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Fracture energy measurements in polycarbonate and PMMA
Polymer Testing 7 (1987) 209-222
Fracture Energy Measurements in Polycarbonate and PMMA R a g n a r Seld6n Swedish Plastics and Rubber Institute, Box 6075, S-850 06 Sundsvall, Sweden (Received 3 November 1986; accepted 17 November 1986)
SUMMARY Fracture energies in polycarbonate and PMMA were measured using different test techniques. Results from instrumented impact tests and slow three-point bend tests on Charpy specimens were compared with tensile test results on Compact Tension (CT) specimens. The Charpy specimens were provided with a blunt Charpy V (0.25ram radius) notch and sharp (251tin radius) notch. It is shown that impact testing of Charpy specimens with blunt notches gives values of the fracture energy which are two to six times higher than those obtained from the CT tensile tests. Only by using a sharp, 251~m notch and performing the three-point bend test at a low rate were similar results obtained.
1 INTRODUCTION The usual procedure for measuring impact strength of plastics uses notched specimens, as in the Charpy and Izod tests. Later developments of these test methods rely on instrumented tests using advanced electronics and computer analysis of the force-time curves. Another improvement is the possibility of obtaining from impact tests fracture mechanics parameters such as the fracture energy or the fracture toughness. According to a theory presented by Williams et al.l'2 the absorbed energy in a Charpy or Izod test can be related to the fracture energy (for brittle failure) according to W = B D ~ G , c + Wk (1) 209 Polymer Testing 0142-9418/87/$03.50 ~ Elsevier Applied Science Publishers Ltd, England, 1987. Printed in Northern Ireland
210
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I
80
w,
,oo
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Imml Fig. 1. Test specimens: (a) Compact Tension (CT); (b) Charpy specimen.
where W is absorbed energy, Wk is kinetic energy, B and D are specimen thickness and width, respectively, q~is a calibration factor and G,c is the fracture energy. Valid fracture toughness parameters can be obtained only if sufficiently sharp notches are used. 3 In this work fracture energies were determined in polycarbonate (PC) and PMMA specimens of different thickness using tensile tests on Compact Tension (CT) specimens. The results were compared with results from instrumented impact tests and slow three-point bend tests on Charpy specimens. The Charpy specimens were provided both with a Charpy V (0.25 mm radius) notch and a sharp 25/~m-radius notch, and the results were analyzed according to eqn. (1). It is shown that impact testing of Charpy specimens with blunt notches gives values of the fracture energy which are two to six times higher than those obtained from the CT tensile tests. Only by using a sharp, 25 ~m notch and performing the three-point bend test at a low rate were similar results obtained. 2 EXPERIMENTAL The polycarbonate material, a commercial quality, 'Makrolon 280' from R6hm GmbH, was received as sheets of thicknesses 3, 6, 8, 10 and 17 mm.
Fracture energy measurements in polycarbonate and P M M A
211
The poly(methyl methacrylate) material was received from Bofors Plastics, Tidaholm, Sweden as sheets of thicknesses 2, 3, 5 and 10 mm. The sheets had been compression-moulded and had a glass transition temperature (Tg) of 110 °C and molecular weights Mw = 1.07 x 107 and M, = 5.0 x 106. Square plates, 2 c m x 2 c m , were cut from the PC sheets and immersed in silicone oil for 1 h at 170 °C. Dimensional changes were measured after the heat treatment and were found to be small both lengthwise and crosswise for all sheet thicknesses. The degree of orientation in the PC sheets was thus concluded to be small.
2.1 Fracture toughness testing Compact Tension (CT) specimens for fracture toughness testing were cut from the sheets, having the dimensions shown in Fig. la. Prior to the mechanical testing the specimens were annealed, PC at 135 °C and P M M A at 80°C, for 15h. Thereafter the temperature was slowly lowered ( = 1 0 ° C / h ) to room temperature. A sharp pre-crack was produced by fatigue testing the specimens in a MTS 50 kN closed-loop servohydraulic testing machine at a frequency of 10 Hz. The fatigue testing was interrupted when a fatigue crack had grown from the chevron notch so that the ratio a/w was between 0-4 and 0.6. The CT specimens were equipped with a 'clip-gauge' and tensile tests were performed at deformation rates varying from 0-175 to 175 mm/ min. Load was measured as a function of crack opening displacement (COD). The fracture toughness, Kic, was calculated using the standard formula: 4 glc
~
Pc n_ . _~rl/2 [29-6 ( a / w )
1/2 -- 185"5 ( a / w ) 3r2 +
- 1017 (a/w) v2 + 638.9 (a/w) 9/2]
655.7 ( a / w ) srz (2)
where Pc = critical (failure) load, B = specimen thickness, a = crack length. For the PC specimens the critical load, Pc, was taken both as the maximum load in the l o a d - C O D curve and as the critical load where crack growth initiated. The crack initiation load was determined from the l o a d - C O D curve by drawing a straight line with a slope of 95% of the initial l o a d - C O D curve. The intersection with the loadCOD curve was taken as the crack initiation l o a d ) Crack initiation load and maximum load were identical for specimens having thicknesses greater than or equal to 8 mm. At the maximum COD (2.5 mm) which could be measured, the testing was terminated even if the specimen had not failed.
