- Email: [email protected]
Fracture of human femoral bone
c
FRACTURE OF HUMAN FEMORAL D. D. MOYLE Department
of Interdtsciplinary
and
R. W.
W?I -9290 a4 I3 a, l 00 1984 Pcrpnmon Press Ltd.
BONE
BOWDEN
Studies. Clemson University.
Clemson, SC 29631. U.S.A.
Abstract-The work-of-fracture of human femoral bone was determined usin! the techntque of Tattersal and Tappin (1966). The work required to fracture a specimen in three pomt bending by slow crack propagation through a triangular cross-section is obtained from the loaddeflection curve. The area of the resulting fracture surface is measured by macrophotographic techniques, and the work-of-fracture is calculated as work per unit area. The work-of-fracture values measured in this way ranged from 3.S to I I3 ( x IO’) J me2 m the samples tested with a mean of 7.8 x IO’J m-2 and a standard deviation of 2.1 x IO-’ J me’. The work-of-fracture was found to be independent ofthe degree ofmineralization within the range of 6&80 weight “,,, and to not vary with transverse variation in location in the femoral shaft. The workof-fracture was also seen to increase with increasing osteon fractional area. Scanning electron microscope photographs of the fracture surfaces indicate that the nature of the failure is similar to that of tiber reinforced composite materials.
ISTRODL’CTIOS of the mechanical properties of bone are important for many reasons. In the orthopedic sciences. they are particularly important for three reasons. First. knowledge of these properties can help predict how bones can be expected to behave in the body, for example, the loads they can and cannot bear or the amount of energy they will absorb before fracturing. Secondly. a thorough knowledge of the mechanical properties of bone will explain the behavior of bone as a material, thereby yielding an understanding of why a particular construction of bone gives it the properties it has. Finally, if other materials are to be substituted for bone, their mechanical properties must be compatible with those of bone to ensure a viable system. This dictates that the mechanical properties of bone be known. This paper is concerned with the determination of the work-of-fracture of human femoral bone and an examination of fracture mechanisms. The work-offracture, or the resistance of a material to fracture, is often described in terms of energy to fracture. The true energy of fracture is not measured in conventional tensile or impact tests and the basic technique used in this study was developed by Tattersal and Tappin (1966) and was applied by them to various materials. Their technique was first applied to tissue by Piekarski (1970) in his investigation of the fracture of bovine bone. and subsequently by Moyle et al. (1978) in a study of the fracture of canine femoral bone. Briefly, the technique involves the controlled propagation of a crack through three point bending of the test specimen (Fig. I). The triangular geometry of the Studies
Rt’crirrd 27 Drcrmhrr
1981: in rrriwdjorm 15 Auytrs~ 1983. *Current address: Becton-Dickenson &Co., 21 Just Road. Fairheld. NJ 07006. U.S.A.
Fig. 1. Test specimen geometry and load configuration.
test area of the specimen and a controlled deformation rate determine the rate of crack propagation. Because of the shape of the test area, the load required for crack initiation is small and no energy is lost to plastic deformation elsewhere in the sample. Because crack propagation is controlled (Fig. 2) and the applied load is gradually reduced to zero no energy is lost to vibration or flying specimen pieces and no energy remains stored in the testing machine. The area under the load-deflection curve represents work which has gone entirely into the creation of fracture surface and to effects which are inextricably connected with crack propagation. The work-of-fracture was calculated as the work measured from the load-deflection curve divided by the nominal area of one of the fracture surfaces (obtained by macrophotography). It is important to note that twice the measured area, sometimes used in
203
D. D.
MOYLE
and
R. W. BOWDEN
03
DEFLECTION Fig. 2. Typical load-deflection
1.0 (mm)
curve as obtained directly from
X-Y
recorder showing controlled nature of
crack propagation.
was not used in this study or in any of the other studies of this type performed in this laboratory. The work-of-fracture measured as described above cannot be related to the quantities normally measured in linear elastic fracture mechanics, namely the critical stress intensity factor, K,, and the critical strain energy release rate, G,. The applicability of linear elastic fracture mechanics to bone has been recently reviewed by Bonfield (1981) and all experimental studies have been on bovine bone. The reason for this restriction to bovine bone is that valid test results cannot be obtained with specimens which are small. Specimen thickness and crack length shoutd exceed 2.5 (&/a,,) where CT,,% is the yield strength of the material. For bovine bone this gives a minimum specimen thickness on the order of 3-4 mm. Given other restrictions on the overall specimen size it is not possible to produce specimens suitable for K, determination using bones from animals smaller than the cow. Wright and Hayes (1977) have indicated that some relaxation of the thickness restriction may be possible but this is still unsettled. fracture mechanics studies,
EXPERIMENTAL
PROCEDURE
Samples of bone were obtained from the diaphysis of the femur during autopsy (with informed consent)at the Veterans Administration Medical Center, Augusta, GA. A short medical history was supplied with each bone specimen. After removal from the cadaver the cylinders of bone were wrapped in saline soaked towelling and frozen using the method of Sedlin and Hirsch (1966). Specimens were tested within one to three weeks of the date of freezing. No specimens were tested immediately upon removal from the cadaver.
