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Mechanisms of brittle-ductile transition in toughened thermoplastics
ELSEVIER
theoretical and applied fracture mechanics Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
Mechanisms of brittle-ductile transition in toughened thermoplastics T. Vu-Khanh *, Z. Yu D~partement de g~nie m~canique. Facult~ des sciences appliqu~es, Universit~ de Sherbrooke, Sherbrooke, Que., Canada J1K 2R1
Abstract
The objective of this work was to investigate the mechanism of brittle-ductile transition in toughened polymers. Two systems, namely, a rubber-toughened nylon 66 (Zytel ST-801) and a high impact polystyrene (HIPS), were chosen for this study. The samples were prepared by injection molding and were tested in three-point bending under various loading rates and temperatures. The brittle-ductile transition temperature (Tb_d) was determined from the observed fracture behavior as a function of temperature. Molecular relaxation temperatures of the polymers were measured by mechanical spectroscopy at various frequencies. The correlation between temperature and loading rate was estimated using the Arrhenius equation. The results show that Tb_d of Zytel ST-801 is only slightly affected by the loading rate, whereas Tb_d of HIPS strongly increases with deformation rate. It is found that for the former, within the experimental errors, an increase in Tb_d with loading rate corresponds to the shift in the secondary relaxation temperature Tb of the nylon 66 matrix. For the latter however, the increase in Tb_d is related to the glass/rubber relaxation of the polystyrene matrix. It seems that the type of molecular relaxation controlling the brittle-ductile transition corresponds to that with lower activation energy.
1. Introduction One of the most important weaknesses of polymers is their poor impact resistance. To improve this performance, much attention has been paid to adding an elastomeric, dispersed phase to the polymer matrix. Presently the role of rubber toughening in the impact performance of polymers is being extensively investigated. However, it is well known that, at relatively low temperatures or high loading rates, the toughened polymer can become brittle. Rubber toughening polystyrene and nylon-6,6 have been commercialized for a number of years. These materials possess good impact properties and have been
* Corresponding author. Tel.: + 1-819-8216997; fax: + 1-8198217163; e-mail: [email protected].
widely used as engineering materials. In terms of fracture performance, they can break in a brittle manner at low temperatures or high loading rates. This brittle-ductile transition has been attributed to the change in fracture mechanism from localized crazing to generalized crazing or shear yielding [1]. The impact fracture behavior of polymers has long been investigated [2-10]. However the fundamental material parameters controlling the brittleductile transition remain unclear. For the case of toughened polymers, it has been suggested that the brittleness at low temperature is due to the glass transition in the rubbery phase [11]. Under impact, it has also been shown that adiabatic heating plays a primary role in the fracture performance [5,8]. In the presence of a defect such as a crack, localized heating can have a very significant effect. Since poly-
0167-8442/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S0167-8442(96)00047-X
178
T. Vu-Khanh, Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
mers are strongly time and temperature dependent, this could lead to opposite effects between increasing impact velocity and the rise in temperature resulting from adiabatic heating due to high loading rate. The effects of molecular relaxations on impact fracture performance should therefore be better understood in order to optimize the impact performance of polymers and prevent brittle fracture to occur. The aim of this study is to investigate the roles played by the various molecular relaxations of each component in rubber toughened polymers. The focus is put on the brittle-ductile transition in fracture behavior, which is a critical condition in the applications of these materials.
striking tup of the impact machine was instrumented with strain gages and the load-time signal during impact was recorded by a rapid data acquisition system. The machine was also equipped with an optical cell, enabling measurement of the velocity of the striker just before impact. By varying the drop height, the impact speed was varied from 2 to 5 m / s . The testing temperature was varied from - 8 5 to 90°C using a Thermotron environmental chamber (model ETS-150-LN2). To reduce the bouncing effect of the sample on the striker in impact, a small amount of plasticine was placed on the striker. The absorbed energy by the sample to break under impact was determined by subtracting the energy absorbed by the plasticine from the total recorded energy to fracture the sample.
2. Experimental High impact polystyrene (HIPS) and toughened nylon 66 were supplied, respectively, by Dow Chemical (STYRON 484C) and by DuPont Canada (Zytel ST-801) in the form of pellets. Rectangular plates of 6 x 27 x 124 mm of these materials were injection molded. The pellets were dried in a vacuum oven prior to molding. Three-point-bend specimens of 6 x 13 x 124 mm were cut out from the molded plates. A sharp notch was also created in the specimens to analyze the impact performance in terms of crack growth resistance. A prenotch was first made by a band saw cut and the final notch in the specimen was created by forcing a razor blade into the specimen in a special jig, The notch depth was varied from 10 to 80% of the specimen width. Measurements of the viscoelastic properties of the materials were performed on a dynamic mechanical thermal analyzer (DMTA) from Polymer Laboratory (Model MKII). Samples of 11.4 × 10 x 1.4 mm were machined from the injection molded plaques. Each sample was cut at the same location in the plaques. Five frequencies; 0.1, 0.33, 1, 3 and 10 Hz were used. The temperature was varied from - 1 2 0 to 110°C. Three-point-bending tests at low loading rate (10 mm/min) were performed on an Instron machine (Model 1123). The testing temperature was varied between - 1 0 0 and 80°C. High loading rate tests were carried out on a Dynatup drop-weight device (Model 8200) with a hammer weight of 3.25 kg. The
3. Fracture characterization
In the Charpy and Izod tests, only the total energy absorbed by the sample to break can be measured and it is well known that this value does not directly correspond to the fracture performance of the material [6,7,9]. Characterization of the impact resistance of the samples was thus made by using the different proposed methods based on fracture mechanics [6,7,9], depending on the type of fracture observed (brittle, semi-ductile, or ductile). It is worth noting that the global concept of fracture mechanics such as the strain energy release rate is unable to properly describe the fracture process [12-16]. However, this approach is presented widely used to characterize the fracture toughness of materials and the strain energy release rate considered in the proposed models can provide a useful alternative method for the characterization of impact performance. For brittle fracture, the critical strain energy release rate, Gc, can be determined by [6]: U = G~BDck
(1)
where U is the absorbed energy by the sample, B and D are, respectively, the sample width and thickness and th is a geometrical function which can be evaluated for any geometry by considering the appropriate calibration factor established for precracked samples [6]. From the slope of the plot of U
179
T. Vu-Khanh, Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
versus BDqb, using samples having different initial crack depths to vary ~b, the fracture energy, G c, can be obtained. For semi-ductile fracture, a mixed stable-unstable period of crack propagation occurs in the same sample during impact fracture and in this case, the total energy absorbed by the sample to break, U, has been determined [7]: U = Gst A l + Ginst.BDCrp I
(3)
G r = G i + TaA
in which Gr is the actual fracture energy, G~ is the fracture energy at crack initiation, T~ represents the rate of change of G, with crack extension and A is the fracture surface. Since the energy absorbed by the specimen is mainly dissipated in the fracture process, the energy absorbed by the specimen becomes: L
@dA=GiA
1
+TTaA
2
(4)
From this equation one can obtain G~ by the intercept and Ta by the slope of the U / A versus A plot.
