TENSILE IMPACT PROPERTIES HUMAN COMPACT BONE*
OF
s. &HA Department of Engineering and Applied Science, Yale University. New Haven. CT 06520. U.S.A. and
W. C. HAYES Department of Applied Mechanics. Stanford University. Stanford CA 94305. U.S.A. Abstract-Longitudinal specimens from human compact bone were tested in a pendulum type instrumented tensile impact tester at a strain rate of 133 set -‘. The recorded load time histories showed marked nonlinearities in the stress strain behavior of some specimens including plastic deformation and strain hardening effects, thus emphasizing that the fracture energy alone is an incomplete representation of the tensile impact behaviour of bone. Mean tensile impact strengths and impact energy capacities were 126.3 + 33.1 MN/m2 and 18790 k 7355 J/m2 for 49 fresh human specimens. Quasi-static tensile strengths for 13 fresh human samples were 34”,, less than the tensile impact strength. Statistically significant correlations were found between elastic properties. ultimate stress and impact energy capacity. Tensile impact strength also correlated negatively with the percentage area of secondary osteons in the specimen.
INTRODUCTION
safety and reduce injury levels in transportation, industrial and recreational accidents must consider the tolerance of human tissues and organs to accelerative and impact forces. Such forces are characterized by abrupt onset, short duration and high magnitude. If protective systems are to be optimally designed, tissue and organ tolerances to such forces must be accurately obtained for a variety of design parameters such as impact velocity, force magnitude and force duration and for such biological factors as age and sex. However, the current state of knowledge concerning human impact tolerance is incomplete and relatively little data is available on the tolerence limits of individual body components against localized impacts. In particular, the impact tolerence of human long bones is poorly understood. The fact that half of all injury producing automobile accidents involve injuries to the extremities (Kihlberg, 1970) emphasizes the need for data with which to better design protective systems and thus reduce the frequency and severity of fractures of the long bones. Most previous studies of the dynamic strength of bone were conducted on whole bones subjected to impact loads (Burstein and Frankel, 1968; Mather. 1968: Evans, 1970: Sammarco et ul., 1971: Kramer er ul.. 1973). These studies provide tolerance limits for individual whole bones, but little information on the dynamic behavior of bone as a material due to difficulties in calculating stresses and strains. Such Attempts
to improve
*Received
10 April
1974.
243
calculations are difficult with whole bones since: (1) the cross-section of a long bone changes shape and size along the length; (2) both compact and cancellous bone are present in varying proportions: (3) simple tension or compression tests produce combined bending and axial loading of the shaft; and (4) inelastic deformation of the bone is likely to be non-uniformly distributed over the whole cross-section (Burstein er al., 1972). Moreover, the thickness of the cortex and the shape and size of a long bone vary with age and between individuals thus making it difficult to compare results obtained by different investigators. For these reasons, this investigation followed other studies which used standardized bone specimens in well-defined loading configurations to determine the mechanical properties of bone as a material (McElhaney. 1966; Wood, 1971). The importance of tensile loading in the fracture mechanisms of bone has long been recognized. Evans and his colleagues (1951, 1952) and Evans (1957) demonstrated with brittle coatings that most bone fractures occur in tension since bone, like most brittle materials. is weak in tension. Brooks er al. (1970) also suggested that bone failure is closely associated with planes of maximum tensile stress. Therefore. it is surprising to note that while the impact tolerence of whole bones and the dynamic strength of standardized bone specimens have been investigated in modes other than tension, few attempts have been made to determine the tensile impact strength of bone at high loading rates. The objective of the present investigation was to provide data on the tensile impact strength and dynamic mechanical properties of human compact bone
244
S. SARA and
and to relate these properties to bone microstructure. Standardized tensile specimens and instrumented testing methods were used to provide accurate determinations of stress and strain throughout impact. This approach represents a significant improvement over previous impact tests of bone which only measured the total energy to fracture. PREVIOUS
INVESTIGATIONS