The origin of each test specimen taken from the cylinder of bone was designated with a letter and number code (Fig. 3). The first number indicates the bone cylinder from which it was obtained, The letter, M or L, indicates the medial or lateral side of the bone. The second number designates a vector area as defined by dividing each medial or lateral half into three specimens, with the number one defining an anterior specimen, the number three a posterior specimen, and the number two an intermediate specimen. For example, 2Ll designates a specimen taken from the lateralanterior area of the second bone cylinder. Bone cylinders I and 2 were obtained from a 70yr old white male who died of cancer. He was 180cm tall and weighed 84 kg. Bone cylinder 3 was obtained from a 56yr old white male who was 180cm tall, weighed 77 kg and died of heart disease. There was no history of connective tissue disease in either case. In preparation for testing a wrapped cylinder of bone was removed from the freezer and the frozen towels were thawed and removed under running tap water. The periosteum was removed, along with any remaining tissue. The cylinder was then cut into six test specimens as given by the vector designation. A diamond saw irrigated with physiological saline was used for cutting the samples. Each test specimen was placed in a container marked with the sample designation and filled with physiological saline. The samples were then ground flat so that they would fit into a jig for cutting notches and so that they would not fall over white being tested. The samples were irrigated in tap water during grinding, and then returned to the containers of saline after grinding. The grinding time never exceeded one minute. Each specimen was required to have a test area of triangular cross-section. With the use of a special jig
Fracturr of human femoral bone RIGHT
FEMUR,
ANTERIOR
VIEW
MEDIAL
CArERAL
POSTERIOR
RIGHT
FEMIJR.
TRANSVFRSE
SECTl!,rl
Fig. 3. Origin and designation of test specimens
and a diamond saw. notches in a triangular shape were cut in the center of each test specimen (Fig. 1). A blade thickness of I mm was used to cut the notches, and the specimens were irrigated in physiological saline during the cutting of the test areas. A sample ready for testing was typically 4Scm in length, about 7mm in height and about 6mm thick. The specimens’ triangular cross-sectional areas varied from 5.4 to 12.8 mm’.
The mechanical testing was performed on an lnstron closed loop hydraulic testing machine with a 4500 Newton load cell. Stroke control mode was used with loading via a ramp function yielding a deflection rateof4.2 x IO-‘ems‘. Thedata was obtained in the form of a loaddeflection curve on an X - Yrecorder. The specimens were never allowed to dry at any time during preparation and testing. The total time between removal of the bone cylinders from the freezer and the testing of the specimens averaged three hours and never exceeded four hours. Following testing, the fracture surfaces of some specimens were held together by threads of bone material when the load reached zero. Nevertheless, those specimens were deemed to be completely fractured and unable to absorb any more energy. One fracture surface from each sample was embedded in a quick setting acrylic mounting medium and then ground and polished for viewing under a reflected light microscope. Standard methods of quantitative microscopy were used to determine osteon ‘density’ (number of osteonsjunit area), average osteon diameter. fractional area of osteons, average void diameter and fractional area ofvoids. The interstitial bone fractional area was calculated for each sample by summing the void and osteon fractional areas and subtracting this value from 1.0. The amount of inorganic mineral content, mostly hydroxypapatite, was measured by weighing a small oven-dried section of each bone specimen before and after decalcification in
a commercially available solution Products, Evanston, IL).
(DscalB,
Scientilic
RESULTS
The results from the mechanical testing. light mlcroscopy and weight percentage mineralization determination for all specimens which failed by controlled crack propagation are presented in Tables 1 and 2. The work-of-fracture mean and standard deviation for all specimens is 7.3 &-2.1 x lO’Jm_*, and the range of values is 3.8-l 1.8 x IO3 J m-‘. These data represent samples obtained from two cadavers. Seventeen specimens were tested, fifteen failed by controlled crack propagation, two catastrophically and one was broken during handling. The data presented in Table 1is for samples from the medial aspect of the femur and that in Table 2 is for samples from the lateral aspect. A comparison of the data obtained for the medial and lateral samples showed no significant difference in work-of-fracture between these two groups. Also, no significant difference was found in the osteon and void parameters, or weight percent mineralization between the medial and lateral aspects of the femur. The mean and standard deviation of the work-of-fracture for the medial samples was 8.5 + 2.0 x lo3 and 7.2 +2.l x IO’Jm- * for the lateral samples. A further breakdown of the data into each vector designation is also shown in Tables 1and 2. No regional variations in any of the measured parameters were found. Since the osteon is the fundamental structural feature of compact human bone, the work-of-fracture was compared with measured osteon parameters. A comparison ot the work-of-fracture against the osteon fractional area data shows a weak positive correlation (r2 = 0.31). Comparison of the work-of-fracture with osteon diameter (Fig. 4) shows a drop in the work-of-fracture at intermediate osteon diameters. No correlation (r* = 0.015) was found by comparing the work-offracture and the osteon density data.
