In this investigation, the thermo-viscoplastic behaviour of the steel AISI 304 has been examined. The experimental characterization of the material has been conducted in tension under wide ranges of strain rates.An analytical description of the macroscopic behaviour of this metal is reported. For such goal, the extended Rusinek-Klepaczko model to viscous drag effects is applied.It allows for proper description of the material behaviour within the whole range of loading conditions considered.In addition, the analytical formulation proposed gathers limited number of material constants and simple calibration procedure

ARIAS, Angel

PESCI, Raphaël

RODRIGUEZ-MARTINEZ, José A.

RUSINEK, Alexis

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Science Arts & Métiers (SAM)
is an open access repository that collects the work of Arts et Métiers ParisTech
researchers and makes it freely available over the web where possible.
This is an author-deposited version published in: https://sam.ensam.eu
Handle ID: .http://hdl.handle.net/10985/11055
To cite this version :
José A. RODRIGUEZ-MARTINEZ, Alexis RUSINEK, Raphaël PESCI, Angel ARIAS - Mechanical
charecterization and analytical modeling of the thermo-viscoplastic behaviour AISI 304  steel
under wide ranges of strain rates at room temperature - 2010
Any correspondence concerning this service should be sent to the repository
Administrator : archiveouverte@ensam.eu
Mechanical characterization and analytical modeling of the thermo-viscoplastic 
behaviour AISI 304 steel under wide ranges of strain rates at room temperature 
 
 
J.A. Rodríguez-Martínez1, A. Rusinek2, R. Pesci3, A. Arias1 
1
 Department of Continuum Mechanics and Structural Analysis, University Carlos III of Madrid, 
Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain 
2
 Laboratory of Mechanic, Biomechanic, Polymers and Structures, National Engineering School of 
Metz (ENIM), Ile du Saulcy, 57045 Metz cedex, France 
3
 Arts et Métiers ParisTech , Laboratory of Physic and Mechanic of Materials, FRE CNRS 3236,          
4 rue Augustin Fresnel, Ile du Saulcy, 57078 Metz cedex 3, France 
 
1. General 
In this contribution, the thermo-viscoplastic behaviour of the steel AISI 304 is analyzed under 
wide ranges of loading conditions. In order to characterize the mechanical behavior of the material, 
tensile tests have been performed within the ranges of strain rates 4 3 110 10 s− −≤ ε ≤ɺ . The analytical 
definition of the material behaviour has been conducted by means of the extended Rusinek-
Klepaczko model to viscous drag effects [1]. Based on such understanding of the material 
behaviour, satisfactory agreement between experiments and analytical modeling is reached for the 
whole range of loading conditions examined. 
2. Experimental characterization at room temperature 
Analysis of the thermo-viscoplastic behaviour of the steel AISI 304 has particular relevance 
since this material is widely used in many engineering applications. The tensile tests performed at 
different strain rates reveal the characteristics high strain hardening and ductility of this metal, 
Figure 1-a. It has to be highlighted that even at high loading rate the strain hardening of the material 
remains approximately constant. It provides to this material of improved mechanical properties for 
absorbing energy under impulsive loads. Dependence of strain rate on the material flow stress level 
is observed. Thus, in Figure 1-b. is illustrated the rate sensitivity of the material from static to 
highly dynamic loading. The original experimental results of this work are compared with those 
reported in [2]. Both data find good agreement within the range of strain rates considered. In 
particular, it has to be noted that beyond certain level of loading rate the flow stress of the material 
sharply increases. Such a behaviour is assumed to be caused by viscous drag deformation mode [2].  
0
100
200
300
400
500
600
700
800
900
1000
0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,5
0.002 1/s
1 1/s
10 1/s
100 1/s
200 1/s
500 1/s
True strain, ε
Material: Steel AISI 304
To = 293 K
Tr
u
e
 
st
re
ss
,
 
σ
 
(M
Pa
)
0.002 s-1
1.0 s-1
10 s-1
100 s-1
200 s-1
500 s-1
 (a) 
0
100
200
300
400
500
600
700
800
900
1000
0,0001 0,01 1 100 104
This work
Follansbee et al. 1986
Average
Tr
u
e
 
st
re
ss
,
 
σ
 
(M
Pa
)
Strain rate, (s-1)
10 %
Material: Steel AISI 304To = 293 K
ε
p
 = 0.1
 (b) 
Figure 1. (a) Flow stress evolution as a function of plastic strain for different strain rates at room 
temperature (b) Flow stress evolution as a function of strain rates and comparison with [3] 
3. Thermo-viscoplastic modeling of 304 stainless steel for a wide range of strain rates 
For modeling the material behaviour, the extended Rusinek-Klepaczko model to viscous drag 
effects [1] is applied: 
(1)  ( ) ( ) ( ) ( )[ ] ( )pvsppppp TTE
TET εσεσεεσεεσ µ ɺɺɺɺ ++= ,,,,,
*
0
 
