Effects of specimen geometry on the measurement of fracture toughness R.E. Kovarik ~ J.W. Ergle 2 C.W. FairhursP
~Assistant Professor Department of Restorative Dentistry 2Research Technician Dental Physical Sciences 3Regents Professor Dental Physical Sciences Medical College of Georgia Augusta, GA 30912-1264 Received May 1, 1990 Accepted May 13, 1991 This investigation was supported in part by the American Fund for Dental Health, Chicago, IL 60611. Dent Mater 7:166-169, July, 1991
Abstract--The objective of this study was to
investigate the use of compact test specimen geometries of reduced size for the measurement of fracture toughness, K~, of dental resin composites. Provisional fracture toughness values were determined for four dental composites by use of a reduced-size compact test specimen. The specimens were volumetrically 8% of the size of compact test specimens used in previous studies on dental composites. The test results and conditions met validity tests. These results were compared with those from previous studies that used large compact test specimens. It is concluded that the reduced-size compact test specimen is an acceptable alternative for measurement of fracture toughness.
racture toughness is an intrinsic property of a materia! and is the measure of a material s resistance to crack propagation. The measuremerit of fracture toughness requires a knowledge of specimen geometry and a pre-existing crack within the material. Several different test methods can be used to measure the fracture toughness of a material. For each test, the internal stress field at the tip ofthe crack must be determined. This is dependent on the geometry of the specimen as well as the geometry of the crack. The calculation of internal stress at the crack tip under a given applied load is the stress intensification factor, K. The stress intensity at which crack instability occurs is designated Kc. This critical stress• intensity, K, varies depending on the triaxial stress-strain conditions. Under plane strain conditions, crack instability occurs at a minimum K and is designated the fracture toughness, K~c. Several different specimen geometries have been used to measure fracture toughness of dental materials. Lloyd and Iannetta (1982), Lloyd(1983), Lloyd and Mitchell (1984), and Lloyd and Adamson (1987) have used a singleedge notched specimen (3 mmx 6 mmx 34 ram) with a geometry conforming to the British standard B5.5447. A precrack was placed in the specimen by means of a straight-edged scalpel blade inserted into the composite before polymerization. De Groot et al. (1988) also used a single-edge notch specimen, forming their pre-crack with a 0.15-mm diamond disk. Goldman (1985) used a double torsion specimen (10 mm x 30 mmx 2 ram) conformingto the technique described by Murray (1977). The precrack was placed by means of an Isomet 11-1180 low-speed saw with a Buehler 0.012" diamond wafer blade. Pilliar et al. (1986) utilized a shortrod fracture toughness specimen design (12 mmx 6 mm diameter) and later were able to reduce the specimen size with a mini-short-rod specimen (7 mmx 4 mm diameter) (Pilliar et al., 1987a,b). A molded notch in these samples was sharpened with a razor blade to expedite
F
166 Kovarik et al. / Effects o f geometry on fracture toughness
crack initiation. This method differs from other methods utilized in that stable crack growth occurs initially, and then fracture toughness is based on the measurement of the load to cause crack instability. Gegauff and Pryor (1987) and Sands et al. (1987, 1988) have both utilized a compact test specimen geometry (14.4 mm x 15 m m x 4.0 ram) conforming to ASTM specification E399-83 (1984). Both used a Bard Parker blade under hand pressure to place the pre-crack in the specimen. E1 Mowafy and Watts (1986) used a compact test specimen geometry of reduced size (4.6 mmx 4.5 m m x 1.6 ram) to measure fracture toughness of human dentin. The specimen size was necessarily constrained by the availability of dentin from an extracted human tooth. The implications and potential errors in reducing the specimen size, some of which did not conform to the standard, were not discussed. A dimensional comparison of the various specimen geometries used for measurement of fracture toughness of dental materials is given in Table 1. Common to all these studies is the need for curing a large bulk of composite up to 4 mm thick. This may lead to difficulties in achieving adequate, uniform cure, and may lead to an artificial temperature increase associated with the curing of a large bulk of composite (Masutani et al., 1988). It is desirable for one to be able to determine fracture toughness on specimen sizes which approximate the sizes of dental restorations, thereby having a specimen which is fabricated close to the actual clinical fabrication technique. The purpose of this study, then, was to determine whether compact test specimen geometries of reduced size resulted in valid fracture toughness measurements.
METHODS The specimen configuration and test fixture design are taken from ASTM Standard E399-83 (1984) for a compact test specimen. The specimen configuration is a rectangular, single-edged
-(
=
"~
:T . 0.4 3 "3
l.
.
.
.
