TITOMANLIO: Compression viscoelastic behaviour of polymethylmethacrylate and effect of temperature rise due to plastic deformation

Acta Polymcriu 31 (1980) Heft 4 261

Compression viscoelastic behaviour of polymethylmethacrylate and effect of temperature rise due to plastic deformation G . TITOMANLIO Istituto di Ingegneria Chimica, Facolti di Ingegneria dell'Universiti di Palermo, PalermolItalia

Compression creep and stress-relaxation tests have been performed on PMMA a t several deformations after the saniple yielding. At large loading rates, the behaviour observed was found significantly affected by the temperature rise due to the plastic deformation. Creep and stress-relaxation data taken holding the samples a t constant temperature after the material loading could be collected into single curves by means of a time shift factor proportional to the loading rate.

Viskoelnstisches Verhalten yon Polymethylmethacrylat bei Druckbeanspruchung und der EinfluQ der durch plastische Deformation bewirkten Temperaturerhdhung Retardations- und Relaxationsuntersuchungen bei Druckbeanspruchung von PMMA wurden hei verschiedenen Defor- mationen oberhalb des FlieBpunktes durchgefuhrt. Bei hohen Beanspruchungsgeschwindigkeiten wurde festgestellt, daS das Deformationsverhalten wesentlich durch die Temperaturerhohung infolge der plastischen Deformation be- einflufit wird. Bei konstant gehaltener Probentemperatur nach erfolgter Belastung erhaltene Retardations- und Relaxa- tionswerte konntcn mit Hilfe eines von der Belastungsgeschwindigkeit abhangigen ZeitverschiebungRfaktors in 3Iasterkurven zusammengefaSt werden.

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1. Introduction

The viscoelastic behaviour of polymeric materials a t small strains is successfully described by the linear viscoelastic theory. Remarkable attention has been given also to the stress range between the linear viscoelasticity limit and the yield stress which has been studied both theoretically and experimentally. Recently [l --31 the creep and stress-relaxation behaviour a t deformations larger than the yield deformation has been considered. In particular it has been shown that the sample loading rate affects remarkably the viscoelastic answer in this zone. Furthermore, simple masterization rules have been sugge- sted in order to collect into single curves data obtained a t diffe- rent loading rates and a t different strain levels.

In this work the behaviour during both constant load creep and stress-relaxation tests performed after compression yielding on polymethylmethacrylate (PLEXIGLASS) is analyzed. Also the effect of the temperature rise which takes place [4] during the plastic deformation is here considered.

2. Experii~reiztnl

Cylindrical samples, with both length and diameter equal to 1 cm, were machined from the material supplied in the form of a rod with 1 cm diameter. A piece of the rod was heated up to 110 O C (about 10 K above the material glass transition temperaturc) in order to reveal frozen in stresses. The length of the test piece did not change and only a slight deformation of its cross section was observed. In particular the cross section became an ellipse with the two principal axis equal to 0.98 and 1.02 cm.

The samples were subjected to constant velocity strain ramps usually followed by either constant force creep or strcss-relaxa- tion tests. All the tests were performed by means of an Instron testing machine model 1115 and during the creep tests the deformation was measured independently by means of a trans- ducer connected to the machine crosshead.

An holc 0.75 mm diameter was drilled in the sample axis in order to mcasurc thc tcmpcrature during the tests. The temperature measurements were made by means of copper-

constantan thermocouple 0.6 mm diameter introduced in the sample through a bronze piece, C in Fig. 1, especially constructed and leaned on the machine die.

The creep and stress-relaxation tests were made after constant velocity compression ramps performed with two values (one tenfold the other) of the loading rate and a t different strains after the material yielding.

The temperature rise accumulated during the sample loading tends to disappear spontaneously (because the sample is in an environment a t constant minor temperature) while the creep or stress-relaxation takes place. During several tests a warm air blow was directed on the samples after loading; the tem- perature of the air blow (never larger than 50 "C) was regulated as to mantain constant, within f 2 K, the temperature measured at the sample axis.