212
Ragnar Seld6n
For the PMMA specimens only brittle failures were obtained. Tests were performed in two mutually perpendicular directions. Similar results were obtained and therefore results for both directions are presented together.
2.2 Impact and three-point bend testing The specimens used for impact testing and (slow) three-point bend testing are shown in Fig. lb. The dimensions were in accordance with the ASTM-D256 standard for Charpy specimens. Both a blunt Charpy notch having a radius of 0.25 mm and a sharp notch using a sharply honed cutter were used. The cutter gave a notch tip radius of approximately 0.025 mm (25 #m) (which could be seen when observing the notch tip in an optical microscope). The crack length (notch depth) was kept constant at 2.54 mm. Prior to testing the specimens were annealed, PC at 135 °C and PMMA at 80 °C for 15 h. Thereafter the temperature was slowly lowered (=10 °C/h) to room temperature. The impact testing was performed in an instrumented falling-weight impact tester. The instrumentation consisted of a microcomputer, a plotter, an analog-to-digital converter and a time-measuring device. The tup was released from a drop height of 1 m corresponding to an impact velocity of 4.4 m/s. The tup-head geometry and the mounting of the specimens were in accordance with the ASTM-D256 standard. With a piezoelectric crystal mounted in series with the tup, load was recorded during the impact event as a function of time. From the calculated tup velocity the computer calculated the absorbed energy as a function of time. The slow three-point bend testing was performed at a testing rate of 10 mm/min in an MTS testing machine. Here also the ASTM-D256 standard for tup geometry and specimen mounting was followed. Load was measured as a function of deflection. The amount of energy absorbed by the specimens was determined by calculating the area under the load-deflection curves. To ensure brittle failures only specimens having thicknesses greater than or equal to 6 mm were tested for the PC material. 3 RESULTS 3.1 Fracture toughness testing Typical load versus crack-opening displacement curves for PC at 17.5 ram/rain and different specimen thicknesses are shown in Fig. 2.
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(ram)
a
b
1 (mm)
(mm) c
1 {mM)
a
(mm)
e
Fig. 2. Load versus crack opening displacement (COD) for PC specimens at 17.5 mm/min cross-head rate and different thicknesses: (a) 3 mm; (b) 6 mm; (c) 8 mm; (d) 10 mm; (e) 17 mm.
At 8, 10 and 1 7 m m thickness almost linear curves were obtained. Failure was brittle and examples of fracture surfaces for the 17 mm thick CT specimens are shown in Fig. 3. It can be seen in Fig. 3 that a small amount of slow crack growth preceded unstable fracture. At a specimen thickness of 6 mm slow crack growth initiates at some critical load. No unstable crack growth is obtained and if the specimen is rapidly unloaded the crack growth will stop. The failure surface shows that ductile tearing preceded crack growth and existence of shear lips 6 was also evident. At 3 mm thickness very little crack propagation was obtained. Extensive shear yielding developed ahead of the fatigue crack. Typical l o a d - C O D curves for P M M A are shown in Fig. 4. Almost linear curves and only brittle failures were obtained. When calculating fracture toughness, eqn. (2) was used. For the PC specimens critical load was taken both as maximum load and as crack initiation load. Results at deformation rates between 17.5 and 175 mm/ min are shown in Fig. 5. Both methods give identical results except for the thinner (3 and 6 mm) specimens. For the 3 mm specimens the ratio between the two values amounts to c a 1.25. This is higher than in the ASTM plane strain fracture toughness standard (E399), which requires that the ratio shall not exceed 1.10. In ASTM E399 the following condition must also be satisfied in order to obtain a valid plane strain
Ragnar Selden
214
Fig. 3. Fracture surfaces for 17mm PC specimens at 17.5 mm/min. Fatigue crack limits are marked with arrows. value of fracture toughness: B > 2"5 (Kic/Oy) z w h e r e K~c = critical plane stress intensity factor and ay = yield stress. Using the K~c value obtained for the thickest 1 7 m m specimens (3.5 MPa~/m) as the plane strain value and taking a y - 60 M P a , 7 one a ( N)100
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I 1
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I 1
(mm)
Fig. 4. Load versus COD for PMMA CT specimens, thickness (a) 2 mm and (b) 5 mm.
Fracture energy measurements in polycarbonate and PMMA
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Valid
3
6
8
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17 THICKNESS (rnm)
Fig. 5. Fracture toughness K~c versus thicknessfor PC: O, Kic at initiation; Q, Ksc at maximum load. obtains valid results for B > 8.5 mm. This is indicated in Fig. 5 as 'Valid LEFM'. Using the crack initiation load as critical load one obtains an approximately thickness-independent value of 3.5 MPa~/m. Fracture toughness as a function of deformation rate is shown in Fig. 6 for the 17 mm-thick PC specimens. It can be seen that the fracture toughness slowly decreases as the deformation rate increases. Similar results have been obtained elsewhere. 8
!
