creeps analysis of thermoplastics

Creep Analysis of Thermoplastics Using Stress Relaxation Data

G. G. GRZYWINSKI and D. A. WOODFORD*

Materials Research Center Rensselaer Polytechnic Institute

Troy, New York 12 180-3590

One of the major factors limiting the use of thermoplastics in engineering applications is the inadequacy of existing design data. Much of the data do not span appropriate ranges of stress, strain, time, or temperature. This study ad- dresses the need to develop an accelerated method for generating long-time design data to support the innovative use of engineering thermoplastics. In particular, stress relaxation tests (SRT) were performed on polycarbonate (PC) and modified polytphenylene oxide)(PPO), and used to generate time-dependent design data through the short-time measurement of the materials current state without dependence on elastic modulus. The test results and analyses reported here indicate the SRT method to be an efficient means of generating accurate and repeatable creep and secant modulus data which may be directly used in design. Therefore, SRT shows great potential both as a design parameter development tool, and as a quality control instrument for assessing batch-to-batch variability.

INTRODUCTION testing (SIIT) (12). This testing method has evolved

uch of the data describing the mechanical be- M havior of thermoplastics available to designers today stem from practices standard for conventional materials which neglect viscoelasticity. While these single-point data can be used for initial material se- lection, they are inadequate for assessing the structural performance of a design since time-dependence may not be properly accounted. In the cases where necessary engineering data do exist, they most often do not span an appropriate range of stress, time, temperature, or strain rate (1, 2). Thus, the current data on engineering thermoplastics may be inadequate to fully support the innovative use of these materials in exacting applications.

To overcome this obstacle, researchers have sought to expand existing databases by increasing testing efforts (3) and by developing constitutive models to predict creep behavior in thermoplastics (4- 1 1). Be-

from ;he stress relaxation analysis of Hart and Solomon (13), where total strain ( e t ) is divided into separate components, and a short-time modulus ( E l is used to get elastic strain (ee) . The data are then plotted in terms of stress vs. inelastic strain rate, covering up to 5 orders of magnitude in strain rate from short time tests (I 24 h). This approach has been recently applied successfully to generate design data for metallic materials (14). Despite favorable results for polycarbonate, the use of a time-indepen- dent elastic modulus gave rise to some uncertainty in the aforementioned analysis (12). To eliminate the ambiguity, this paper reports further efforts to generate both creep and time-dependent secant modulus ( S ) data for both polycarbonate (PC) and modified polyphenylene oxide (PPO) through the use of SRT without specifically isolating the elastic strain compo nent.

cause of the many complications associated with both EXPERIMENTAL, PROCEDURE long time creep testing and detailed mathematical modeling (12). an alternative method for generating high temperature design data which avoids such traditional strategies would undoubtedly be useful to designers. In an effort to satisfy designers needs for more complete thermoplastic design data, the authors have previously reported a practical, innovative approach to generating tensile and creep curves for polycarbonate through the use of stress relaxation

*Current address: Materials Performance Analysis, Inc.. 1737 Union St. Schenectady, NY 12309.

Standard dogbone-type tensile specimens of Gen- eral Electric Plastics Lexan polycarbonate and Noryl modified poly(2.6 dimethyl 1,4 phenylene oxide) (PPO) were stress relaxation tested in an Instron 4204 mechanical testing system operating in the closed-loop control mode. Samples were loaded at a constant displacement rate of 25 mm/min, with an exten- someter attached to record strain in the specimen gage length. When the desired strain level was reached, the displacement setting was reduced to .5 mm/min, and a constant strain was maintained in

POLYMER ENGINEERING AND SCIENCE, DECEMBER 1995, Vol. 35, No. 24 1931

G. G. Grzywinski and D. A. Woodford

- 1 1 a E to Lo 0 9 - u1 K i- v)

(3 0 7 - 0,

0 5

the specimen. This practice of maintaining constant

compliance encountered in most similar stress relaxation studies (15). The reduction of nominal stress,

40

strain eliminated concerns associated with machine 1 5% strain

0 1 0% strain 0 0 5% strain

30 u, with time, t , was then measured for - 24 h on a strip-chart recorder, as the elastic strain was p r e gressively replaced with inelastic strain, E,. Using n.

E E., polynomial equations were then fit to these data, F which were subsequently differentiated to yield stress

- a these relaxation data, u vs. In t was plotted, and

w

v)

rate, du/dt . This procedure was performed at total strain levels of 0.5, 1.0, 1.5, and 2.0% strain, and at temperatures of 50, 65, and 80C. These curves were then used in the construction of iso-stress rate pseudo-tensile (u - E ) curves, which were subse-

10

quently used to generate creep and secant modulus curves. To eliminate history and aging effects ( 121, an

0 0 2 4 6 8 10 12

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i

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0

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individual specimen was used in each separate test.