0.742 0.416 0.528
9.9 9.1 8.0
6.7 6.6 5.1
IL2 3L2 2L2
3L3 2L3 5L3
0.496 0.528 0.462
0.544 0.464
Fractional (Osteons)
8.6 3.8
Work-of-fracture (IO’Jm-I)
2Ll 1Ll
Sample
0.120 0.088 0.176
0.224 0.128 0.144 0.056
arca (Voids)
150 209 173
215 201 195 160 285 76 239
101 152 86 59
Avcragc diameter (Irm) (Voids) (Osteons)
60.52 70.83 75.90
19.54 58.64 65.30 65.74
Weigh1 pcrccnt mincralizllion
0.112 0.072 0.162
o.oxx 0.144 0.112
0.144 0.096
area (Voids)
196 167 IX3
214 165 193
167 176
82 57 154
93 91 76
98 65
Average diameter (jrm) (Voids) (Osteons)
75.36 69.57 76.30
71.65 72.09 64.42
12.15 15.15
Weight percent minerah~~tion
and
19.2 25.4 16.6
22.4 20.8 22.4
20.8 22.8
Osteon density (No. mm- ‘)
and osteon
25.4 15.0 11.4
23.8 24.4
I X.8
18.8
Ostcou density (No.mnC ‘) _-
weight percent mineralization
osteon and void fractional areas, osteon and void average diameters, weight percent mineralization density for the lateral samples tested
0.536 0.616 0.403
8.6 8.4 5.1
2M3 IM3 3M3
Table 2. Work-of-fracture,
0.656 0.424 0.576 0.504
It.8 9.8 8.3 1.7
IMI 2M2 lM2 3M2
Fractional (Ostcons)
osteon and void fractional areas, osteon and void average diameters, osteon density for the medial samples tested
Work-of-fracture (lO’Jm_‘)
1. Work-of-fracture,
Sample
Table
Fracture
of human femoral bone
1
150
I60
170 AVERAGE
160
I90
OSTEON
DIAMETER
200
210
220
(pm)
Fig. 4. A plot of work-of-fracture vs average osteon diameter
To determine the combined elTect of resorption spaces and Haversian canal areas, the work-of-fracture was compared with the void fractional area and average void diameter. No correlations were found. A comparison of the work-of-fracture with the weight percent mineralization data also exhibits no correlation between these parameters. A scanning electron microscope was used to examine and photograph the fracture surfaces. A typical fracture surface of a specimen which failed by controlled crack growth is shown in Fig. 5. The appearance of the fracture surface is very irregular. The rough texture indicates the crack did not propagate perpendicularly through all the bone constituents, resulting in valleys and ridges. Complete pull-out of osteons, partial pull-out of osteons and torn osteon fragments are easily discernable. This type of crack propagation maximizes the surface area and allows for maximum energy absorption. No areas of rapid crack growth are contained in this fracture area. A brittle mode of fracture in a specimen which failed by uncontrolled crack growth is illustrated in the fracture surface photography of Fig. 6. The surface is generally rippled in appearance, the valleys and ridges of the samples which failed by controlled crack growth are not evident. There is no evidence of osteon pullout. In this case the crack has moved indiscriminately through all the microconstituents, thereby yielding low energy absorption. A closer examination of a fracture surface from a specimen which failed by controlled crack propagation is seen in Fig. 7. Various degrees of osteonal fracture can be noted. Complete osteon pull-out is evident, though not the dominant mode of fracture. It can be seen that the crack is diverted along the lamellar bone of the osteons resulting in a step-like appearance. This preference for thecrack to follow the interface between
the osteon and interstitial lamellae indicates the prrsence of a relatively weak bond. A higher magnification of a fracture surface is shown in Fig. 8. An osteon which has pulled-out can be seen in the left portion of the photo. The concentric circumferential osteon lamellae and Haversian canal are easily seen. The step-like fracture of the surrounding interstitial lamellae is also evident. Of the seventeen specimens mechanically tested, two failed by uncontrolled crack propagation. These were not included in the results because the rapid crack growth does not allow the energy absorbing mechanisms of bone to function. Since it is not readily possible to quantify how much energy is dissipated by postfracture processes, it is not possible to determine what part of the work put into the system has been consumed by the fracture process, and therefore, the fracture energy. The specimens that failed by uncontrolled crack growth were analyzed by the same methods used for the samples which failed by controlled crack growth. The data for the osteon, void and mineralization parameters appears in Table 3. A comparison with the values for specimens which failed by controlled crack propagation reveals no significant differences.
DISCUSSIOS
A comparison of the work-of-fracture data from this study with data for canine bone from an earlier study (Moyle et al., 1978) in this laboratory has been made. A comparison of the means and standard deviations for some of the relevant data is given in Table 4. Statistical analysis of the data from this study and the canine bone study referred to reveals a significant difference in the work-of-fracture (0.02 < p < 0.05).Extending the
708
D. D.
MOYLE
and R.
comparison to the osteon parameters indicates significant differences (p < O.CQl) between all the human and canine values presented in Table 4 except osteon density. There was no significant difference in the work-offracture between the medial and lateral samples in this stud>. This is in contrast to the results of the canine stud?. which showed the lateral samples to have a significantly higher work-of-fracture than the medial samples. No explanation for this difference was offered at the time of publication of the canine study but it could be hypothesized that the method of loading on the femur is responsible. When the typical canine is standing at rest, the hind legs present a ‘bow-legged’ appearance. The resultant line of action of the hip joint reaction force passes medial to the femur. This situation creates a bending moment, which along with the compressive loads, places the medial aspect of the femur in much higher compression continuously than the lateral aspect. This could account for the difference in the work-offracture. The loading on the human femur presents a different, perhaps more complex. situation. The line of force passes through the femur in some cases. or medial to it. depending on the placement of the feet. This creates a bending situation which is more complex, the medial and lateral aspects of the femur experience both high and low compressive stresses alternately., This might account for the lack of a significant difference in the work-of-fracture between the medial and lateral samples. The mechanisms of fracture were found to be essentially the same as those described by Piekarski (1970). Cooke ef al. (1973) and Moyle rl al. (1978). With controlled crack propagation, the crack passed through the weak interface of the lamellae of the osteons or through the interstitial