I-
I[ ~g
10"!
10o
101
102
CROSS- HEAD RATE(mm/min)
Fig. 6. Kzc versus cross-head rate for 17 mm PC specimens.
Ragnar SeldEn
216
s u N
1
2 THICKNESS (ram)
Fig. 7.
K~c versus thickness for PMMA specimens.
Results for P M M A are presented in Fig. 7 at a deformation rate of 1 mm/min. The fracture toughness is approximately independent of thickness and a value of - 1 . 5 MPa~/m is obtained. The ASTM E399 requirements are met here (taking ay - 80 MPa and Kic = 1.5 MPaX/m) for thicknesses greater than or equal to 0-9 mm. The fracture energy G~c can be calculated from the fracture toughness, Kic, using the relation: 9 Gic ~--- (1 -
v2)r2c/e
(3)
where v is Poisson's ratio and E is the (short-time) value of Young's modulus. This calculation has been performed on the fracture toughness values of PC and P M M A shown in Figs 6 and 7 and the results are given in Table 1. TABLE 1
Fracture Energy Determined from Different Test Methods.
Material
PMMA PC
Glc(kJ / m 2) Impact Charpy
Slow bend Charpy
CT tensile test
Sharp notch
Blunt notch
Sharp notch
Blunt notch
0-62 4-4-6.8
2.8 3.1
3.7 12
0.75 5-7
1.2 14
217
Fracture energy measurements in polycarbonate and PMMA
3.2 Impact and three-point bend testing A typical impact test result for PC having a sharp (25/zm radius) notch is shown in Fig. 8a. Here applied force and absorbed energy are displayed as a function of time. Only one maximum in the force-time diagram is obtained. Figure 8b shows typical results for PC having a blunt (0.25 mm) notch. Here two maxima in the force-time diagram are obtained. This effect is attributed to specimen bouncings,l° against the tup before unstable fracture is obtained. The difference in behavior between sharp and blunt notches is also reflected in the amount of absorbed energy. Less than a three-fold lower energy absorption is obtained with the sharp notches. Figure 9 shows typical results for PMMA specimens with sharp and blunt notches. Only one maximum in the force-time diagrams is obtained in both cases. The absorbed energy is only moderately affected by notch tip radius. According to eqn. (1) the absorbed energy in a notched impact test a
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.8
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!.6
21.1
2.6
12
i,
,',
4.2 ' TIME(ms)
Impact results for 17mm PC specimens:(a) sharp notches; (b) blunt notches. Absorbed energycalculatedup to vertical (broken) line.
Ragnar Selden
218
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.v
.6 %-
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.2"
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3.7
4.2
4.8
TIME (ms)
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3.7
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1~. 9, Impact results for 5 mm PMMA specimens: (a) sharp notches; and (b) blunt notches.
can be related to the fracture energy, G~c, through the relation: W = BDdpG~c + Wk
Thus, by plotting absorbed energy in an impact test versus BDdp a straight line will result with a slope equal to G~c and an intercept WK. Here the absorbed energy was varied by testing specimens of different thicknesses. Figure 10 shows results from such plots for PC having blunt and sharp notches. In both cases straight lines are obtained which pass through the origin. From the slope of the lines a fracture energy of 12kJ/m z is obtained for the blunt-notched and 3.1 kJ/m 2 for the sharp-notched specimens. Results for PMMA with sharp and blunt notches are shown in Fig. 11. In this case fracture energies of 2.8 and 3.7 kJ/m z, respectively, were obtained. Typical load-displacement records in slow three-point bend testing of blunt-notched PMMA and PC are shown in Fig. 12. From these diagrams the absorbed energy was calculated as the area under the
Fracture energy measurements in polycarbonate and PMMA
219
.-j
Gc: 1 2 k J / m 2 I
I ~
i
i f kJ/m z
I 5
I0
15.10" 5 B.O.O Cmz)
Fig. 10. Absorbed energy in impact versus BD¢ for PC specimens with sharp (O) and blunt (0) notches.
load-deflection curves. The absorbed energy was then plotted against BDdp to obtain Gic in the same way as for the impact tests. Typical results are shown in Fig. 13 for PC specimens with sharp and blunt notches. A similar plot for the P M M A specimens gave the following values of the fracture energy: sharp notches 0.75 k J / m 2 and blunt notches 1.2 k J / m 2.
.5 ¸
.4
.2
.I ~
O
5
10 e.O.tl
15. iO"s (m z ,
Fig. 11. Absorbed energy in impact versus BD¢ for PMMA specimens with sharp (O)
and blunt (0) notches.