Gc (bdttle) I Gi (ductile)
,t 8
~5 ff
eA
6 4
,&A
•
oo
&
2 0 -150
- 100
-50
0
50
100
Temperature ('C)
Fig. 1. Variation of fracture energy as a function of temperature for HIPS tested at 10 ram/rain. m / s are shown in Figs. 1 and 2, respectively. It is observed that, for low loading rate (Fig. 1), stable fracture occurs at around - 100 to - 9 0 ° C . When the velocity of loading is increased to 2 m / s , the britfie-ductile transition temperature (Tb_ d) shifts to the region between - 5 0 to - 3 0 ° C (Fig. 2): In this region of temperatures, a mixed stable-unstable crack propagation (semi-ductile fracture) occurs. When the temperature is increased, the onset of stable crack propagation is observed above about -30°C. It is worth noting that one cannot base only on these reported values of fracture energy to determine the material's impact performance but the type of crack propagation should also be considered. With the same value of Gc and G i, the material exhibiting a stable crack propagation performs better in terms of impact resistance since after initiation, fracture can only continue with further supply of energy by external loads, whereas in the case of brittle fracture, the 24
• • •
~20 E
!16
Gc (brittle) II Ginst (semi-ductile) Gi (ductile)
I
~5
12
iO o" O
4. Results and discussion
• •
14 ~12 N 10
(2)
where Gst is the average fracture energy during the first stable crack propagation stage, A I is the fracture surface area of the first stable crack propagation zone, G~,~,. is the fracture energy at the onset of unstable crack propagation and q~ is the calibration factor corresponding to the crack length at the instability of crack propagation. By plotting U / A l against B D d P J A ~ , G,t and Ginst" can be obtained, respectively, from the intercept and the slope of the straight line. For the ductile fracture behavior, another approach taking into account the crack initiation and crack propagation energies in the material has been proposed [9]. Assuming that the fracture energy of the polymer with ductile behavior varies linearly with crack extension and is given by:
U=
16
8 4 @ . . . .
0 - 100
I -50
. . . .
I
0
. . . .
I 50
,
,
,
, 100
Temper'atum (°C)
The fracture energy as a function of temperature for HIPS at the loading speed of l0 m m / m i n and 2
Fig. 2. Variation of fracture energy as a function of temperature for HIPS tested at 2 m/s.
180
T. V u - K h a n h , Z. Yu / T h e o r e t i c a l a n d A p p l i e d F r a c t u r e M e c h a n i c s 2 6 ( 1 9 9 7 ) 1 7 7 - 1 8 3 60
0.2
5O &
0.16
4o
a °°.
3o
0.12
° °':~
d
¢ 20
J
10 , , I . , , I , , , I,,,
0
•
Ginst (semi-ductile)
•
Gi (ductile)
I...
0.08
•.. 0.04
-80
-60
-40
-20
0
Temperature
20 ('C)
40
60
80
.'*...,.
+ ,,
":°'"
Fig. 3. Variation of fracture energy as a function of temperature for Zytel ST-801 tested at 10 mm/min.
J~ .
+°'"
-100
"r.,,,
.** .*,*,~"
i -50
0
50
Temperature
crack accelerates without any additional supply of energy from the external forces, leading to the phenomenon of shattering of the part. Figs. 3 and 4 show the parameters representing the fracture energy corresponding to different fracture behaviors, measured at various temperatures for the case of Zytel ST-801. It can be seen that in this case, the same increase in the loading rate results in a lesser shift in the ductile-brittle transition temperature. At 10 mm/min, with increasing temperature, stable fracture starts to occur at about - 2 0 ° C and at 2 m / s , stable crack propagation is observed from about 10°C. The above results also show that a peak in the fracture energy is always observed at the brittleductile transition temperature. Multiple impact peaks have been reported for several polymers [2,17-20] and, although it is still a controversial subject, attempts have been made to relate the observed impact
.~ .."
• .°
i -150
".--.....