bone and the fracture surfaces were rough and textured. Pull-out of Haversian systems was observed, though not as dramatic as that seen by Moyle et al. (1978) or Piekarski (1970). This could suggest that the osteons in human bone contain many more points of weakness than that of canine and bovine bone, which would explain the close proximity of the osteon fracture to the fracture surface. With uncontrolled propagation, the crack moved through all the constituents of bone indiscriminately and the fracture surfaces were smooth and rippled. A pull-out type of failure is characteristic of fiber reinforced composite materials containing short fibers or fibers with many points of weakness in them which fail some distance from the crack plane. Pull-out of osteons did occur at varying distances from the fracture surface. It can then be said that failure of human femoral bone in bending, at low deformation rates. is like that ofa fibrouscomposite with osteons as fibers and interstitial material as matrix. The relationship between the degree of mineralization and work-of-fracture is not obvious. The data
W. BONDEX
showed no correlation between the weight percent mineralization and the work-of-fracture. The weight percent mineralization figures obtained were high when compared to ash weight data typically found in the literature (Currey. 1979). It is likely that errors arose due to the necessity of making two weight measurements. The use of a decalcifying solution may not be the best method for determining calcium content. The work-of-fracture was seen to increase with increasing osteon fractional area. and drop at intermediate osteon diameters. No concrete explanation can be offered to explain this behavior. The osteon density, average void diameter and void fractional area did not have any significant effect on the work-offracture of the samples which failed by controlled crack propagation. Finally, we should point out that the results represent samples taken from only two individuals and it is possible that variations from individual to individual may exist which we could not have measured. The total number of samples tested successfully was fifteen and the standard deviation in the work-of-fracture is 27 ‘I,, of the mean. Although this seems large it in fact compares favorably with quantitative data from other fracture mechanics studies. For example Wright and Hayes (1977) divide their K, data into 4 groups in which the standard deviations are 2 I I’,. 23 !A, 12 y;, and 15 y,, of the means. Further, their data on G,, the critical strain energy release rate, which is perhaps more comparable to the fracture energy reported in this paper, shows for each of the four groups standard deviations which are 62 %. 49%. 21% and 34% of the means. Bonfield (1981) does not report standard deviations for any of his data, only averages. Bonfield and Datta (1976) report no standard deviations because they did not perform more than one test per initial crack length (each data point in the paper represents only one sample). Impact testing data gives standard deviations similar to ours. For example, Currey (1979) does not calculate means and standard deviations but an examination of his curves shows very large scatter (we estimate S.D./mean of 40-50%) and Currey states, ‘This is not unusual for impact tests’. While it is possible that the sample-to-sample variation encountered in our test may be due to variations in some unmeasured variable (e.g. density) it is also true that cumulative effects of small variations in measured variables can produce sizeable but not statistically significant alterations in the test result. This normal sample to sample variation is typical of biological materials and is a reflection of the fact that individual samples cannot be reproduced. COKCLUSlONS
The results of this investigation lead to the following conclusions: at slow fracture rates, bone behaves like a
Fig. 5. SEM photograph
of a specimen
which failed by controlled
209
crack propagation.
Fig. 6. SEM photograph
of a specimen
210
which failed by rapid crack propagation.
Fig. 7. SEM photograph
illustrating
rough
texture
211
_---. typical of controlled
--
---
crack growth.
Fig. 8. SEM photograph illustrating osteon ‘pull-out’.
212
Fracture
Table 3. @[eon
Sample 7MI 7Ll
of human
femoral
213
bone
and void fractional areas, osteon and void average diameters of the samples which failed catastrophically
FractIonal (Osteons)
area (Voids) 0.064 0.160
0.485 0.360
Average diameter (pm) (Osteons) (Voids)
and weight percent mineralizatton
Weight percent mineralization
47 95
171 190
Osteon density (No. mm-‘)
77.90 73.59
16.8 18.0
Table 4. Comparison of work-of-fracture, osteon fractional area. osteon density and average osteon diameter for canine and human femoral bone Work-of-fracture (X lO-‘Jm-‘) Canine Human
9.0 * 3.3 7.8k2.1
Fractional osteon area
Osteon density (No. rnrn-l~
Average osteon diameter (pm)
0.290 f 0.06 1 0.516+0.094
19.8_+6.5 20.8 + 3.5
148k22 185+21
fiber reinforced composite with osteons as fibers and interstitial bone as the matrix. The work-of-fracture is independent of the degree of mineralization within the range of 60-80 weight percent. For human specimens taken from the diaphysis of the femur, there is no relationship between the work-of-fracture and the origin of the specimen around the circumference of the bone shaft. Work-of-fracture appears to increase with increasing fractional area of osteons. AcAnowlrdyrmmr-We thank Dr. Richard B. Schuessler the V. A. Medical Center. Augusta, GA for his assistance obtaining the bone specimens.
of in
REFERENCES Bonfield. W. (1981) Mechanisms of fracture in bone. Mechanical Properties o/Bone, AMD-Vol. 45, (Edited by
Cowin, S. C.) American Society of Mechanical Engineers, New York. Bonfield W. and Dana, P. K. (1976) Fracture toughness of compact bone. J. Biomechanics 9, 13 I -I 34. Cooke, F. W., Zeidman, H. and Scheifele, S. J. (1973) The fracture mechanics of bone-another look at composite modeling. J. Biomrd. Mar. Res. Symp. 4, 383-399. Currey, J. D., (1979) Changes in the impact energy absorption of bone with age. J. Biomrchanics 12, 459469. Moyle. D. D.. Welborn, J. W. III and Cooke, F. W. (1978). Work to fracture of canine femoral bone. J. Biomechanirs I I, 435440. Piekarski, K. (1970) Fracture of bone. J. appl. Phys. 41, 215-223. Sedlin, E. D. and Hirsch. C. (1966) Factors affecting the determination of the physical properties of femoral cortical bone. Ac~a orthop. stand. 37, 2948. Tatter&l, H. G. and Tappin, G. (1966) The work of fracture and its measurement in metals, ceramics and other materials. J. Mater. Sci. I. 296-301.
Wright, T. M. and Hayes, W. C. (1977) Fracture mechanics parameters for compact bone-effects of density and specimen thickness. J. Biomerhanics IO, 419430.
