Loading History Effects on the Creep and Relaxation Behavior of Thermoplastics

[+] Author and Article Information
Fazeel Khan

Department of Mechanical and Manufacturing Engineering, 145 Kreger Hall, Miami University, Oxford, OH 45056

J. Eng. Mater. Technol 128(4), 564-571 (May 30, 2006) (8 pages) doi:10.1115/1.2345448 History: Received August 24, 2005; Revised May 30, 2006

Experimental investigations have been performed to understand the effects of prior loading on the creep and stress relaxation behavior of an amorphous polymer (polyphenylene oxide) and a semi-crystalline polymer (high density polyethylene) at room temperature. Of particular interest was the positioning of creep and relaxation tests on the unloading segment of stress-strain curves for tensile and compressive loading. The data was found to be quite unlike that obtained in typical tests performed on the loading segment; i.e., with no unloading history. Specifically, in relaxation tests, rather than registering a monotonic drop, the stress first increases then decreases. The rate of change of stress, therefore, is initially positive and then becomes negative. Similarly, in creep tests, the strain was found to decrease at first, and then began to increase. This has been labeled as rate-reversal in the context of relaxation and creep test data, and, furthermore, the test point has been found to influence the stress-time and strain-time data, respectively. In relaxation, for instance, at large strain values, the initial increase in stress is considerably smaller than the subsequent drop and the rate reversal occurs very rapidly. Conversely, at smaller strain values, the initial increase in stress dominates and the rate reversal may occur only after several hours. Analogous changes are observed during creep as tests are performed at lower stress values. Preliminary attempts at modeling the aforementioned creep and relaxation behavior have been made by modifying the existing formulation of the viscoplasticity theory based on overstress, which is a constitutive state-variable based model. A modified, single-element standard linear solid serves as a suitable descriptor of the model. Linking of two elements in series has shown some promise towards the modeling of the rate-reversal behavior. Experimental data and results of preliminary simulations are presented in this study.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 12

Spring-dashpot representation of VBO. In this single-element model, the total strain equals the sum of the strain of spring 1 and that across spring 2 and the dashpot. The total rate is expressed as a time derivative.

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Figure 13

General stress-strain curve output of VBO. The time evolution of the equilibrium and kinematic stress is illustrated. Governed by the sign of the overstress, the relaxation, and creep response is shown at points A, P1, and P2.

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Figure 14

VBO simulation of a stress-strain curve for a hypothetical material. Modifications discussed in the text yield two equilibrium stress curves labeled g and h. The significance of having two equilibrium stress curves is illustrated in the following figure which provides a magnified view of the unloading segment of the curve. The qualitative response of relaxation during loading remain unaffected.

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Figure 2

Material: PPO, Loading rate: ε̇=1×10−4s−1. The stress-strain curves of two specimen undergoing 1‐h stress-relaxation at 5% and 7% strain followed by a resumption in loading are shown. The convergence of the plots provides evidence of fading memory vis-à-vis subsequent deformation behavior. The inset plot highlights the stress-time response, but more importantly suggests that the drop in stress can be independent of the test point.

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Figure 3

Material: PES. Data from three specimens shows that the drop in stress during relaxation is found to increase as tests are performed at higher strain values along the (quasi) elastic portion of the stress-strain curve.

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Figure 4

Material: PPO. Data from two specimen with a prior loading rate of 1×10−4s−1 has been appended to the relaxation data presented in Fig. 2. It can be seen that the faster prior loading rate results in a larger drop in stress. Simulation results from VBO are included in the figure as well.

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Figure 5

Material: PPO. Creep strain increases nonlinearly with increasing stress. The dotted line represents an uninterrupted loading curve. A strain rate of ε̇=1×10−3s−1 was used for loading the specimen to all test points.

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Figure 6

Material: PPO. Creep response at 47MPa with two prior strain rates. Simulation results are shown in solid lines.

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Figure 7

Material: HDPE. Strain rate magnitude for loading and unloading: ε̇=1×10−3s−1. The relaxation behavior of three specimen at 4.5%, 4.0%, and 3.5% strain shows the occurrence of an increase in the stress magnitude followed by a decrease. The relative swing in each direction changes with the placement of the test.

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Figure 8

Material: HDPE. One-hour relaxation tests in compression with a prior tension-compression loading history. The test at −3.5% strain on the unloading segment clearly displays the occurrence of a decrease followed by an increase in the magnitude of the stress. The arrowhead lines highlight this behavior. Strain rate: ε̇=1×10−3s−1.

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Figure 9

Material: HDPE. Results of eight specimen are shown to highlight the transformation in the creep behavior as tests are performed at various stress levels. At point E(5MPa), strain during creep only decreases during the 1‐h load hold. Specimen H was loaded directly into compression. Strain rate: ε̇=1×10−3s−1.

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Figure 10

Material: HDPE. Comparison of the creep response over 1200s at 15MPa on the loading and unloading segment. In the latter, the strain decreases, then begins to increase. The dashed gray line is provided to compare the post-creep stress-strain curve to one representing uninterrupted loading. Loading and unloading strain rate: ε̇=1×10−3s−1.

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Figure 11

Material: HDPE. Comparison of the creep response at ±10MPa shows good similitude in the data.

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Figure 1

The strain controlled loading history imposed on the specimen undergoing a relaxation test is shown. For a test on the loading segment, AB represents the strain hold interval, while DE=0. Alternatively, for tests performed on the unloading segment, AB=0 implying uninterrupted loading from O to C followed by immediate unloading to D. DE represents the relaxation response. Sr is the residual strain recorded upon unloading the specimen to zero load.

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Figure 15

Positive overstress quantities associated with each of the g-curves permit only negative stress rates during relaxation. In region B, however, opposing signs can allow the stress rate to swing from positive to negative to describe the reversal behavior observed in Fig. 7. Increase in stress during relaxation in region C is predicted under this formulation and agrees with experimental observations.

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Figure 16

Simulation of relaxation response at 7.9% (initial stress: 5.1MPa) strain using the proposed two-element VBO model shows the occurrence of the experimentally observed up-down behavior. The test point lies in region B of Fig. 1 and the full loading-unloading path is shown in Fig. 1. Though the changes in magnitude indicated in the plot are smaller than observed in experiment, an attempt has not yet been made to match the data. Only the potential for modeling such phenomena is being demonstrated.



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