~
Water
i . . . t . . , i • i
100
160
( °C )
Fig. 5. Example of DMTA spectra for HIPS at different frequencies.
peaks to the molecular relaxation peaks of the polymer. For toughened polymers, the cause of ductilebrittle transition has often been attributed to the glass transition of the rubbery phase [11]. In order to verify this assumption, the viscoelastic properties of the samples were generated over a wide range of temperature at various frequencies. Figs. 5-7 show the DMTA spectra obtained for the two materials. For HIPS (Fig. 5), two clear transitions corresponding to the glass transition of the butadiene rubber and the polystyrene matrix can be seen. For Zyel ST 801, the or, /3 and ",/ transitions have been well documented [21] and can also be identified in Fig. 6. 0.2
0.16
60 A 5O
0.12 °
~40 0.08 . 30
o . % ° . +o
r
~ 2O 0
.-.',...
°,
10 0
-10
0.04
•
t u ." I
. . . .
-50
" , , . :. ~.., . . . .
%. o. °o*,
"-~'o %. .
~i~ltu~l~i-ductie) I } ~<~"t''') I
. . . .
0 Temperature
#
I
50
,
,
,
.....
I
i
-150 100
('C)
Fig. 4. Variation of fracture energy as a function of temperature for Zytel ST-80I tested at 2 m / s .
-100
i
i
-50
o Temperature
,
~o
.
i
100
150
( °C )
Fig. 6. Example of DMTA spectra for Zytel ST-801 at different frequencies.
T. Vu-Khanh. Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
Tg PS
.1
Table 2 Molecular transition temperatures in Zytel ST-801, as measured by DMTA
.
,08
T~ Rubber
°
.06
.0,1.02
-100
-
Frequency (Hz)
T/~ (nylon 66) (°C)
Tg (nylon 66) (°C)
0.1 0.33 1 3 10
- 49.5 -48,6 - 44.0 - 42.2 -41.8
54.2 55.1 56.2 56.5 58.2
] ~ ¢ . : : ......
•
I
-15,
181
510
I
i
I
0
50
100
150
Temperature ( °C I
Fig, 7. Example of DMTA spectra for dried Zytel ST-801 at different frequencies.
It is well known that the time-temperature dependence of molecular relaxation in polymers can be expressed/by ~a~ ~arhenius equation: f=Aexp~)
Because of commercial reasons, the rubber structure has not been released. A transition around - 5 1 ° C has been reported from the work of Wu [22] in a hydrocarbon rubber/nylon 66 blend. This might correspond to second peak in the region o f / 3 transition around - 70°C in Fig. 6. However it has been shown that this peak could also be associated with the presence of water [22]. Measurements performed on dried samples (Fig. 7) show that the second peak in the region of/3 transition disappears, suggesting that it is not related to the glass transition of the rubbery phase (which, in fact, has never been reported in the literature). A possible explanation for the absence of the glass transition peak of the rubbery phase in Zytel ST 801 is that it may overlap with the /3 transition of the Nylon matrix. Tables 1 and 2 summarize the various transition temperatures recorded at different frequencies for HIPS and Zytel ST 801,
Table 1 Molecular transition temperatures in HIPS, as measured by DMTA Frequency (Hz)
Tg (rubber) (°C)
Tg (polystyrene) (°C)
0.t 0.33 1 3 10
-78.5 -78.6 - 76.4 - 75.5 - 74.4
81.7 82.4 84.3 108. I 112.7
(5)
where f is the testing frequency, A is a constant, A H is the activation energy, R is the gas constant and T is the temperature (K), which can be either Tg or Tt3. Eq. ( 5 ) ~ be rearranged as: In f = In A - - -
RT
(6)
From the intercept and the slope of the plot of In f versus 1 / T , A and A H can be obtained. The values of In A and A H / R obtained for various molecular transitions in HIPS and Zytei ST-801 are shown in Table 3. In order to compare the time-temperature dependence of the brittle-ductile transition with that of the above molecular relaxations, an equivalent frequency corresponding to the loading rate in the three-pointbending test was determined from the time to fracture t e This time being the time spent from the first striker/specimen contact to the onset of fracture and can be measured from the recorded load versus time signal. The equivalent frequency was thus considered to be 1/(2tf). Using the values of A H and A determined in Table 3, the various molecular transition temperatures in HIPS and Zytel ST 801 at the equivalent frequencies corresponding to the loading rates of 10 m m / m i n and 2 m / s were calculated and are shown in Tables 4 and 5. In Tables 4 and 5 the observed brittle-ductile transition temperatures at these loading rates are also shown. From Tables 4 and 5 comparison can be made between the shift in the temperatures corresponding to the molecular relaxation (at the two equivalent frequencies as discussed
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T. Vu-Khanh, Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
Table 3 Measured values of In A and A H / R in Eq. (6) for the time-temperature dependence of molecular relaxations in HIPS and Zytel ST-801 Molecular relaxation
In A
A H / R (X 103 K)
Correlation coefficient
Tg (rubber, HIPS) Tg (PS, HIPS) T/3 (Pa 66, ST-801) (PA 66, ST 801)
184.64 45.239 107.97 386.47
36.246 10.679 24.590 127.160
0.963 0.967 0.951 0.984
PS = polystyrene matrix; PA 66 = Nylon 66 matrix.