Recent reviews of the mechanical properties of bone (Evans, 1957, 1973: Kraus, 1968: Currey, 1970: Swanson. 1971: Herrmann and Liebowitz. 1972: Reilly and Burstein. 1974) emphasize that few data are available on the dynamic behavior of small bone specimens. Some workers have reported the use of Charpy impact tests to study dynamic fracture of bone (Tsuda. 1957: Hert er (II., 1965: Bonfield and Li. 1966: Swanson. 1971). However, the large scatter evidenced in these results makes it difficult to draw meaningful conclusions. Moreover, because of uncertainties concerning plastic deformation in such experiments, bending tests cannot be used to calculate maximum stresses and strains during impact (Burstein rr al.. 1972). Compared to the number of transverse impact tests, few attempts have been made to study the longitudinal impact properties of bone. Bird and Becker (1966) and their associates (Bird et al., 1968) performed compressive impact tests on specimens from fresh beef femurs in order to establish a relationship between failure mode and impactor velocity. They found that the modulus of elasticity decreased and the ultimate stress increased with stress rate. They also noted that whole bones were more impact resistant than were small specimens. McElhaney and Byars (1965) and McElhaney (1966) performed constant velocity compressive tests at strain rates of from OGOl to 1500 see-’ on specimens from embalmed human and fresh beef femurs. For human bone, the ultimate compressive stress increased from 21% ksi at the lowest strain rate to 46.0 ksi at the highest. The energy absorption capacity and maximum strain first increased to a maximum and then decreased with increases in strain rate. The only detailed study on the dynamic response of bone in tension was conducted by Wood (1971) in tests of cranial bone specimens at strain rates ranging from 0005 to 150 set- I. While the breaking stress and modulus of elasticity increased with strain rate, the breaking strain decreased. The energy absorption capacity was independent of strain rate. Black and Korostoff (1973) also studied the frequency response of the elastic modulus of excised human compact bone specimens in tension. Elastic moduli were found to increase with loading frequency in the range of 354353.6 Hz. Previous investigations of the influence of bone microstructure on mechanical properties have concentrated mainly on the effects of the size and num-
W. C. HAYES
ber of osteons in specimens tested quasi-statically. Evans and Bang (1967) demonstrated negative correlations between ultimate tensile strength and the percentage area of osteons in the specimen break area for embalmed human compact bone. Evans and Vincentelli (1974) found a positive correlation between bone compressive strength and percentage osteon area. Evans and Riolo (1970) also found a positive correlation between the fatigue life and percentage of osteon area in bone. Recently. Burstein and co-workers have focused considerable interest on the importance of plastic deformation in the mechanical behavior of bone. Using tensile tests on bovine bone at relatively low strain rates. Burstein et t/l. (1972) demonstrated the existence of significant regions of plastic deformation in bone. They later demonstrated that this deformation is truly plastic by conducting quasi-static tensile loading and unloading tests on bovine bone and showing irreversible and successively additive deformations beyond yield (Burstein et d.. 1973). Using standard histological techniques the authors were unable to determine the exact mechanisms for plastic flow but assumed that they included osteon pull out. microcracking and void coalescence. Similar plastic deformation has also been observed in specimens of human compact bone tested at low strain rates (O.OS/sec)in both tension and compression (Reilly et al., 1974). In a recent paper. Currey and Brear (1974) have examined the microstructural changes that are associated with tensile yield in bone.
MATERIALS
AND METHODS
The initial stages of this investigation utilized bone specimens from fresh adult beef femurs and tibias. These results are reported elsewhere (Saha and Hayes, 1974). Subsequently, human compact bone specimens were obtained from both femurs of an embalmed adult human skeleton and from the right femur of a 38 yr old male autopsy specimen with no history of bone disease. All compact bone specimens were removed from the femoral diaphysis and were longitudinally oriented as it was not possible to obtain sufficiently long test specimens from the circumferential or radial directions. The dimensions of the tensile specimens were chosen acccording to the ATSM specifications for the tensile impact testing of plastics (D-1822-61T, Type L). The standard specimen used in this investigation is shown in Fig. 1. To prepare tensile test specimens, each femur was sectioned into five segments along its length and each segment was divided into quadrants. Parallel sided strips of the required thickness were removed from each quadrant using a diamond saw thin sectioning machine. The finished necked shape was produced in a standard mill. All machining operations were performed using copious irrigation to minimize thermal
(Facing p. 244)
Tensile
impact
properties
ENERDI SCALE
PENDULUM HEAD
Q”ARTZ LOAD TEST CELL SPECIMEN
Fig. 2. Schematic
diagram
of the tensile
impact
test set-up.