220
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i
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i
8
1001
250-
i
i
501
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5 10 16 Displacement , ram,
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201
d
101
100-
5
I
0 10
10
15
Displacement ,mill,
16
D i s p l a c e m e n t , ram.
Fig. 12. Load versus displacement in three-point bending (blunt notches); (a) PC, 6 mm thickness; (b) PC, 17 mm; (c) PMMA, 5 mm; (d) PMMA, 10 mm.
4 DISCUSSION Table 1 shows the results from the fracture energy measurements using different test methods. It can be seen that impact testing of bluntnotched Charpy specimens provides values of the fracture energy which are higher than those obtained from the CT tensile tests. The difference is a factor of six for P M M A and a factor of two for PC. Reducing the test speed in the Charpy test significantly decreases the fracture energy values for PMMA whereas the values for PC slightly increase. However, only by using the sharp (25 #m) notch and performing the
Fracture energy measurements in polycarbonate and P M M A 31
221
I
k
kJ/m z
; ~
I0
Gc" 5.7 kJ n~
1 5 . 1 0 "s
e.o.O (m z)
Fig. 13. Absorbed energy in three-point bending versus BDdp for sharp-(O) and blunt-(O) notched PC.
Charpy test at a low rate, do G~c values for both P M M A and PC become close to the CT results. Impact testing of the sharp-notched P M M A specimens increases the fracture energy to 2 . 8 k J / m 2, compared with 0 . 7 k J / m 2 in the slow three-point bend test. This behavior of P M M A has been noted earlier ~,~2 and was explained by thermal blunting of the crack tip at high crack speeds. However, this effect is not pronounced for the PC material. For the sharp-notched specimens the fracture energy decreases from 5.7 k J / m 2 at low test rate to 3-1 kJ/m 2 at high test rate. Figure 6 also shows that the fracture toughness becomes lower as the test rate is increased. Assuming a distribution of the fracture energy where the surface regions are in plane stress over a thickness corresponding to the plastic zone size (1/2~r)(EGc2/a 2) where Gc2 is the fracture energy of regions in plane stress, E the elastic modulus and ay the yield stress, and assuming that the central regions are in the plane strain one obtains: 2 G~ = G c l +
(EGc2/~rBaZ)(Gc2-- Gcl)
where G~ is measured fracture energy, Gc~ the fracture energy of regions in plane strain and B the specimen thickness. Assuming that ay increases with test rate, a lower value of Gc will be obtained since Gc will become closer to Gc~. 2
222
Ragnar Selden 5 CONCLUSIONS
The following conclusions apply to the fracture energy measurements using different test methods: (1)
(2)
(3) (4)
Three-point bend testing of Charpy specimens gives results which are close to results from fracture toughness testing of CT specimens when 25 #m-radius notches are used and the test rate is kept low. The standard Charpy V-notch gives values of the fracture energy which are two to six times higher than those obtained from the fracture toughness tests. The increase in Glc obtained for PMMA at impact testing can be explained by crack tip blunting at high crack velocities. The reduction of G~c obtained for PC in impact testing is probably caused by an increasing yield stress and a corresponding reduction in size of regions in plane stress.
REFERENCES 1. Plati, E. and Williams, J. G. (1975). Polym. Eng. Sci., 15, 470. 2. Idem. (1975). Polymer 16(12), 915. 3. Williams, J. G. (1984). Fracture Mechanics of Polymers, p. 130. Chichester, Ellis Horwood. 4. Brown, W. F. and Srawley, J. E. (1966). Plane Strain Crack Toughness Testing of High Strength Metallic Materials, ASTM-STP 410, American Society for Testing and Materials. 5. ASTM E399, (1981). Standard Test Methods for Plane-Strain Fracture Toughness of Metallic Materials, American Society for Testing and Materials. 6. Fraser, R. A. W. and Ward, I. M. (1978). Polymer, 19, 220. 7. Ryan, J. T. (1978). Polym. Eng. Sci., 18, 264. 8. Glover, A. P., Johnson, F. A. and Radon, J. C. (1974). Polym. Eng. Sci., 14(6), 420. 9. Williams, J. G. (1977). Polym. Eng. Sci., 17(3), 144. 10. Arends, C. B. (1965). J. Appl. Polym. Sci., 9, 3531. 11. Williams, J. G. and Hodgkinson, J. (1981). Proc. Roy. Soc. London, A375, 231. 12. Clutton, E. Q. and Williams, J. G. (1981) J. Mater. Sci., 16(9), 2583.
Fracture Energy Measurements in Polycarbonate and PMMA R a g n a r Seld6n Swedish Plastics and Rubber Institute, Box 6075, S-850 06 Sundsvall, Sweden (Received 3 November 1986; accepted 17 November 1986)
SUMMARY Fracture energies in polycarbonate and PMMA were measured using different test techniques. Results from instrumented impact tests and slow three-point bend tests on Charpy specimens were compared with tensile test results on Compact Tension (CT) specimens. The Charpy specimens were provided with a blunt Charpy V (0.25ram radius) notch and sharp (251tin radius) notch. It is shown that impact testing of Charpy specimens with blunt notches gives values of the fracture energy which are two to six times higher than those obtained from the CT tensile tests. Only by using a sharp, 251~m notch and performing the three-point bend test at a low rate were similar results obtained.
