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RESEARCH PAPERS

Experimentally Evaluating the Equilibrium Stress in Shear of Glassy Polycarbonate

[+] Author and Article Information
Mehrdad Negahban

Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526mnegahban@unl.edu

Ashwani Goel, Pierre Delabarre, Ruqiang Feng, Amy Dimick

Department of Engineering Mechanics, University of Nebraska, Lincoln, NE 68588-0526

J. Eng. Mater. Technol 128(4), 537-542 (Apr 12, 2006) (6 pages) doi:10.1115/1.2345445 History: Received October 14, 2005; Revised April 12, 2006

One group of models proposed for characterizing the mechanical response of glassy polymers is based on a structure that resembles finite plasticity. In most cases, a constitutive equation for stress is proposed, which depends on the elastic deformation gradient, supplemented by a flow rule for the plastic deformation, which depends on the “over stress.” The over stress is a properly invariant difference between the stress and the back stress (equilibrium stress). The back stress represents conditions under which relaxation events should stop and the material should be able to carry an applied load indefinitely without a need to change the strain. Questions that arise in using these models are whether such equilibrium stresses exist, how can they be evaluated, and what experiments can be used to characterize the flow rule. One challenge in accurately evaluating the locus of equilibrium conditions is the fact that the relaxation process substantially slow down around these points, and, therefore, a method that does not directly require being at the equilibrium is desirable. Focusing on shear, a thermodynamic theory for characterizing the response of glassy polymers, similar to models currently used for this purpose, is developed, and using this model it is shown that one can set up a method to calculate the plastic strain rate. This method is based on evaluating the slope of stress-strain response under conditions of similar elastic and plastic strain, but different strain rates. Since the equilibrium stress occurs when the plastic strain rate goes to zero, the evaluated plastic strain rates allow evaluation of the needed information for developing the flow rule and obtaining the back stress. This method is used to evaluate the plastic strain rate and back stress at room temperature for polycarbonate. The evaluated results match well with results obtained by direct probing of the equilibrium stress, in which one searches for points at which the stress remains constant at a constant strain over long durations. The method proposed looks promising in evaluating the back stress of glassy polymers. The added advantage of this method is that it also provides a map of plastic strain rate and tangent modulus over a large range of loading conditions.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Stress buildup and stress relaxation seen in PMMA above its glass-transition temperature

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Figure 2

Schematic of sample geometry and loading method, and pictures of the deformed sample

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Figure 3

Stress response of PC under shear at room temperature at four strain rates

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Figure 4

Equilibrium stress in PC after initial loading: Stress-time response

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Figure 5

Equilibrium stress in PC after initial loading: Stress-strain response

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Figure 6

Cyclic loading and unloading of PC in shear. The loading and unloading are different in value.

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Figure 7

Cyclic loading and unloading of PC in shear. The loading and unloading are different in value. Also shown on the plot are the loci of constant plastic strain rate with the plastic strain rates indicated on the legend.

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Figure 8

Shear strain history of the sample during cyclic loading and unloading for the response shown in Fig. 6

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Figure 9

The two points on adjacent loading cycles used to evaluate γ̇p

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Figure 10

Plastic shear strain rate evaluated as a function of stress using the mismatch in the loading and unloading slopes (cycles 1, 2, and 3)

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Figure 11

Plastic shear strain rate evaluated as a function of stress using the mismatch in the loading and unloading slopes

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Figure 12

Equilibrium stress τb as a function of plastic strain at room temperature. Also shown are the loci of constant plastic strain rate.

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