.
6.3
-~
.
. .55W
-!--! . . . . '
....
,
~P"1.7[.~1=
5.5 ZW]
.
.
.
.
.
.
l
1.2W
.
,,,
~',I
Iwl
-'4I ',
Fig. 1. Compact test specimen geometry. (a) Specimen dimensions used for this investigation. (b) General specimen dimensions forcompact test specimens.
notched type with dimensions 6.3 mmx 6.6 mm x 1.7 mm (Fig. la). These dimensions are near the limit of the smallest potential dimensions which would still conform to the ASTM Standard. For determination of the validity of using the reduced-size compact test specimen, four materials of various filler concentrations were chosen; these had been previously studied by Sands et al. (1988), and are listed in Table 2. Twenty samples of Occlusin (Coe Laboratories, Inc., Chicago, IL) and ten samples of each additional material were fabricated. The composite materials were injected into a chrome-cobalt mold. A clear plastic film and a piece of metal were placed on the top surface of the mold. This assembly was placed in a hydraulic hand press and compressed under 1500 psi for 30 s so that the material could flow completely into the mold. The metal plate was removed, and the material was cured through the plastic film under a curing light with a 6ram-diameter tip. The specimens were cured 1/4 at a time for 20 s, then released from the mold and cured over the center of the specimen for an additional 20 s. The rectangular specimen (6.3 mm x 6.6 mm) was then lightly planed on abrasive paper for removal of any irregularities from the mold. A #4 round bur in a drill press with a micrometer stage was used to prepare holes so that the specimen could be gripped in the Universal Testing Machine (Instron Model TTB, Instron Corp., Canton, MA), and a notch was cut into the specimen by means ofa 0.3-mm
separating disk. For each specimen, a pre-crack was placed at the end of the notch by use of a razor blade with hand pressure. This method is consistent with the type of pre-crack used by Sands et al. (1987, 1988), with which the results of this study are compared. This method of pre-cracking is also consistent with that used by Gegauff and Pryor (1987) and Ferracane et al. (1987). Measurements
of the dimensional parameters a, W, and B for each specimen (Fig. lb) were then recorded with use of a measuring microscope. The specimens were then tested in tension in theUniversal Testing Machine, with the direction of the force perpendicular to the plane of the preformed notch in the specimen. All specimens conformed to the geometric, material, and test constraints in the ASTM Standard (Table 3).
TABLE 1 DIMENSIONALCOMPARISONSOF SPECIMENGEOMETRIESUSED FOR MEASURINGFRACTURETOUGHNESS Volume(mm3)
Type of Specimen
Dimensions(mm)
Single-edge notch
3 x 6 x 34
612
Lloyd eta/. (1987)
Doubletorsion
30 x 10 x 2
600
Goldman (1985)
Short rod
12 x 6 diameter
339
Pilliar etal. (1986)
Mini short rod
7 x 4 diameter
88
Pilliar et al. (1987a)
Compact test
14 x 15 x 4
Mini compacttest
6.3 x 6.6 x 1,7
840 71
Reference
Gegauff etal. (1987), Sands etal. (1988) Used in this study
TABLE 2 MATERIALS USED
Material
Code
Batch No.
Manufacturer
Occlusin
OC
AO 60B
Coe Labs., Inc., IL
Visiomolar
Vl
0005
ESPE Premier, PA
Adaptic II
AD
5K5207
Johnson & Johnson, NJ
Distalite
DI
344501
Johnson & Johnson, NJ
Dental Materials~July 1991 167
2.5
Large s p e c i m e n Mini
specimen
2.0
I--I l
1.0
I--J I
.5
Occlusin
Visiomolar
Adaptic
II
Distalite
Material Fig. 2. Bar graph comparingfracturetoughnessmeasuredwith use of a largecompacttest specimenwithfracture toughnessmeasuredwithuse of a reduced-sizecompacttest specimen. Bothgroupswere pre-crackedby means of a Bard Parker blade underhandpressure.