1 INTRODUCTION The usual procedure for measuring impact strength of plastics uses notched specimens, as in the Charpy and Izod tests. Later developments of these test methods rely on instrumented tests using advanced electronics and computer analysis of the force-time curves. Another improvement is the possibility of obtaining from impact tests fracture mechanics parameters such as the fracture energy or the fracture toughness. According to a theory presented by Williams et al.l'2 the absorbed energy in a Charpy or Izod test can be related to the fracture energy (for brittle failure) according to W = B D ~ G , c + Wk (1) 209 Polymer Testing 0142-9418/87/$03.50 ~ Elsevier Applied Science Publishers Ltd, England, 1987. Printed in Northern Ireland
210
Ragnar Selden
I
80
w,
,oo
i 4
r
i
127
,.- ~
Imml Fig. 1. Test specimens: (a) Compact Tension (CT); (b) Charpy specimen.
where W is absorbed energy, Wk is kinetic energy, B and D are specimen thickness and width, respectively, q~is a calibration factor and G,c is the fracture energy. Valid fracture toughness parameters can be obtained only if sufficiently sharp notches are used. 3 In this work fracture energies were determined in polycarbonate (PC) and PMMA specimens of different thickness using tensile tests on Compact Tension (CT) specimens. The results were compared with results from instrumented impact tests and slow three-point bend tests on Charpy specimens. The Charpy specimens were provided both with a Charpy V (0.25 mm radius) notch and a sharp 25/~m-radius notch, and the results were analyzed according to eqn. (1). It is shown that impact testing of Charpy specimens with blunt notches gives values of the fracture energy which are two to six times higher than those obtained from the CT tensile tests. Only by using a sharp, 25 ~m notch and performing the three-point bend test at a low rate were similar results obtained. 2 EXPERIMENTAL The polycarbonate material, a commercial quality, 'Makrolon 280' from R6hm GmbH, was received as sheets of thicknesses 3, 6, 8, 10 and 17 mm.
Fracture energy measurements in polycarbonate and P M M A
211
The poly(methyl methacrylate) material was received from Bofors Plastics, Tidaholm, Sweden as sheets of thicknesses 2, 3, 5 and 10 mm. The sheets had been compression-moulded and had a glass transition temperature (Tg) of 110 °C and molecular weights Mw = 1.07 x 107 and M, = 5.0 x 106. Square plates, 2 c m x 2 c m , were cut from the PC sheets and immersed in silicone oil for 1 h at 170 °C. Dimensional changes were measured after the heat treatment and were found to be small both lengthwise and crosswise for all sheet thicknesses. The degree of orientation in the PC sheets was thus concluded to be small.
2.1 Fracture toughness testing Compact Tension (CT) specimens for fracture toughness testing were cut from the sheets, having the dimensions shown in Fig. la. Prior to the mechanical testing the specimens were annealed, PC at 135 °C and P M M A at 80°C, for 15h. Thereafter the temperature was slowly lowered ( = 1 0 ° C / h ) to room temperature. A sharp pre-crack was produced by fatigue testing the specimens in a MTS 50 kN closed-loop servohydraulic testing machine at a frequency of 10 Hz. The fatigue testing was interrupted when a fatigue crack had grown from the chevron notch so that the ratio a/w was between 0-4 and 0.6. The CT specimens were equipped with a 'clip-gauge' and tensile tests were performed at deformation rates varying from 0-175 to 175 mm/ min. Load was measured as a function of crack opening displacement (COD). The fracture toughness, Kic, was calculated using the standard formula: 4 glc
~
Pc n_ . _~rl/2 [29-6 ( a / w )
1/2 -- 185"5 ( a / w ) 3r2 +
- 1017 (a/w) v2 + 638.9 (a/w) 9/2]
655.7 ( a / w ) srz (2)
where Pc = critical (failure) load, B = specimen thickness, a = crack length. For the PC specimens the critical load, Pc, was taken both as the maximum load in the l o a d - C O D curve and as the critical load where crack growth initiated. The crack initiation load was determined from the l o a d - C O D curve by drawing a straight line with a slope of 95% of the initial l o a d - C O D curve. The intersection with the loadCOD curve was taken as the crack initiation l o a d ) Crack initiation load and maximum load were identical for specimens having thicknesses greater than or equal to 8 mm. At the maximum COD (2.5 mm) which could be measured, the testing was terminated even if the specimen had not failed.
212
Ragnar Seld6n
For the PMMA specimens only brittle failures were obtained. Tests were performed in two mutually perpendicular directions. Similar results were obtained and therefore results for both directions are presented together.
