An Overstress Model for Non-proportional Loading of Nylon 66

Nylon 66의 무비례 하중에 대한 과응력 모델

  • Published : 2001.12.01


Non-proportional loading tests of Nylon 66 at room temperature exhibit path dependent behavior and plasticity-relaxation interactions. The uniaxial formulation of the viscoplasticity theory based on overstress (VBO), which has been used to reproduce the nonlinear strain rate sensitivity, relaxation, significant recovery and cyclic softening behaviors of Nylon 66, is extended to three-dimensions to predict the response in strain-controlled, comer-path tests. VBO consists of a flow law that is easily written for either the stress or the strain as the independent variable. The flow law depends on the overstress, the difference between the stress and the equilibrium stress that is a state variable in VBO. The evolution law of the equilibrium stress in turn contains two additional state variables, the kinematic stress and the isotropic stress. The simulations show that the constitutive model is competent at modeling the deformation behavior of Nylon 66 and other solid polymers.


  1. McKenna, G.B. and Zappas, L.J., 1979, 'Nonlinear Viscoelastic Behavior of Poly(Methly Methacrylate)in Torsion,' Journal of Rheology, Vol. 23, pp. 151-166
  2. Knauss, W.G. and Emri, I., 1987, 'Volume Change and the Nonlinear Thermo-Viscoelastic Constitution of Polymers,' Polymer Engineering and Science, Vol. 27, pp. 86-100
  3. Schapery, R.A., 1998, 'Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics,' Mechanics of Time-Dependent Materials, Vol. 1, pp. 209-240
  4. Bordnaro, C.M. and Krempl, E., 1992, 'The Effect of Strain Rate on the Deformation and Relaxation Behavior of 66 Nylon at Room Temperature,' Polymer Engineering and Science, Vol. 32, pp. 1066-1072
  5. Bordonaro, C.M. and Krempl, E., 1995, 'A State Variable Model for High Strength Polymers,' Polymer Engineering and Science, Vol. 35, pp. 310-316
  6. Krempl, E., 1996, 'A Small Strain Viscoplasticity Theory Based on Overstress,' in Krausz, A. S. and Krausz, K., Editors, United Constitutive Laws of Plastic Deformaion, Academic Press, San Diego, pp. 281-318
  7. Krempl, E. and Ho, K., 2000, 'An Overstress Model for Solid Polymer Deformation Behavior Applied to Nylon 66,' Time Dependent and Nonlinear Effects in Polymers and Composites, ASTM STP 1357, American Society for Testing and Materials, West Conshohocken PA, pp.118-137
  8. Krempl, E. and Bordonaro, C.M., 1999, 'Non Proportional Loading of Nylon 66 at Room Temperature,' International Journal of Plasticity, Vol. 14, pp. 245-258
  9. Krempl, E. and Nakamura, T., 1999, 'The Influence of the Equillbrium Stress Growth Formulation on the Modeling of Recently Observed Relasation Behaviors,' JSME International Journal A, Vol. 41, pp. 103-111
  10. Ho, K. and Krempl, E., 2000, 'Modeling of Positive, Negative and Zero Rate Sensitivity by Using the Viscoplasticity Theory Based on Overstress(VBO),' Mechanics of Time-Dependent Materials, Vol. 4, pp. 21-42