Table 4 Transition temperatures at the equivalent frequencies corresponding to low (10 m m / m i n ) and high loading rates (2 m / s ) in three-pointbending tests for HIPS Relaxation temperature (°C)
Tg (rubber) Tg (PS) Tb- d
temperature T I (Vl = 10 m m / m i n )
temperature T2 (V2 = 2 m / s )
AT = T2 -
- 79.56 74.65 -- 95 _+ 5
- 70.26 150.5 -- 25 _+ 5
9.30 75.85 70 _+ 10
T I
Table 5 Transition temperatures at the equivalent frequencies corresponding to low (10 m m / m i n ) and high loading rates (2 m / s ) in three-pointbending tests for Zytel ST-801 Relaxation temperature (°C)
Tt~ (PA 66) Tg (PA 66) T0-d
temperature T I (V~ = 10 m m / m i n )
temperature T 2 (V~ = 2 m / s )
AT = T2 - T I
- 53.26 52.71 -25±5
- 32.10 61.12 5!5
21.66 8.41 3 0 + 10
above) and the shift in the brittle-ductile transition temperature. It can be observed that for HIPS, the time-temperature dependence, represented by AT, of the brittle-ductile transition is closer to that of the glass-rubber transition of the polystyrene matrix. For Zytel ST 801, with reservations about the glass transition of the rubbery phase being overlapsed by the /3 transition of the Nylon matrix, the shift of the temperature of the brittle-ductile transition with such increase in loading rate, seems to be equivalent to the shift in the temperature of the matrix /3 transition. It is also interesting to note that the molecular relaxation corresponding to the brittle-ductile transition always has a lower value of activation energy. The lower value of activation energy could therefore explain the more significant contribution of the cot-
responding relaxation process in the mechanism of brittle-ductile transition.
5. Conclusion The brittle-ductile transition in both HIPS and Zytel ST-801 have been analyzed as a function of the molecular relaxation mechanisms of the rubbery and matrix phases in these materials. It has been found that the type of molecular relaxation with a lower activation energy seems to be related to the brittle-ductile transition phenomenon. In the case of HIPS, the relaxation process involved seems to be the glass-rubber transition of the polystyrene matrix. In the case of Zytel ST-801, the /3 transition of the
T. Vu-Khanh, Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183 N y l o n 66 s e e m s to b e r e l a t e d to the b r i t t l e - d u c t i l e t r a n s i t i o n o f fracture.
References [1] C.B. Bucknall, Toughened Plastics (Applied Science Publishers, London, 1977). [2] P.I. Vincent, Impact strength and mechanical losses in thermoplastics, Polymer 15, 111-116 (1974). [3] E. Plati and J.G. Williams, Effect of temperature on the impact fracture toughness of polymers, Polymer 16, 9l 5-920 (1975). [4] S. Yamini and R.J. Young, Stability of crack propagation in epoxy resin, Polymer 18, 1075-1080 (1977). [5] J.G. Williams and J.M. Hodgkinson, Crack-blunting mechanisms in impact tests on polymers, Proc. R. Sac. London Ser. A 375, 231-247 (1981). [6] E. Plati and J.G. Williams, The determination of the fracture parameters for polymers in impact, Polym. Eng. Sci. 15, 470-477 (1975). [7] T. Vu-Khanh and F.X. de Charentenay, Mechanics and mechanisms of impact fracture in semi-ductile polymers, Polym. Eng. Sci. 25, 841-850 (1985). [8] T. Vu-Khanh and B. Fisa, Impact fracture of glass-flakes reinforced polypropylene, Polym. Compos. 7, 375-382 (1986). [9] T. Vu-Khanh, Determination of the impact fracture parameters in ductile polymers, Polymer 29, 1979-1984 (1988). [10] K. Dijkstra, J. ter Laak and R.J. Gaymans, Nylon 6/rabber blends 6: Notched tensile impact testing of nylon 6/(ethylene-propylene rubber)blends, Polymer 35, 315-331 (1994).
183
[l 1] C.B. Bucknall, Brittle-tough transition temperatures in impact tests on rubber-toughened plastics, Makromol. Chem. MakromoL Synp. 16, 209-224 (1988). [12] G.C. Sih and B. MacDonald, Fracture mechanics applied to engineering problems: Strain energy density criterion, Eng. Fract. Mech. 6, 361-386 (1974). [13] G.C. Sih, Some basic problem in fracture mechanics and new concept, Eng. Fract. Mech. 5, 365-377 (1983). [14] G.C. Sih and E. Madenci, Crack growth resistance characterized by the strain energy density function, Eng. Fract. Mech. 18, 1159-1171 (1983). [15] E.E. Gdoutos and G.C. Sih, Crack growth characteristics influenced by load time record, Theor. Appl. Fract. Mech. 3, 95-103 (1984). [16] T. Vu-Khanh and B. Fisa, Effects of fillers on fracture performance of thermoplastics: Strain energy density criterion, Theor. Appl. Fract. Mech. 13, 11-19 (1990). [17] J. Heifboer, Dynamic mechanical properties and impact strength, J. Polym. Sei. C 16, 3755-3763 (1968). [18] R.F. Boyer, Dependence of mechanical properties on molecular motion in polymers, Polym. Eng. Sci. 8, 161-185 (1968). [19] B. Hartmann and G.F. Lee, Impact resistance and secondary transitions, J. Appl. Polym. &'i. 23, 3639-3650 (1979). [20] E.S. Clark and F.C. Wilson, in: M.I. Kohan (ed.), Nylon Plastics (Wiley-lnterscience Publication, New York, 1973). [21] L. Woo, S. Westphal and M.T.K. Ling, Dynamic mechanical analysis and its relationship to impact transitions, Polym. Eng Sci. 34, 420-427 (1994). [22] S. Wu, Impact fracture mechanisms in polymer blends: Rubber toughened nylon, J. Polym. Sci. Polym. Phys'. Ed. 21, 699-716 (1983).
