Kimberly Maciejewski1, Yaofeng Sun1, Otto Gregory2, Hamouda Ghonem1

1Department of Mechanical Engineering and Applied Mechanics, 2Department of Chemical Engineering, University of Rhode Island, Kingston, RI, 02881, USA

The microstructural and mechanical properties of low carbon steel as a function of temperature and post thermal exposure are characterized. The amounts and morphology of carbides present were monitored as a function of thermal exposure parameters. An Internal State Variable (ISV) model has been employed to simulate the flow behavior of the steel for multiple temperatures, ranging from 20-700°C and loading rate conditions. Low cycle fatigue tests are carried out to determine the material parameters required for implementation in constitutive equations.

This work provides a fundamental understanding of the deformation response associated with fire loadings. It also gives insight on the effects of microstructural components related to the deformation response of post-fire loading conditions. This knowledge represents the foundation of predictive modeling of new designs, materials and protocols for mitigation methods aiming at infrastructure protection.

This material is based upon work supported by the U.S. Department of Homeland Security under Award Number 2008-ST-061-ED0001. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied of the U.S. Department of Homeland Security.

This ISV model is being extended to 2-D and 3-D simulations suitable for implementation of steel-structures subjected to fire and loading conditions. It will also be extended for simulation of deformation response of structural steel under combined blast/fire loadings

K. Maciejewski, Y. Sun, O. Gregory and H. Ghonem, Time-Dependent Deformation of Low Carbon Steel at Elevated Temperatures, Int. J. Steel and Iron Research, March 2011

Deformation and Hardening Characteristics of Structural Steel

Under Post-Fire and Fire Conditions

Abstract

Relevance

1) Effects of temperature and time on Vol% pearlite and grain size of low carbon steel have been examined. 2) An ISV material model combining kinematic and isotropic hardening has been employed. 3) An experimental program was carried out to determine material parameters for model implementation. 4) Numerical modeling was carried out for 1-D simulation to check validity of model and its ability to predict material behavior for variable loading conditions.

Accomplishments Through Current Year

Future Work Journal Publications

Technical Approach

4. Microstructural 5. Heat Treatment Characterization Test Setup

v

R

k

ijX

ij

p

ij

v

R

k

ijX

1 2

1

μqmax

p

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( )

( )

Q Q 1 e

max( ε ,q)

exp ( )

( )

i

v

r

i i i p i p i i i

p

n n

v vp

t p

X R k

X X X

X C a X X X

R b Q R

q

sign XK K

E

Extensometer

Induction Coil

TC 1 TC 2 TC 3

Specimen

Extensometer

Specimen

Alpha-Ferrite

Pearlite Colony/ Plates - Cementite - Ferrite

Temperature range: 300-700°C

Exposure times range: 0-200min

Vertical Furnaces

Ice Salt Water Baths

Nickel-Chromium Wire

Temperature (°C)

0 200 400 600 800

Vol%

Pearlite

0

2

4

6

8

10

12

14

Marked decrease in Vol% Pearlite at 700°C

Exposure Time (minutes)

-50 0 50 100 150 200 250

Vo

l% P

ea

rlite

0

2

4

6

8

10

12

14 20°C, 300°C, 500°C, 600°C

700°C

Exposure Time (minutes)

-50 0 50 100 150 200 250

Gra

in S

ize

(m

icro

me

ters

)

30

40

50

60

70

80

90

100

20°C, 300°C, 500°C, 600°C

700°C

Temperature (°C)

0 200 400 600 800

Gra

in S

ize

(m

icro

me

ters

)

30

40

50

60

70

80

90

100

Increase in variations of grain size at 700°C

(bimodal distribution)

As Received

600°C, 200min

700°C, 200min

Critical Post Fire Conditions

• As Received • 600°C, 200min,

Quenched in Ice Salt Water Bath

• 700°C, 200min, Quenched in Ice Salt Water Bath

Grain Size (micrometers)