damage. Specimens were equilibrated in Ringer’s SOlution and stored at from - 10 to -20-C. For testing specimens were thawed and kept submerged in Ringer‘s solution at room temperature. Impact testing was accomplished within 3 min of removal from the solution and exposed surfaces were continually saturated to minimize surface drying. These preparation. storage and testing procedures have been shown by other workers to optimally preserve the mechanical properties of bone (McElhaney er trl.. 1964: Sedlin and Hirsch. 1966). A schematic diagram of the experimental apparatus used for tensile impact testing is shown in Fig. 2. An instrumented pendulum type tensile impact tester (Modified Custom Scientific Instruments model CS-137) at a striking velocity of 11.3 ft,isec (3-44 m:secl was used throughout. The bone specimens were gripped at one end using fixed, serrated jaws and at the other end by a freely movable end clamp. A 500 lb (22365N) capacity quartz load cell (Kistler Model 910) with a signal rise time of Sp/sec and a natural frequency of 100 kc was used to monitor load during testing. The load cell output was amplified and recorded on a storage oscilloscope (Tektronix model 564) as a load-time curve. Triggering was accomplished internally by using a vertical plug-in with a built-in delay line (Tektronix mode1 3A6) in the oscilloscope. With this arrangement it was possible to use internal triggering without any loss of the initial portion of the load-time curve. ENERGY ABSORBED
DURING
CATASTROPHIC
of human
compact
hone
Combining all the losses during impact due to air resistance, friction and the kinetic energy imparted to the clamp. the velocity of the pendulum head was reduced by less than 4’,, during impact. Therefore. it is reasonable to assume a constant velocity impact and to calculate total specimen deformation on the basis of an average velocity of 133.9 inset. Thus. the Inad-time cur\es also represent dynamic stress-strain curses. The dynamic mechanical properties cl\lculuted from the load-time curves are shown in Fig. 3. The proportional limit. (T;. was defined as the maximum stress the samples sustained without an appreciable deviation from linearity. Strain was calculated on the bases of an effective length of one inch. a value verified by strain gaged specimens (Saha. 1973; Saha and Hayes. 1974). A secant modulus of elasticity. Ei. was also calculated from the stress-strain data at the proportional limit. indicating the slope of the straight line joining the point of yield stress to the origin. The total energy absorption capacity was obtained by measuring the area under the load-time curve with a planimeter. In all cases the values agreed with scale reading of the pendulum impact tester after corrections were made for windage and friction losses and for clamp kinetic energy. The use of instrumented testing methods also allowed the separation of the total energy to fracture into: (1) Energy absorbed during elastic deformation: (2) Energy absorbed during plastic deformation: and (3) Energy absorbed during tearing (Fig. 3). The’total impact energy. U. was considered the sum of the energy absorbed during elastic and plastic deformation. The total numbers of human compact bone specimens tested at a strain rate of 133 set were 58 fresh and 42 embalmed. Thirteen additional fresh human specimens were tested quasi-statically in tension using a speciallv designed loading rig at a cross-head speed of OGOl2 in:sec (0.031 mm’secl. The same load cell used for tensile impact testing was used to monitor load during quasi-static testing. After mechanical testing. the specimens were imbedded in cold metallurgical mound, polished on a series of rotating metallurgical wheels and photopmphed at 50x magnification in a reflected-light metallurgical microscope. The percentage of the total area occupied by osteons was measured with a planimeter by tracing osteon outlines on transparent paper and joining the outlines. This method resulted in osteon area measurements repeatable to within five percmt. RESULTS
AND DISCCSSION
PROPAGATION STRAIN
(TIME)
’
Fig. 3. Idealized stress-strain (or load-time) curve in tenslle impact showing the energy absorbed during elastic, plastic and tearing phases.
