Transcript PPVC-2 yield stresses where (a) strain rate data (triangles)

Rate dependence of poly(vinyl chloride), the effects of
plasticizer and time–temperature superposition
by Michael J. Kendall, and Clive R. Siviour
Proceedings A
Volume 470(2167):20140012
July 8, 2014
©2014 by The Royal Society
Yield stress dependence on absolute temperature of an arbitrary polymer, with multiple strain
rates shown to obey a linear time–temperature superposition.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PMMA yield data as a function of temperature mapped onto strain rate yield data to create
master curves at 100°C in uniaxial compression.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Comparison of the PC variation of peak stress with temperature, and the variation of peak stress
with strain rate mapped onto temperature. [8].
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Representative behaviour of PVC. (a) True stress–true strain response in uniaxial compression
over all rates tested at 20°C and (b) the true yield stress as a function of strain rate over a
logarithmic scale.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Representative behaviour of PVC. (a) True stress–true strain response in uniaxial compression
over all temperatures tested at 10−2 s−1 and (b) the true yield stress as a function of temperature
over a linear scale in °C.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Representative behaviour of PPVC-2.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Representative behaviour of PPVC-2.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
True yield stress of PPVC-2 as a function of strain rate over a logarithmic scale presenting the
influences of two different rate-activated processes (α and β).
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Representative behaviour of PPVC-4.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Representative behaviour of PPVC-4.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Representative behaviour of PPVC-6.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
Representative behaviour of PPVC-6.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PVC elastic modulus (solid lines) and loss modulus (dashed lines) curves at 0.035 s−1 (1 Hz,
light grey), 0.35 s−1 (10 Hz, dark grey) and 3.5 s−1 (100 Hz, black). β- and α-transitions are
centred, respectively, at approximately (i) −45°C and (ii) 82°C.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PPVC-2 elastic modulus and loss modulus curves at 0.035 s−1 (1 Hz, light grey), 0.35 s−1 (10 Hz,
dark grey) and 3.5 s−1 (100 Hz, black) starting at (a) −100°C and (b) −150°C. β- and α-transitions
are centred, respectively, at approximately −150 and 45°C.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PPVC-4 elastic modulus and loss modulus curves at 0.035 s−1 (1 Hz, light grey), 0.35 s−1 (10 Hz,
dark grey) and 3.5 s−1 (100 Hz, black). β- and α-transitions are centred, respectively, at
approximately −150 and 0°C.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PPVC-6 elastic modulus and loss modulus curves at 0.035 s−1 (1 Hz, light grey), 0.35 s−1 (10 Hz,
dark grey) and 3.5 s−1 (100 Hz, black). β- and α-transitions are centred, respectively, at
approximately −150 and −20°C.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PVC yield stresses where (a) temperature data (squares) are mapped onto strain rate data
(triangles) and (b) strain rate data are mapped onto temperature data using D=13.5°C/decade ε˙.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PPVC-2 yield stresses where (a) temperature data (squares) are mapped onto strain rate data
(triangles) and (b) strain rate data are mapped onto temperature data using D=11°C/decade ε˙.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PPVC-4 yield stresses where (a) temperature data (squares) are mapped onto strain rate data
(triangles) and (b) strain rate data are mapped onto temperature data using D=8.5°C/decade ε˙.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PPVC-6 yield stresses where (a) temperature data (squares) are mapped onto strain rate data
(triangles) and (b) strain rate data are mapped onto temperature data using D=7.5°C/decade ε˙.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PVC (a), PPVC-2 (b), PPVC-4 (c) and PPVC-6 (d) with yield stress data at 10−2 s−1 superimposed
onto elastic modulus data at 0.035 s−1 (1 Hz, light grey), 0.35 s−1 (10 Hz, dark grey) and 3.5 s−1
(100 Hz, black).
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PPVC-2 yield stresses where (a) strain rate data (triangles) are mapped onto temperaturedependent data (squares) and (b) temperature data (squares) are mapped onto strain rate
(triangles) data using D=6°C/decade ε˙.
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PPVC-2 (a) strain rate data (triangles and circles) mapped onto temperature data (squares), and
(b) PPVC-2 temperature data (squares and circles) mapped onto strain rate data (triangles).
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society
PVC (a) strain rate data (triangles and circles) mapped onto temperature data (squares) and (b)
temperature data (squares and circles) mapped onto strain rate data (triangles).
Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A
2014;470:20140012
©2014 by The Royal Society