The inelastic deformation behavior of the PMR-15 neat resin, a high-temperature thermoset polymer, was investigated at temperatures in the 274–316 °C range. The experimental program was designed to explore the influence of strain rate on monotonic loading at various temperatures. In addition, the effects of prior strain rate on relaxation response and on creep behavior following strain-controlled loading were examined at temperatures in the range of interest. Positive, nonlinear strain rate sensitivity is observed in monotonic loading at all temperatures investigated. Both relaxation behavior and creep are profoundly influenced by prior strain rate at all temperatures. The time-dependent mechanical behavior of the PMR-15 polymer is also strongly affected by temperature. The elastic modulus decreases and the departure from quasi-linear behavior is accelerated with increasing temperature. Stress levels in the region of inelastic flow decrease as the temperature increases. The relaxation behavior as well as the creep response is strongly influenced by temperature. The viscoplasticity theory based on overstress for polymers (VBOP) is augmented to model the effects of temperature on the inelastic deformation behavior of PMR-15. VBOP is a unified state variable theory with growth laws for three state variables: the equilibrium stress, the kinematic stress, and the isotropic stress. Based on the experimental findings several VBOP model parameters are developed as functions of temperature. The augmented model is employed to predict the response of the material under both strain- and stress-controlled loading histories at temperatures in the range of interest. Comparison with experimental data demonstrates that the augmented VBOP successfully predicts the inelastic deformation behavior of PMR-15 polymer under various loading histories at temperatures between 274 and 316 °C.

References

1.
NASA
,
2003
, “
DMBZ Polyimides Provide an Alternative to PMR-15 for High-Temperature Applications
,” http://www.grc.nasa.gov/WWW/RT/RT1995/5000/5150c.htm.
2.
Ellyin
,
F.
, and
Xia
,
Z.
,
2006
, “
Nonlinear Viscoelastic Constitutive Model for Thermoset Polymers
,”
ASME J. Eng. Mater. Technol.
,
128
,
pp.
579
585
.10.1115/1.2345450
3.
Shaw
,
S.
,
Warby
,
M. K.
, and
Whiteman
,
J. R.
,
1997
,
An Introduction to the Theory and Numerical Analysis of Viscoelasticity Problems
,
Brunel University
,
England
.
4.
Schapery
,
R. A.
,
2000
, “
Nonlinear Viscoelastic Solids
,”
Int. J. Solids. Struct.
,
37
,
pp.
359
366
.10.1016/S0020-7683(99)00099-2
5.
Losi
,
G. U.
, and
Knauss
,
W. G.
,
1992
, “
Free Volume Theory and Nonlinear Thermoviscoelasticity
,”
Polym. Eng. Sci.
,
32
(
8
),
pp.
542
557
.10.1002/(ISSN)1548-2634
6.
Knauss
,
W. G.
, and
Emri
,
I.
,
1987
, “
Volume Change and the Nonlinearly Thermo-Viscoelastic Constitution of Polymers
,”
Polym. Eng. Sci.
,
27
(
1
),
pp.
86
100
.10.1002/(ISSN)1548-2634
7.
Shay
,
R. M.
, Jr.
, and
Caruthers
,
J. M.
,
1990
, “
A Predictive Model for the Effects of Thermal History on the Mechanical Behavior of Amorphous Polymers
,”
Polym. Eng. Sci.
,
30
(
20
),
pp.
1266
1280
.10.1002/(ISSN)1548-2634
8.
Schapery
,
R. A.
,
1969
, “
On the Characterization of Nonlinear Viscoelastic Materials
,”
Polym. Eng. Sci.
,
9
(
4
),
pp.
295
310
.10.1002/(ISSN)1548-2634
9.
O'Connell
,
P. A.
, and
McKenna
,
G. B.
,
2002
, “
The Non-Linear Viscoelastic Response of Polycarbonate in Torsion: An Investigation of Time-Temperature and Time-Strain Superposition
,”
Mech. Time-Depend. Mater.