2.2 Impact and three-point bend testing The specimens used for impact testing and (slow) three-point bend testing are shown in Fig. lb. The dimensions were in accordance with the ASTM-D256 standard for Charpy specimens. Both a blunt Charpy notch having a radius of 0.25 mm and a sharp notch using a sharply honed cutter were used. The cutter gave a notch tip radius of approximately 0.025 mm (25 #m) (which could be seen when observing the notch tip in an optical microscope). The crack length (notch depth) was kept constant at 2.54 mm. Prior to testing the specimens were annealed, PC at 135 °C and PMMA at 80 °C for 15 h. Thereafter the temperature was slowly lowered (=10 °C/h) to room temperature. The impact testing was performed in an instrumented falling-weight impact tester. The instrumentation consisted of a microcomputer, a plotter, an analog-to-digital converter and a time-measuring device. The tup was released from a drop height of 1 m corresponding to an impact velocity of 4.4 m/s. The tup-head geometry and the mounting of the specimens were in accordance with the ASTM-D256 standard. With a piezoelectric crystal mounted in series with the tup, load was recorded during the impact event as a function of time. From the calculated tup velocity the computer calculated the absorbed energy as a function of time. The slow three-point bend testing was performed at a testing rate of 10 mm/min in an MTS testing machine. Here also the ASTM-D256 standard for tup geometry and specimen mounting was followed. Load was measured as a function of deflection. The amount of energy absorbed by the specimens was determined by calculating the area under the load-deflection curves. To ensure brittle failures only specimens having thicknesses greater than or equal to 6 mm were tested for the PC material. 3 RESULTS 3.1 Fracture toughness testing Typical load versus crack-opening displacement curves for PC at 17.5 ram/rain and different specimen thicknesses are shown in Fig. 2.
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Fracture energy measurements in polycarbonate and PMMA tN)
~ND
500
v
F
213
/
5OO
I 1
I 2
1
(ram)
a
b
1 (mm)
(mm) c
1 {mM)
a
(mm)
e
Fig. 2. Load versus crack opening displacement (COD) for PC specimens at 17.5 mm/min cross-head rate and different thicknesses: (a) 3 mm; (b) 6 mm; (c) 8 mm; (d) 10 mm; (e) 17 mm.
At 8, 10 and 1 7 m m thickness almost linear curves were obtained. Failure was brittle and examples of fracture surfaces for the 17 mm thick CT specimens are shown in Fig. 3. It can be seen in Fig. 3 that a small amount of slow crack growth preceded unstable fracture. At a specimen thickness of 6 mm slow crack growth initiates at some critical load. No unstable crack growth is obtained and if the specimen is rapidly unloaded the crack growth will stop. The failure surface shows that ductile tearing preceded crack growth and existence of shear lips 6 was also evident. At 3 mm thickness very little crack propagation was obtained. Extensive shear yielding developed ahead of the fatigue crack. Typical l o a d - C O D curves for P M M A are shown in Fig. 4. Almost linear curves and only brittle failures were obtained. When calculating fracture toughness, eqn. (2) was used. For the PC specimens critical load was taken both as maximum load and as crack initiation load. Results at deformation rates between 17.5 and 175 mm/ min are shown in Fig. 5. Both methods give identical results except for the thinner (3 and 6 mm) specimens. For the 3 mm specimens the ratio between the two values amounts to c a 1.25. This is higher than in the ASTM plane strain fracture toughness standard (E399), which requires that the ratio shall not exceed 1.10. In ASTM E399 the following condition must also be satisfied in order to obtain a valid plane strain
Ragnar Selden
214
Fig. 3. Fracture surfaces for 17mm PC specimens at 17.5 mm/min. Fatigue crack limits are marked with arrows. value of fracture toughness: B > 2"5 (Kic/Oy) z w h e r e K~c = critical plane stress intensity factor and ay = yield stress. Using the K~c value obtained for the thickest 1 7 m m specimens (3.5 MPa~/m) as the plane strain value and taking a y - 60 M P a , 7 one a ( N)100
i iV1\
51)-
I 1
0
I 1
(mm)
Fig. 4. Load versus COD for PMMA CT specimens, thickness (a) 2 mm and (b) 5 mm.
Fracture energy measurements in polycarbonate and PMMA
I
I
!
4.
g IE
215
3
i
Valid
3
6
8
10
17 THICKNESS (rnm)
Fig. 5. Fracture toughness K~c versus thicknessfor PC: O, Kic at initiation; Q, Ksc at maximum load. obtains valid results for B > 8.5 mm. This is indicated in Fig. 5 as 'Valid LEFM'. Using the crack initiation load as critical load one obtains an approximately thickness-independent value of 3.5 MPa~/m. Fracture toughness as a function of deformation rate is shown in Fig. 6 for the 17 mm-thick PC specimens. It can be seen that the fracture toughness slowly decreases as the deformation rate increases. Similar results have been obtained elsewhere. 8
!