3. Results and Discussion

The behaviour observed during constant velocity com- pression tests performed at room temperature is shown i n Fig. 2, where the stress u and t h e temperature rise T are reported as function of t h e strain e=Z/l0 (where 1 is t h e sample height and Zo i ts initial value). Two values of t h e initial deformation r a t e a r V/Zo (where V is t h e velocity of t h e machine cross-head) are considered i n Fig. 2 and t h e temperature rise is obviously much more relevant for t h e larger one t h a n for t h e smaller one when

I I Fig. 1. A sample, B machine dice, C bronze piece used to intro-

duce the thermocouple in the sample axis

Act. Polymeria 31 (1980) Heft 4 TJTOMANLIO: Compression viscoelastic behaviour of polgmethvlmethacrglate

lo-'

e %

10-2

I 1.0 0.8 0.6

e = l / / o

-

-

0.4

Fig. 2. Compressive true stress, u, and temperature rise at sample axis, AT, vs. strain 0; a =V& is initial deformation rat.e

I . . A -

02t - - A A =- 101 5

01 I I -*AhA I I I

1 10 102 , 103 f o b s 105

Fig. 3. Compressive stress-relaxation data at different strains e, and loading rates a; AT is the temperature increment with

the sample has enough time to disperse the heat generated with deformation. The fact that curves a t different defor- mation rates cross each other a t e zw 0.6 is probably due to the difference in temperature rise.

Stress relaxation data taken under three strain levels e, are plotted in Fig. 3 as u/uo (where uo is the stress just prior to the relaxation! versus the time t . The data show a remarkable effect of the loading rate and to a good appro- ximation the two curves a t the smallest deformation level, i.e. for e, = 0.74, may be superimposed by means of a time shift factor proportional to the loading rate. This effect was already shown by both stress-relaxation and creep data taken in the plastic region on other materials [I-31. The data of Fig. 3 taken a t larger deformations, i.e. for e, = 0.62 and e, = 0.5, satisfy this rule only a t very small times. At larger times the relaxation rate of tests conducted after fast,er loading rates becomes smaller than that (at the same value of u/uo) of tests performed after slower loading ramps. This starts to happen about a t the same time when the temperature rise a t the sample axis, which for one of the samples is reported in the same figure, starts to decrease significantly. The temperature decrease, as far as it lasts, counteracts partially the relaxa- tion process. When the temperature becomes again constant the sample starts relaxing again a t a faster pace. During tests conducted using the slower loading rate the tempera-

- and effect of temperature rise d i e tb plasiic deformation

0.75 0 352 PMUA 063 w v 35%

0.48 0 J5'C (149. A s p c n l d i n g

104 I 10-3 10-2 10'' * 1 I0 10'

Fig. 4. Master stress relaxation curve. 0 is a dimensionless time as defined by Eq. (1). - master curve obtained in [2] for poly-

carbonate (Lexan)

10-31 I I I I I 10-3 10-2 10-1 1 lo lo2

Fig. 5. Master creep curve. 0 is a dimensionless time as defined by Eq. (1). - master curve obtained in 121 for polycarbonate

(Lexan)

turr rise is much smaller, as shown in Fig. 2, and its effect can be considered negligible.

Analogous ohservations have been made with creep tests and also in this case tests performed with the same starting creep strain e, = Zc/Zo (where Z, is the sample height a t the end of the loading ramp) but with different loading rates could he superimposed, by means of a time shift factor proportional to the loading rate, only a t very short times; during creep tests conducted after fast loading ramps the creep rate showed a sensible decrease when the tem- perature a t the sample axis started to diminish.