,
6
(
3
),
pp.
207
229
.10.1023/A:1016205712110
10.
Xia
,
Z.
,
Shen
,
X.
, and
Ellyin
,
F.
,
2005
, “
An Assessment of Nonlinearly Viscoelastic Constitutive Models for Cyclic Loading: The Effect of a General Loading/Unloading Rule
,”
Mech. Time-Depend. Mater.
,
9
(
4
),
pp.
79
98
.10.1007/s11043-006-9004-3
11.
Popelar
,
C. F.
, and
Liechti
,
K. M.
,
2003
, “
A Distortion-Modified Free Volume Theory for Nonlinear Viscoelastic Behavior
,”
Mech. Time-Depend. Mater.
,
7
(
2
),
pp.
89
141
.10.1023/A:1025625430093
12.
Lustig
,
S. R.
,
Shay
,
R. M.
, Jr., and
Caruthers
,
J. M.
,
1996
, “
Thermodynamic Constitutive Equations for Materials With Memory on a Material Time Scale
,”
J. Rheol.
,
40
,
pp.
69
106
.10.1122/1.550789
13.
Krempl
,
E.
, and
Khan
,
F.
,
2003
, “
Rate (Time)-Dependent Deformation Behavior: An Overview of Some Properties of Metals and Solid Polymers
,”
Int. J. Plast.
,
19
(
7
),
pp.
1069
1095
.10.1016/S0749-6419(03)00002-0
14.
Krempl
,
E.
,
McMahon
,
J. J.
, and
Yao
,
D.
,
1986
, “
Viscoplasticity Based on Overstress With a Differential Growth Law for the Equilibrium Stress
,”
Mech. Mater.
,
5
(
1
),
pp.
35
48
.10.1016/0167-6636(86)90014-1
15.
Krempl
,
E.
,
1996
, “
A Small-Strain Viscoplasticity Theory Based on Overstress
,”
Unified Constitutive Laws of Plastic Deformation
,
A. S.
Krausz
and
K.
Krauszeds
, eds.,
Academic Press
,
San Diego
,
pp.
281
318
.
16.
Krempl
,
E.
, and
Ho
,
K.
,
2001
, “
Inelastic Compressible and Incompressible, Isotropic, Small Strain Viscoplasticity Theory Based on Overstress VBO
,”
Handbook of Materials Behavior Models
,
J.
Lemaitre
, ed.,
Academic Press
,
San Diego
,
pp.
336
348
.
17.
Krempl
,
E.
,
1995
, “
From the Standard Linear Solid to the Viscoplasticity Theory Based on Overstress
,”
Proceedings of the International Conference on Computational Engineering Science
,
S. N.
Atluri
,
G.
Yagawa
, and
T. A.
Cruse
, eds.,
Vol.
2
,
pp.
1679
1684
.
18.
Kitagawa
,
M.
, and
Matsutani
,
T.
,
1988
, “
Effect of Time and Temperature on Nonlinear Constitutive Equation in Polypropylene
,”
J. Mater. Sci.
,
23
(
11
),
pp.
4085
4090
.10.1007/BF01106840
19.
Kitagawa
,
M.
,
Zhou
,
D.
, and
Qiu
,
J.
,
1995
, “
Stress-Strain Curves for Solid Polymers
,”
Polym. Eng. Sci.
,
35
(
22
),
pp.
1725
1732
.10.1002/(ISSN)1548-2634
20.
Bordonaro
,
C. M.
, and
Krempl
,
E.
,
1992
, “
The Effect of Strain Rate on the Deformation and Relaxation Behavior of 6/6 Nylon at Room Temperature
,”
Polym. Eng. Sci.
,
32
(
16
),
pp.
1066
1072
.10.1002/(ISSN)1548-2634
21.
Krempl
,
E.
, and
Ho
,
K.
,
2000
, “
An Overstress Model for Solid Polymer Deformation Behavior Applied to Nylon 66
,”
Proceedings of the ASTM Symposium
,
R. A.
Schapery
and
C. T.
Sun
, eds.,
Vol.