Typical load-time curves for human compact bone specimens in tensile impact are shown in Fig. 4. The observed failure modes ranged from nearly brittle fracture as in Fig. 4(a) to fracture with plastic deformation as in Fig. 4(b). Some specimens also indicated
246
S. SAHA and
(b)
(a)
(d
Fig. 4. Characteristic load-time or stress-strain curves for fresh human bone in tensile impact: (a) elastic failure: specimen from proximal femur, medial quadrant: V. Scale = 501b or 6017 psi/div. H. Scale = 20~ set or 0.002658 in/in/div. (b) plastic deformation; specimen from distal femur. anterior quadrant; V. Scale = 25 lb or 3161 psi/div. H. Scale = 20 !1 set or 0.002658 in/in/div. (c) strain hardening; specimen from distal femur. medial quadrant: V. Scale = 25 lb or 2941 psi/div. H. Scale = 20 p set or 0.002658 in/in/div. strain hardening effects as shown in Fig. 4(c). Specimens with markedly nonlinear stress-strain relations exhibited an initial elastic region followed by a smooth transition to a plastic region which usually included some strain hardening. Similar stress-strain relations were reported by Reilly er c/l. (1974) in quasistatic tensile tests of human compact bone. In the present investigation. bone specimens with similar impact energy absorption capacities (as measured by the area under the stress-strain curves) often exhibited large differences in ultimate stress and strain. Since the energy to fracture is a function of the applied force times the distance through which the force operates. equal tensile impact energies may result from a large force associated with a small elongation and from a small force associated with a large elongation. The results presented here suggest that the failure characteristics of bone are not adequately described by the failure energy alone since significant deviations from linearity often occur. The use of the total energy to fracture as a tolerance limit for bone is thus an oversimplification which may preclude optimum use of tolerance data in the design of protective systems. Means and standard deviations for the tensile impact properties for 49 fresh and 42 embalmed human compact bone specimens are presented in Table 1. Of the total of 58 fresh human bone samples tested. nine specimens had cavities in their structure which were visible to the naked eye and subsequent examin-
W. C. HAW
ation of their microstructure indicated that they were partially cancellous in character. Thus their mechanical properties were not included in the values shown in Table 1. The data show that the ultimate tensile strength of fresh human bone specimens is higher than that of embalmed specimens. These results are in agreement with data on the effect of embalming in beef bone (McElhaney et trl.. 1964) but contradict the results reported by Evans (1973) on wet-tested human cortical bone. The fact that the embalmed specimens were from an older person in this study may the the reason for this difference. Table 1 also shows that the modulus of elasticity (with a coefficient of variation of 23.706) is the most consistent of the mechanical properties of bone. Wood (1969). in this study of the dynamic tensile behavior of cranial bone, also observed that the modulus of elasticity was the least variable of the mechanical properties. Of the 49 fresh human bone samples tested, 19 showed a decrease in the initial slope of the stress strain curve (E in Fig. 3) beyond the proportional limit (ai) which indicated the onset of some plastic deformation. The yield stress. Ui. was 9.79 + 2.72 ksi (67.5 + 18.8 MN/m’) for these 19 fresh human bone specimens. This agreed with our previous result of plastic deformation of beef bone samples in tensile impact (Saha and Hayes. 1974). Other investigators have also noted plastic deformation of bone in static tension (Ascenzi et trl.. 1966: Bonfield and Li, 1966, 1967; Burstein ef al.. 1973; Reilly et al., 1974). shear (Bonfield and Li, 1967). bending (Burstein rt trl.. 1972) and dynamic compression (McElhaney, 1966: Bird et al., 1968). While the mechanism leading to this plastic deformation has not been definitely established, most workers assume that it represents a combination of microcrack formation. osteon pullout, and void coalescence (Chamay, 1970: Reilly et al., 1974: Currey and Brear, 1974). Data on the biological effects of plastic deformation in bone is not available. Such information would be helpful in determining whether the tolerance limits for bone should be based on the prevention of plastic deformation or whether some plastic deformation may be allowed. Sttrtic. rs trttsilr
iriprcf
strmgtk
The mean yield stress. oi. for 13 specimens of fresh human compact bone tested in quasi-static tension
was Il.13 ~fr2.25 ksi (76.74 f 15.51 MN/m*).
