UDK 678.7:66.017	ISSN 1580-2949
Original scientific article/Izvirni znanstveni članek	MTAEC9, 48(3)315(2014)
EFFECT OF THE QUENCHING TEMPERATURE ON THE
IZOD IMPACT STRENGTH OF POLYCARBONATE: EXPERIMENTAL DATA AND EMPIRICAL MODELING
VPLIV TEMPERATURE KALJENJA NA IZOD UDARNO TRDNOST POLIKARBONATA: EKSPERIMENTALNI PODATKI IN EMPIRIČNO
MODELIRANJE
Farid Rouabah1, Abdallah Bouguettoucha2, Laurent Ibos3, Nacerddine Haddaoui1
1Laboratoire de Physico-Chimie des Hauts Polymeres, Universite Ferhat Abbes, 19000 Setif, Algerie
2Laboratoire de Genie des Procedes Chimique (LGPC), Universite Ferhat Abbes, 19000 Setif, Algerie 3Universite Paris-Est, CERTES, 61 Avenue du General De Gaulle, 94010 Creteil, France f_rouabah2002@yahoo.fr
Prejem rokopisa - received: 2012-07-04; sprejem za objavo - accepted for publication: 2013-08-27
In this study, the development of a mathematical model of the effects of free quenching on the Izod impact strength of polycarbonate (PC) has been investigated. Three different thermal treatments were used: the first quenching from the melt state to different temperatures, the second quenching from Tg + 15 °C and, finally, the annealing. The results have shown that an improvement in the impact strength can be obtained after the second quenching at 40 °C. The impact tests experimentally performed on the molding prototypes yield useful data for a particular structural and impact-loading case. But, it is generally not practical, in terms of time and cost, to experimentally characterize the effects of a wide range of design variables. A successful numerical model for the Izod impact strength of polymers can provide convenient and useful guidelines on product design and, therefore, decrease the disadvantages arising from purely experimental trial and error. It is expensive to prepare the samples for the tests. Therefore, it is necessary to develop a mathematical model that will predict the fracture toughness of polycarbonate as a function of the quenching temperature. Mathematical models for the mechanical properties like the tensile strength, Young's modulus and Izod impact strength as functions of the quenching temperature are not available. There is no sign that they can be built up from a simple theory; a polynomial interpolation was, therefore, used to generate a fracture-toughness model using the data obtained from the experiments. The shifted model represents the Izod impact of the samples as a function of the first- and second-quenching temperatures.
Keywords: Izod impact strength, polycarbonate, quenching temperature, mathematical modeling
Ta študija preučuje razvoj matematičnega modela vpliva prostega kaljenja na Izod udarno trdnost polikarbonata (PC). Uporabljeni so bili trije različni načini toplotne obdelave: najprej prosto kaljenje iz staljenega stanja na različne temperature, nato drugo kaljenje iz Tg + 15 °C in nato končno žarjenje. Rezultati so pokazali, daje mogoče doseči izboljšanje Izod udarne trdnosti po drugem kaljenju pri 40 °C. Eksperimentalno izvedeni preizkusi na modeliranih prototipih so dali uporabne podatke za posebne primere strukturno in udarno obremenjenih primerov. Vendar pa na splošno ni praktično - s stališča časa in stroškov - eksperimentalno določanje vplivov različnih oblik. Uspešen numerični model za Izod udarno trdnost polimerov lahko zagotovi zanesljive in uporabne napotke za načrtovanje proizvodov in s tem zmanjša pomanjkljivosti, ki izvirajo iz eksperimentalnih preizkusov in napak. Priprava vzorcev za preizkuse je draga. Zato je treba razviti matematični model, ki bo napovedoval lomno žilavost polikarbonata v odvisnosti od temperature kaljenja. Na razpolago ni modelov za mehanske lastnosti, kot so natezna trdnost, Youngov modul in Izod udarna trdnost, v odvisnosti od temperature kaljenja. Ni znamenj, da se lahko postavijo z enostavno teorijo: zato je bila z uporabo eksperimentalnih podatkov uporabljena interpolacija polinomov za izdelavo modela lomne žilavosti. Predstavljeni model predstavlja Izod udarno trdnost v odvisnosti od prve in druge temperature kaljenja.