FRACTURE OF HUMAN FEMORAL D. D. MOYLE Department
of Interdtsciplinary
and
R. W.
W?I -9290 a4 I3 a, l 00 1984 Pcrpnmon Press Ltd.
BONE
BOWDEN
Studies. Clemson University.
Clemson, SC 29631. U.S.A.
Abstract-The work-of-fracture of human femoral bone was determined usin! the techntque of Tattersal and Tappin (1966). The work required to fracture a specimen in three pomt bending by slow crack propagation through a triangular cross-section is obtained from the loaddeflection curve. The area of the resulting fracture surface is measured by macrophotographic techniques, and the work-of-fracture is calculated as work per unit area. The work-of-fracture values measured in this way ranged from 3.S to I I3 ( x IO’) J me2 m the samples tested with a mean of 7.8 x IO’J m-2 and a standard deviation of 2.1 x IO-’ J me’. The work-of-fracture was found to be independent ofthe degree ofmineralization within the range of 6&80 weight “,,, and to not vary with transverse variation in location in the femoral shaft. The workof-fracture was also seen to increase with increasing osteon fractional area. Scanning electron microscope photographs of the fracture surfaces indicate that the nature of the failure is similar to that of tiber reinforced composite materials.
ISTRODL’CTIOS of the mechanical properties of bone are important for many reasons. In the orthopedic sciences. they are particularly important for three reasons. First. knowledge of these properties can help predict how bones can be expected to behave in the body, for example, the loads they can and cannot bear or the amount of energy they will absorb before fracturing. Secondly. a thorough knowledge of the mechanical properties of bone will explain the behavior of bone as a material, thereby yielding an understanding of why a particular construction of bone gives it the properties it has. Finally, if other materials are to be substituted for bone, their mechanical properties must be compatible with those of bone to ensure a viable system. This dictates that the mechanical properties of bone be known. This paper is concerned with the determination of the work-of-fracture of human femoral bone and an examination of fracture mechanisms. The work-offracture, or the resistance of a material to fracture, is often described in terms of energy to fracture. The true energy of fracture is not measured in conventional tensile or impact tests and the basic technique used in this study was developed by Tattersal and Tappin (1966) and was applied by them to various materials. Their technique was first applied to tissue by Piekarski (1970) in his investigation of the fracture of bovine bone. and subsequently by Moyle et al. (1978) in a study of the fracture of canine femoral bone. Briefly, the technique involves the controlled propagation of a crack through three point bending of the test specimen (Fig. I). The triangular geometry of the Studies
Rt’crirrd 27 Drcrmhrr
1981: in rrriwdjorm 15 Auytrs~ 1983. *Current address: Becton-Dickenson &Co., 21 Just Road. Fairheld. NJ 07006. U.S.A.
Fig. 1. Test specimen geometry and load configuration.
test area of the specimen and a controlled deformation rate determine the rate of crack propagation. Because of the shape of the test area, the load required for crack initiation is small and no energy is lost to plastic deformation elsewhere in the sample. Because crack propagation is controlled (Fig. 2) and the applied load is gradually reduced to zero no energy is lost to vibration or flying specimen pieces and no energy remains stored in the testing machine. The area under the load-deflection curve represents work which has gone entirely into the creation of fracture surface and to effects which are inextricably connected with crack propagation. The work-of-fracture was calculated as the work measured from the load-deflection curve divided by the nominal area of one of the fracture surfaces (obtained by macrophotography). It is important to note that twice the measured area, sometimes used in
203
D. D.
MOYLE
and
R. W. BOWDEN
03
DEFLECTION Fig. 2. Typical load-deflection
1.0 (mm)
curve as obtained directly from
X-Y
recorder showing controlled nature of
crack propagation.
was not used in this study or in any of the other studies of this type performed in this laboratory. The work-of-fracture measured as described above cannot be related to the quantities normally measured in linear elastic fracture mechanics, namely the critical stress intensity factor, K,, and the critical strain energy release rate, G,. The applicability of linear elastic fracture mechanics to bone has been recently reviewed by Bonfield (1981) and all experimental studies have been on bovine bone. The reason for this restriction to bovine bone is that valid test results cannot be obtained with specimens which are small. Specimen thickness and crack length shoutd exceed 2.5 (&/a,,) where CT,,% is the yield strength of the material. For bovine bone this gives a minimum specimen thickness on the order of 3-4 mm. Given other restrictions on the overall specimen size it is not possible to produce specimens suitable for K, determination using bones from animals smaller than the cow. Wright and Hayes (1977) have indicated that some relaxation of the thickness restriction may be possible but this is still unsettled. fracture mechanics studies,
EXPERIMENTAL
PROCEDURE
Samples of bone were obtained from the diaphysis of the femur during autopsy (with informed consent)at the Veterans Administration Medical Center, Augusta, GA. A short medical history was supplied with each bone specimen. After removal from the cadaver the cylinders of bone were wrapped in saline soaked towelling and frozen using the method of Sedlin and Hirsch (1966). Specimens were tested within one to three weeks of the date of freezing. No specimens were tested immediately upon removal from the cadaver.
