Creep Analysis of a Thermoplastic Using Stress Relaxation Data
Shane Reif Gravelle, author

CONTENTS

• Abstract
• Introduction
• Experimental Procedure
• Results
• Discussion
• Conclusion
• References
• List of Figures

Recent development in the field of polymer design and engineering have been limited by the inadequacy of existing data. More specifically, innovative designs using thermoplastics are limited by the mechanical behavior data which often do not span appropriate ranges of stress, time, strain, or temperature. In an effort to improve the design process, a methodology using short time (less than twenty-four hours) stress relaxation tests has been developed to provide long-time design information.

This study uses stress relaxation tests to investigate the creep properties of VALOX, a poly(butylene terephthalate), or PBT, developed by General Electric. The results confirm that this technique can accurately generate creep curves. Secant modulus curves as a function of strain, time, and temperature can also be produced. The stress relaxation testing technique thus show great promise as a tool to be used in the design of thermoplastic components.

INTRODUCTION

Recent developments associated with the innovative use of thermoplastics in structural applications demands accurate engineering data. More specifically, the assessment of structural performance requires data that spans appropriate ranges of stress, time, temperature, and strain rate.[1,2] Traditionally, data available to designers have neglected vicoelasticity which is unacceptable for applications involving time-dependent behavior.

In an effort to address these shortcomings, new methodologies are continually being developed to predict creep behavior. The desire to avoid long time creep testing has led to the development of a practical, innovative approach to generating tensile and creep curves through the use of stress relaxation tests (SRT).[3] The SRT methodology was first developed for metals and subsequently shown to be applicable to polymers.[3,4,5,6] Short time (less than twenty-four hours) SRT are used to generate plots of stress versus inelastic strain rate. The previous work demonstrated a high degree of accuracy using SRT to determine creep curve for polycarbonate and polyphenylene oxide.[6] The present study investigates the mechanical behavior of VALOX, a poly(butylene terephthalate), or PBT, provided by General Electric, using the same approach.

EXPERIMENTAL PROCEDURE

Standard tensile specimens of General Electric Plastics' VALOX, with a cross-sectional area of 38.97 mm , were stress relaxation tested using an Instron 4204 testing system with a closed-loop control configuration. Each sample was loaded at a constant displacement rate of 10 mm/min using an attached extensometer to measure the strain directly. When the desired level of strain was reached, the displacement rate was reduced to 0.5 mm/min and the strain held constant. By maintaining a constant strain in the specimen, concerns about machine compliance are eliminated. [7]

Subsequently, a strip chart recorder monitored the reduction of stress with time over approximately a twenty-four hour period, as the elastic strain was continuously being replaced by inelastic strain. Time and stress data were taken from the charts to yield a plot of stress versus time which was subsequently fit with a fourth order polynomial equation (See figures 1a-c These equations were differentiated to yield stress rate.)

The aforementioned experimental procedure was repeated for total strain levels of 0.5%, 1.0%, 1.5%, and 2.0% and at the temperatures of 50 degrees Celsius, 65 degrees Celsius, and 80 degrees Celsius. To eliminate the effects of history and aging, a separate specimen was tested at each of the desired conditions. Curves of log stress versus stress rate were used to generate pseudo tensile curves at iso-stress rates which in turn were used to construct creep and secant modulus curves.

RESULTS

Construction of Pseudo-Tensile Curves: Using the stress-stress rate curves shown in figures 2a-c families of iso-stress rate psuedo curves for VALOX were constructed using a cross-plotting technique. Vertical cuts of constant stress rate were taken across the stress-rate curves. Values of stress were recorded corresponding to the intersection between the cuts and the curves. Subsequently, these stresses were plotted against their respective total strains to yield pseudo-tensile curves, as shown in figures 3a-c.

Generations of Creep Data: Using the previously constructed pseudo-tensile plots, horizontal cuts of constant stress were made and each intersecting strain value was recorded. The time to each of these strains were then calculated using the following formula:

After converting time to units of hours, creep curves of strain versus time were plotted. This procedure was performed at stress levels of 1.72, 3.45, and 5.2 MPa (250, 500, and 750 psi, respectively). Results are presented in figures 4a-c.