RESULTS

Representative stress relaxation and stress-stress rate curves for Noryl and Lexan at 65C are presented in N s . la and b and 2a and b, respectively. The repeatability of these curves was assessed by performing a duplicate test sequence on Noryl at 65C as was the repeatability of such curves for Lexan in our previous work (1 2). As illustrated in Figs 3a to d , excellent agreement was observed between the original and repeat test data at each strain level.

Construction of Pseudo-Tensile Curves

Using the stress-stress rate curves (as in Figs. 1 b and Zb), families of iso-stress rate pseudo tensile curves for both Noryl and Lexan were constructed through a simple cross-plotting procedure. Vertical cuts of constant stress rate were taken across the stress rate curves. By recording the values at which each of the curves was intersected by such a vertical cut, and subsequently plotting these stresses against their respective total strains, pseudo-tensile curves (v - E ) were produced. Resulting curves for Noryl and Lexan at 65C are presented in Figs. 4 and 5, resp.

Generation of Creep Data

Through the use of another cross-plotting procedure, creep data were obtained from pseudo-tensile curve families. Horizontal cuts of constant stress were made across the iso-stress rate pseudo-tensile curves, and each intersecting strain value was recorded. The times to each of these strains were then calculated using the following:

a/ ( d u / d t ) = t( S ) (1)

After converting t into units of hours, creep curves ( E - t ) were generated. For Noryl, this procedure was performed at stress levels of 1.72, 3.45, and 5.2 MPa (250, 500, and 750 psi), and the resulting creep data are presented in Fig. 6. Stresses of 6.9, 13.8, and 20.7 MPa (1000,2000, and 3000 psi) were used for Lexan, and Fig. 7 displays the resulting creep data for this

in I ( 5 )

(a)

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STRESS RATE x - 1 (MPahec) 10-7 10-6 10-5 10-4 10.3 10-2 10-1 l o o

(b) Rg. 1 . ( a ) Stress relaxation curves in N o y l at 65C. (b) Stress rate curves in N o y l at 65C.

material. Note that, for comparison, actual creep results for both Noryl and Lexan, taken from the G. E. Engineering Design Database (EDD), are also presented on Figs. 6 and 7.

Results for Noryl indicate excellent agreement between predicted (from SRT) and experimental creep data at each stress examined. This agreement is less impressive for Lexan, but is still reasonable.

Generation of Secant Modulus Data

In addition to tensile and creep data, designers also rely heavily on modulus data in the context of mechanical performance of thermoplastics. Most published "modulus" values represent Young's Modulus ( E), or the slope of a tangent to the u - E curve at the origin. For thermoplastics, however, this modulus is not a constant, and is therefore not useful for design purposes. Since this tangent modulus is often diffi- cult to determine with precision, a secant modulus,

1932 POLYMER ENGINEERINGAND SCIENCE, DECEMBER 1995, Vol. 35, No. 24


40

30

- a. L (0 20 cn Lu E in

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(a)

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(b) Fg. 2. ( a ) Stress relaxation curves in Lexan at 65C. (b) Stress rate curves in Lexan at 65C.

$ 6 , i, TI, may be used to incorporate the time/temperature dependence.

Having constructed pseudo-tensile curves through the use of SRT, these curves were used in the generation of secant modulus (S) values for both Noryl and Lexan. The procedure for generating these values is similar to that by which creep curves were determined. Vertical cuts of constant strain were taken across families of pseudo-tensile curves at a particular T, and the stress at which each of the stress rate curves was intersected was recorded. By taking these stress points and dividing by the strain, secant modulus ( S ) was determined at a particular E and T. This procedure was performed at strains of 0.5, 1.0, 1.5, and 2.0%, and at temperatures of 50, 65, and 80C. Plots of S vs. t at these temperatures were then produced at each strain. For Noryl, these plots are presented in Figs. 8a to d, and similar plots for Lexan are presented in Figs. 9a to d.

DISCUSSION

Creep data generated through the use of SRT for both Noryl and Lexan have shown good correlation with those generated by experiment. In comparing experimental and SRT-generated creep data for N e ryl, exceptionally good correlation is observed. This correlation is perhaps even better than should be expected from such a data generation procedure. The agreement between experimental and SRT-generated data for Lexan is less impressive in terms of accuracy, but the general trend observed in the predicted data at all stresses closely matches those seen in the experimental curves. There are a number of possible explanations as to why the SRT-generated creep curves better match data for Noryl than for Lexan. Batch-to-batch variability is one possibility where, in this case, essentially no variability exists between Noryl samples subjected to both creep testing and SRT, whereas there is some variability between the Lexan samples tested. Another possible explanation stems from the creep testing procedure itself. Due to the loading procedure involved in experimental creep testing, there is considerable uncertainty in deter- mining the point of zero strain. Such uncertainty could result in a vertical shift of the entire strain-time curve to higher (or lower) strains than are actually present in the test specimen. This may explain why the strains observed in all points of the experimental creep curves in Lexan, are, at all times, greater than those in the SRT-generated curves. It should also be noted, however, that the degree of variation observed in Lexan, although considerably greater than that seen in Noryl, may not be any more severe than that which would be observed in actual creep tests performed on samples from different batches.

