This subject is important because evidence of conoidal rough cracks is observed experimentally on various macrographs of broken specimens, under fatigue for instance. Our recent works (see below in answers) provides associated physical quantities.
Corresponding works [1, 2] are given below. The various physical quantities displayed there depend implicitly on time t through the dependence on time of the horizontal circular basis with radius R ≡ a0 + vt (v and a0 are constants) of the conoidal crack.
[1] - P.N.B. ANONGBA, Rough conoidal crack under general loading: dislocation, crack-tip stress and crack extension force
(a) ResearchGate (2022), DOI: 10.13140/RG.2.2.31913.88166
(b) Rev. Ivoir. Sci. Technol., 40 (2022) 177 - 206
[2] – P.N.B. ANONGBA (2022), Rough conoidal crack under general loading: crack extension force as a function of the average cone angle, ResearchGate, DOI: 10.13140/RG.2.2.13078.01600
Again with this work at hand, it becomes possible to follow the evolution (propagation) of highest complexity cracks that nucleate from defects (such as heterogeneities, inclusions ...) located inside materials. The provided G (the crack extension force per unit length of the crack front) is function of highest number of variables and parameters.
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