The origin of each test specimen taken from the cylinder of bone was designated with a letter and number code (Fig. 3). The first number indicates the bone cylinder from which it was obtained, The letter, M or L, indicates the medial or lateral side of the bone. The second number designates a vector area as defined by dividing each medial or lateral half into three specimens, with the number one defining an anterior specimen, the number three a posterior specimen, and the number two an intermediate specimen. For example, 2Ll designates a specimen taken from the lateralanterior area of the second bone cylinder. Bone cylinders I and 2 were obtained from a 70yr old white male who died of cancer. He was 180cm tall and weighed 84 kg. Bone cylinder 3 was obtained from a 56yr old white male who was 180cm tall, weighed 77 kg and died of heart disease. There was no history of connective tissue disease in either case. In preparation for testing a wrapped cylinder of bone was removed from the freezer and the frozen towels were thawed and removed under running tap water. The periosteum was removed, along with any remaining tissue. The cylinder was then cut into six test specimens as given by the vector designation. A diamond saw irrigated with physiological saline was used for cutting the samples. Each test specimen was placed in a container marked with the sample designation and filled with physiological saline. The samples were then ground flat so that they would fit into a jig for cutting notches and so that they would not fall over white being tested. The samples were irrigated in tap water during grinding, and then returned to the containers of saline after grinding. The grinding time never exceeded one minute. Each specimen was required to have a test area of triangular cross-section. With the use of a special jig
Fracturr of human femoral bone RIGHT
FEMUR,
ANTERIOR
VIEW
MEDIAL
CArERAL
POSTERIOR
RIGHT
FEMIJR.
TRANSVFRSE
SECTl!,rl
Fig. 3. Origin and designation of test specimens
and a diamond saw. notches in a triangular shape were cut in the center of each test specimen (Fig. 1). A blade thickness of I mm was used to cut the notches, and the specimens were irrigated in physiological saline during the cutting of the test areas. A sample ready for testing was typically 4Scm in length, about 7mm in height and about 6mm thick. The specimens’ triangular cross-sectional areas varied from 5.4 to 12.8 mm’.
The mechanical testing was performed on an lnstron closed loop hydraulic testing machine with a 4500 Newton load cell. Stroke control mode was used with loading via a ramp function yielding a deflection rateof4.2 x IO-‘ems‘. Thedata was obtained in the form of a loaddeflection curve on an X - Yrecorder. The specimens were never allowed to dry at any time during preparation and testing. The total time between removal of the bone cylinders from the freezer and the testing of the specimens averaged three hours and never exceeded four hours. Following testing, the fracture surfaces of some specimens were held together by threads of bone material when the load reached zero. Nevertheless, those specimens were deemed to be completely fractured and unable to absorb any more energy. One fracture surface from each sample was embedded in a quick setting acrylic mounting medium and then ground and polished for viewing under a reflected light microscope. Standard methods of quantitative microscopy were used to determine osteon ‘density’ (number of osteonsjunit area), average osteon diameter. fractional area of osteons, average void diameter and fractional area ofvoids. The interstitial bone fractional area was calculated for each sample by summing the void and osteon fractional areas and subtracting this value from 1.0. The amount of inorganic mineral content, mostly hydroxypapatite, was measured by weighing a small oven-dried section of each bone specimen before and after decalcification in
a commercially available solution Products, Evanston, IL).
(DscalB,
Scientilic
RESULTS
The results from the mechanical testing. light mlcroscopy and weight percentage mineralization determination for all specimens which failed by controlled crack propagation are presented in Tables 1 and 2. The work-of-fracture mean and standard deviation for all specimens is 7.3 &-2.1 x lO’Jm_*, and the range of values is 3.8-l 1.8 x IO3 J m-‘. These data represent samples obtained from two cadavers. Seventeen specimens were tested, fifteen failed by controlled crack propagation, two catastrophically and one was broken during handling. The data presented in Table 1is for samples from the medial aspect of the femur and that in Table 2 is for samples from the lateral aspect. A comparison of the data obtained for the medial and lateral samples showed no significant difference in work-of-fracture between these two groups. Also, no significant difference was found in the osteon and void parameters, or weight percent mineralization between the medial and lateral aspects of the femur. The mean and standard deviation of the work-of-fracture for the medial samples was 8.5 + 2.0 x lo3 and 7.2 +2.l x IO’Jm- * for the lateral samples. A further breakdown of the data into each vector designation is also shown in Tables 1and 2. No regional variations in any of the measured parameters were found. Since the osteon is the fundamental structural feature of compact human bone, the work-of-fracture was compared with measured osteon parameters. A comparison ot the work-of-fracture against the osteon fractional area data shows a weak positive correlation (r2 = 0.31). Comparison of the work-of-fracture with osteon diameter (Fig. 4) shows a drop in the work-of-fracture at intermediate osteon diameters. No correlation (r* = 0.015) was found by comparing the work-offracture and the osteon density data.
