6 Tool Model Building and Research on Cutting Simulation …
67
Table 6.1 Material physical
property parameters
(W m −1 K −1 )
Thermal conductivity
6.8
T (°C)
Temperature
100
E (GPa)
Elastic modulus
108
P (Kg m −3 )
Density
4428.8
C (J kg −1 K −1 )
Specific heat capacity
520
where, λ is the material thermal conductivity, T is the temperature,
•
q represents that
the heat source intensity is time-dependent, ρ is the material density, C is the specific
heat capacity, and
•
T shows that the temperature is time-dependent. x, y, and z are
vectors of directions in the cartesian coordinate system. The default value of inelastic
heat fraction (0.8) is accepted. Physical property parameters of materials are shown
in Table 6.1 [10–12].
Johnson–Cook material constitutive model. Material constitutive model defines
mechanical properties of materials. The correctness of constitutive model directly
affects the reliability of simulation results. The constitutive model must reflect the
relationship among temperature, strain rate, stress and strain of the model itself
in the simulation of metal cutting. In the current simulation constitutive model,
Johnson–Cook material constitutive model covers the relationship among temperature, strain rate, stress and strain. The Johnson–Cook constitutive model is shown in
the following Eq. (6.5):
σ =
A + Bε
n
1 + C ln
˙
ε
˙
ε 0
1 −
T − T r
T m − T r
m
(6.5)
where, (A + Bε
n
) refers to the relationship between strain and stress in a material,
1 + C ln
•
ε
•
ε 0
is the relationship between stress and strain rate,
1 −
T −T r
T m −T r
m
represents the relation between stress and temperature, σ is the stress, ε is the strain;
•
ε is the strain rate,
•
ε 0 is the reference strain rate, T is the temperature, T r is the room
temperature, T m is the melting point of the material, A is the yield strength under
quasi-static conditions, B and n are the parameters related to strain hardening, m is
the strain softening parameter, C is the strain strengthening parameter. These values
are shown in Table 6.2 [12].
Table 6.2 Constitutive
model parameters of the
Johnson–Cook materials
A
Initial yield stress (MPa)
792
B
Hardening modulus (MPa)
510
C
Strain strengthening coefficient
0.033
n
Strain hardening coefficient
0.47
m
Strain softening coefficient
1.02
67
Table 6.1 Material physical
property parameters
(W m −1 K −1 )
Thermal conductivity
6.8
T (°C)
Temperature
100
E (GPa)
Elastic modulus
108
P (Kg m −3 )
Density
4428.8
C (J kg −1 K −1 )
Specific heat capacity
520
where, λ is the material thermal conductivity, T is the temperature,
•
q represents that
the heat source intensity is time-dependent, ρ is the material density, C is the specific
heat capacity, and
•
T shows that the temperature is time-dependent. x, y, and z are
vectors of directions in the cartesian coordinate system. The default value of inelastic
heat fraction (0.8) is accepted. Physical property parameters of materials are shown
in Table 6.1 [10–12].
Johnson–Cook material constitutive model. Material constitutive model defines
mechanical properties of materials. The correctness of constitutive model directly
affects the reliability of simulation results. The constitutive model must reflect the
relationship among temperature, strain rate, stress and strain of the model itself
in the simulation of metal cutting. In the current simulation constitutive model,
Johnson–Cook material constitutive model covers the relationship among temperature, strain rate, stress and strain. The Johnson–Cook constitutive model is shown in
the following Eq. (6.5):
σ =
A + Bε
n
1 + C ln
˙
ε
˙
ε 0
1 −
T − T r
T m − T r
m
(6.5)
where, (A + Bε
n
) refers to the relationship between strain and stress in a material,
1 + C ln
•
ε
•
ε 0
is the relationship between stress and strain rate,
1 −
T −T r
T m −T r
m
represents the relation between stress and temperature, σ is the stress, ε is the strain;
•
ε is the strain rate,
•
ε 0 is the reference strain rate, T is the temperature, T r is the room
temperature, T m is the melting point of the material, A is the yield strength under
quasi-static conditions, B and n are the parameters related to strain hardening, m is
the strain softening parameter, C is the strain strengthening parameter. These values
are shown in Table 6.2 [12].
Table 6.2 Constitutive
model parameters of the
Johnson–Cook materials
A
Initial yield stress (MPa)
792
B
Hardening modulus (MPa)
510
C
Strain strengthening coefficient
0.033
n
Strain hardening coefficient
0.47
m
Strain softening coefficient
1.02