An additional stress component ( )pvsσ εɺ  originally proposed by [3] is added to the original Rusinek-
Klepaczko formulation in order to describe the viscous drag effects at high strain rates. The 
following set of constants for the model calibration has been found, Table 1.  
B0 (MPa) ν  (-) n0 (-) D2 (-) 0ε  (-) *0σ (MPa) *m  (-) D1 (-) χ (MPa) α (-) *θ  
1243.6 0.001 0.36 0.035 0.0118 117.72 1.29 0.55 200.83 0.0009774 0.9 
Table 1. Material constants for the steel AISI 304, equation 1 
 
 
 
By means of such analytical 
description of the material 
behaviour, good agreement between 
experiments and modeling is found 
at room temperature for the whole 
range of loading conditions 
considered, Figure 2.  
 
 
Figure 2. Comparison between experiments and analytical 
predictions for wide ranges of strain rates  
4. Conclusions 
In this investigation, the thermo-viscoplastic behaviour of the steel AISI 304 has been 
examined. The experimental characterization of the material has been conducted in tension under 
wide ranges of strain rates. An analytical description of the macroscopic behaviour of this metal is 
reported. For such goal, the extended Rusinek-Klepaczko model to viscous drag effects is applied. 
It allows for proper description of the material behaviour within the whole range of loading 
conditions considered. In addition, the analytical formulation proposed gathers limited number of 
material constants and simple calibration procedure. 
References 
[1] A. Rusinek and J. A. Rodríguez-Martínez (2009). Thermo-viscoplastic constitutive relation 
for aluminium alloys, modeling of negative strain rate sensitivity and viscous drag effects, 
Mater. Des., 30, 4377–4390. 
[2] P.S Follansbee (1986). High-Strain-Rate Deformation of FCC Metals and Alloys, 
Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, 451-479. 
[3] R. Kapoor and S. Nemat-Nasser (1999). Comparison between high strain-rate and low strain-
rate deformation of tantalum, Metall. Mater. Trans., 31A, 815–823. 


English

Mechanical charecterization and analytical modeling of the thermo-viscoplastic behaviour AISI 304  steel under wide ranges of strain rates at room temperature