theoretical and applied fracture mechanics Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
Mechanisms of brittle-ductile transition in toughened thermoplastics T. Vu-Khanh *, Z. Yu D~partement de g~nie m~canique. Facult~ des sciences appliqu~es, Universit~ de Sherbrooke, Sherbrooke, Que., Canada J1K 2R1
Abstract
The objective of this work was to investigate the mechanism of brittle-ductile transition in toughened polymers. Two systems, namely, a rubber-toughened nylon 66 (Zytel ST-801) and a high impact polystyrene (HIPS), were chosen for this study. The samples were prepared by injection molding and were tested in three-point bending under various loading rates and temperatures. The brittle-ductile transition temperature (Tb_d) was determined from the observed fracture behavior as a function of temperature. Molecular relaxation temperatures of the polymers were measured by mechanical spectroscopy at various frequencies. The correlation between temperature and loading rate was estimated using the Arrhenius equation. The results show that Tb_d of Zytel ST-801 is only slightly affected by the loading rate, whereas Tb_d of HIPS strongly increases with deformation rate. It is found that for the former, within the experimental errors, an increase in Tb_d with loading rate corresponds to the shift in the secondary relaxation temperature Tb of the nylon 66 matrix. For the latter however, the increase in Tb_d is related to the glass/rubber relaxation of the polystyrene matrix. It seems that the type of molecular relaxation controlling the brittle-ductile transition corresponds to that with lower activation energy.
1. Introduction One of the most important weaknesses of polymers is their poor impact resistance. To improve this performance, much attention has been paid to adding an elastomeric, dispersed phase to the polymer matrix. Presently the role of rubber toughening in the impact performance of polymers is being extensively investigated. However, it is well known that, at relatively low temperatures or high loading rates, the toughened polymer can become brittle. Rubber toughening polystyrene and nylon-6,6 have been commercialized for a number of years. These materials possess good impact properties and have been
* Corresponding author. Tel.: + 1-819-8216997; fax: + 1-8198217163; e-mail: [email protected].
widely used as engineering materials. In terms of fracture performance, they can break in a brittle manner at low temperatures or high loading rates. This brittle-ductile transition has been attributed to the change in fracture mechanism from localized crazing to generalized crazing or shear yielding [1]. The impact fracture behavior of polymers has long been investigated [2-10]. However the fundamental material parameters controlling the brittleductile transition remain unclear. For the case of toughened polymers, it has been suggested that the brittleness at low temperature is due to the glass transition in the rubbery phase [11]. Under impact, it has also been shown that adiabatic heating plays a primary role in the fracture performance [5,8]. In the presence of a defect such as a crack, localized heating can have a very significant effect. Since poly-
0167-8442/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S0167-8442(96)00047-X
178
T. Vu-Khanh, Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
mers are strongly time and temperature dependent, this could lead to opposite effects between increasing impact velocity and the rise in temperature resulting from adiabatic heating due to high loading rate. The effects of molecular relaxations on impact fracture performance should therefore be better understood in order to optimize the impact performance of polymers and prevent brittle fracture to occur. The aim of this study is to investigate the roles played by the various molecular relaxations of each component in rubber toughened polymers. The focus is put on the brittle-ductile transition in fracture behavior, which is a critical condition in the applications of these materials.
striking tup of the impact machine was instrumented with strain gages and the load-time signal during impact was recorded by a rapid data acquisition system. The machine was also equipped with an optical cell, enabling measurement of the velocity of the striker just before impact. By varying the drop height, the impact speed was varied from 2 to 5 m / s . The testing temperature was varied from - 8 5 to 90°C using a Thermotron environmental chamber (model ETS-150-LN2). To reduce the bouncing effect of the sample on the striker in impact, a small amount of plasticine was placed on the striker. The absorbed energy by the sample to break under impact was determined by subtracting the energy absorbed by the plasticine from the total recorded energy to fracture the sample.
2. Experimental High impact polystyrene (HIPS) and toughened nylon 66 were supplied, respectively, by Dow Chemical (STYRON 484C) and by DuPont Canada (Zytel ST-801) in the form of pellets. Rectangular plates of 6 x 27 x 124 mm of these materials were injection molded. The pellets were dried in a vacuum oven prior to molding. Three-point-bend specimens of 6 x 13 x 124 mm were cut out from the molded plates. A sharp notch was also created in the specimens to analyze the impact performance in terms of crack growth resistance. A prenotch was first made by a band saw cut and the final notch in the specimen was created by forcing a razor blade into the specimen in a special jig, The notch depth was varied from 10 to 80% of the specimen width. Measurements of the viscoelastic properties of the materials were performed on a dynamic mechanical thermal analyzer (DMTA) from Polymer Laboratory (Model MKII). Samples of 11.4 × 10 x 1.4 mm were machined from the injection molded plaques. Each sample was cut at the same location in the plaques. Five frequencies; 0.1, 0.33, 1, 3 and 10 Hz were used. The temperature was varied from - 1 2 0 to 110°C. Three-point-bending tests at low loading rate (10 mm/min) were performed on an Instron machine (Model 1123). The testing temperature was varied between - 1 0 0 and 80°C. High loading rate tests were carried out on a Dynatup drop-weight device (Model 8200) with a hammer weight of 3.25 kg. The
3. Fracture characterization
In the Charpy and Izod tests, only the total energy absorbed by the sample to break can be measured and it is well known that this value does not directly correspond to the fracture performance of the material [6,7,9]. Characterization of the impact resistance of the samples was thus made by using the different proposed methods based on fracture mechanics [6,7,9], depending on the type of fracture observed (brittle, semi-ductile, or ductile). It is worth noting that the global concept of fracture mechanics such as the strain energy release rate is unable to properly describe the fracture process [12-16]. However, this approach is presented widely used to characterize the fracture toughness of materials and the strain energy release rate considered in the proposed models can provide a useful alternative method for the characterization of impact performance. For brittle fracture, the critical strain energy release rate, Gc, can be determined by [6]: U = G~BDck
(1)
where U is the absorbed energy by the sample, B and D are, respectively, the sample width and thickness and th is a geometrical function which can be evaluated for any geometry by considering the appropriate calibration factor established for precracked samples [6]. From the slope of the plot of U
179
T. Vu-Khanh, Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
versus BDqb, using samples having different initial crack depths to vary ~b, the fracture energy, G c, can be obtained. For semi-ductile fracture, a mixed stable-unstable period of crack propagation occurs in the same sample during impact fracture and in this case, the total energy absorbed by the sample to break, U, has been determined [7]: U = Gst A l + Ginst.BDCrp I
(3)
G r = G i + TaA
in which Gr is the actual fracture energy, G~ is the fracture energy at crack initiation, T~ represents the rate of change of G, with crack extension and A is the fracture surface. Since the energy absorbed by the specimen is mainly dissipated in the fracture process, the energy absorbed by the specimen becomes: L
@dA=GiA
1
+TTaA
2
(4)
From this equation one can obtain G~ by the intercept and Ta by the slope of the U / A versus A plot.
