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

8.10. Example.
The Delft Sand, Clay & Rock Cutting Model.
In this chapter and in Appendix W many graphs are given with a red or green rectangle giving the value of the
different parameters for an α=60º blade and an internal friction angle φ=20º. The external friction angle is assumed
to be δ=2/3·φ. Most graphs are dimensionless, but Figure 8-49, Figure 8-50, Figure 8-51 and Figure 8-52 are based
on a compressive strength UCS=100 MPa, a blade width w=0.1 m and a layer thickness hi=0.1 m.
8.10.1. Step 1: Brittle Shear.
The the shear angle β=43.3º, horizontal force coefficient λHF=1.912, the verticle force coefficient λVF=0.572 and
the Esp/UCS ratio=0.669. This gives a horizontal force Fh=0.669 MN, a vertical force Fv=0.200 MN and a specific
energy of Esp=66.9 MPa. These values are peak values, but for comparison reasons these values will be used.
8.10.2. Step 2: The Transition Brittle Shear/Brittle Tensile.
The transitions brittle shear/brittle tensile occur for UCS/BTS=4.985 and UCS/BTS=11.75. This can also be
written as BTS=0.085·UCS and BTS=0.2·UCS, so BTS=8.5 MPa and BTS=20 MPa. BTS or UTS are
considered positive numbers, while tensile strength is considered to be negative in this book.
This means that below the Lower Limit BTS=8.5 MPa brittle shear failure cannot exist, so there is always brittle
tensile failure. Above the Upper Limit BTS=20 MPa brittle tensile failure cannot exist, so there is always brittle
shear failure. In between, both can exist , even at the same time, according to Figure 8-19 the Chip Type. Figure
8-49 and Figure 8-50 show the horizontal and vertical cutting forces as a function of the tensile strength for the
case considered. Interpolation curves are shown, simulating the simultaneous occurrence of brittle shear and brittle
tensile failure according to the Chip Type. For this interpolation the following method is used:
First define a factor f according to:
BTS LowerLimit BTS f 1
BTS UpperLimit BTS f 0
BTS LowerLimit BTS
BTS UpperLimit BTS
UpperLimit BTS BTS
f
UpperLimit BTS LowerLimit BTS
p
(8-140)
Now the resulting cutting forces can be determined with:
F F f F 1
f
h h,TearType h,ShearType
F F f F 1
f
v v,TearType v,ShearType
(8-141)
The power p used in Figure 8-49 and Figure 8-50 is p=1, a linear transition from tensile failure to shear failure,
the Chip Type.
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