The specimens were tested in mode I (tension) by means of the Universal Testing Machine. Provisional fracture toughness values, K_, were calculated ~t from the fracture toughness equation for compact test specimen:
KQ = (P~W'2); t~a/W) where: Pc = maximum load prior to catastrophic crack advance (KN), B = average specimen thickness (cm), W = average specimen width (cm), and a = crack length (cm).
f(a/W) = (2+a/W)(0.866+4.64a/W- 13.32a2/ W2+14.72a3/W3- 5.6a4/W4) (1- a/W)3/2
RESULTS
All specimens fractured in a straight line from the pre-formed notch to the base (+ 5°), and the fracture surfaces were flat. The provisional fracture toughness values, KQ,for all the materials met the validity tests given in the ASTM Standard for the reduced-size compact test specimen (Table 4). Therefore, the provisional Ko values are accepted as true fracture toughness, KIc. The mean fracture toughness values and standard deviations, ~c -+ SD, for the geometric comparison are shown in Fig. 2. Unpaired t tests comparing each material showed no significant differences in the mean fracture toughness when large compact test specimen geometries were compared with the reduced-size specimen at a confidence level of 0.99. A power function curve for the test showed that the probability for find-
ing a difference in the true mean of 0.15 MN*mI.5 is 0.93 for n = 10 and SD = 0.15. DISCUSSION
The validity of reducing specimen size is not obvious. In order for true fracture toughness to be measured, plane strain conditions must exist at the crack tip. Under plane strain conditions, the stress intensity levels for crack instability are lower than those for other tri-axial stressstrain conditions. In order for this requirement of plane strain to be satisfied, at least on a theoretical basis, the specimen would have to be infinitely thick. However, if the plastic zone ahead of the crack tip is very small compared with the thickness of the crack front, then the effects of having finite thickness are negligible, and plane strain conditions are essentially met. Thus, the problem with reducing specimen size is associated with reducing the thickness of the specimen. Infinitely thick specimens adhere to plane strain conditions, while infinitely thin specimens adhere to plane stress conditions. The ASTM Standard for the compact test specimen geometry permits the thickness, B, to be a minimum of 1.6 mm; however, a safety factor of 2 is usually applied. The concern, then, is whether plane strain conditions are met for the reduced-size specimens. This cannot be assumed, since the mean thickness used in the study (1.7 mm) borders on the limits of the standard. Also, there is some uncertainty involved in the testing of a polymeric material as opposed to a metallic material for which the standard was written. The results of this study support the conclusion that plane strain conditions are satisfied. The appearance of the fracture surface is one indicator of the tri-axial stress-strain conditions. The planar or flat fracture surface exhibited by the specimens is characteristic of plane strain conditions. Furthermore, under plane stress conditions or any
TABLE 3
TABLE 4
CONSTRAINTS
TESTS FOR VALIDITY
Geometric
Material/Test
W/4 < B < W/2
oy,/E = 0.01
g _>2.5(KJ~y,)2
0.55 MPa*m°%
~Assistant Professor Department of Restorative Dentistry 2Research Technician Dental Physical Sciences 3Regents Professor Dental Physical Sciences Medical College of Georgia Augusta, GA 30912-1264 Received May 1, 1990 Accepted May 13, 1991 This investigation was supported in part by the American Fund for Dental Health, Chicago, IL 60611. Dent Mater 7:166-169, July, 1991
Abstract--The objective of this study was to
investigate the use of compact test specimen geometries of reduced size for the measurement of fracture toughness, K~, of dental resin composites. Provisional fracture toughness values were determined for four dental composites by use of a reduced-size compact test specimen. The specimens were volumetrically 8% of the size of compact test specimens used in previous studies on dental composites. The test results and conditions met validity tests. These results were compared with those from previous studies that used large compact test specimens. It is concluded that the reduced-size compact test specimen is an acceptable alternative for measurement of fracture toughness.
