Dear Nikolay:

It clearly is of not of no importance as the transgranular cleavage needs to form along low energy crystallographic planes. However, aside from that, personally I do not think that it has that much influence on the resulting fracture resistance.

ROR

Cleavage runs along the crystallografic plane with minimal energy, like {001} in BCC ferrite. If one known the rules of microstructure (globular or lamellar) and micro texture (solidication, rolling etc.) than it allows to control the properties and their anisotropy, and deformation and fracture mechanisms.

Dear Nikolay Orlov . See the following useful link: Article Microstructure-based cleavage modelling to study grain size ...

Also check kindly the following RG link: Article Effect of tilt and twist angles on the cleavage crack propag...

The following link is also very useful: https://www.sciencedirect.com/topics/materials-science/cleavage-fracture

Aref Wazwaz Stepan I. Stepanov Robert O Ritchie

I am very grateful for your answers! Thank you very much!

I'm interested in one more question. Perhaps you can answer it.

How does preliminary plastic deformation affect the misorientation angle of the facets? (During further testing in liquid nitrogen?) Should the degree of plastic deformation increase, the misorientation angle of the facets should become larger?

Cleavage facets may help in finding equilibrium crack configurations. Equilibrium states are those observed during extended time (the stable motion of earth around the sun for instance) in other words over large crack propagation distances (say of the order of 1 micron meter in small specimen or 1mm in large specimen). Observing a crack configuration during a large interval of time or distance is the signature that this is an equilibrium state. Fractography may help researchers to detect equilibrium configurations. A valid theoretical calculation should predict these.

Equilibrium configurations of the crack do not depend on plasticity, be this introduced by external load or generated from the tip of the crack. This is demonstrated in existing literatures.

Fracture is defined by a system {S}: S is the fracture plane; T the fracture propagation direction on S. The plane S may have different types of fracture propagation direction. Fractography of broken specimens is helpful in determining fracture systems. In laboratory experiments, we may have a tension σ22in the vertical x2-direction and shears σ21and σ23 in the horizontal Ox1x3-plane along x1 and x3, respectively. Changing the loadings may change the fracture systems. can be detected from the markings on micrographs. Please, for experiments see: “A study of the brittle fracture characteristics of CoSi2 using laser beam reflections”, Acta Metall. Mater. 43 (1995) 2275 – 2285. For theoretical prediction, see “Conoidal crack with elliptic bases, within cubic crystals, under arbitrarily applied loadings – III. Application to brittle fracture systems of CoSi2single crystals, ResearchGate, DOI: 10.13140/RG.2.2.34719.37282”.

Regards

Nikolay Orlov

Detailed explanation:

When a material undergoes plastic deformation, the crystal structure of the material becomes distorted and the atomic lattice becomes misaligned. This creates local variations in the crystal orientation, leading to the formation of sub-grains and an increase in the overall misorientation angle between different regions of the material.

During testing in liquid nitrogen, the continued plastic deformation of the material can further increase the misorientation angle of the facets. The lower temperature of the liquid nitrogen environment can make the material more susceptible to additional plastic deformation, leading to a greater degree of crystal lattice distortion and a larger misorientation angle.

So in general, as the degree of plastic deformation increases, the misorientation angle of the facets should become larger, particularly when the material is tested in the low-temperature liquid nitrogen environment. The increased misorientation angle is a result of the cumulative plastic deformation and the corresponding distortion of the crystal structure.

Good luck; partial credit AI

Mohammad Imam Patrick N.B. Anongba Thank you very much!

Please, the comments that follow are necessary for clarification. Deformation modes (plastic slip, twinning, and fracture, for examples) in loaded materials decrease the energy of the system E (elastic energy and potential energy of the loading mechanism). A measure of the decrease of E during deformation evolution over time is given by what is called in fracture “energy release rate or crack extension force G per unit length of the crack front”. An expression for G depending on the shape of the crack front is available only under stationary conditions. For a crack with arbitrary front, it is necessary to consider an average (G averaged over all the positions on the crack front). Observed fracture systems fulfil the condition d=0 ( being function of crack-front configuration, applied loadings, material elastic constants…) and are not guided by pre-existing atomic planes.