by Michael J. Kendall, and Clive R. Siviour 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. Yield stress dependence on absolute temperature of an arbitrary polymer, with multiple strain rates shown to obey a linear time–temperature superposition. An equivalent yield stress is found corresponding to a chosen temperature. 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. PMMA yield data as a function of temperature mapped onto strain rate yield data to create master curves at 100°C in uniaxial compression. The dashed curve is calculated from the two-process Ree–Eyring equation [5]. 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]. 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 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. 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. (Online version in colour.)‏ Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A 2014;470:20140012 ©2014 by The Royal Society

Representative behaviour of PVC 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. 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. (Online version in colour.)‏ Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A 2014;470:20140012 ©2014 by The Royal Society

Representative behaviour of PPVC-2. Representative behaviour of PPVC-2. (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. (Online version in colour.)‏ Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A 2014;470:20140012 ©2014 by The Royal Society

Representative behaviour of PPVC-2. Representative behaviour of PPVC-2. (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 strain rate over a temperature scale in °C. (Online version in colour.)‏ 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). 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). All tests were conducted at 20°C. Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A 2014;470:20140012 ©2014 by The Royal Society

Representative behaviour of PPVC-4. Representative behaviour of PPVC-4. (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 (yield is determined by the stress at 10% true strain for this material). (Online version in colour.)‏ Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A 2014;470:20140012 ©2014 by The Royal Society

Representative behaviour of PPVC-4. Representative behaviour of PPVC-4. (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 strain rate over a temperature scale in °C. (Online version in colour.)‏ Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A 2014;470:20140012 ©2014 by The Royal Society

Representative behaviour of PPVC-6. Representative behaviour of PPVC-6. (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 (yield is determined by the maximum stress at 5% true strain for this material). (Online version in colour.)‏ Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A 2014;470:20140012 ©2014 by The Royal Society

Representative behaviour of PPVC-6. Representative behaviour of PPVC-6. (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 strain rate over a temperature scale in °C. (Online version in colour.)‏ 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. 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. These transitions correspond to the loss modulus peaks at these temperatures. 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 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. 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 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. 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 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. 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˙. 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˙. 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˙. The dashed (strain rate data) and dotted lines (temperature data) are used to help present the subtleties of the two different sets of data. These data are described in greater detail in §5. 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˙. 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˙. 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). 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 temperature-dependent data (squares) and (b) temperature data (squares) are mapped onto strain rate (triangles) data using D=6°C/decade ε˙. PPVC-2 yield stresses where (a) strain rate data (triangles) are mapped onto temperature-dependent 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). 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). Using Dα=6.0°C/decade ε˙ (triangles) for low to moderate strain rates (0.001–85 s−1) and using Dβ=13.0°C/decade ε˙ (circles) for high strain rates (2020–7600 s−1) where both values were obtained from DMTA data. 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). 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). Using Dα=5.35°C/decade ε˙ (squares) for low strain rates (0.001–0.1 s−1) and using Dβ=11.80°C/decade ε˙ (circles) for moderate to high strain rates (1–6330 s−1) where β influences were confirmed by DMTA data. Michael J. Kendall, and Clive R. Siviour Proc. R. Soc. A 2014;470:20140012 ©2014 by The Royal Society