Gc (bdttle) I Gi (ductile)
,t 8
~5 ff
eA
6 4
,&A
•
oo
&
2 0 -150
- 100
-50
0
50
100
Temperature ('C)
Fig. 1. Variation of fracture energy as a function of temperature for HIPS tested at 10 ram/rain. m / s are shown in Figs. 1 and 2, respectively. It is observed that, for low loading rate (Fig. 1), stable fracture occurs at around - 100 to - 9 0 ° C . When the velocity of loading is increased to 2 m / s , the britfie-ductile transition temperature (Tb_ d) shifts to the region between - 5 0 to - 3 0 ° C (Fig. 2): In this region of temperatures, a mixed stable-unstable crack propagation (semi-ductile fracture) occurs. When the temperature is increased, the onset of stable crack propagation is observed above about -30°C. It is worth noting that one cannot base only on these reported values of fracture energy to determine the material's impact performance but the type of crack propagation should also be considered. With the same value of Gc and G i, the material exhibiting a stable crack propagation performs better in terms of impact resistance since after initiation, fracture can only continue with further supply of energy by external loads, whereas in the case of brittle fracture, the 24
• • •
~20 E
!16
Gc (brittle) II Ginst (semi-ductile) Gi (ductile)
I
~5
12
iO o" O
4. Results and discussion
• •
14 ~12 N 10
(2)
where Gst is the average fracture energy during the first stable crack propagation stage, A I is the fracture surface area of the first stable crack propagation zone, G~,~,. is the fracture energy at the onset of unstable crack propagation and q~ is the calibration factor corresponding to the crack length at the instability of crack propagation. By plotting U / A l against B D d P J A ~ , G,t and Ginst" can be obtained, respectively, from the intercept and the slope of the straight line. For the ductile fracture behavior, another approach taking into account the crack initiation and crack propagation energies in the material has been proposed [9]. Assuming that the fracture energy of the polymer with ductile behavior varies linearly with crack extension and is given by:
U=
16
8 4 @ . . . .
0 - 100
I -50
. . . .
I
0
. . . .
I 50
,
,
,
, 100
Temper'atum (°C)
The fracture energy as a function of temperature for HIPS at the loading speed of l0 m m / m i n and 2
Fig. 2. Variation of fracture energy as a function of temperature for HIPS tested at 2 m/s.
180
T. V u - K h a n h , Z. Yu / T h e o r e t i c a l a n d A p p l i e d F r a c t u r e M e c h a n i c s 2 6 ( 1 9 9 7 ) 1 7 7 - 1 8 3 60
0.2
5O &
0.16
4o
a °°.
3o
0.12
° °':~
d
¢ 20
J
10 , , I . , , I , , , I,,,
0
•
Ginst (semi-ductile)
•
Gi (ductile)
I...
0.08
•.. 0.04
-80
-60
-40
-20
0
Temperature
20 ('C)
40
60
80
.'*...,.
+ ,,
":°'"
Fig. 3. Variation of fracture energy as a function of temperature for Zytel ST-801 tested at 10 mm/min.
J~ .
+°'"
-100
"r.,,,
.** .*,*,~"
i -50
0
50
Temperature
crack accelerates without any additional supply of energy from the external forces, leading to the phenomenon of shattering of the part. Figs. 3 and 4 show the parameters representing the fracture energy corresponding to different fracture behaviors, measured at various temperatures for the case of Zytel ST-801. It can be seen that in this case, the same increase in the loading rate results in a lesser shift in the ductile-brittle transition temperature. At 10 mm/min, with increasing temperature, stable fracture starts to occur at about - 2 0 ° C and at 2 m / s , stable crack propagation is observed from about 10°C. The above results also show that a peak in the fracture energy is always observed at the brittleductile transition temperature. Multiple impact peaks have been reported for several polymers [2,17-20] and, although it is still a controversial subject, attempts have been made to relate the observed impact
.~ .."
• .°
i -150
".--.....