30 40 50 60 70 80 90

Vol%

Pearlite

0

2

4

6

8

10

12

14

20°C - 600°C

700°C

Bimodal Distribution

Formation of Spheroidized

Carbide

For the same temperature, exposure time had less than 2% effect on Vol% Pearlite

600°C, 200min

Spheroidized Carbide

700°C, 200min

Spheroidized Carbide

Strain controlled tests carried at 5 temperatures to determine Kinematic Hardening, Isotropic Hardening, and Viscous Stress Material Constants. Tests required at each temperature are: 1. Monotonic – constant strain rate 2. Stress Relaxation – constant strain rate with hold at constant strain values 3. Cyclic – constant strain rate with fully reversed loading at different strain ranges 4. Strain Rate Sensitivity – varying strain rates

2. High & Room Temperature Test Setup

3. Experimental Program & Parameter Determination

1. Internal State Variable Model

Digital Temperature

Readout

6. Quantitative Analysis

For T 20°C- 600°C, exposure time has no effect on grain size.

At 700°C, “average” GS increases with exposure time

Strain (mm/mm)

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

Str

ess

(M

Pa

)

-200

-150

-100

-50

0

50

100

150

200

600°C - Experimental

Strain (mm/mm)

-0.008 -0.006 -0.004 -0.002 0.000 0.002 0.004 0.006 0.008

Str

ess

(M

Pa)

-80

-60

-40

-20

0

20

40

60

80

700°C - Experimental

Strain (mm/mm)

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

Str

ess

(M

Pa

)

-400

-200

0

200

400300°C - Experimental

Numerical

Strain (mm/mm)

-0.006 -0.004 -0.002 0.000 0.002 0.004 0.006

Str

ess

(M

Pa)

-300

-200

-100

0

100

200

300

500°C - Experimental

500°C 300°C

600°C 700°C

Strain (mm/mm)

0.000 0.002 0.004 0.006 0.008 0.010

Str

ess (

MP

a)

0

100

200

300

400

500

300°C - Experimental

500°C - Experimental

600°C - Experimental

700°C - Experimental

Numerical

Strain (mm/mm)

0.000 0.005 0.010 0.015 0.020 0.025

Str

ess

(M

Pa

)

0

50

100

150

200

250

300

5e-4 s-1

5e-6 s-1

5e-7 s-1

500°C - Numerical

Strain (mm/mm)

0.000 0.002 0.004 0.006 0.008 0.010

Str

ess

(M

Pa

)

0

100

200

300

400

500

5e-6s-1

5e-5s-1

5e-4s-1

300°C - Numerical

300°C

500°C

Strain (mm/mm)

0.000 0.005 0.010 0.015 0.020

Str

ess (

MP

a)

0

100

200

300

400

500

20°C - Experimental

20°C - Numerical

Strain (mm/mm)

0.000 0.005 0.010 0.015 0.020

Str

ess (

MP

a)

0

100

200

300

400

500

20°C - Post 600°C - Experimental

20°C - Post 600°C - Numerical

Strain (mm/mm)

0.000 0.005 0.010 0.015 0.020

Str

ess (

MP

a)

0

100

200

300

400

500

20°C - Post 700°C - Experimental

20°C - Post 700°C - Numerical

Strain (mm/mm)

-0.008 -0.006 -0.004 -0.002 0.000 0.002 0.004 0.006 0.008

Str

ess (

MP

a)

-600

-400

-200

0

200

400

600

20°C - Post 600°C - Experimental

20°C - Post 600°C - Numerical

Strain (mm/mm)

-0.010 -0.008 -0.006 -0.004 -0.002 0.000 0.002 0.004 0.006 0.008 0.010

Str

ess (

MP

a)

-600

-400

-200

0

200

400

600

20°C - Post 700°C - Experimental

20°C - Post 700°C - Numerical

Strain (mm/mm)

-0.004 -0.003 -0.002 -0.001 0.000 0.001 0.002 0.003 0.004

Str

ess (

MP

a)

-600

-400

-200

0

200

400

600

20°C - Experimental

20°C - Numerical

As Received Post 600°C Post 700°C

Strain Rate Independent

The ISV model is capable of modeling: Monotonic and cyclic loading for all temperature conditions:

A) 20°C and 300°C - strain rate independent behavior B) 500°C, 600°C, and 700°C - strain rate dependent behavior

7. Simulation Results & Validation

Fire Conditions

Post-Fire Conditions

Strain Rate Dependent