The paper shows the results of the researches concerning the deformation behavior of alloyed steel with chromium and molybdenum. The plastic deformation behavior is researched in the experimental way, using the torsion test method. The result of the research program including the various temperatures and strain rates is systematized

G. GURAU

L. GURAU

N. CANANAU

P. ALEXANDRU

The Annals of “Dunarea de Jos” University of Galati Fascicle IX Metallurgy and Materials Science

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FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
 
 
RESEARCHES ON THE VISCOPLASTIC BEHAVIOR 
OF A CrMo ALLOYED STEEL 
 
N. CANANAU, P ALEXANDRU, L. GURAU, G. GURAU 
“Dunărea de Jos” University of Galati 
email: ncananau@ugal.ro 
 
ABSTRACT 
 
The paper shows the results of the researches concerning the deformation 
behavior of alloyed steel with chromium and molybdenum. The plastic deformation 
behavior is researched in the experimental way, using the torsion test method. The 
result of the research program including the various temperatures and strain rates 
is systematized.  
 
KEYWORDS: constitutive equation, torsion test, stress, strain, temperature. 
 
1. Introduction 
 
The knowledge of constitutive equation is 
necessary for the evaluation, modeling, simulation 
and optimization of the plastic deformation processes. 
For this aim, in the calculus program, it is applied the 
three-dimensional constitutive equation [1, 2]:  
 ijij S⋅⋅=
0
0
3
2
σ
εε
&
&            (1) 
In this equation ijε&  - is the component of the 
strain rate tensor, 0ε&  - is the strain rate intensity, 0σ -
stress intensity, in real deformation conditions, Sij -
component of the deviator tensor of stress state. This 
component is defined by: 
 mijijijS σδσ ⋅−=            (2) 
σij is the component of the stress tensor, δij – 
Kronecker’s symbol, σm – mean normal stress of the 
stress tensor. 
This equation is defined if the mono-
dimensional constitutive equation is known. In this 
paper are presented the results of researches for 
establishing of the constitutive equation for steel 
alloyed with chromium and molybdenum. 
 
2. Experimental conditions 
 
The deformation behavior is established through 
experimental way using a torsion testing machine.  
The chemical composition of the researched 
material is rendered in table 1. 
 
Table 1. Chemical composition of steel, [%] 
C Mn Si P S Cr Mo 
0,43 0,55 0,45 0,037 0,035 1,01 0,35 
The form of active zone of the sample is 
cylindrical and has the dimensions 
( ) ( )1.03602.06 ±×±φ  mm. 
 
The torsion testing installation is equipped with: 
electro-hydraulic system for action of sample with the 
power of 5kW, the revolution is 1-2000 rpm, Spider 8 
data acquisition system, heating system, temperature 
max 11000C and precision ±5 0C [3,4]. 
The research program covers a temperature area, 
according to the researched material and a domain of 
the strain rate values. A test corresponds to a certain 
strain rate value and a certain temperature according 
to the established research program. As a result of the 
torsion test we obtain the torque diagram ( ) TtM ,ε&  
where t is the time, which may be transformed in 
strain. Thus, we obtain the ( ) TM ,εε &  diagram.  
 
3. Experimental data 
 
The research program consists in: research 
temperatures of 20, 400, 600, 750, 850, 900, 950, 
1000 0C and the revolution of 0.319; 0.943; 2.962; 
10.01 rev/s. 
The influence of the temperature on the torsion 
moment, at the 0.319 rev/s, is rendered in figure 1. 
The maximum torque connected with the 
temperature is shown in figure 2. 
The maximum strain connected with the 
temperature is shown in figure 3. 
Up to a temperature of 600 0C, the maximum 
torque has great values and the maximum strain has 
small values.  
The plastic deformation is difficult.  
 