~
Water
i . . . t . . , i • i
100
160
( °C )
Fig. 5. Example of DMTA spectra for HIPS at different frequencies.
peaks to the molecular relaxation peaks of the polymer. For toughened polymers, the cause of ductilebrittle transition has often been attributed to the glass transition of the rubbery phase [11]. In order to verify this assumption, the viscoelastic properties of the samples were generated over a wide range of temperature at various frequencies. Figs. 5-7 show the DMTA spectra obtained for the two materials. For HIPS (Fig. 5), two clear transitions corresponding to the glass transition of the butadiene rubber and the polystyrene matrix can be seen. For Zyel ST 801, the or, /3 and ",/ transitions have been well documented [21] and can also be identified in Fig. 6. 0.2
0.16
60 A 5O
0.12 °
~40 0.08 . 30
o . % ° . +o
r
~ 2O 0
.-.',...
°,
10 0
-10
0.04
•
t u ." I
. . . .
-50
" , , . :. ~.., . . . .
%. o. °o*,
"-~'o %. .
~i~ltu~l~i-ductie) I } ~<~"t''') I
. . . .
0 Temperature
#
I
50
,
,
,
.....
I
i
-150 100
('C)
Fig. 4. Variation of fracture energy as a function of temperature for Zytel ST-80I tested at 2 m / s .
-100
i
i
-50
o Temperature
,
~o
.
i
100
150
( °C )
Fig. 6. Example of DMTA spectra for Zytel ST-801 at different frequencies.
T. Vu-Khanh. Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
Tg PS
.1
Table 2 Molecular transition temperatures in Zytel ST-801, as measured by DMTA
.
,08
T~ Rubber
°
.06
.0,1.02
-100
-
Frequency (Hz)
T/~ (nylon 66) (°C)
Tg (nylon 66) (°C)
0.1 0.33 1 3 10
- 49.5 -48,6 - 44.0 - 42.2 -41.8
54.2 55.1 56.2 56.5 58.2
] ~ ¢ . : : ......
•
I
-15,
181
510
I
i
I
0
50
100
150
Temperature ( °C I
Fig, 7. Example of DMTA spectra for dried Zytel ST-801 at different frequencies.
It is well known that the time-temperature dependence of molecular relaxation in polymers can be expressed/by ~a~ ~arhenius equation: f=Aexp~)
Because of commercial reasons, the rubber structure has not been released. A transition around - 5 1 ° C has been reported from the work of Wu [22] in a hydrocarbon rubber/nylon 66 blend. This might correspond to second peak in the region o f / 3 transition around - 70°C in Fig. 6. However it has been shown that this peak could also be associated with the presence of water [22]. Measurements performed on dried samples (Fig. 7) show that the second peak in the region of/3 transition disappears, suggesting that it is not related to the glass transition of the rubbery phase (which, in fact, has never been reported in the literature). A possible explanation for the absence of the glass transition peak of the rubbery phase in Zytel ST 801 is that it may overlap with the /3 transition of the Nylon matrix. Tables 1 and 2 summarize the various transition temperatures recorded at different frequencies for HIPS and Zytel ST 801,
Table 1 Molecular transition temperatures in HIPS, as measured by DMTA Frequency (Hz)
Tg (rubber) (°C)
Tg (polystyrene) (°C)
0.t 0.33 1 3 10
-78.5 -78.6 - 76.4 - 75.5 - 74.4
81.7 82.4 84.3 108. I 112.7
(5)
where f is the testing frequency, A is a constant, A H is the activation energy, R is the gas constant and T is the temperature (K), which can be either Tg or Tt3. Eq. ( 5 ) ~ be rearranged as: In f = In A - - -
RT
(6)
From the intercept and the slope of the plot of In f versus 1 / T , A and A H can be obtained. The values of In A and A H / R obtained for various molecular transitions in HIPS and Zytei ST-801 are shown in Table 3. In order to compare the time-temperature dependence of the brittle-ductile transition with that of the above molecular relaxations, an equivalent frequency corresponding to the loading rate in the three-pointbending test was determined from the time to fracture t e This time being the time spent from the first striker/specimen contact to the onset of fracture and can be measured from the recorded load versus time signal. The equivalent frequency was thus considered to be 1/(2tf). Using the values of A H and A determined in Table 3, the various molecular transition temperatures in HIPS and Zytel ST 801 at the equivalent frequencies corresponding to the loading rates of 10 m m / m i n and 2 m / s were calculated and are shown in Tables 4 and 5. In Tables 4 and 5 the observed brittle-ductile transition temperatures at these loading rates are also shown. From Tables 4 and 5 comparison can be made between the shift in the temperatures corresponding to the molecular relaxation (at the two equivalent frequencies as discussed
182
T. Vu-Khanh, Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183
Table 3 Measured values of In A and A H / R in Eq. (6) for the time-temperature dependence of molecular relaxations in HIPS and Zytel ST-801 Molecular relaxation
In A
A H / R (X 103 K)
Correlation coefficient
Tg (rubber, HIPS) Tg (PS, HIPS) T/3 (Pa 66, ST-801) (PA 66, ST 801)
184.64 45.239 107.97 386.47
36.246 10.679 24.590 127.160
0.963 0.967 0.951 0.984
PS = polystyrene matrix; PA 66 = Nylon 66 matrix.