SRT certainly shows promise as a creep data generation tool. This conclusion is based on both the a p parent accuracy of SRT-generated creep data, and the obvious advantages this method offers over traditional creep testing. The SRT approach is a far more economical method than traditional creep testing, as this approach is capable of predicting creep data to several hundred hours from tests lasting - 24 h (as illustrated in Figs. 6 and 7 for a wide range of stresses. Also, it has been shown that the creep data generation procedure can be performed in terms of total strain, without the need to specify a time-dependent elastic modulus. Although the stress for which the longest time data may be predicted is limited to the highest stress attained in the lowest stress rate pseudo-tensile curve, this stress range could be eas- ily increased by running relaxation tests from higher strains. In addition, the predictable time range itself may be expanded by allowing longer relaxation times and thus producing families of stress-stress rate curves extending into lower stress rates. It must be stated, however, that broad conclusions regarding the accuracy of this data generation procedure can- not yet be drawn. Before such generalizations may be stated, additional testing is needed to assess the issues of variability and repeatability.

POLYMER ENGINEERING AND SCIENCE, DECEMBER 1995, Vol. 35, No. 24 1933

G. G. Grzywinski a n d D. A. Woodford

0 5% strain

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&I. 3. Repeatability of stress rate da ta in Noyl a t 65C. (a ) 0.5% strain, (b) ~.WO strain, ( c ) 1.5% strain, ( d ) 2.W0 strain.

In addition to creep and tensile data, designers rely quite heavily upon modulus data, in the broadest sense of the term, in performing structural performance calculations for thermoplastic components. There are, however, incompatibilities between many of the published modulus data, and those which are actually needed by designers (3). Published data are traditionally generated by plastics producers, and are thus geared toward the development and production of new and improved material grades. These data thus tend to fall within the framework of chemistry/ chemical engineering. Designers, or data users, on the other hand, require data applicable to the cre- ation of end-products. These needs, then, lie more within the framework of mechanical engineering. These incompatibilities are especially significant in the case of modulus data, such as: creep modulus [fc t, u , TI]; relaxation modulus, [f( t, E , T)]; complex modulus, [$frequency, TI]; and secant modulus

[ fc E , i, T)]. These variations, while convenient for plastics producers, serve as a source of confusion to designers, who probably have little understanding of the polymer physics defining the various modulus functions, and simply require appropriate numerical values for use in design calculations.

This confusion in the communication of modulus data between data generators and users can have serious consequences. Modulus values typically quoted in print [the primary, or reference, modulus value (3)] are normally generated through constant strain rate tests, and tend to be higher than most other moduli generated by alternative test methods or exhibited by in-service components. Owing to the combined effects of high strain, long times, and vari- able molecular alignment, the effective modulus of a thermoplastic may be as low as one-tenth the com- monly published value (3). Elevated temperatures, of course, reduce this value even further. I t is therefore,

1934 POLYMER ENGINEERINGAND SCIENCE, DECEMBER 1995, Vol. 35, No. 24


0 stress rate = 18- stress rate = le-5

- LL

I cn 10 v) u1 CT I- cn

0 0 1 2

STRAIN (X)

Fig. 4. Iso-stress rate pseudo-tensile curves in N o y l at 65C.

40 1

30 -

20 -

stress rate = 1 e-3 o stress rate = le-2 A stress rate = le-l

0 1 2 STRAIN (%)

Fg. 5. lso-stress rate pseudo-tensile curves in Lexan at 65C.

absolutely critical that downstream users of design data recognize that the modulus and other mechanical properties of engineering plastics are multi-val- ued, and highly time- and temperature-dependent.

To clear some of this uncertainty, it has been p r e posed that the formal distinctions between various types of moduli be disregarded. Although these data would thus lose their uniqueness, and even some of their original precision, the resulting time-dependent effective moduli would be more consistent and useful to designers as a whole (3).

The procedure for generating modulus data through the use of SRT shows enormous potential as a means of producing effective modulus data, as is currently needed in the thermoplastics design community (3, 16). This procedure is efficient-capable of generating secant modulus values (in MPa) over a wide range. Furthermore, there is no fundamental reason why the conventional means of generating secant modu-

0.020

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Flg. 6. Comparison of experimental creep data us. creep curves generated from SRT in N o y l at 65C.