1357
,
pp.
118
137
.
22.
Khan
,
F.
, and
Krempl
,
E.
,
2004
, “
Pre-Necking and Post-Necking Relaxation and Creep Behavior of Polycarbonate: A Phenomenological Study
,”
Polym. Eng. Sci.
,
44
(
9
),
pp.
1783
1791
.10.1002/(ISSN)1548-2634
23.
Khan
,
F.
, and
Krempl
,
E.
,
2006
, “
Amorphous and Semicrystalline Solid Polymers: Experimental and Modeling Studies of Their Inelastic Deformation Behaviors
,”
ASME J. Eng. Mater. Technol.
,
128
,
pp.
64
72
.10.1115/1.1925289
24.
Khan
,
F.
,
2006
, “
Loading History Effects on the Creep and Relaxation Behavior of Thermoplastics
,”
ASME J. Eng. Mater. Technol.
,
128
,
pp.
564
571
.10.1115/1.2345448
25.
Khan
,
F.
,
2002
, “
The Deformation Behavior of Solid Polymers and Modeling With the Viscoplasticity Theory Based on Overstress
,”
Ph.D. thesis, Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute
,
Troy, NY
.
26.
Colak
,
O. U.
,
2005
, “
Modeling Deformation Behavior of Polymers With Viscoplasticity Theory Based on Overstress
,”
Int. J. Plast.
,
21
(
1
),
pp.
145
160
.10.1016/j.ijplas.2004.04.004
27.
Colak
,
O. U.
, and
Dusunceli
,
N.
,
2006
, “
Modeling Viscoelastic and Viscoplastic Behavior of High Density Polyethylene (HDPE)
,”
ASME J. Eng. Mater. Technol.
,
128
(
4
),
pp.
572
578
.10.1115/1.2345449
28.
Bowles
,
K. J.
,
Papadopoulos
,
D. S.
, and
Inghram
,
L. L.
,
2001
, “
Longtime Durability of PMR-15 Matrix Polymer at 204, 260, 288 and 316 C
,”
NASA Glenn Research Center, Report No. NASA TM-2001-210602
.
29.
Odegard
,
G.
, and
Kumosa
,
M.
,
2000
, “
Elastic-Plastic and Failure Properties of a Unidirectional Carbon/PMR-15 Composite at Room and Elevated Temperatures
,”
Compos. Sci. Technol.
,
60
(
16
),
pp.
2979
2988
.10.1016/S0266-3538(00)00163-9
30.
Schoeppner
,
G. A.
,
Tandon
,
G. P.
, and
Ripberger
,
E. R.
,
2007
, “
Anisotropic Oxidation and Weight Loss in PMR-15 Composites
,”
Composites, Part A
,
38
(
3
),
pp.
890
904
.10.1016/j.compositesa.2006.07.006
31.
Tsuji
,
L. C.
,
McManus
,
H. L.
, and
Bowles
,
K. J.
,
1998
, “
Mechanical Properties of Degraded PMR-15 Resin
,”
NASA Lewis Research Center, Report No. TM-1998-208487
.
32.
Falcone
,
C. M.
, and
Ruggles-Wrenn
,
M. B.
,
2009
, “
Rate Dependence and Short-Term Creep Behavior of a Thermoset Polymer at Elevated Temperature
,”
ASME J. Pressure Vessel Technol.
,
131
, p.
011403
.10.1115/1.3027475
33.
McClung
,
A. J. W.
, and
Ruggles-Wrenn
,
M. B.
,
2008
, “
The Rate (Time)-Dependent Mechanical Behavior of the PMR-15 Thermoset Polymer at Elevated Temperature
,”
Polym. Test.
,
27
(
7
),
pp.
908
914
.10.1016/j.polymertesting.2008.07.007
34.