Table 4 Transition temperatures at the equivalent frequencies corresponding to low (10 m m / m i n ) and high loading rates (2 m / s ) in three-pointbending tests for HIPS Relaxation temperature (°C)
Tg (rubber) Tg (PS) Tb- d
temperature T I (Vl = 10 m m / m i n )
temperature T2 (V2 = 2 m / s )
AT = T2 -
- 79.56 74.65 -- 95 _+ 5
- 70.26 150.5 -- 25 _+ 5
9.30 75.85 70 _+ 10
T I
Table 5 Transition temperatures at the equivalent frequencies corresponding to low (10 m m / m i n ) and high loading rates (2 m / s ) in three-pointbending tests for Zytel ST-801 Relaxation temperature (°C)
Tt~ (PA 66) Tg (PA 66) T0-d
temperature T I (V~ = 10 m m / m i n )
temperature T 2 (V~ = 2 m / s )
AT = T2 - T I
- 53.26 52.71 -25±5
- 32.10 61.12 5!5
21.66 8.41 3 0 + 10
above) and the shift in the brittle-ductile transition temperature. It can be observed that for HIPS, the time-temperature dependence, represented by AT, of the brittle-ductile transition is closer to that of the glass-rubber transition of the polystyrene matrix. For Zytel ST 801, with reservations about the glass transition of the rubbery phase being overlapsed by the /3 transition of the Nylon matrix, the shift of the temperature of the brittle-ductile transition with such increase in loading rate, seems to be equivalent to the shift in the temperature of the matrix /3 transition. It is also interesting to note that the molecular relaxation corresponding to the brittle-ductile transition always has a lower value of activation energy. The lower value of activation energy could therefore explain the more significant contribution of the cot-
responding relaxation process in the mechanism of brittle-ductile transition.
5. Conclusion The brittle-ductile transition in both HIPS and Zytel ST-801 have been analyzed as a function of the molecular relaxation mechanisms of the rubbery and matrix phases in these materials. It has been found that the type of molecular relaxation with a lower activation energy seems to be related to the brittle-ductile transition phenomenon. In the case of HIPS, the relaxation process involved seems to be the glass-rubber transition of the polystyrene matrix. In the case of Zytel ST-801, the /3 transition of the
T. Vu-Khanh, Z. Yu / Theoretical and Applied Fracture Mechanics 26 (1997) 177-183 N y l o n 66 s e e m s to b e r e l a t e d to the b r i t t l e - d u c t i l e t r a n s i t i o n o f fracture.
References [1] C.B. Bucknall, Toughened Plastics (Applied Science Publishers, London, 1977). [2] P.I. Vincent, Impact strength and mechanical losses in thermoplastics, Polymer 15, 111-116 (1974). [3] E. Plati and J.G. Williams, Effect of temperature on the impact fracture toughness of polymers, Polymer 16, 9l 5-920 (1975). [4] S. Yamini and R.J. Young, Stability of crack propagation in epoxy resin, Polymer 18, 1075-1080 (1977). [5] J.G. Williams and J.M. Hodgkinson, Crack-blunting mechanisms in impact tests on polymers, Proc. R. Sac. London Ser. A 375, 231-247 (1981). [6] E. Plati and J.G. Williams, The determination of the fracture parameters for polymers in impact, Polym. Eng. Sci. 15, 470-477 (1975). [7] T. Vu-Khanh and F.X. de Charentenay, Mechanics and mechanisms of impact fracture in semi-ductile polymers, Polym. Eng. Sci. 25, 841-850 (1985). [8] T. Vu-Khanh and B. Fisa, Impact fracture of glass-flakes reinforced polypropylene, Polym. Compos. 7, 375-382 (1986). [9] T. Vu-Khanh, Determination of the impact fracture parameters in ductile polymers, Polymer 29, 1979-1984 (1988). [10] K. Dijkstra, J. ter Laak and R.J. Gaymans, Nylon 6/rabber blends 6: Notched tensile impact testing of nylon 6/(ethylene-propylene rubber)blends, Polymer 35, 315-331 (1994).
183
[l 1] C.B. Bucknall, Brittle-tough transition temperatures in impact tests on rubber-toughened plastics, Makromol. Chem. MakromoL Synp. 16, 209-224 (1988). [12] G.C. Sih and B. MacDonald, Fracture mechanics applied to engineering problems: Strain energy density criterion, Eng. Fract. Mech. 6, 361-386 (1974). [13] G.C. Sih, Some basic problem in fracture mechanics and new concept, Eng. Fract. Mech. 5, 365-377 (1983). [14] G.C. Sih and E. Madenci, Crack growth resistance characterized by the strain energy density function, Eng. Fract. Mech. 18, 1159-1171 (1983). [15] E.E. Gdoutos and G.C. Sih, Crack growth characteristics influenced by load time record, Theor. Appl. Fract. Mech. 3, 95-103 (1984). [16] T. Vu-Khanh and B. Fisa, Effects of fillers on fracture performance of thermoplastics: Strain energy density criterion, Theor. Appl. Fract. Mech. 13, 11-19 (1990). [17] J. Heifboer, Dynamic mechanical properties and impact strength, J. Polym. Sei. C 16, 3755-3763 (1968). [18] R.F. Boyer, Dependence of mechanical properties on molecular motion in polymers, Polym. Eng. Sci. 8, 161-185 (1968). [19] B. Hartmann and G.F. Lee, Impact resistance and secondary transitions, J. Appl. Polym. &'i. 23, 3639-3650 (1979). [20] E.S. Clark and F.C. Wilson, in: M.I. Kohan (ed.), Nylon Plastics (Wiley-lnterscience Publication, New York, 1973). [21] L. Woo, S. Westphal and M.T.K. Ling, Dynamic mechanical analysis and its relationship to impact transitions, Polym. Eng Sci. 34, 420-427 (1994). [22] S. Wu, Impact fracture mechanisms in polymer blends: Rubber toughened nylon, J. Polym. Sci. Polym. Phys'. Ed. 21, 699-716 (1983).