-  23  -
FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
At the temperature of 600 0C the torsion 
moment increases until the maximum value. The 
increasing of the strain leads to the decreasing of the 
value of torque because the effective temperature 
increases as a result of the caloric effect of the plastic 
deformation. 
At the 750 0C the value of the maximum torque 
is small and the maximum strain is very high. 
Consequently, the plastic deformation behavior of the 
researched material, at this temperature, is very good.  
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
At the temperatures greater than the 8000C we 
have the hot plastic deformation regime. The 
deformation stress is small and the deformation 
capacity is high. 
The explanation of this behavior consists in the 
structural transformation of the material in function of 
the temperature. Thus at the 700 – 750 0C we have a 
favorable structural state as result of the perlite-
austenite transformation and the very good 
deformation behavior of the ferrite at these 
temperatures. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The explanation of this behavior consists in the 
structural transformation of the material in function of 
the temperature. Thus at 700 – 750 0C we have a 
favorable structural state as a result of the perlite-
austenite transformation and the very good 
deformation behavior of the ferrite at these 
temperatures. 
For temperatures greater than 750 0C the steel 
has a viscoplastic behavior specific for hot 
deformation. 
The diagrams of the torsion moment, at the hot 
deformation area, are shown in figures 4, 5, 6 and 7. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Fig. 1. Influence of temperature on 
the torque diagrams, at 0.319 rev/s 
4 
8 
12 
16 
20 
24 
28 
32 
1 2 3 4 5 6 7 8 9 10
200C 
4000C 
6000C 
7500C 8500C 
9000C 
10000C 
9500C 
To
rs
io
n 
m
om
en
t, 
[N
m
] 
Deformation degree, ε 
Fig. 2. Influence of temperature on the 
maximum torque, at 0.319rev/s 
4
8
12
16
20
24
28
32
200 400 600 800 1000
To
rs
io
n 
m
om
en
t, 
[N
m
] 
Temperature, 0C 
Fig. 3. Influence of temperature on the 
maximum strain, at 0.319rev/s 
1
2
200 400 600 800 1000 
D
ef
or
m
at
io
n 
de
gr
ee
, ε
 
Temperature, 0C 
3
4
5
6
7
8
9
10
Fig. 4. The torque diagrams 
 at the 0.319 rev/s 
0 1 2 3 4 5 6 7 8 9 
Strain intensity 
8500C
9000C 
9500C 
10000C 
1 
2 
3 
4 
To
rq
ue
, [
N
m
] 
-  24  -
FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The influence of the strain rate and temperature 
on the deformation resistance of the researched steel 
may be described by the variation of the maximum 
torsion moment with these deformation factors. 
In figures 8 and 9 are shown the graphics of the 
dependence Mmax( ),Tε& . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The increasing of the temperature leads to the 
decreasing of the maximum torsion moment. This 
variation is determined by the increasing of the 
dislocations mobility when the temperature increases 
and, consequently, the activation stress decreases. 
Considering the exponential variation of the 
atomic and dislocations mobility with temperature 
(Arrhenius law), the variation of the deformation 
resistance is, also, an exponential function. 
With the increasing of the strain rate the strength 
of the researched steel increases. The mathematical 
expression of the variation of the maximum torsion 
moment with the strain rate is defined by a power law 
(Norton law). The plasticity of material may be 
defined by the maximum value of the strain. In the 
table 2 are rendered the values of the maximum strain 
connected with the temperature and strain rate. 
 
Fig. 5. The torque diagrams at the 0.94 rev/s 
8500C 
9000C 
10000C 9500C T
or
qu
e,
 [N
m
] 
1 
2 
3 
4 
5 
6 
0 1 2 3 4 5 6 7 8 9
Strain intensity 
Fig. 6. The torque diagrams  
at the 2,962 rev/s 
8500C 
9000C 
9500C 10000C 
0 1 2 3 4 5 6 7 8 9
Strain intensity 
1 
2 
3 
4 
To
rq
ue
, [
N
m
] 
5 
6 
7 
Fig. 7. The torque diagrams  
at the 10.01 rev/s 
1 
2 
3 
4 
To
rq
ue
, [
N
m
] 5 
6 
7 
0 1 2 3 4 5 6 7
Strain intensity 
8500C 
9000C 
9500C 
10000C 
Fig. 8. Variation of the maximum 
torque with temperature and strain 
rate 
Temperature, 0C 
M
ax
im
um
 to
rq
ue
, N
m
 