0.742 0.416 0.528
9.9 9.1 8.0
6.7 6.6 5.1
IL2 3L2 2L2
3L3 2L3 5L3
0.496 0.528 0.462
0.544 0.464
Fractional (Osteons)
8.6 3.8
Work-of-fracture (IO’Jm-I)
2Ll 1Ll
Sample
0.120 0.088 0.176
0.224 0.128 0.144 0.056
arca (Voids)
150 209 173
215 201 195 160 285 76 239
101 152 86 59
Avcragc diameter (Irm) (Voids) (Osteons)
60.52 70.83 75.90
19.54 58.64 65.30 65.74
Weigh1 pcrccnt mincralizllion
0.112 0.072 0.162
o.oxx 0.144 0.112
0.144 0.096
area (Voids)
196 167 IX3
214 165 193
167 176
82 57 154
93 91 76
98 65
Average diameter (jrm) (Voids) (Osteons)
75.36 69.57 76.30
71.65 72.09 64.42
12.15 15.15
Weight percent minerah~~tion
and
19.2 25.4 16.6
22.4 20.8 22.4
20.8 22.8
Osteon density (No. mm- ‘)
and osteon
25.4 15.0 11.4
23.8 24.4
I X.8
18.8
Ostcou density (No.mnC ‘) _-
weight percent mineralization
osteon and void fractional areas, osteon and void average diameters, weight percent mineralization density for the lateral samples tested
0.536 0.616 0.403
8.6 8.4 5.1
2M3 IM3 3M3
Table 2. Work-of-fracture,
0.656 0.424 0.576 0.504
It.8 9.8 8.3 1.7
IMI 2M2 lM2 3M2
Fractional (Ostcons)
osteon and void fractional areas, osteon and void average diameters, osteon density for the medial samples tested
Work-of-fracture (lO’Jm_‘)
1. Work-of-fracture,
Sample
Table
Fracture
of human femoral bone
1
150
I60
170 AVERAGE
160
I90
OSTEON
DIAMETER
200
210
220
(pm)
Fig. 4. A plot of work-of-fracture vs average osteon diameter
To determine the combined elTect of resorption spaces and Haversian canal areas, the work-of-fracture was compared with the void fractional area and average void diameter. No correlations were found. A comparison of the work-of-fracture with the weight percent mineralization data also exhibits no correlation between these parameters. A scanning electron microscope was used to examine and photograph the fracture surfaces. A typical fracture surface of a specimen which failed by controlled crack growth is shown in Fig. 5. The appearance of the fracture surface is very irregular. The rough texture indicates the crack did not propagate perpendicularly through all the bone constituents, resulting in valleys and ridges. Complete pull-out of osteons, partial pull-out of osteons and torn osteon fragments are easily discernable. This type of crack propagation maximizes the surface area and allows for maximum energy absorption. No areas of rapid crack growth are contained in this fracture area. A brittle mode of fracture in a specimen which failed by uncontrolled crack growth is illustrated in the fracture surface photography of Fig. 6. The surface is generally rippled in appearance, the valleys and ridges of the samples which failed by controlled crack growth are not evident. There is no evidence of osteon pullout. In this case the crack has moved indiscriminately through all the microconstituents, thereby yielding low energy absorption. A closer examination of a fracture surface from a specimen which failed by controlled crack propagation is seen in Fig. 7. Various degrees of osteonal fracture can be noted. Complete osteon pull-out is evident, though not the dominant mode of fracture. It can be seen that the crack is diverted along the lamellar bone of the osteons resulting in a step-like appearance. This preference for thecrack to follow the interface between
the osteon and interstitial lamellae indicates the prrsence of a relatively weak bond. A higher magnification of a fracture surface is shown in Fig. 8. An osteon which has pulled-out can be seen in the left portion of the photo. The concentric circumferential osteon lamellae and Haversian canal are easily seen. The step-like fracture of the surrounding interstitial lamellae is also evident. Of the seventeen specimens mechanically tested, two failed by uncontrolled crack propagation. These were not included in the results because the rapid crack growth does not allow the energy absorbing mechanisms of bone to function. Since it is not readily possible to quantify how much energy is dissipated by postfracture processes, it is not possible to determine what part of the work put into the system has been consumed by the fracture process, and therefore, the fracture energy. The specimens that failed by uncontrolled crack growth were analyzed by the same methods used for the samples which failed by controlled crack growth. The data for the osteon, void and mineralization parameters appears in Table 3. A comparison with the values for specimens which failed by controlled crack propagation reveals no significant differences.
DISCUSSIOS
A comparison of the work-of-fracture data from this study with data for canine bone from an earlier study (Moyle et al., 1978) in this laboratory has been made. A comparison of the means and standard deviations for some of the relevant data is given in Table 4. Statistical analysis of the data from this study and the canine bone study referred to reveals a significant difference in the work-of-fracture (0.02 < p < 0.05).Extending the
708
D. D.
MOYLE
and R.
comparison to the osteon parameters indicates significant differences (p < O.CQl) between all the human and canine values presented in Table 4 except osteon density. There was no significant difference in the work-offracture between the medial and lateral samples in this stud>. This is in contrast to the results of the canine stud?. which showed the lateral samples to have a significantly higher work-of-fracture than the medial samples. No explanation for this difference was offered at the time of publication of the canine study but it could be hypothesized that the method of loading on the femur is responsible. When the typical canine is standing at rest, the hind legs present a ‘bow-legged’ appearance. The resultant line of action of the hip joint reaction force passes medial to the femur. This situation creates a bending moment, which along with the compressive loads, places the medial aspect of the femur in much higher compression continuously than the lateral aspect. This could account for the difference in the work-offracture. The loading on the human femur presents a different, perhaps more complex. situation. The line of force passes through the femur in some cases. or medial to it. depending on the placement of the feet. This creates a bending situation which is more complex, the medial and lateral aspects of the femur experience both high and low compressive stresses alternately., This might account for the lack of a significant difference in the work-of-fracture between the medial and lateral samples. The mechanisms of fracture were found to be essentially the same as those described by Piekarski (1970). Cooke ef al. (1973) and Moyle rl al. (1978). With controlled crack propagation, the crack passed through the weak interface of the lamellae of the osteons or through the interstitial