Simi-
Table 1. Means and standard deviations of the mechanical properties of human bone specimens in tensile impact (values in S.I. units are shown within parentheses)
Condition
No. of samples
Ultimate stress 0, in ksi (MN/m’)
Impact energy U in in. lb/in’
(Jim’)
Maximum strain (:‘/,)
Fresh
49
18.32 i 4.80 (1263 + 33.1)
107.3 + 42 (18790 + 7355)
1.15 + 030
Embalmed
42
14.3 * 3.7 (98.6 + 25.5)
81.7 + 31.5 (14308 f 5517)
0.982 k 0.225
Modulus of elasticity in IO’ psi (GN/m’) Secant, E, Tangent. E 2.11 f 0.50 (145 k 3.4)
1.80 f 0.42 (12.4 f 2.9) 1.76 k 023 (12.1 + 1.6)
Tensile impact properties of human compact bone larly. the ultimate stress. uu. was 13.72 + 1.47 ksi (94.60 & 1013 MN,m’). The static tensile strength of each fresh human bone sample was compared with the impact strength of another sample of the same region. i.e. from the same quadrant, longitudinal segment and approximate radial distance from the center of the shaft. The percentage of increase in strength was calculated for each pair using the formula
.a .
.
C”.____-ll”,FKl)- 01,,.!.>,I‘, ‘1oagrincrease = _ x 100 rs” (\l&lCI and the ultimate stress in tensile impact was 34.4 & 30.1”,, higher than the static strength for 13 fresh compact human bone specimens. This difference. using a paired r-test, is significantly different from zero at the P < OQOl level. Wood (1971) also found an increase in ultimate stress of approx. 409, for cranial bone specimens tested at strain rates of 0.01 and 100 set-‘. An increase in maximum stress with increasing strain rates has also been observed for bone in compression (McElhaney and Byars. 1965: Bird et r/l.. 1968). This increased bone strength in tensile impact is in agreement with similar observations for engineering materials. Clark and Duwez (1950) compared the static tensile strength with the dynamic strength of steel at a strain rate of 190 set-’ and showed increases in ultimate strength of 30-450,,. Clark and Wood (1950) also showed that the ultimate strength of some metals and alloys was greater under dynamic conditions than under static conditions. Similar observations, indicating an increase in ultimate stress with higher strain rates. have been reported for other engineering materials (Ely. 1960). For embalmed human compact bone in static tension. Evans and Lebow (1951. 1952) obtained an energy absorption capacity of 83.6 in. lb/in.3 The tensile impact energy of 81.7 in. lb/in3 obtained in this investigation (Table 1. expressed per unit volume). agrees with the value obtained by Evans and Lebow. The present results do not exhibit the increase in energy absorption capacity that was observed by Mather (1968) and Burstein and Franked (1968) in their comparison of static and dynamic properties. Hc,\\c‘\cr. the rc5ults are similar to Wood’s (1971) hndlngs of no Increase in the energy absorption capacity of cranial bone when tested in dynamic tension. McElhaney and Byars (1965) further reported a critical strain rate of 1 set-’ at which the energy absorption capacity was a maximum for bone in compression. Experiments over a wide range of strain rates are presently underway to determine if such a critical strain rate exists for bone in tension. On the basis of tests of 242 specimens from the human femur in static tension. Evans and Lebow (1951 j obtained percentage elongations of from 1.15 to 1.27”,, which is slightly higher than the 0.98’- -+ 0.3’5” -0. obtained in tensile impact for embalmed bone in this investigation. This is to be expected. however. since with higher strain rates. the
. . /.