Name not available

Science Arts & Métiers (SAM)is an open access repository that collects the work of Arts et Métiers ParisTechresearchers and makes it freely available over the web where possible.This is an author-deposited version published in: http://sam.ensam.euHandle ID: .http://hdl.handle.net/10985/11055To cite this version :José A. RODRIGUEZ-MARTINEZ, Alexis RUSINEK, Raphaël PESCI, Angel ARIAS - Mechanicalcharecterization and analytical modeling of the thermo-viscoplastic behaviour AISI 304  steelunder wide ranges of strain rates at room temperature - 2010Any correspondence concerning this service should be sent to the repositoryAdministrator : archiveouverte@ensam.euMechanical characterization and analytical modeling of the thermo-viscoplastic behaviour AISI 304 steel under wide ranges of strain rates at room temperature   J.A. Rodríguez-Martínez1, A. Rusinek2, R. Pesci3, A. Arias1 1 Department of Continuum Mechanics and Structural Analysis, University Carlos III of Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain 2 Laboratory of Mechanic, Biomechanic, Polymers and Structures, National Engineering School of Metz (ENIM), Ile du Saulcy, 57045 Metz cedex, France 3 Arts et Métiers ParisTech , Laboratory of Physic and Mechanic of Materials, FRE CNRS 3236,          4 rue Augustin Fresnel, Ile du Saulcy, 57078 Metz cedex 3, France  1. General In this contribution, the thermo-viscoplastic behaviour of the steel AISI 304 is analyzed under wide ranges of loading conditions. In order to characterize the mechanical behavior of the material, tensile tests have been performed within the ranges of strain rates 4 3 110 10 s− −≤ ε ≤ɺ . The analytical definition of the material behaviour has been conducted by means of the extended Rusinek-Klepaczko model to viscous drag effects [1]. Based on such understanding of the material behaviour, satisfactory agreement between experiments and analytical modeling is reached for the whole range of loading conditions examined. 2. Experimental characterization at room temperature Analysis of the thermo-viscoplastic behaviour of the steel AISI 304 has particular relevance since this material is widely used in many engineering applications. The tensile tests performed at different strain rates reveal the characteristics high strain hardening and ductility of this metal, Figure 1-a. It has to be highlighted that even at high loading rate the strain hardening of the material remains approximately constant. It provides to this material of improved mechanical properties for absorbing energy under impulsive loads. Dependence of strain rate on the material flow stress level is observed. Thus, in Figure 1-b. is illustrated the rate sensitivity of the material from static to highly dynamic loading. The original experimental results of this work are compared with those reported in [2]. Both data find good agreement within the range of strain rates considered. In particular, it has to be noted that beyond certain level of loading rate the flow stress of the material sharply increases. Such a behaviour is assumed to be caused by viscous drag deformation mode [2].  010020030040050060070080090010000 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,50.002 1/s1 1/s10 1/s100 1/s200 1/s500 1/sTrue strain, εMaterial: Steel AISI 304To = 293 KTrue stress, σ (MPa)0.002 s-11.0 s-110 s-1100 s-1200 s-1500 s-1 (a) 010020030040050060070080090010000,0001 0,01 1 100 104This workFollansbee et al. 1986AverageTrue stress, σ (MPa)Strain rate, (s-1)10 %Material: Steel AISI 304To = 293 Kεp = 0.1 (b) Figure 1. (a) Flow stress evolution as a function of plastic strain for different strain rates at room temperature (b) Flow stress evolution as a function of strain rates and comparison with [3] 3. Thermo-viscoplastic modeling of 304 stainless steel for a wide range of strain rates For modeling the material behaviour, the extended Rusinek-Klepaczko model to viscous drag effects [1] is applied: (1)  ( ) ( ) ( ) ( )[ ] ( )pvsppppp TTETET εσεσεεσεεσ µ ɺɺɺɺ ++= ,,,,,*0 An additional stress component ( )pvsσ εɺ  originally proposed by [3] is added to the original Rusinek-Klepaczko formulation in order to describe the viscous drag effects at high strain rates. The following set of constants for the model calibration has been found, Table 1.  B0 (MPa) ν  (-) n0 (-) D2 (-) 0ε  (-) *0σ (MPa) *m  (-) D1 (-) χ (MPa) α (-) *θ  1243.6 0.001 0.36 0.035 0.0118 117.72 1.29 0.55 200.83 0.0009774 0.9 Table 1. Material constants for the steel AISI 304, equation 1    By means of such analytical description of the material behaviour, good agreement between experiments and modeling is found at room temperature for the whole range of loading conditions considered, Figure 2.    Figure 2. Comparison between experiments and analytical predictions for wide ranges of strain rates  4. Conclusions In this investigation, the thermo-viscoplastic behaviour of the steel AISI 304 has been examined. The experimental characterization of the material has been conducted in tension under wide ranges of strain rates. An analytical description of the macroscopic behaviour of this metal is reported. For such goal, the extended Rusinek-Klepaczko model to viscous drag effects is applied. It allows for proper description of the material behaviour within the whole range of loading conditions considered. In addition, the analytical formulation proposed gathers limited number of material constants and simple calibration procedure. References [1] A. Rusinek and J. A. Rodríguez-Martínez (2009). Thermo-viscoplastic constitutive relation for aluminium alloys, modeling of negative strain rate sensitivity and viscous drag effects, Mater. Des., 30, 4377–4390. [2] P.S Follansbee (1986). High-Strain-Rate Deformation of FCC Metals and Alloys, Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, 451-479. [3] R. Kapoor and S. Nemat-Nasser (1999). Comparison between high strain-rate and low strain-rate deformation of tantalum, Metall. Mater. Trans., 31A, 815–823. 

