TY - JOUR
T1 - A new constitutive equation for the long-term creep of polymers based on physical aging
AU - Zheng, S. F.
AU - Weng, G. J.
N1 - Funding Information: This work was supported by the National Science Foundation, under Grants CMS-9625304 and CMS-0114801.
PY - 2002
Y1 - 2002
N2 - Based on the observation that during long-term creep the viscosity of polymers will continue to increase due to physical aging, a new constitutive equation is derived to describe the long-term creep behavior of polymers that are chrono-rheologically simple. The theory is developed using the concept of effective time for such materials whose long-term creep compliances with various aging times are characterized by a horizontal shift on the log(t)-scale. The derivation makes use of the basic mathematical structure for such a horizontal shift, with a result that is both sufficient and necessary. A linear viscosity function is found to be required for such a material, and the corresponding shift rate for both the long-term creep and the short-time creep is found to increase with aging time te, reaching an asymptotic value of unity. This theory improves Struik's (1978) classic theory for the special class of chrono-rheologically simple materials, in that, when the aging time is sufficiently long, both theories are identical, but when it is short, the present one can account for the transition to the asymptotic state. The developed effective-time theory is then extended to a polymer-matrix composite to predict the effect of physical aging on the long-term creep of a fiber-reinforced composite material.
AB - Based on the observation that during long-term creep the viscosity of polymers will continue to increase due to physical aging, a new constitutive equation is derived to describe the long-term creep behavior of polymers that are chrono-rheologically simple. The theory is developed using the concept of effective time for such materials whose long-term creep compliances with various aging times are characterized by a horizontal shift on the log(t)-scale. The derivation makes use of the basic mathematical structure for such a horizontal shift, with a result that is both sufficient and necessary. A linear viscosity function is found to be required for such a material, and the corresponding shift rate for both the long-term creep and the short-time creep is found to increase with aging time te, reaching an asymptotic value of unity. This theory improves Struik's (1978) classic theory for the special class of chrono-rheologically simple materials, in that, when the aging time is sufficiently long, both theories are identical, but when it is short, the present one can account for the transition to the asymptotic state. The developed effective-time theory is then extended to a polymer-matrix composite to predict the effect of physical aging on the long-term creep of a fiber-reinforced composite material.
KW - Constitutive equations
KW - Long-term creep
KW - Polymers and composites
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U2 - https://doi.org/10.1016/S0997-7538(02)01215-9
DO - https://doi.org/10.1016/S0997-7538(02)01215-9
M3 - Article
VL - 21
SP - 411
EP - 421
JO - European Journal of Mechanics, A/Solids
JF - European Journal of Mechanics, A/Solids
SN - 0997-7538
IS - 3
ER -