Creep Design Analysis for Thermoplastics

02014099(95)00009-9

Creep design analysis for a thermoplastic from stress relaxation measurements

S. K. Reif, K. J. Amberge and D. A. ~oo~ord ~ateria/s ~e~orrna~~e a~a/ys~s, Inc., 1737 ff~io~ Street, Suite 543, Schenectady, NY 72309, USA

Received 29 September 7994; accepted 16 February 1995

Innovative designs using thermoplastics have been limited by available mechanical property data which often do not span appropriate ranges of stress, time, strain and temperature. In an effort to improve the design process, a methodology using short-time (less than 24-hour) high- precision stress relaxation tests has been developed to provide comprehensive design information. This study uses stress relaxation tests to investigate the creep properties of VALOX, a polybutylene terephthalate, or PBT, developed by General Electric. The approach is extremely efficient, and the data generated can be presented in several convenient formats. For example, pseudo-stress-strain curves may be used to generate strain versus time (at a constant stress) or stress versus time (at a constant strain). Secant modulus curves as a function of strain, time and temperature can also be produced. The results are in good agreement with those generated by traditional test methods. The stress relaxation testing technique thus shows great promise as a tool to be used in the design of thermoplastic components.

Keywords: stress relaxation; creep; secant modulus; design analysis

Introduction The assessment of structural performance in plastics, as in all materials operating at high homologous temperatures, requires property data covering appropriate ranges of stress, strain, time and temperature1-3. The traditional approach to generate the data has involved the testing of many specimens for long times at fixed values of stress and temperature. This is a costly and inefficient procedure and is a major obstacle to the development of new or improved materials. The desire to avoid long-time creep testing has led to the development of a practical, innovative approach to generating high-temperature design curves through the use of stress relaxation tests (SRT)4. The SRT methodology was first developed for metals and subsequently shown to be applicable to polymers&. Short-time (less than 24 hours) SRT are used to generate plots of stress versus either stress rate or inelastic strain rate. The high- temperature pe~o~an~e may then be represented in several ways using these basic plots.

For polymers the scarcity of design-quality creep data is especially acute because of the great variety of grades and the batch-to-batch variability. The previous work on a polycarbonate and polyphenylene oxide showed great potential in the SRT methodology to provide the desired acceleration of data generatio#.. The results were accurate, reproducible and consistent with traditional constant load creep data. Moreover, it was

Correspondence to David A. Woodford

0261-3069/95/0~001~7 8 1995 Elsevier Science

shown that ambiguities associated with strain on loading and with the time-dependence of elastic modulus could be eliminated using the SRT approach and total strain analysis.

The present study investigates the mechanical behaviour of VALOX, a polybutylene terephthalate, or PBT, provided by General Electric, using this approach.

Experimental procedure Standard flat tensile specimens of VALOX, with a cross-sectional area of 39 mm2, were stress relaxation tested in an Instron 4204 testing system with a closed- loop control configuration and an oven capable of controlling the specimen temperature to within 1C. Each sample was loaded at a constant displacement rate of 10 mm/min, using an attached extensometer on a 25.4 mm gauge to measure the strain directly. When the desired level of total strain was reached, the displacement rate was automatically reduced to 0.5 mm/min for increased control stability, and the strain then held constant. By maintaining a constant strain in the specimen, concerns about machine compliance for fixed crosshead control are eliminated8. Subsequently, a strip- chart recorder monitored the reduction of stress with time over approximately a 24-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 Figure I). These equations were then differentiated to yield stress rate as a function of stress. In constructing

Materials & Design Volume 16 Number 1 1995 15

Creep design analysis for a thermoplastic: S. U. Reif et al.

14

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16 Materials & Design Volume 16 Number 1 1995

Creep design analysis for a thermoplastic: S. K. Reif et al.

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these curves (see Figure 2) care was taken to limit the analyses to times not exceeding the actual test duration.

Relaxation tests were run from total strain levels of 0.5%, l.O%, 1.5% and 2.0% and at temperatures of 50C 65C and 80C. To eliminate the effects of deformation history and ageing, 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 Figure 2, families of iso-stress rate pseudo-tensile curves for VALOX were constructed using a cross-plotting technique. Vertical cuts of constant stress rate were taken across the stress-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 Figure 3.

Generation of creep curves Using the previously constructed pseudo-tensile plots, horizontal cuts of constant stress (s) were made and each intersecting strain value was recorded. The times (t) to each of these strains were then calculated using the following formula:

s / (dsldt) = t (seconds) (1)

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). Figure 4 is an example of a set of curves at 65C. These generated creep curves are plotted against effective time with no extrapolation of actual data, and it should be noted that the times are much longer than the relaxation test duration. This effective acceleration for creep analysis will be discussed subsequently.

From the pseudo-stress-strain plots, vertical cuts of constant strain were made and each intersecting stress value was recorded. The times to each of these strains were again calculated using equation (1). These data were plotted in terms of stress versus time and shown in Figure 5 for the case of 1% strain.

