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RESEARCH PAPERS: Special Issue on Time-Dependent Behaviors of Polymer Matrix Composites and Polymers

Amorphous and Semicrystalline Solid Polymers: Experimental and Modeling Studies of Their Inelastic Deformation Behaviors

[+] Author and Article Information
Fazeel Khan

Department of Manufacturing and Mechanical Engineering, Miami University, Oxford, OH 45056khanfj@muohio.edu

Erhard Krempl

Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY 12180

J. Eng. Mater. Technol 128(1), 64-72 (Mar 09, 2005) (9 pages) doi:10.1115/1.1925289 History: Received September 26, 2004; Revised March 09, 2005

The study of the inelastic deformation behavior of six amorphous and semicrystalline polymers was performed to develop and verify the capabilities of a constitutive material model. The test conditions consisted of piecewise constant strain rates for loading and unloading. Immediate control mode switching capability permitted using load control for creep and recovery tests. Positive, nonlinear rate sensitivity was observed in all cases for monotonic loading and the prior loading rate was found to have a strong influence on creep, relaxation and strain recovery (emulating creep at zero stress) tests. In particular, a fast prior rate engenders a larger change in the output variable: strain in conditions of creep and stress drop in relaxation. Based on the absence of any distinctive deformation traits, the preponderance of data collected in the experimentation program suggests that both categories of polymers can be modeled using the same phenomenological approach. Modeling of the experimental data is introduced with a uniaxial form of the Viscoplasticity Theory Based on Overstress for Polymers (VBOP). Simulations and model predictions are provided for various loading histories. Additional modifications necessary to extend the theory to finite deformation and inelastic compressibility are then presented. An objective formulation is obtained in the Eulerian framework together with the recently proposed logarithmic spin by Xiao [Xiao, H., Bruhns, O., and Meyers, A., 1997, “Hypoelesticity Model Based Upon the Logarithmic Stress Rate  ,” J. Elast., 47, pp. 51–68].

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Material: PPO. Experimental tensile data at three strain rates illustrates the equidistant trend of the stress–strain curves. The inset illustrates the influence of prior rate on recovery behavior.

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Figure 2

Material: HDPE. Symbols represent experimental data for specimen in tension. The material exhibits pronounced nonlinear rate sensitivity. Beyond 4% strain, the stress–strain curves become equidistant. This region is called the flow stress region. The solid lines represent VBO simulation data.

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Figure 3

Material: PES. Tensile experimental data showing increasing divergence between the stress–strain curves. Necking was imminent beyond 9% strain.

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Figure 4

Material: PC. Solid lines represent tensile experimental data which was available only for the loading segment shown. Strain controlled loading to 5% strain shows divergence in the stress-strain curves accompanied by very little rate sensitivity. Necking occurs at approximately 5.5%–6.0% strain accompanied by a precipitous drop in stress. Symbols represent VBO simulation data.

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Figure 5

Material: PC. Multiple relaxation tests on the loading and unloading segments of the stress–strain curve. The drop in stress increases as the test point is shifted to a higher strain value (on loading). The dotted line represents the postulated path of the equilibrium stress and does not illustrate the change in magnitude during relaxation. Its placement relative to the stress–strain curve allows for increasing positive overstress (σ–G) during loading and negative overstress during unloading.

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Figure 6

Material: HDPE. Drop in stress during relaxation at 4% and 5% strain. Experimental and simulation results are shown for the two indicated strain rates. The drop in stress is found to be independent of the test point, but strongly influenced by the prior strain rate. A faster prior rate engenders a larger drop in stress.

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Figure 7

Material: PC (Simulation data: solid symbols). Creep stress level 44MPa (loading stress–strain segment). Prior rate effects are apparent in the material’s behavior.

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Figure 8

Material: HDPE, experimental data. Change in strain following loading to 10% strain, unloading to zero stress, and holding at zero load. Effect of prior rate is in evidence. The vertical axis indicates the amount of strain recovered as a percentage of the initial value, i.e., the inelastic strain value measured immediately upon complete unloading.

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Figure 9

Schematic of a stress–strain path generated by VBO. Also shown in the figure are the equilibrium (G) and kinematics (K) stress curves. Values for σ–G (overstress) and G–K reach steady state values in the flow stress region.

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Figure 10

Schematic of a VBO stress–strain curve. Of considerable importance is the equilibrium stress curve because its position relative to the σ curve governs the sign of change in stress and strain during relaxation and creep, respectively. At point A, the overstress (σ–G) is positive and relaxation occurs from A to C as shown. At P1, a positive overstress yields similar behavior. However, at P2, the model will yield upwards relaxation and decreasing strain during creep.

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Figure 11

Material: PC. Comparison of the experimental and simulation data for a fourteen hour relaxation test at 4.0% strain. Material constants are the same as those used in Fig. 4.

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Figure 12

Material: PC. Illustration of the drop in stress versus time for the data shown in Fig. 1. While the model slightly over predicts the rapid initial drop, the long-time behavior is reproduced quite accurately.

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Figure 13

Material: HDPE. Experimental data (open symbols) and VBO prediction (lines) of the creep response at 10MPa with two prior loading rates. Material constants are the same as those used in Figs.  26.

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