I-
I[ ~g
10"!
10o
101
102
CROSS- HEAD RATE(mm/min)
Fig. 6. Kzc versus cross-head rate for 17 mm PC specimens.
Ragnar SeldEn
216
s u N
1
2 THICKNESS (ram)
Fig. 7.
K~c versus thickness for PMMA specimens.
Results for P M M A are presented in Fig. 7 at a deformation rate of 1 mm/min. The fracture toughness is approximately independent of thickness and a value of - 1 . 5 MPa~/m is obtained. The ASTM E399 requirements are met here (taking ay - 80 MPa and Kic = 1.5 MPaX/m) for thicknesses greater than or equal to 0-9 mm. The fracture energy G~c can be calculated from the fracture toughness, Kic, using the relation: 9 Gic ~--- (1 -
v2)r2c/e
(3)
where v is Poisson's ratio and E is the (short-time) value of Young's modulus. This calculation has been performed on the fracture toughness values of PC and P M M A shown in Figs 6 and 7 and the results are given in Table 1. TABLE 1
Fracture Energy Determined from Different Test Methods.
Material
PMMA PC
Glc(kJ / m 2) Impact Charpy
Slow bend Charpy
CT tensile test
Sharp notch
Blunt notch
Sharp notch
Blunt notch
0-62 4-4-6.8
2.8 3.1
3.7 12
0.75 5-7
1.2 14
217
Fracture energy measurements in polycarbonate and PMMA
3.2 Impact and three-point bend testing A typical impact test result for PC having a sharp (25/zm radius) notch is shown in Fig. 8a. Here applied force and absorbed energy are displayed as a function of time. Only one maximum in the force-time diagram is obtained. Figure 8b shows typical results for PC having a blunt (0.25 mm) notch. Here two maxima in the force-time diagram are obtained. This effect is attributed to specimen bouncings,l° against the tup before unstable fracture is obtained. The difference in behavior between sharp and blunt notches is also reflected in the amount of absorbed energy. Less than a three-fold lower energy absorption is obtained with the sharp notches. Figure 9 shows typical results for PMMA specimens with sharp and blunt notches. Only one maximum in the force-time diagrams is obtained in both cases. The absorbed energy is only moderately affected by notch tip radius. According to eqn. (1) the absorbed energy in a notched impact test a
1.6 1.2 "~
a~1.5
.'i¢
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f .8
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O .5
1.
!16
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2.1
2.6
3.2
317
4,'2 4.8 TIME c msJ
3.2
I I
~1.5
_F~ll I
~"
f
E-
2.4 ,., 1.6
,5
° F i g . 8.
Z zz~
.8
.5
1.
!.6
21.1
2.6
12
i,
,',
4.2 ' TIME(ms)
Impact results for 17mm PC specimens:(a) sharp notches; (b) blunt notches. Absorbed energycalculatedup to vertical (broken) line.
Ragnar Selden
218
.4.
.v
.6 %-
v
.3"
.2"
-F
-" .4
Z
.2
.1-
iAi .5
1.
1.6
2.1
2.6
3.2
3.7
4.2
4.8
TIME (ms)
i,
,
.6 %-
la. ,IF
--~1
.4
E i i.u
.1
1 I
0
I .5
1.
,
116
,.
2.1
2.6
.
3.2
',
3.7
,
4.2 4.8 TIME(ms)
1~. 9, Impact results for 5 mm PMMA specimens: (a) sharp notches; and (b) blunt notches.
can be related to the fracture energy, G~c, through the relation: W = BDdpG~c + Wk
Thus, by plotting absorbed energy in an impact test versus BDdp a straight line will result with a slope equal to G~c and an intercept WK. Here the absorbed energy was varied by testing specimens of different thicknesses. Figure 10 shows results from such plots for PC having blunt and sharp notches. In both cases straight lines are obtained which pass through the origin. From the slope of the lines a fracture energy of 12kJ/m z is obtained for the blunt-notched and 3.1 kJ/m 2 for the sharp-notched specimens. Results for PMMA with sharp and blunt notches are shown in Fig. 11. In this case fracture energies of 2.8 and 3.7 kJ/m z, respectively, were obtained. Typical load-displacement records in slow three-point bend testing of blunt-notched PMMA and PC are shown in Fig. 12. From these diagrams the absorbed energy was calculated as the area under the
Fracture energy measurements in polycarbonate and PMMA
219
.-j
Gc: 1 2 k J / m 2 I
I ~
i
i f kJ/m z
I 5
I0
15.10" 5 B.O.O Cmz)
Fig. 10. Absorbed energy in impact versus BD¢ for PC specimens with sharp (O) and blunt (0) notches.
load-deflection curves. The absorbed energy was then plotted against BDdp to obtain Gic in the same way as for the impact tests. Typical results are shown in Fig. 13 for PC specimens with sharp and blunt notches. A similar plot for the P M M A specimens gave the following values of the fracture energy: sharp notches 0.75 k J / m 2 and blunt notches 1.2 k J / m 2.