Some tests where performed in order to verify whether the simple superposition rules mentioned above, and veri- fied with MYIAR [I] and LEXAN [2], for which the effect of temperature rise due to plastic deformation was found negligible, are obeyed also by PMMA under isothermal conditions. During tests performed with the larger loading rate, isothermal conditions where mantained by blowing, starting from the end of the loading ramp, warm air on the sample. Furthermore the initial temperature of each test was chosen as to obtain a t the end of the sample loading always the same temperature. At this temperature and a t the same initial strains, trsts whrre performed also with the lower loading rate (when the temperature rise may be neglected).

Together with the effect of the sample loading rate, which is the more relevant, also the effect of the initial test strain (eC and e,) could he simply described in previous communications [I-31. In particular compression creep data taken in the plastic region on LEXAN could be collected into a single curve by plotting AZ/Zc (where AZ is the sample

TITOIKANLIO: Compression viscoelastic behaviour of polymethylmethacrylate and effect of temperature rise due to plastic deformation

k t a Polymciicr 31 (1980) Heft 4 263

deformation as measured since the end of the loading ramp) versus the dimensionless time

0 = hie , ,

where ai is the deformation rate just prior t o the creep. The exigency of having mi instead of a in Eq. (1) was demonstrated by means of tests performed with complex loading histories [2] ; the effect of the starting creep strain was satisfactory accounted for by e,. As far as stress-relaxa- tion data are concerned, the exigency of having a stress measure considering a t each strain only the relaxable part of stress [2, 5, 61 suggested plotting (ao - o)/uoe, versus the dimensionless time 0.

The creep and stress-relaxation data taken under iso- thermal conditions a t 35°C are plotted in Figures 4 and 5 respectively in terms of the groups mentioned above (that is A&, (ao - a)/aoe, and 0). For comparison also two curves relating to tests performed with the larger loading rate considered here (that is a = 30 h-l) having a t the end of the loading ramp a temperature of 35"C, as the others, but left t o cool spontaneously (in absence of the warm air blow) afterwards are reported in these Figures. These curves, a t large times, when the cooling effect starts t o have a significant influence? remain sensibly below the respective master curves which collect satisfactory all the other data.

4. Concluding remarks

A significant temperature rise has been measured during constant force compression tests performed on PMMA (PLEXIQLASS). The decrease of the temperature accumulated during fast sample loading affects both the creep and stress-relaxation curves a t strains larger than the yield strain.

Data obtained conducting the creep and stress-relaxation under constant temperature obeyed simple masterization rules already verified with LEU (at room temperature), which thus may be considered of rather general use.

I t may be worth noticing tha t the master curves ob- tained in this work are very similar t o those obtained with LEU, also reported for comparison in the corresponding figures. In particular a t small times the master curves obtained with PMMA and those obtained previously with LEU are very close, a t larger times both the creep defor- mation and the stress relaxation shown by the data pre- sented here are sensibly larger. This is probably related to the fact tha t a temperature closer t o the material glass transition temperature has been adopted here than in the case of LEXAN.

Acknowledgemeni

This work has been supported by C. N. R. Grant N. 78.00935.03

References

[ l ] TITOMANLIO, G., and Rrzzo, G.: J. appl. Polymer Sci. 21 (1977) 2933.

[2] TITOMANLIO, G., and RIZZO, G.: Polymer, submitted for publication.

[3] TITOMANLIO, G., and R~zzo, G.: ,,Effect of plastic detor- mation on creep behaviour of solid polymers", presented a t t h e Joint Conference of the British, Italian and Netherlands Societies of Rheology, Amsterdam, April 18- 20, 1979.

[4] BINDER, G., and MULLER, F. H.: Kolloid-Z. 177 (1961) 129. [5] KUBAT, J., PETERMAN, J., and RIQDAHL, M.: Mater. Sci.

[6] KUBAT, J., PETERMAN, J., and RIQDAHL, M.: J. Mater. Sci. Engng. (Amsterdam) 19 (1975) 185.

10 (1975) 2071.

Received June 26, 1979