When a planar crack is loaded in tension (mode I) in brittle materials, the velocity V of the crack is observed to increase from zero to a terminal velocity VT, then follows crack branching on further increasing V. VT falls well below the Rayleigh wave velocity VR.
To our knowledge, one attempt has been made to estimate theoretically VT. This attempt makes use of Mott (1948) extension of the Griffith concept to dynamic fracture. This is expounded by Lawn (1993). This estimate gives VT ≈ 0.38cl where cl is the velocity of longitudinal sound wave.
Does any other estimate exist?
In a very recent work, we have found that the crack extension force G(I) increases with V from G(I)0 at V=0 to a maximum G(I)max≈ 1.32 G(I)0 at VE≈ 0.52ct (Poisson ratio ν=1/3) where ct is the velocity of transverse sound wave. In agreement with experiments, we take VE =VT. The equation yielding VT is then “ d G(I) / dV =0 “. This is a second estimate of the terminal velocity.
Our recent work: “Planar cracks in uniform motion under mode I and II loadings”; see our contribution in ResearchGate.
From its maximum value, G(I) decreases continuously to zero at V = ct. No reference is made to Rayleigh wave velocity CR for mode I tensile crack. This contrasts with many who argue that Rayleigh wave velocity should be the maximum velocity for any moving surface discontinuity (see Freund (1990), for example).
May be, you should explain your understandings here and not report us in other places, this is much helpful, ah ah ah, isn't it?
Try it by Conservation of energy equation (energy balance equation) analytically. Velocity increases to terminal velocity in a short span of time
The conservation of energy corresponds to Griffith Energy-balance concept. This may be stated as
G(I)max=2*Gamma
where Gamma is the surface energy. We observe that this is valid at G(I)max only. Here, G(I)max is known separately first, before we can reach the Griffith equation.
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