Will fracture occur under very high hydrostatic pressure? In the case of tensile loading, the distances between atoms or molecules increase and finally the material is broken because of bonds breakage between atoms or molecules. But, what about the hydrostatic loading? Will the atomic bonds break when they close to each other very very much? In other words, will a body be damaged under sufficiently high hydrostatic pressure loading?
About hydrostatic loading, I mean stress state of
$$\mathbf{\sigma}=-P\mathbf{I}$$
where $\mathbf{I}$ is the identity tensor and $P$ is constant.
 A: In the context of everyday forces and pressures (i.e., no neutron stars or black holes), consensus is that homogeneous (non-porous) materials can withstand arbitrarily high hydrostatic pressure without failure (although other transformations  not involving fracture, such as a phase change, might of course occur). In other words, strength criteria (e.g., 1, 2) do not predict failure from $\sigma=-P\mathbf{I}$ for any positive value of $P$.
Ductile materials fail through shear (mediated by dislocation movement), generalized as deviatoric stress, which is exactly the opposite of hydrostatic stress in the sense that it occurs off the stress tensor diagonal. Pressure doesn't create a driving force to move dislocations in this way.
Brittle materials fail when the strain energy induced by a load exceeds the energy required to create a new surface that would relieve that strain energy; under hydrostatic pressure, however, there's no mechanism by which a new surface would relieve the strain energy.
As a side note, hydrostatic pressure is well known to alter the mechanisms of failure induced by other types of loading, such as tensile and shear. Early work in this area was performed by Bridgman (e.g., "Effects of High Hydrostatic Pressure on the Plastic Properties of Metals", Rev. Mod. Phys. 17 1945) and has continued in the areas of polymers and rock.