bone and the fracture surfaces were rough and textured. Pull-out of Haversian systems was observed, though not as dramatic as that seen by Moyle et al. (1978) or Piekarski (1970). This could suggest that the osteons in human bone contain many more points of weakness than that of canine and bovine bone, which would explain the close proximity of the osteon fracture to the fracture surface. With uncontrolled propagation, the crack moved through all the constituents of bone indiscriminately and the fracture surfaces were smooth and rippled. A pull-out type of failure is characteristic of fiber reinforced composite materials containing short fibers or fibers with many points of weakness in them which fail some distance from the crack plane. Pull-out of osteons did occur at varying distances from the fracture surface. It can then be said that failure of human femoral bone in bending, at low deformation rates. is like that ofa fibrouscomposite with osteons as fibers and interstitial material as matrix. The relationship between the degree of mineralization and work-of-fracture is not obvious. The data
W. BONDEX
showed no correlation between the weight percent mineralization and the work-of-fracture. The weight percent mineralization figures obtained were high when compared to ash weight data typically found in the literature (Currey. 1979). It is likely that errors arose due to the necessity of making two weight measurements. The use of a decalcifying solution may not be the best method for determining calcium content. The work-of-fracture was seen to increase with increasing osteon fractional area. and drop at intermediate osteon diameters. No concrete explanation can be offered to explain this behavior. The osteon density, average void diameter and void fractional area did not have any significant effect on the work-offracture of the samples which failed by controlled crack propagation. Finally, we should point out that the results represent samples taken from only two individuals and it is possible that variations from individual to individual may exist which we could not have measured. The total number of samples tested successfully was fifteen and the standard deviation in the work-of-fracture is 27 ‘I,, of the mean. Although this seems large it in fact compares favorably with quantitative data from other fracture mechanics studies. For example Wright and Hayes (1977) divide their K, data into 4 groups in which the standard deviations are 2 I I’,. 23 !A, 12 y;, and 15 y,, of the means. Further, their data on G,, the critical strain energy release rate, which is perhaps more comparable to the fracture energy reported in this paper, shows for each of the four groups standard deviations which are 62 %. 49%. 21% and 34% of the means. Bonfield (1981) does not report standard deviations for any of his data, only averages. Bonfield and Datta (1976) report no standard deviations because they did not perform more than one test per initial crack length (each data point in the paper represents only one sample). Impact testing data gives standard deviations similar to ours. For example, Currey (1979) does not calculate means and standard deviations but an examination of his curves shows very large scatter (we estimate S.D./mean of 40-50%) and Currey states, ‘This is not unusual for impact tests’. While it is possible that the sample-to-sample variation encountered in our test may be due to variations in some unmeasured variable (e.g. density) it is also true that cumulative effects of small variations in measured variables can produce sizeable but not statistically significant alterations in the test result. This normal sample to sample variation is typical of biological materials and is a reflection of the fact that individual samples cannot be reproduced. COKCLUSlONS
The results of this investigation lead to the following conclusions: at slow fracture rates, bone behaves like a
Fig. 5. SEM photograph
of a specimen
which failed by controlled
209
crack propagation.
Fig. 6. SEM photograph
of a specimen
210
which failed by rapid crack propagation.
Fig. 7. SEM photograph
illustrating
rough
texture
211
_---. typical of controlled
--
---
crack growth.
Fig. 8. SEM photograph illustrating osteon ‘pull-out’.
212
Fracture
Table 3. @[eon
Sample 7MI 7Ll
of human
femoral
213
bone
and void fractional areas, osteon and void average diameters of the samples which failed catastrophically
FractIonal (Osteons)
area (Voids) 0.064 0.160
0.485 0.360
Average diameter (pm) (Osteons) (Voids)
and weight percent mineralizatton
Weight percent mineralization
47 95
171 190
Osteon density (No. mm-‘)
77.90 73.59
16.8 18.0
Table 4. Comparison of work-of-fracture, osteon fractional area. osteon density and average osteon diameter for canine and human femoral bone Work-of-fracture (X lO-‘Jm-‘) Canine Human
9.0 * 3.3 7.8k2.1
Fractional osteon area
Osteon density (No. rnrn-l~
Average osteon diameter (pm)
0.290 f 0.06 1 0.516+0.094
19.8_+6.5 20.8 + 3.5
148k22 185+21
fiber reinforced composite with osteons as fibers and interstitial bone as the matrix. The work-of-fracture is independent of the degree of mineralization within the range of 60-80 weight percent. For human specimens taken from the diaphysis of the femur, there is no relationship between the work-of-fracture and the origin of the specimen around the circumference of the bone shaft. Work-of-fracture appears to increase with increasing fractional area of osteons. AcAnowlrdyrmmr-We thank Dr. Richard B. Schuessler the V. A. Medical Center. Augusta, GA for his assistance obtaining the bone specimens.
of in
REFERENCES Bonfield. W. (1981) Mechanisms of fracture in bone. Mechanical Properties o/Bone, AMD-Vol. 45, (Edited by
Cowin, S. C.) American Society of Mechanical Engineers, New York. Bonfield W. and Dana, P. K. (1976) Fracture toughness of compact bone. J. Biomechanics 9, 13 I -I 34. Cooke, F. W., Zeidman, H. and Scheifele, S. J. (1973) The fracture mechanics of bone-another look at composite modeling. J. Biomrd. Mar. Res. Symp. 4, 383-399. Currey, J. D., (1979) Changes in the impact energy absorption of bone with age. J. Biomrchanics 12, 459469. Moyle. D. D.. Welborn, J. W. III and Cooke, F. W. (1978). Work to fracture of canine femoral bone. J. Biomechanirs I I, 435440. Piekarski, K. (1970) Fracture of bone. J. appl. Phys. 41, 215-223. Sedlin, E. D. and Hirsch. C. (1966) Factors affecting the determination of the physical properties of femoral cortical bone. Ac~a orthop. stand. 37, 2948. Tatter&l, H. G. and Tappin, G. (1966) The work of fracture and its measurement in metals, ceramics and other materials. J. Mater. Sci. I. 296-301.
Wright, T. M. and Hayes, W. C. (1977) Fracture mechanics parameters for compact bone-effects of density and specimen thickness. J. Biomerhanics IO, 419430.