racture toughness is an intrinsic property of a materia! and is the measure of a material s resistance to crack propagation. The measuremerit of fracture toughness requires a knowledge of specimen geometry and a pre-existing crack within the material. Several different test methods can be used to measure the fracture toughness of a material. For each test, the internal stress field at the tip ofthe crack must be determined. This is dependent on the geometry of the specimen as well as the geometry of the crack. The calculation of internal stress at the crack tip under a given applied load is the stress intensification factor, K. The stress intensity at which crack instability occurs is designated Kc. This critical stress• intensity, K, varies depending on the triaxial stress-strain conditions. Under plane strain conditions, crack instability occurs at a minimum K and is designated the fracture toughness, K~c. Several different specimen geometries have been used to measure fracture toughness of dental materials. Lloyd and Iannetta (1982), Lloyd(1983), Lloyd and Mitchell (1984), and Lloyd and Adamson (1987) have used a singleedge notched specimen (3 mmx 6 mmx 34 ram) with a geometry conforming to the British standard B5.5447. A precrack was placed in the specimen by means of a straight-edged scalpel blade inserted into the composite before polymerization. De Groot et al. (1988) also used a single-edge notch specimen, forming their pre-crack with a 0.15-mm diamond disk. Goldman (1985) used a double torsion specimen (10 mm x 30 mmx 2 ram) conformingto the technique described by Murray (1977). The precrack was placed by means of an Isomet 11-1180 low-speed saw with a Buehler 0.012" diamond wafer blade. Pilliar et al. (1986) utilized a shortrod fracture toughness specimen design (12 mmx 6 mm diameter) and later were able to reduce the specimen size with a mini-short-rod specimen (7 mmx 4 mm diameter) (Pilliar et al., 1987a,b). A molded notch in these samples was sharpened with a razor blade to expedite
F
166 Kovarik et al. / Effects o f geometry on fracture toughness
crack initiation. This method differs from other methods utilized in that stable crack growth occurs initially, and then fracture toughness is based on the measurement of the load to cause crack instability. Gegauff and Pryor (1987) and Sands et al. (1987, 1988) have both utilized a compact test specimen geometry (14.4 mm x 15 m m x 4.0 ram) conforming to ASTM specification E399-83 (1984). Both used a Bard Parker blade under hand pressure to place the pre-crack in the specimen. E1 Mowafy and Watts (1986) used a compact test specimen geometry of reduced size (4.6 mmx 4.5 m m x 1.6 ram) to measure fracture toughness of human dentin. The specimen size was necessarily constrained by the availability of dentin from an extracted human tooth. The implications and potential errors in reducing the specimen size, some of which did not conform to the standard, were not discussed. A dimensional comparison of the various specimen geometries used for measurement of fracture toughness of dental materials is given in Table 1. Common to all these studies is the need for curing a large bulk of composite up to 4 mm thick. This may lead to difficulties in achieving adequate, uniform cure, and may lead to an artificial temperature increase associated with the curing of a large bulk of composite (Masutani et al., 1988). It is desirable for one to be able to determine fracture toughness on specimen sizes which approximate the sizes of dental restorations, thereby having a specimen which is fabricated close to the actual clinical fabrication technique. The purpose of this study, then, was to determine whether compact test specimen geometries of reduced size resulted in valid fracture toughness measurements.
METHODS The specimen configuration and test fixture design are taken from ASTM Standard E399-83 (1984) for a compact test specimen. The specimen configuration is a rectangular, single-edged
-(
=
"~
:T . 0.4 3 "3
l.
.
.
.
.
6.3
-~
.
. .55W
-!--! . . . . '
....
,
~P"1.7[.~1=
5.5 ZW]
.
.
.
.
.
.
l
1.2W
.
,,,
~',I
Iwl
-'4I ',
Fig. 1. Compact test specimen geometry. (a) Specimen dimensions used for this investigation. (b) General specimen dimensions forcompact test specimens.
notched type with dimensions 6.3 mmx 6.6 mm x 1.7 mm (Fig. la). These dimensions are near the limit of the smallest potential dimensions which would still conform to the ASTM Standard. For determination of the validity of using the reduced-size compact test specimen, four materials of various filler concentrations were chosen; these had been previously studied by Sands et al. (1988), and are listed in Table 2. Twenty samples of Occlusin (Coe Laboratories, Inc., Chicago, IL) and ten samples of each additional material were fabricated. The composite materials were injected into a chrome-cobalt mold. A clear plastic film and a piece of metal were placed on the top surface of the mold. This assembly was placed in a hydraulic hand press and compressed under 1500 psi for 30 s so that the material could flow completely into the mold. The metal plate was removed, and the material was cured through the plastic film under a curing light with a 6ram-diameter tip. The specimens were cured 1/4 at a time for 20 s, then released from the mold and cured over the center of the specimen for an additional 20 s. The rectangular specimen (6.3 mm x 6.6 mm) was then lightly planed on abrasive paper for removal of any irregularities from the mold. A #4 round bur in a drill press with a micrometer stage was used to prepare holes so that the specimen could be gripped in the Universal Testing Machine (Instron Model TTB, Instron Corp., Canton, MA), and a notch was cut into the specimen by means ofa 0.3-mm
separating disk. For each specimen, a pre-crack was placed at the end of the notch by use of a razor blade with hand pressure. This method is consistent with the type of pre-crack used by Sands et al. (1987, 1988), with which the results of this study are compared. This method of pre-cracking is also consistent with that used by Gegauff and Pryor (1987) and Ferracane et al. (1987). Measurements
of the dimensional parameters a, W, and B for each specimen (Fig. lb) were then recorded with use of a measuring microscope. The specimens were then tested in tension in theUniversal Testing Machine, with the direction of the force perpendicular to the plane of the preformed notch in the specimen. All specimens conformed to the geometric, material, and test constraints in the ASTM Standard (Table 3).