Generation of Secant Modulus Data: In a procedure similar to the construction of creep curves, vertical cuts of constant strain were taken across families of pseudo-tensile curves for a particular temperature. The stress at which each of the stress rate curves was intersected was recorded. By dividing these stress values by strain, secant modulus values were determined for specific strains and temperatures. Plots of secant modulus versus time are presented in figures 5a-d.

DISCUSSION

Creep curves generated using SRT show excellent agreement with experimentally determined data for VALOX. As shown in figure 6, the SRT predictions are well within expected experimental error.

The attractiveness of the SRT methodology goes beyond its apparent accuracy. Because it can predict creep curves to several hundred hours on the basis of a twenty-four hour test without actual data exploitation, SRT is far more economical as a design tool than conventional experimental creep testing. Furthermore, the SRT technique can be analyzed in terms of total strain, eliminating the need to consider a separate time-dependent elastic contribution. The SRT methodology could be further improved by running stress relaxation tests from higher strains, subsequently enlarging the usable stress range. In addition, longer SRT could be run to expand the predictable time range, producing families of stress-stress rate curves which encompass lower stress rates.

To determine the structural integrity of thermoplastics, designers rely heavily on modulus data. The variability of published data available to designers is perplexing. For example, modulus data may be presented as any of the following:

Each of these values varies enough to result in serious consequences in the design process.

In an effort to minimize confusion to designers, the use of a single effective modulus has been proposed. The SRT technique shows great promise as a basis for producing such effective modulus data. The procedure is capable of generating secant modulus data for a wide range of time and temperature. Furthermore, there is no indication that the usual procedure for calculating secant moduli, based on constant strain rate, is superior to the SRT method which relies on constant stress rate.

In summary, the SRT approach is an accurate and efficient means of producing long-time design information for use in pseudo-elastic design. Despite the apparent success of this methodology the SRT does not rigorously model the may time-dependent and deformation path-dependent phenomena seen in polymers at elevated temperatures. However, it does represent a significant advance in the compilation of sound thermoplastic engineering data.

CONCLUSIONS

1. Trantina, G.G. and Ysseldyke, D.A. An Engineering Design Database for Plastics. Materials Engineering. Oct., 1987. pp 35-38.
2. Trantina, G.G. and Ysseldyke, D.A. An Engineering Design System for Thermoplastics. Society of Plastics Engineers, 1989 ANTEC Technical Conference Proceeding. pp. 635-639.
3. Woodford, D.A. Test Methods for Development, Design, and Life Assessment of High Temperature Materials. Materials and Design 14(5), 1993. pp 279-284.
4. Hart, E.W. and Solomon, H.D. Load relaxation studies of polycrystalline high purity aluminum. Acta Met 1973, 21, pp 295-307.
5. Grzywinski, G.G. and Woodford, D.A. Design Data for polycarbonate from stress-relaxation test. Materials and Design 14 (5), 1993. pp 279-284.
6. Grzywinski, G.G. and Woodford, D.A. Creep Analysis of Thermoplastics Using Stress Relaxation Data. Polymer Engineering and Science, to be published.
7. Gillis, P.P. and Medrano, R.E. A Consistency Criterion Applicable to Strain Rate and Stress Relaxation Tests. J. Mater. 6, 1971. pp 514-523.

LIST OF FIGURES

Figure 1a: Stress relaxation curves for 50 degrees Celsius
Figure 1b: Stress relaxation curves for 65 degrees Celsius
Figure 1c: Stress relaxation curves for 80 degrees Celsius

Figure 2a: Stress rate curves for 50 degrees Celsius
Figure 2b: Stress rate curves for 65 degrees Celsius
Figure 2c: Stress rate curves for 80 degrees Celsius

Figure 3a: Pseudo-tensile curves for 50 degrees Celsius
Figure 3b: Pseudo-tensile curves for 65 degrees Celsius
Figure 3c: Pseudo-tensile curves for 80 degrees Celsius

Figure 4a: Creep curves for 50 degrees Celsius
Figure 4b: Creep curves for 65 degrees Celsius
Figure 4c: Creep curves for 80 degrees Celsius

Figure 5a: Time dependence of secant modulus at 0.5% strain
Figure 5b: Time dependence of secant modulus at 1.0% strain
Figure 5c: Time dependence of secant modulus at 1.5% strain
Figure 5d: Time dependence of secant modulus at 2.0% strain

Figure 6: Comparison between experimental and predicted curves at 50 degrees Celsius