main concern, am I right?

Normally the strength of concrete (in ordinary mixes), does not take in to account the strength of the coarse aggregates, and the reason lies in the concrete microstructure.

Concrete is a multiphase material, and as such porosity of each component of the microstructure is a strength limiting feature, coarse aggregates are often much stronger than the cement paste matrix as well as the interfacial transition zone between the matrix and the coarse aggregate, which determines the strength of ordinary concrete mixes.

I believe that cracking in coarse aggregate will make it brittle and will reduce it´s compressive strength, how ever the confinement that the cement paste matrix has over the aggregate should be taken in to account as well (it might mitigate the loss of strength); that being said the elasticity modulus of concrete greatly changes with the selection of aggregate and a brittle coarse aggregate could toll on it.

Thanks, this is very helpful@Vidriales