31.6 Comparison of Experimental and Calculation Results
403
σ m = T , p = 0, , = 1, τ o = T
2
3
, SG(σ n ) = 1.
Then the dependency gives
ε 1 = T
1
2G
+ η
1
G
−
1
G o
, ε 2 = 0,
ε 3 = −T
1
2G
− η
1
G
−
1
G o
,
(31.7)
where the function G is calculated using formulas (30.14)–(30.16) or (30.19) at
= 1, whereas v still designates the change rate of octahedral tangential stress.
31.5 Determination of Model Parameters
To verify the model, it is required to find the parameters b (or a), η, c, and τ
from experiments. They can be defined, for example, if we have experimental
material test diagrams for elongation, shear, compression testing, as well as one
of creep curves. After selecting one point from these diagrams and using the
dependencies (31.2), (31.5), (31.6), and (31.7), we will have four equations relative
to the sought parameters. By identical transformations, they can be brought to the
system of two transcendent equations relative to η and τ :
η = F 1 (η, τ ), τ = F 2 (η, τ ),
(31.8)
where the functions F 1 and F 2 , apart from their arguments, depend on the
coordinates for four selected points on experimental curves.
A solution to the system (31.8) can be obtained by the method of iteration
[1]. The process convergence depends on the zero approximation quality. The
experience showed that for the sought materials, good zero approximation was
η = 0.1 . . . 0.3 and vτ = 10 5 . . . 10 7 Pa.
Determining the parameters using the described methodology when setting G
using formula (30.13), the loading rate of v = 500 Pa/s, G o = 60 MPa and using
the experimental results [2, 3] gave the following values of model parameters: b =
4.25 · 10 −5 Pa −1 ; η − 0.14; τ = 200 −1 c; c = 0.4.
31.6 Comparison of Experimental and Calculation Results
Figure 31.1 shows experimental results taken from [2, 3] with dashed lines
and computational dependencies with solid lines for the above values of model
403
σ m = T , p = 0, , = 1, τ o = T
2
3
, SG(σ n ) = 1.
Then the dependency gives
ε 1 = T
1
2G
+ η
1
G
−
1
G o
, ε 2 = 0,
ε 3 = −T
1
2G
− η
1
G
−
1
G o
,
(31.7)
where the function G is calculated using formulas (30.14)–(30.16) or (30.19) at
= 1, whereas v still designates the change rate of octahedral tangential stress.
31.5 Determination of Model Parameters
To verify the model, it is required to find the parameters b (or a), η, c, and τ
from experiments. They can be defined, for example, if we have experimental
material test diagrams for elongation, shear, compression testing, as well as one
of creep curves. After selecting one point from these diagrams and using the
dependencies (31.2), (31.5), (31.6), and (31.7), we will have four equations relative
to the sought parameters. By identical transformations, they can be brought to the
system of two transcendent equations relative to η and τ :
η = F 1 (η, τ ), τ = F 2 (η, τ ),
(31.8)
where the functions F 1 and F 2 , apart from their arguments, depend on the
coordinates for four selected points on experimental curves.
A solution to the system (31.8) can be obtained by the method of iteration
[1]. The process convergence depends on the zero approximation quality. The
experience showed that for the sought materials, good zero approximation was
η = 0.1 . . . 0.3 and vτ = 10 5 . . . 10 7 Pa.
Determining the parameters using the described methodology when setting G
using formula (30.13), the loading rate of v = 500 Pa/s, G o = 60 MPa and using
the experimental results [2, 3] gave the following values of model parameters: b =
4.25 · 10 −5 Pa −1 ; η − 0.14; τ = 200 −1 c; c = 0.4.
31.6 Comparison of Experimental and Calculation Results
Figure 31.1 shows experimental results taken from [2, 3] with dashed lines
and computational dependencies with solid lines for the above values of model