Ključne besede: Izod udarna trdnost, polikarbonat, temperatura kaljenja, matematično modeliranje
1 INTRODUCTION	is subject to a dramatic brittle failure at relatively low
loads. PC applications are also limited to thin molded
Engineering polymers have been increasingly used in	articles because its impact strength is highly sensitive to
the applications such as housings for electronic appli-	the presence of notches. The presence of sharp notches,
ances, lenses and windows that have to sustain accidental	or even small notches, caused by a microscopic surface
impact without showing signs of damage. Due to good	degradation decreases the impact strength.5 However, an thermal- and electrical-insulation properties, low density
high resistance to chemicals and ease of manufacturing
addition of appropriate polymers or terpolymers and
enlinelrin^'polyme'rlhavebeenincreasinglyusedinihe core-shell impact modifiers can be an effective
applications where the impact performance is the pri-	toughening method for the PCs used in thick sections.6,7
mary concern.1-4 One of the biggest advantages of poly-	To expand the usefulness of PC in a variety of
carbonate (PC) is its impact strength. It is widely used as	applications, it is important to explore the ways to pre-
a transparent protective material because of its low	vent or minimize the loss of toughness during sub-Tg
density and excellent mechanical properties. However,	annealing and to reduce the sensitivity to the presence of
when defects such as cracks or notches are introduced, it	notches and, consequently, the loss of the impact
strength. Residual-stress (RS) generation with the quenching process under severe conditions (0 °C) is known to be an effective method of toughening glassy polymers.8-11 Recently, our study showed that, in the case of polycarbonate, the improvement of the impact strength after the second quench at 40 °C is linked to the existence of the relaxation mode located around 35 °C.12
Notched Izod testing is a common qualitative measure of the toughness of a material, measuring the energy absorbed prior to failure under high triaxiality and highrate loading conditions. In industrial applications, it is important to know the impact behavior and the safe operating limits of polymeric structures. In our case, the evaluation of the impact-design failure of polymeric structures has to be experimentally performed on molding prototypes. The experimental trial-and-error method significantly delays the design progress and optimization, wasting a lot of time, money and efforts.
There are several types of standard tests to evaluate the impact strength of polymers. The most commonly used are the Charpy and Izod tests.13 A successful numerical model for an impact deformation and failure of polymers can provide convenient and useful guidelines on the product design, therefore decreasing the disadvantages arising from just experimental trial and error. In this work, we have investigated the development of a mathematical model predicting the effects of the first-and second-quenching temperatures on the Izod impact strength of PC.
2 EXPERIMENTAL PROCEDURE 2.1 Materials
The polymer used in this study is a commercial polycarbonate, Makrolon® 2620, supplied by Bayer (Germany) with the average molecular mass of about 57 400. The melt index at 300 °C is 19.6 g/(10 min), the polydispersity index is 2.16 and the glass transition temperature is about 144 °C (the value obtained from DMA measurements14).
2.1.1	First-quench procedure
Pellets were dried in an oven at 120 °C and then put into the mold and pressed at 25 bar for 12 min at 230 °C. Then the samples were immediately quenched from the moulding temperature in the water baths at three different temperatures of (0, 20 and 80) °C or in the air at room temperature for 15 min. All the samples have a thickness of 3 mm and this step was named "the first quench".
2.1.2	Second-quench procedure
Another free quenching was carried out only for the samples molded at 230 °C at different quenching temperatures. These specimens were heated in the oven at 160 °C (Tg+ 15 °C) for 3 h and were immediately quenched for the second time in the water baths at different temperatures (0, 20, 30, 35, 40, 45 and 60) °C for 15 min. This procedure was named "the second quench".
2.1.3 Annealed samples
Finally, in order to get reference samples, an annealing was performed. The annealed specimens were prepared using the samples first quenched in air at 25 °C. Then, these samples were heated at 160 °C for a period of 2 h and, finally, slowly cooled in the oven at room temperature at a rate of about 0.5 °C min-1. These samples were named "annealed samples".
2.2	Notched Izod impact strength
Izod impact-strength properties were determined at room temperature with a CEAST 6546/000 machine with a 15 J pendulum according to ASTM D256-73. The specimens with the dimensions of 3 mm x 12.7 mm x 63 mm were compression molded. Parts of them were milled with a notch radius of 0.5 mm. This radius was chosen so that the tip of the notch was located in the residual compressive zone. These stress zones were determined with a photoelastic examination of a sample between the cross Polaroids under white light. In the case of the thermal stress (symmetrical free quenching), due to the non-uniform cooling of the outer and central layers, compressive and tensile stresses are formed in the material. Two neutral lines symmetrically separate the stress zones. The extension of this zone can reach a certain percentage of the sample thickness.14
These stresses are frozen in, and the material conserves some internal stresses, revealed in the polarized light by certain colors. Using a standard polariscope, the photoelastic color sequence, with the increasing stress, observed from the neutral line includes: black (zero), yellow, red, blue-green, yellow, red, green, yellow, red, green and so on.14 At least five specimens were tested and the average value was used for plotting the experimental data.