McClung
,
A. J. W.
, and
Ruggles-Wrenn
,
M. B.
,
2009
, “
Strain Rate Dependence and Short-Term Relaxation Behavior of a Thermoset Polymer at Elevated Temperature: Experiment and Modeling
,”
ASME J. Pressure Vessel Technol.
,
131
, p.
031405
.10.1115/1.3110025
35.
Ruggles-Wrenn
,
M. B.
, and
Ozmen
,
O.
,
2010
, “
The Rate (Time)-Dependent Mechanical Behavior of the PMR-15 Thermoset Polymer at 316 °C: Experiments and Modeling
,”
ASME J. Pressure Vessel Technol.
,
132
, p.
041403
.10.1115/1.4000730
36.
Ruggles-Wrenn
,
M. B.
, and
Broeckert
,
J. L.
,
2008
, “
Effects of Prior Aging at 288 °C in Air and in Argon Environments on Creep Response of PMR-15 Neat Resin
,”
J. Appl. Polym. Sci.
,
111
,
pp.
228
236
.10.1002/app.v111:1
37.
Diedrick
,
B. K.
,
2010
, “
Effects of Prior Aging at 260 °C in Argon on Inelastic Deformation Behavior of PMR-15 Polymer at 260 °C: Experiment and Modeling
,”
M.S. thesis, Air Force Institute of Technology
,
Wright-Patterson Air Force Base, Ohio
.
38.
Ruggles
,
M. B.
,
Cheng
,
S.
, and
Krempl
,
E.
,
1994
, “
The Rate-Dependent Mechanical Behavior of Modified 9wt.%Cr-1wt.%Mo Steel at 538 °C
,”
Mater. Sci. Eng., A
,
186
(
1–2
),
pp.
15
21
.10.1016/0921-5093(94)90301-8
39.
Ruggles
,
M. B.
, and
Krempl
,
E.
,
1991
, “
Rate Sensitivity and Short-Term Relaxation Behavior of AISI Type 304 Stainless Steel at Room Temperature and at 650 °C; Influence of Prior Aging
,”
ASME J. Pressure Vessel Technol.
,
113
(
3
),
pp.
385
391
.10.1115/1.2928771
40.
Ozmen
,
O.
,
2009
, “
Effects of Prior Aging at 316 °C in Argon on Inelastic Deformation Behavior of PMR-15 Polymer at 316 °C: Experiment and Modeling
,”
M.S. thesis, Air Force Institute of Technology
,
Wright-Patterson Air Force Base, Ohio
.
41.
Ho
,
K.
,
1998
, “
Application of the Viscoplasticity Theory Based on Overstress to the Modeling of Dynamic Strain Aging of Metals and to the Modeling of the Solid Polymers, Specifically to Nylon 66
,”
Ph.D. thesis, Rensselaer Polytechnic Institute
,
Troy, New York
.
42.
Ho
,
K.
, and
Krempl
,
E.
,
2002
, “
Extension of the Viscoplasticity Theory Based on Overstress (VBO) to Capture Non-Standard Rate Dependence in Solids
,”
Int. J. Plast.
,
18
(
7
),
pp.
851
872
.10.1016/S0749-6419(01)00011-0
43.
Bordonaro
,
C. M.
,
1995
, “
Rate Dependent Mechanical Behavior of High Strength Plastics: Experiment and Modeling
,” Ph.D. thesis,
Rensselaer Polytechnic Institute
,
Troy, New York
.
44.
Cernocky
,
E. P.
, and
Krempl
,
E.
,
1980
, “
A Theory of Thermoviscoplasticity Based on Infinitesimal Total Strain
,”
Int. J. Solids. Struct.
,
16
(
8
),
pp.
723
741
.10.1016/0020-7683(80)90014-1
45.
Maciucescu
,
L.
,
2002
, “
A Simplified Viscoplasticity Theory Based on Overstress for Low to High Homologous Temperature and Quasi-Static to Dynamic Applications
,”
Ph.D. thesis, Rensselaer Polytechnic Institute
,
Troy, New York
.
You do not currently have access to this content.