SAM : Science Arts et Métiers

Science Arts & Métiers (SAM)is an open access repository that collects the work of Arts et Métiers Institute ofTechnology researchers and makes it freely available over the web where possible.This is an author-deposited version published in: https://sam.ensam.euHandle ID: .http://hdl.handle.net/10985/11055To cite this version :José A. RODRIGUEZ-MARTINEZ, Alexis RUSINEK, Raphaël PESCI, Angel ARIAS - Mechanicalcharecterization and analytical modeling of the thermo-viscoplastic behaviour AISI 304  steelunder wide ranges of strain rates at room temperature - 2010Any correspondence concerning this service should be sent to the repositoryAdministrator : archiveouverte@ensam.euMechanical characterization and analytical modeling of the thermo-viscoplastic behaviour AISI 304 steel under wide ranges of strain rates at room temperature   J.A. Rodríguez-Martínez1, A. Rusinek2, R. Pesci3, A. Arias1 1 Department of Continuum Mechanics and Structural Analysis, University Carlos III of Madrid, Avda. de la Universidad 30, 28911 Leganés, Madrid, Spain 2 Laboratory of Mechanic, Biomechanic, Polymers and Structures, National Engineering School of Metz (ENIM), Ile du Saulcy, 57045 Metz cedex, France 3 Arts et Métiers ParisTech , Laboratory of Physic and Mechanic of Materials, FRE CNRS 3236,          4 rue Augustin Fresnel, Ile du Saulcy, 57078 Metz cdex 3, France  1. General In this contribution, the thermo-viscoplastic behaviour of the steel AISI 304 is analyzed under wide ranges of loading conditions. In order to characterize the mechanical behavior of the material, tensile tests have been performed within the ranges of strain rates 4 3 110 10 s− −≤ ε ≤ɺ . The analytical definition of the material behaviour has been conducted by means of the extended Rusinek-Klepaczko model to viscous drag effects [1]. Based on such understanding of the material behaviour, satisfactory agreement between experiments and analytical modeling is reached for the whole range of loading conditions examined. 2. Experimental characterization at room temperature Analysis of the thermo-viscoplastic behaviour of the steel AISI 304 has particular relevance since this material is widely used in many engineering applications. The tensile tests performed at different strain rates reveal the characteristics high strain hardening and ductility of this metal, Figure 1-a. It has to be highlighted that even at high loading rate the strain hardening of the materil remains approximately constant. It provides to thismaterial of improved mechanical properties for absorbing energy under impulsive loads. Dependence of strain rate on the material flow stress level is observed. Thus, in Figure 1-b. is illustrated the rate sensitivity of the material from static to highly dynamic loading. The original experimental results of this work are compared with those reported in [2]. Both data find good agreement within the range of strain rates considered. In particular, it has to be noted that beyond certain level of loading rate the flow stress of the materil sharply increases. Such a behaviour is assumed to be caused by viscous drag deformation mode [2].  010020030040050060070080090010000 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 0,45 0,50.002 1/s1 1/s10 1/s100 1/s200 1/s500 1/sTrue strain, εMaterial: Steel AISI 304To = 293 KTrue stress, σ (MPa)0.002 s-11.0 s-110 s-1100 s-1200 s-1500 s-1 (a) 010020030040050060070080090010000,0001 0,01 1 100 104This workFollansbee et al. 1986AverageTrue stress, σ (MPa)Strain rate, (s-1)10 %Material: Steel AISI 304To = 293 Kεp = 0.1 (b) Figure 1. (a) Flow stress evolution as a function of plastic strain for different strain rates at room temperature (b) Flow stress evolution as a function of strain rates and comparison with [3] 3. Thermo-viscoplastic modeling of 304 stainless steel for a wide range of strain rates For modeling the material behaviour, the extended Rusinek-Klepaczko model to viscous drag effects [1] is applied: (1)  ( ) ( ) ( ) ( )[ ] ( )pvsppppp TTETET εσεσεεσεεσ µ ɺɺɺɺ ++= ,,,,,*0 An additional stress component ( )pvsσ εɺ  originally proposed by [3] is added to the original Rusinek-Klepaczko formulation in order to describe the viscous drag effects at high strain rates. The following set of constants for the model calibration has been found, Table 1.  B0 (MPa) ν  (-) n0 (-) D2 (-) 0ε  (-) *0σ (MPa) *m  (-) D1 (-) χ (MPa) α (-) *θ  1243.6 0.001 0.36 0.035 0.0118 117.72 1.29 0.55 200.83 0.0009774 0.9 Table 1. Material constants for the steel AISI 304, equation 1    By means of such analytical description of the material behaviour, good agreement between experiments and modeling is found at room temperature for the whole range of loading conditions considered, Figure 2.    Figure 2. Comparison between experiments and analytic l predictions for wide ranges of strain rates  4. Conclusions In this investigation, the thermo-viscoplastic behaviour of the steel AISI 304 has been examined. The experimental characterization of the material has been conducted in tension under wide ranges of strain rates. An analytical description of the macroscopic behaviour of this metal is reported. For such goal, the extended Rusinek-Klepaczko model to viscous drag effects is applied. It allows for proper description of the material behaviour within the whole range of loading conditions considered. In addition, the analytical formulation proposed gathers limited number of material constants and simple calibration procedure. References [1] A. Rusinek and J. A. Rodríguez-Martínez (2009). Thermo-viscoplastic constitutive relation for aluminium alloys, modeling of negative strain rate sensitivity and viscous drag effects, Mater. Des., 30, 4377–4390. [2] P.S Follansbee (1986). High-Strain-Rate Deformation of FCC Metals and Alloys, Metallurgical Applications of Shock-Wave and High-Strain-Rate Phenomena, 451-479. [3] R. Kapoor and S. Nemat-Nasser (1999). Comparison between high strain-rate and low strain-rate deformation of tantalum, Metall. Mater. Trans., 31A, 815–823. 

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Mechanical charecterization and analytical modeling of the thermo-viscoplastic behaviour AISI 304 steel under wide ranges of strain rates at room temperature

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