2.3	Numerical method
The polynomial curve-fitting technique was used to derive analytical terms that match the given data points.15 Polynomial curve fitting is a mathematical procedure for finding the best fitting curve for a given set of points by minimizing the sum of the squares of the offsets of the points from the curve. This includes finding the coefficients of polynomial p(x) of degree n that fits the computed values p(x,) with experimental data ji, where i G {1, 2, ..., N) and N is the number of experimental data points. The following definition has been used for determining the residual standard deviation (RSD), which is a statistical term used to describe the standard deviation of the points formed around a function, and it is an estimate of the accuracy of the dependent variable being measured. The lower the RSD, the greater is the agreement between the experimental data and the model. The RSD is computed as follows:
RSD =
1L [y^ - p(Xi)]2
N - q
(1)
i =1
where q is the number of estimated parameters (note that for a polynomial fit, q = n + 1) and the yi values correspond to the experimental results of the Izod impact strength (at).
3 RESULTS AND DISCUSSIONS
3.1 Effects of the first and second quenching on the
Izod impact strength
The evolution of the milled notched Izod impact strength is presented as the function of the second-quenching temperature (Figure 1). In both cases, the maximum second-quenching temperature is 40 °C. The second thermal treatment including a heat treatment for 3 h at 160 °C (i.e., at Tg + 15 °C) has not totally erased the first thermal treatment. Indeed, the same evolution is observed for the samples that were first quenched in water at (0, 20 and 80) °C and in air at room temperature (25 °C). The influence of the first quenching is reflected on all the properties. The properties obtained after the first quenches at 0 °C and 20 °C are close; they correspond to the rapid first quench. Again, the properties corresponding to the first-quenching temperature of 80 °C and to the cooling in air are close, indicating a slower first quench.
In a previous work,12 the minimum density observed for the second-quenching temperature of 35 °C was associated with an increase in the free volume. This increase leads to a higher molecular mobility. This explains the increase in the Izod impact strength. The maximum ductility reached during the second quenching from 160 °C to 40 °C is linked to the existence of the ßi molecular relaxation at around 35 °C.12
As already reported for the PMMA and PS,14 the Izod impact-strength values are maximum at the same
second-quenching temperature, i.e., at 40 °C. However, with polycarbonate, the improvement in the Izod impact strength is more pronounced.
3.2 Comparison of the experimental data with the empirical model
In order to obtain an analytical expression of the variation of the Izod impact strength of PC with the thermal-treatment parameters, i.e., the first- and second-quenching temperatures, we decided to use an empirical model. First of all, the model chosen in this study to fit the experimental behavior as the function of the second-quenching temperature has a third-degree polynomial form as follows:
ak = a0 + a 1 xT2 + a2 xT22 + a3 xT^	(2)
where ak is the notched Izod impact strength (expressed in kJ m-2), T2 is the absolute second-quenching temperature (in K) and a0, a1, a2 and as are the constants obtained by fitting.
The parameters estimated from the polynomial model (equation 2) are displayed in Table 1. The expression chosen to describe the experimental result, with the usual meanings for constants a0, a1, a2, and a3, gives a fairly good agreement between the calculated and the experimental values, as seen in Figure 1. Indeed, it can be seen that the model matched the experimental data for the entire process. This is supported by the low RSD values obtained. However, we must note a slightly higher value of the RSD for the first quench in water at 80 °C, indicating a lower agreement between the experimental data and the model in this particular case.