.5 ¸
.4
.2
.I ~
O
5
10 e.O.tl
15. iO"s (m z ,
Fig. 11. Absorbed energy in impact versus BD¢ for PMMA specimens with sharp (O)
and blunt (0) notches.
220
Ragnar Selden i 500 -
v o u
i
I
i
8
1001
250-
i
i
501
f
0
i
b
10 15 Dis tlacement . r a m ,
5 10 16 Displacement , ram,
i 200 -
A ae
C
201
d
101
100-
5
I
0 10
10
15
Displacement ,mill,
16
D i s p l a c e m e n t , ram.
Fig. 12. Load versus displacement in three-point bending (blunt notches); (a) PC, 6 mm thickness; (b) PC, 17 mm; (c) PMMA, 5 mm; (d) PMMA, 10 mm.
4 DISCUSSION Table 1 shows the results from the fracture energy measurements using different test methods. It can be seen that impact testing of bluntnotched Charpy specimens provides values of the fracture energy which are higher than those obtained from the CT tensile tests. The difference is a factor of six for P M M A and a factor of two for PC. Reducing the test speed in the Charpy test significantly decreases the fracture energy values for PMMA whereas the values for PC slightly increase. However, only by using the sharp (25 #m) notch and performing the
Fracture energy measurements in polycarbonate and P M M A 31
221
I
k
kJ/m z
; ~
I0
Gc" 5.7 kJ n~
1 5 . 1 0 "s
e.o.O (m z)
Fig. 13. Absorbed energy in three-point bending versus BDdp for sharp-(O) and blunt-(O) notched PC.
Charpy test at a low rate, do G~c values for both P M M A and PC become close to the CT results. Impact testing of the sharp-notched P M M A specimens increases the fracture energy to 2 . 8 k J / m 2, compared with 0 . 7 k J / m 2 in the slow three-point bend test. This behavior of P M M A has been noted earlier ~,~2 and was explained by thermal blunting of the crack tip at high crack speeds. However, this effect is not pronounced for the PC material. For the sharp-notched specimens the fracture energy decreases from 5.7 k J / m 2 at low test rate to 3-1 kJ/m 2 at high test rate. Figure 6 also shows that the fracture toughness becomes lower as the test rate is increased. Assuming a distribution of the fracture energy where the surface regions are in plane stress over a thickness corresponding to the plastic zone size (1/2~r)(EGc2/a 2) where Gc2 is the fracture energy of regions in plane stress, E the elastic modulus and ay the yield stress, and assuming that the central regions are in the plane strain one obtains: 2 G~ = G c l +
(EGc2/~rBaZ)(Gc2-- Gcl)
where G~ is measured fracture energy, Gc~ the fracture energy of regions in plane strain and B the specimen thickness. Assuming that ay increases with test rate, a lower value of Gc will be obtained since Gc will become closer to Gc~. 2
222
Ragnar Selden 5 CONCLUSIONS
The following conclusions apply to the fracture energy measurements using different test methods: (1)
(2)
(3) (4)
Three-point bend testing of Charpy specimens gives results which are close to results from fracture toughness testing of CT specimens when 25 #m-radius notches are used and the test rate is kept low. The standard Charpy V-notch gives values of the fracture energy which are two to six times higher than those obtained from the fracture toughness tests. The increase in Glc obtained for PMMA at impact testing can be explained by crack tip blunting at high crack velocities. The reduction of G~c obtained for PC in impact testing is probably caused by an increasing yield stress and a corresponding reduction in size of regions in plane stress.
REFERENCES 1. Plati, E. and Williams, J. G. (1975). Polym. Eng. Sci., 15, 470. 2. Idem. (1975). Polymer 16(12), 915. 3. Williams, J. G. (1984). Fracture Mechanics of Polymers, p. 130. Chichester, Ellis Horwood. 4. Brown, W. F. and Srawley, J. E. (1966). Plane Strain Crack Toughness Testing of High Strength Metallic Materials, ASTM-STP 410, American Society for Testing and Materials. 5. ASTM E399, (1981). Standard Test Methods for Plane-Strain Fracture Toughness of Metallic Materials, American Society for Testing and Materials. 6. Fraser, R. A. W. and Ward, I. M. (1978). Polymer, 19, 220. 7. Ryan, J. T. (1978). Polym. Eng. Sci., 18, 264. 8. Glover, A. P., Johnson, F. A. and Radon, J. C. (1974). Polym. Eng. Sci., 14(6), 420. 9. Williams, J. G. (1977). Polym. Eng. Sci., 17(3), 144. 10. Arends, C. B. (1965). J. Appl. Polym. Sci., 9, 3531. 11. Williams, J. G. and Hodgkinson, J. (1981). Proc. Roy. Soc. London, A375, 231. 12. Clutton, E. Q. and Williams, J. G. (1981) J. Mater. Sci., 16(9), 2583.