0217.3=ε&  
0.8949 
0.2849 
0.0964 
850 1000 900 
0 
1 
2 
3 
4 
5 
6 
7 
950 
Fig. 8. Variation of the maximum 
torque with strain rate and 
temperature 
Strain rate, 1/s 
M
ax
im
um
 to
rq
ue
, N
m
 
 
8500C 
10000C 
9000C 
0 
1 
2 
3 
4 
5 
6 
7 
9500C 
0.5 1.5 2.5  
-  25  -
FO N D ATĂ
197 6
 
 
THE ANNALS OF “DUNAREA DE JOS” UNIVERSITY OF GALATI. 
FASCICLE IX. METALLURGY AND MATERIALS SCIENCE 
N0. 1 – 2009, ISSN 1453 – 083X 
 
 
Table 2. Values of maximum strain 
 
 Strain rate, 1/s 
Temperature 
0C 
0.0964 0.2849 0.8949 3.0217 
850 4.305 6.152 7.501 1.882 
900 4.751 5.749 7.401 4.849 
950 5.802 5.951 7.249 5.701 
1000 7.898 8.651 8.902 0.655 
 
The values of the maximum strain are 
represented in the graphic form in the figure 9. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
For the temperature of 850 0C, the maximum 
strain has an important dispersion connected to the 
strain rate. For a greater temperature, 900 and 950 0C, 
the maximum strain increases and the dispersion of 
values is smaller. For a temperature of 1000 0C and 
not great values of the strain rate the values of the 
maximum strain are the greatest. If the strain rate is 
great, for this temperature, the maximum strain is 
smallest.  
Figure 10 shows the variation of the maximum 
strain with the strain rate and temperature. It is 
evident the maximum values of the strain correspond 
to the favorable strain rate (0.8949s-1). 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4. Conclusions 
 
The knowledge of the constitutive equation of 
the material is necessary for the modelling, simulation 
and optimization of the plastic deformation process.  
The best method for establishing the constitutive 
equation is the torsion testing.  
Experimental researches showed, that the 
strength of the researched steel decreases with the 
temperature and increases with the strain rate. The 
variation of the plasticity has a complex character 
connected to the temperature and strain rate.  
This is the justification of the necessity of the 
experimental research establishing the deformation 
behavior of the metallic material.  
 
References 
 
[1]. Cănănău N., Teoria deformării plastice, Universitatea 
Dunarea de Jos din Galati, 1994. 
[2]. Dumitrescu A.T.- Contribuţii la modelarea laminarii in 
calibre. Teza de doctorat, Institutul Politehnic Bucureşti, 1986. 
[3]. Moussy F, Franciosi P.- Physique et mecanique de la mise en 
forme des meteaux. Presses du CNRS, Paris, 1990, ISBN 2-87682-
023-4 
[4]. Cananau N., Petrea I, Corobete G. - Modelling of the flow 
and deformation fields at the profiles rolling by field lines method , 
The Annals of “Dunarea de Jos” University of Galati, Fascicle IX, 
Nov. 2005. 
 
 
 
 
 
ε&  
Fig. 9. Variation of the maximum 
strain with temperature and strain 
rate 
Temperature, 0C 
M
ax
im
um
 st
ra
in
 
3.0217 
0.8949 
0.2849 
0.0964 
850 1000 900 
0 
1 
2 
3 
4 
5 
6 
7 
950 
8 
M
ax
im
um
 st
ra
in
 
 
 
Fig. 10. Variation of the maximum 
strain with strain rate and 
temperature 
Strain rate, 1/s 
M
ax
im
um
 st
ra
in
  
8500
10000C
9000C 
0
1
2
3
4
5
6
7
9500C 
0.5 1.5 2.5 3.5 
8
-  26  -


Researches on the Viscoplastic Behavior of a CrMo Alloyed Steel

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Researches on the Viscoplastic Behavior of a CrMo Alloyed Steel

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