* . /
. l *
.‘* . .* . . .. ’ . / I l
J.
I
*
i 0.5
I.0
2.0
I.5
Max. Strain
2.5
1%)
Fig. 5. Relationship between the impact energy absorption capacity and maximum strain of fresh human compact bone specimens in tensile impact. material has less chance to deform plastically before failure. These results also agree with Wood (1969) who observed a decrease in breaking strain with increases in strain rate. Correltrtions
between
eltrstic
properties
ctnd strength
Pearson’s product moment correlation coefficients were used to determine correlations between elastic properties and bone strength. The correlation matrix for 49 fresh human samples tested in tensile impact is shown in Table 2. An extremely high positive correlation (P < OQOl) was noted between impact energy absorption capacity. U. and ultimate strain. E. This relationship is shown graphically in Fig. 5. Using a HP 9805 A calculator. the linear regression equation (Fig. 5) was obtained as (coefficient of determination 1.’ = 0.7180) I! = -48.87
+ 14@0 E
(1)
where the energy absorption capacity U is given in in. lb/in* and c is the percentage of ultimate strain. This indicates that the failure energy of bone in tensile impact can best be estimated from ultimate strain. Evans and Lebow (1951, 1952) also reported a strong correlation between maximum strain and energy absorption in static tensile testing of human femoral specimens. In most cases, the correlation coefficient between U and E is higher than the coefficient between U and ultimate stress 0,. This suggests that it may be more appropriate to base the tolerance limits of bone on maximum strain rather than on maximum stress. as is customary. Table 2 also shows that statistically significant positive correlations exist for: (1)
248
S. SAHA and
Table 2. Correlation
Ult. tensile
Impact
matrix
elastic and strength
stress @,I
energy
(U)
Tan mod of elasticity
Ult. strain
between
(E)
(E)
Sec. mod. elasticity
(&)
Yield stress (ci)
properties
2.0
HAYES
for fresh human
bone (coefficient;(cases)~significancek
0”
u
E
E
-5
0,
1GOOO (0) S=O.oOl 0.6926 (49) S = oNl1 05303 (49) s = O+Ol 0.1660 (49) S = 0127 05458 (49) S=OOOl 04734 (19) s = 0.020
06926 (49) S=OOOl 1WOO (0) S=OOOl - 0.0549 (49) s = 0354 08473 (49) S=OOOl - 0.0673 (49) S = 0323 04142 (19) s = 0039
0.5303 (49) S = OQOl - 0.0549 (49) s = 0.354 1.0000 (0) s = OGOl -0.4144 (49) s = oGO2 0.8701 (50) s = OQOl 0.7589 (19) S=OOOl
0.1660 (49) S = 0.127 0.8473 (49) s = 0.001 -0.4144 (49) s = oGO2 1+)000 (0) s = OQOl - 0.4738 (49) s = 0.001 01568 (19) s = 0.261
05458 (49) S = 0~001 - 0.0673 (49) s = 0323 0.8701 (501 s = oNl1 -0.4738 (49) s = OGOl 1GOOO (0) s = 0001 0.7774 (19) s = 0001
04734 (19) S = 0.020 04142 (19) s = 0.039 0.7589 (19) s = OXKll 0.1568 (19) S = 0.261 0.7774 (19) S=OOOl 1WOO (0) s = 0001
25-
I.5
W. C.
25
3.0
Mod. 01 ElaSticv?y (IO’pri)
Fig. 6. Relationship between the ultimate stress and the modulus of elasticity of fresh human compact bone specimens in tensile impact.
proportional limit, bi. and maximum stress, bU, with both moduli of elasticity, E and Ei; and (2) energy absorption capacity, U, and maximum stress ati. Figure 6 shows the relationship between the maximum stress (a,) and tangent modulus of elasticity (E) for fresh human bone specimens. The linear regression equation describing this relationship is given by (coefficient of determination r2 = 028).