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Ftg. 7. Comparison of experimental creep data us. creep curves generated from SRT in Lexan at 65C.

lus data (constant strain rate) should be considered superior to the SRT method (constant stress rate). Finally, while these moduli generated through SRT may be approximations to the values applicable to any single application, they are nevertheless likely to be more realistic estimates' than standard, unad- justed reference moduli.

In summary, what has been developed here is a methodology by which long-time data for use in a pseudo-elastic design approach may be generated with reasonable accuracy and greatly improved effi- ciency. This methodology is not, however, rigorous under all circumstances. Since the many time-dependent phenomena manifested in polymers exposed to elevated temperatures, such as physical and thermal aging, may not be accommodated, this methodology

P O L Y M E R ENGINEERING A N D S C I E N C E , D E C E M B E R 1995, Vol. 35, N o . 24 1935

G. G. Grzywinski and D. A. Woodford

o r . . . . . . . . ' . . . . . . . . ' . . . . . . . . ' . . . . .01 1 1 10 100 1000

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(d) FUJ. 8. (a) Time-dependence of secant modulus in Noryl at 0.5% strain, generatedfrom SRT. ( b ) rime-dependence of secant modulus in Noryl at 1 .WO strain, generatedfrom SRT. (c ) Tim-dependence of secant modulus in Noryl at 1.5% strain, generated from S m . ( d ) Time-dependence of secant modulus in Noryl at 2.Wo strain, generatedfrom SRT.

does not claim to characterize thermoplastics for all themomechanical histories. I t does, however, pro- vide a significant advance as a basis for efficient engineering design with thermoplastics.

CONCLUSIONS

1) Data from Stress Relaxation Testing (SRT) can be correlated with traditional design data.

2) Constructed iso-stress rate pseudo-tensile curves may be used as a means of quality control to assess batch-to-batch variability.

4) Secant moduli generated though SRT show promise in providing useful effective modulus data over a wide range of times and temperatures, and thus may prove to be a significant aid in the thermoplastic component design process.

5) The SRT methodology for generating design data is significantly more time and cost efficient than traditional long-time tensile and creep testing a p proaches.

ACKNOWLEDGMENTS

3) Long-time creep curves generated through SRT show close agreement with creep data, and thus show potential as a design tool. Additional testing is necessary to assess accuracy and repeatability.

The authors wish to acknowledge the continued experimental support and advice from Donald Van Steele. The contributions of Dr. Gerald G. Trantina are also greatly appreciated.

1936 POLYMER ENGINEERING AND SCIENCE, DECEMBER 1995, Vol. 35, No. 24


TIME (HRS )

(a)

m. 9. (a ) Time-dependence of secant modulus in Lexan at 0.5% strain, generated from SRT. ( b ) Time-dependence of secant modulus in Lexan at 1.0% strain, generatedfrom SRT. ( c ) Time-dependence of secant modulus in Lexan at 1.5% strain, generated from SRT. ( d ) Time-dependence of secant modulus in Lexan at 2.0% strain, generatedfrom SRT.

REFERENCES 1. G. G. Trantina and D. A. Ysseldyke, Materials Engineer- -

ing, October 1987, p . 35. 2. G. G . Trantina and D. A. Ysseldvke. SPE ANTEC Tech

Papers, 35, 635 (1989).

137 (1990).

Papers, 33. 1480 (1987).

3. S. Turner and G. Dean, Plastics Rubber Proc. AppL, 14.

4. D. A. Ysseldyke and J. Messaros, SPE ANTEC Tech

5. G. G. Trantina, PoZyrn Eng. Sci. 26. 776 (1986). 6. R. K. Penny and D. L. Maniott, Design for Creep, Mc-

7. J. Duxbury and I. M. Ward, J. Mater. Sci. 22. 1215 Graw-Hill Book Co., (U.K.) Limited, London (1971).

(1987).

8. B. E. Read, G. D. Dean, and P. E. Tomlins, Plastics

9. 0. S. Brueller. Polyrn Eng. Sci., 33. 97 (1993). 10. J. Amodeo and D. Lee, PoLyrn Eng. Sci., 32. 1055 (1992). 11. P. Krishnaswamy, M. E. Tuttle, A. F. Emery, and J.

12. G. G. Grzywinski and D. k Woodford, Materials and

13. E. W. Hart and H. D. Soloman, ActaMet, 21. 295 (1973). 14. D. A. Woodford. Mater. Design, 14, 231 (1993). 15. P. P. Gillis and R. E. Medrano, J. Mater., 6, 514 (1971). 16. H. F. Rondeau, Machine Design, March 1976, p . 67.

Rubber Proc. Appl , 14, 153 (1990).

Ahmad. Polyrn Eng. Sci., 32, 1086 (1992).

Design, 14, 279 (1993).

Revised May 1994

POLYMER ENGINEERING AND SCIENCE, DECEMBER 1995, Yo/. 35, No. 24 1937

creeps analysis of thermoplastics

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