Close values of the estimated parameters were obtained for both the samples first quenched in water at 0 °C and the ones first quenched in air. Moreover, the values of the Izod impact strength are higher for the samples first quenched at 0 °C than for the ones first
Figure 1: Milled notched Izod impact strength of PC as a function of second-quenching temperature T2 of the PC first quenched in water at (■) 0 °C, (•) 20 °C, (^) 80 °C and (►) in air at 25 °C; for the milled annealed sample, ak = 45 kJ m-2
Slika 1: Izod udarna trdnost brušenega in z zarezo PC-vzorca v odvisnosti od druge temperature kaljenja T2 PC-vzorca, ki je bil najprej kaljen v vodi pri (■) 0 °C, (•) 20 °C, (^) 80 °C in (►) na zraku pri 25 °C; pri brušenem žarjenem vzorcu je bila ak = 45 kJ m 2
Figure 2: Plot of the normalized ai coefficients from equation 2 as a function of first-quenching temperature T1 (for the samples quenched in water)
Slika 2: Prikaz normaliziranih koeficientov ai iz enačbe 2 v odvisnosti od kalilne temperature T1 prvega kaljenja (za vzorce, kaljene v vodi)
Table 1: Parameters estimated from the model and residual standard deviation between the experimental Izod impact strength (at) and the calculated one, for the PC first quenched at different temperatures (r1) in air and water
Tabela 1: Parametri, dolo~eni iz modela in preostale standardne deviacije med eksperimentalno dolo~eno Izod udarno trdnostjo (at) in izra~unano za polikarbonat, ki je bil najprej kaljen pri razli~nih temperaturah (r1) na zraku in v vodi
Sample	First quenched in water			First quenched in air
T1/°C	0 °C	20 °C	80 °C	25 °C
a0 (kJ m-2)	20422	16556	10326	21591
a1 (kJ m 2 K1)	-204.89	-166.00	-105.97	-214.28
a2 (kJ m 2 K 2)	0.68764	0.55780	0.36427	0.71084
a3 (kJ m 2 K-3)	-7.6663 X 10-4	-6.2266 X 10-4	-4.1476 X 10-4	-7.8382 X 10-4
RSD	1.25	1.61	4.02	2.22
Table 2: Parameters bi of equation 3 estimated from the plots of normalized coefficients ai presented in Figure 2 Tabela 2: Parametri bi iz ena~be 3, dolo~eni iz odvisnosti od normaliziranih koeficientov ai, predstavljenih na sliki 2
Estimated parameter of Eq. 3	Values for each Eq. 2 polynomial coefficient ai			
	a0	a1	a2	a3
b1/°C-1	-1.056 X 10-2	-1.064 X 10-2	-1.063 X 10-2	-1.061 X 10-2
b2/°C-2	5.476 X 10-5	5.759 X 10-5	5.938 X 10-5	6.088 X 10-5
quenched in air. The selected first quench in ambient atmosphere is generally preferred because it is moderate and less costly than the first quench in water at 0 °C, which requires more resources and is more expensive. These results are supported by the model used. It has to be noted that we could not find a model in the literature to compare it with our results.
Even if the model proposed is in agreement with the experimental behavior, we must note that the fitting parameters ai obtained do not have, at this time, any physical significance. However, it seems interesting to study their dependence upon first-quenching temperature T1, when the samples are first quenched in water. In order to describe the general variation of these para-
Figure 3: Chart of Izod impact strength at (expressed in kJ m 2) of PC as a function of the first- and second-quenching temperatures, namely Ti and T2 (quenching in water); computation done using equations 2 and 3, the model and data from Tables 1 and 2 Slika 3: Diagram Izod udarne trdnosti at (izražene v kJ m 2) poli-karbonata v odvisnosti od prve in druge temperature kaljenja T1 in T2 (kaljeno v vodi); izra~un je izdelan z uporabo ena~b 2 in 3, modela in podatkov iz tabele 1 in 2
meters with Ti, we present, in Figure 2, a plot of the a^ values normalized to the values obtained for the first quenching at 0 °C as the function of Ti. We can see that the normalized values of polynomial coefficients ai of equation 2 seem to obey the general rule that can be approximated using the following relationship:
a.(T1) = ai.(0°C)x[l + b1 xT1 +b2xT12] Vi e {1,2,3,4} (3)
where T1 is the first-quenching temperature expressed in °C, while b1 and b2 are the coefficients, whose values are given in Table 2. The values of the b1 parameter seem to be quite independent of the polynomial coefficient order i, whereas a slight dependence on this coefficient order can be noted for the b2 parameter. By using equations 2 and 3, along with the empirical values of parameters ai and bi reported in Tables 1 and 2, it is now possible to compute the Izod impact strength of PC as the function of the first- and second-quenching temperatures, namely, T1 and T2. The results of this computation are presented in Figure 3. This kind of simple modeling can be useful for manufacturing polymers since it can predict the value of the impact strength as the function of the parameters characterizing the thermal treatments imposed on the material. This kind of modeling can be carried out on the basis of the experiments performed for a limited number of the selected quenching temperatures.
4 CONCLUSION
The effect of the quenching process on the mechanical properties of PC was investigated via Izod impact measurements. The predicted Izod impact strength as the function of the second-quenching temperature was compared with the experimental data and a good agreement was obtained. The results indicated that a generalized constitutive model accurately predicts the Izod impact strength of PC over a wide range of first- and second-
quenching temperatures. This kind of modeling could be useful for manufacturers as it can reduce the number of experimental tests necessary to design a manufacturing process. It should be interesting, in future research, on the one hand, to check if this kind of behavior can be extrapolated to the other polymers (e.g., PMMA, polystyrene) and, on the other hand, to find a physical significance of some of these empirical parameters.
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