The Delft Sand, Clay & Rock Cutting Model, 2019a

Rock Cutting: Atmospheric Conditions.
8.7. Correction on the Tear Type and the Chip Type.
The equations for the Tear Type are derived based on the shear angle β of the Flow Type. It is however a question
whether this is correct under all circumstances. At the moment of transition of Flow Type to Tear Type this may
be the case, but far away from this transition there may be another optimum shear angle β. Combining equations
(7-68), (7-69) and (7-88) with the shear angle β as a variable and determining the minimum horizontal force, gives
a different value for the shear angle β.
Shear Angle β (Degrees)
B: Shear Angle β vs. Blade Angle α, Based on Tensile Failure
90
85
80
75
70
65
60
55
50
45
40
35
30
25
20
15
10
5
0
15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
Blade Angle α (Degrees)
φ=00°
φ=05°
φ=10°
φ=15°
φ=20°
φ=25°
φ=30°
φ=35°
φ=40°
φ=45°
© S.A.M.
Figure 8-44: The shear angle β as a function of the blade angle α and
the internal friction angle φ.
A shear angle β is found, exactly 22.5° smaller than the shear angle β of the Flow Type (see Figure 8-44).
/4
(8-133)
2 2
Figure 8-45 and Figure 8-46 show the horizontal and the vertical cutting force coefficients which are slightly
smaller than the horizontal and vertical cutting force coefficients in Figure 8-42 and Figure 8-43. Now there exists
a set of parameters where both shear failure and tensile failure give a possible solution. In this range of parameters
shear failure will not give tensile stresses that exceed the tensile strength while tensile failure would lead to smaller
forces. The occurrence of the Flow Type or the Tear Type will depend on the history of the cutting process.
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