Generation of secant modulus design curves Because of the strong time-dependence of elastic modulus in polymers a secant modulus is often used in design. This is the slope of the line drawn from the origin on a stress-strain plot to intersect the curve at a given strain. It is dependent on strain rate (or stress rate), temperature and strain. In practice, the secant modulus is normally plotted against time so that a pseudo-elastic design may be made for the anticipated service life of a part, i.e. the appropriate value of the


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Creep design analysis for a thermoplastic: S. K. Reij et al.

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secant modulus may be used in place of Youngs modulus.

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, A plot of secant modulus versus time for the three temperatures is shown in Figure 6 for the case of 1% strain. This indicates up to 50% reduction in effective modulus with increasing test times to 100 hours.

Discussion High-temperature properties are generally evaluated using either constant stress (in practice, constant load) or constant strain rate (in practice, constant machine displacement rate). Much discussion centres on the conversion of data generated in one test mode to the other, i.e. the development of a constitutive relation- ship. This has been extensively pursued in the plastics literatureg-12, where the viscoelastic behaviour and the various ageing phenomena common in thermoplastics create considerable complexities. Nevertheless, design practice often uses constant load creep data cross- plotted to produce isochronous or isostrain curves, as if



TIME (hr)

Figure 6 Time dependence of secant modulus at three temperatures for 1% strain

a simple mechanical equation of state existed. Similarly, these data, or data generated at constant machine displacement rate, are used to generate secant moduli for pseudo-elastic design analysis.

In reality, neither test method provides a unique mechanical characterization; each relates to a specific deformation path which may bear little connection to the deformation path of a part in a device or machine. In fact, in many cases, stress relaxation and stress redis- tribution are of major concern, so that an argument may be made that the stress relaxation test could be fundamentally more appropriate. Here, we advocate the SRT test simply because it is more efficient and can be used in the same way to generate the various design curves as can the conventional test methods.

In fact, creep curves generated from SRT tests have been shown to give good agreement with actual constant load data6p7, so that any discussion of which test should be used as a fundamental standard becomes moot. Likewise, Figure 7 shows that creep curves generated using SRT show excellent agreement with experi- mentally determined data for VALOX.

The attractiveness of the SRT methodology goes beyond its ability to generate families of creep curves at any stress. Because it can predict creep performance to several hundred hours on the basis of a 24-hour test without actual data extrapolation, SRT is far more economical as a design tool than conventional experimental creep testing. For example, the data of Figure 2(b) show stress rates to about 10 MPa/s. A conventional tensile test (at this constant stress rate) would reach a stress of 6 MPa (corresponding to the highest strain point of 2%) in 1667 hours, which should be compared with the actual SRT test time of 24 hours. In plotting the data here we have conservatively limited the analysis to a stress rate of 1O-5 in all cases, but the enor- mous acceleration potential of the SRT method is readily apparent. Furthermore, the SRT analysis is done in terms of total strain, eliminating the need to


consider a separate time-dependent elastic contribution. Nethertheless, if desired, by dividing the stress rate by a time-independent Youngs modulus it is possible to separate elastic and inelastic strain$. Although this is normally preferred for the analysis of metals and ceram- ics, the viscoelastic behaviour of polymers makes a total strain analysis simpler to perform and to apply. The SRT methodology could be further improved by running stress relaxation tests from higher strains, subsequently enlarging the usable stress range. In addi- tion, 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: creep modulus, [f(t, e, r)]; relaxation modulus, [f(t, s, ZJ]; complex modulus, [f(freq, r)]; and secant modulus, [f(e, k, Z)]. Each of these values varies enough to result in serious conse- quences in the design process.

In an effort to minimize confusion to designers, the use of a single effective modulus has been proposed3. 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 modului, based on constant strain rate, is supe- rior 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 model the many time-dependent and deformation path- dependent phenomena seen in polymers at elevated temperatures. However, it does represent a significant

Creep design analysis for a thermoplastic: S. K. Reij et al.

Fignre 7 Comparison

2.76 MPa -

experimental and predicted creep curves at 50C for three stress levels

advance in the compilation of sound thermoplastic engineering data.

Conclusions Stress relaxation testing (SRT) can provide an enor- mous amount of information in a short time, which can be used to compare projected performance of different grades of a thermoplastic, and also rapidly evaluate batch-to-batch variability. By representing the SRT data for VALOX in the form of stress versus stress rate plots, a series of pseudo-tensile curves can be constructed to serve as the basis of performance analysis and design. Design creep curves based on strain versus time or stress versus time were constructed and compare well with experimental data generated from constant load creep tests. SRT produces effective secant moduli values over a wide range of time and temperature. This development could significantly aid the pseudo-elastic design procedure for thermoplastics.

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Creep Design Analysis for Thermoplastics