Nonlinearly Viscoelastic Behavior of Polycarbonate. II. The Role of Volumetric Strain

The creep responses of (bisphenol A) polycarbonate at 80°C undercombined two-dimensional shear with superposed tensile and compressivestress states were measured on Arcan specimens in the nonlinearlyviscoelastic regime. Of particular interest is the influence of thedilatational deformation component on the nonlinearly viscoelastic creepbehavior. Because the nonlinear material response determines the stressdistribution under fixed deformation or load, but is not known a priori,a re-estimation of the latter is essential to verify or adjust thestress state(s). This is accomplished by approximating isochronalstress-strain relations derived from shear creep behavior, encompassingthe nonlinear domain, by a classical incremental elasto-plastic materialdescription at appropriate times. To the extent that the two-dimensionalcharacter of the test configuration permits accessing three-dimensionalinformation, a coherent representation of the results is examined interms of maximum shear and/or octahedral representation.It is found that the creep behavior under shear and normal stressor deformation imposition differ significantly: When viewed as aresponse to the imposition of a maximum shear stress, the creepresponses differ depending on whether one or the other dominates. On theother hand, if the response is formulated in terms of an octahedraldescription the representation becomes less sensitive to normal vs.shear behavior. It is clear in either case, however, that normal strainhas a disproportionately large effect on creep response in shear. Withinthe precision underlying the measurements it is found that the shear andnormal strain components accumulate under creep in nearly constantratios. Under this scenario it is demonstrated clearly that theinfluence of negative dilatational stress (or deformation) on pure sheardeformation leads to distinctly lower creep rates. The converse is true,if positive dilatational stresses are added, though not monotonically so.

[1]  W. Knauss,et al.  Non-linear viscoelasticity based on free volume consideration , 1981 .

[2]  G. Adam,et al.  On the Temperature Dependence of Cooperative Relaxation Properties in Glass‐Forming Liquids , 1965 .

[3]  W. F. Ranson,et al.  Determination of displacements using an improved digital correlation method , 1983, Image Vis. Comput..

[4]  J. Ferry,et al.  Mathematical Structure of the Theories of Viscoelasticity , 1955 .

[5]  Richard Schapery.  An engineering theory of nonlinear viscoelasticity with applications , 1966 .

[6]  James M. Caruthers,et al.  Thermodynamic constitutive equations for materials with memory on a material time scale , 1996 .

[7]  K. Liechti,et al.  An evaluation of the arcan specimen for determining the shear moduli of fiber-reinforced composites , 1997 .

[8]  G. Vendroux,et al.  Submicron deformation field measurements: Part 2. Improved digital image correlation , 1998 .

[9]  R. Christensen.  Theory of viscoelasticity : an introduction , 1971 .

[10]  R. E. Robertson,et al.  The elastic, anelastic and plastic components of strain in the load-extension curve for bisphenol-A polycarbonate† , 1972 .

[11]  Igor Emri,et al.  Volume change and the nonlinearly thermo‐viscoelastic constitution of polymers , 1987 .

[12]  G. McKenna,et al.  A torsional dilatometer for volume change measurements on deformed glasses: Instrument description and measurements on equilibrated glasses , 1990 .

[13]  M. Goldstein.  Some Thermodynamic Aspects of the Glass Transition: Free Volume, Entropy, and Enthalpy Theories , 1963 .

[14]  Mircea Arcan,et al.  The iosipescu shear test as applied to composite materials , 1984 .

[15]  K. Liechti,et al.  Finite Element Analysis of the Arcan Specimen for Fiber Reinforced Composites under Pure Shear and Biaxial Loading , 1999 .

[16]  A. Wineman,et al.  Yieldlike response of a compressible nonlinear viscoelastic solid , 1995 .

[17]  Richard Schapery.  Nonlinear Viscoelastic and Viscoplastic Constitutive Equations Based on Thermodynamics , 1997 .

[18]  Z. Hashin,et al.  A method to produce uniform plane-stress states with applications to fiber-reinforced materials , 1978 .

[19]  M. Arcan,et al.  On the Most Suitable Specimen Shape for Testing Shear Strength of Plastics , 1959 .

[20]  Hongbing Lu,et al.  The Role of Dilatation in the Nonlinearly Viscoelastic Behavior of PMMA under Multiaxial Stress States , 1998 .

[21]  John Henry Poynting,et al.  On the changes in the dimensions of a steel wire when twisted, and on the pressure of distortional waves in steel , 1912 .

[22]  Wolfgang G. Knauss,et al.  Nonlinearly Viscoelastic Behavior of Polycarbonate. I. Response under Pure Shear , 2002 .

[23]  Y. Liang,et al.  On the large deformation and localization behavior of an epoxy resin under multiaxial stress states , 1996 .

[24]  W. Knauss,et al.  The Time-Dependent Bulk Response of Poly (Methyl Methacrylate) , 2001 .

[25]  W. Knauss,et al.  Strain inhomogeneity and discontinuous crack growth in a particulate composite , 1998 .