Journal of Materials Science

, Volume 42, Issue 12, pp 4562–4574 | Cite as

A constitutive equation for the dynamic deformation behavior of polymers

  • F. J. Zerilli
  • R. W. ArmstrongEmail author


A constitutive equation based on the generalized concept of thermally activated flow units is developed to describe the stress–strain behavior of polymers as a function of temperature, strain-rate, and superposed hydrostatic pressure under conditions in which creep and long-term relaxation effects are negligible. The equation is shown to describe the principal features of the dynamic stress–strain behavior of polytetrafluoroethylene and, also, the yield stress of polymethylmethacrylate as a function of temperature and strain rate. A key feature of the model, not utilized in previous constitutive equation descriptions, is an inverse shear stress dependence of the shear activation volume. In contrast to metal deformation behavior, an enhanced strain hardening with increasing strain at higher strain rates and pressures is accounted for by an additional rate for immobilization of flow units. The influence of hydrostatic pressure enters through a pressure activation volume and also through the flow unit immobilization term. The thermal activation model is combined with a temperature dependent Maxwell–Weichert linear viscoelastic model that describes the initial small strain part of the stress strain curve.


PMMA PTFE Flow Unit Creep Compliance Brittle Transition 



This work was principally supported by the NSWC Independent Research Program with partial support from the Office of Naval Research. Additional partial support was provided by NSWC for Ronald Armstrong. Appreciation is expressed to Stephen Mitchell and Wayne Reed for the NSWC IR support, Chester Clark for the NSWC support, and to Judah Goldwasser for the ONR support. Appreciation is also expressed to G. T. Gray, III for providing us his Hopkinson bar data on PTFE in advance of publication.


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Research and Technology DepartmentNaval Surface Warfare CenterIndian HeadUSA
  2. 2.Center for Energetic Concepts DevelopmentUniversity of MarylandCollege ParkUSA

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