TABLE 1 DIMENSIONALCOMPARISONSOF SPECIMENGEOMETRIESUSED FOR MEASURINGFRACTURETOUGHNESS Volume(mm3)
Type of Specimen
Dimensions(mm)
Single-edge notch
3 x 6 x 34
612
Lloyd eta/. (1987)
Doubletorsion
30 x 10 x 2
600
Goldman (1985)
Short rod
12 x 6 diameter
339
Pilliar etal. (1986)
Mini short rod
7 x 4 diameter
88
Pilliar et al. (1987a)
Compact test
14 x 15 x 4
Mini compacttest
6.3 x 6.6 x 1,7
840 71
Reference
Gegauff etal. (1987), Sands etal. (1988) Used in this study
TABLE 2 MATERIALS USED
Material
Code
Batch No.
Manufacturer
Occlusin
OC
AO 60B
Coe Labs., Inc., IL
Visiomolar
Vl
0005
ESPE Premier, PA
Adaptic II
AD
5K5207
Johnson & Johnson, NJ
Distalite
DI
344501
Johnson & Johnson, NJ
Dental Materials~July 1991 167
2.5
Large s p e c i m e n Mini
specimen
2.0
I--I l
1.0
I--J I
.5
Occlusin
Visiomolar
Adaptic
II
Distalite
Material Fig. 2. Bar graph comparingfracturetoughnessmeasuredwith use of a largecompacttest specimenwithfracture toughnessmeasuredwithuse of a reduced-sizecompacttest specimen. Bothgroupswere pre-crackedby means of a Bard Parker blade underhandpressure.
The specimens were tested in mode I (tension) by means of the Universal Testing Machine. Provisional fracture toughness values, K_, were calculated ~t from the fracture toughness equation for compact test specimen:
KQ = (P~W'2); t~a/W) where: Pc = maximum load prior to catastrophic crack advance (KN), B = average specimen thickness (cm), W = average specimen width (cm), and a = crack length (cm).
f(a/W) = (2+a/W)(0.866+4.64a/W- 13.32a2/ W2+14.72a3/W3- 5.6a4/W4) (1- a/W)3/2
RESULTS
All specimens fractured in a straight line from the pre-formed notch to the base (+ 5°), and the fracture surfaces were flat. The provisional fracture toughness values, KQ,for all the materials met the validity tests given in the ASTM Standard for the reduced-size compact test specimen (Table 4). Therefore, the provisional Ko values are accepted as true fracture toughness, KIc. The mean fracture toughness values and standard deviations, ~c -+ SD, for the geometric comparison are shown in Fig. 2. Unpaired t tests comparing each material showed no significant differences in the mean fracture toughness when large compact test specimen geometries were compared with the reduced-size specimen at a confidence level of 0.99. A power function curve for the test showed that the probability for find-
ing a difference in the true mean of 0.15 MN*mI.5 is 0.93 for n = 10 and SD = 0.15. DISCUSSION
The validity of reducing specimen size is not obvious. In order for true fracture toughness to be measured, plane strain conditions must exist at the crack tip. Under plane strain conditions, the stress intensity levels for crack instability are lower than those for other tri-axial stressstrain conditions. In order for this requirement of plane strain to be satisfied, at least on a theoretical basis, the specimen would have to be infinitely thick. However, if the plastic zone ahead of the crack tip is very small compared with the thickness of the crack front, then the effects of having finite thickness are negligible, and plane strain conditions are essentially met. Thus, the problem with reducing specimen size is associated with reducing the thickness of the specimen. Infinitely thick specimens adhere to plane strain conditions, while infinitely thin specimens adhere to plane stress conditions. The ASTM Standard for the compact test specimen geometry permits the thickness, B, to be a minimum of 1.6 mm; however, a safety factor of 2 is usually applied. The concern, then, is whether plane strain conditions are met for the reduced-size specimens. This cannot be assumed, since the mean thickness used in the study (1.7 mm) borders on the limits of the standard. Also, there is some uncertainty involved in the testing of a polymeric material as opposed to a metallic material for which the standard was written. The results of this study support the conclusion that plane strain conditions are satisfied. The appearance of the fracture surface is one indicator of the tri-axial stress-strain conditions. The planar or flat fracture surface exhibited by the specimens is characteristic of plane strain conditions. Furthermore, under plane stress conditions or any
TABLE 3
TABLE 4
CONSTRAINTS
TESTS FOR VALIDITY
Geometric
Material/Test
W/4 < B < W/2
oy,/E = 0.01
g _>2.5(KJ~y,)2
0.55 MPa*m°%