*
where U is given in in. lb/in’ and 0” in lo3 psi. A parabolic relation U = 91.28 - 5524 a, + 0.3245 au2 fitted the data slightly better (coefficient by determination. r2 = 05483). The highly significant correlations between initial modulus of elasticity Ei and both proportional limit ui and maximum stress u, is significant. Since the in ~iuo strength of living bone cannot be determined by destructive testing, methods are being developed whereby the modulus of elasticity may be measured in citlo ultrasonically (Abendschein and Hyatt, 1970). Thus, with the correlations suggested here it may be possible to develop improved estimates for bone strength from non-invasive tests.
r
250
l
. ..
.
a,, = 7.73 + 5.0 E.
(2)
.
U = -9.94 + 6.354 a,
. . .
l
(3)
where a, is given in 10’ psi and E in lo6 psi. Both equations (2 and 3) have been shown graphically in Fig. 6. The relationship between the energy absorption capacity. U, and the maximum stress, 0, for fresh human bone specimens is,shown in Fig. 7. The linear regression equation is given by (coefficient of determination rz = @509) (4)
’
.
Although a linear relationship is simple to use, but a parabolic equation fitted the data better (coefficient of determination rz = 0.41) a, = -24.22 + 35.1 E - 7 E2,
.
$
Ip “I,.
. .
/
.
.
l* . . . . *l*
/
.I
I$
2p
Q
P
strmaUdPSi)
Fig. 7. Relationship between the impact energy absorption capacity and ultimate stress of fresh human compact bone specimens in tensile impact.
Tensile
0
IO
20
40
30
50
60
impact
70
properties
00
90
S. Osteons (YJ
Fig. 8. Relation between the tensile impact strength of fresh human bone and the percentage area of secondary osteons in the specimen. Co~~lurior~s hrtwrrn
impact
properties
and
rnicrostruc-
IUJY Correlation coefficients were also calculated between tensile impact properties and percentage area of secondary osteons in the fresh human bone specimens. Highly significant negative correlations (P < O+Ml) between the percentage area of secondary osteons and both the tensile impact strength and the impact energy absorption capacity were obtained Saha. 1974). The relation between the tensile impact strength and percentage osteon area is shown graphically in Fig. 8. The regression equation describing this relation is CT,= 30.88 - 0.269 X.
(5)
where 0, is given in ksi, and X is the percentage area of secondary osteons in the specimen. This result is similar to the observation by Currey (1959) of a significant negative correlation between static tensile strength and percentage area of Haversian systems in beef bone specimens.
of human
compact
249
bone
In light of these relationships between bone microstructure and mechanical properties it is possible to question if the correlations between elastic and strength properties are due to a dependence on the percentage area of secondary osteons or are instead an inherent property of bone irrespective of the histe logical structure. To answer this question. partial correlation coefficients were calculated between elastic and strength properties. controlling for the area of the secondary osteons (Table 3). Table 3 shows that statistically significant correlation coefficients do change slightly from the values shown in Table 2 but the values and the levels of significance for these correlations are not changed appreciably. Thus. the significant correlations between mechanical properties shown in Table 2 can be assumed to be inherent properties of compact bone, irrespective of the percentage area of secondary osteons. Therefore. attempts to use the modulus of elasticity to obtain bone strength by non-invasive methods may regard the relationship between modulus of elasticity and strength as independent of bone microstructure. SUMMARY
AND CONCLUSIONS
I. Standardized longitudinal specimens from human femoral diaphyses were tested in tensile impact at a strain rate of 133 set-‘. Dynamic mechanical properties were determined from the load-time histories of 49 fresh and 42 embalmed human compact bone specimens. For the fresh human bone specimens. the maximum stress, ultimate strain and impact absorption energy capacity were respectively 18.32 + 4.80 ksi. 1.15 k @309, and 107.3 + 42 in. lb/ in’. 2. Stress-strain behavior during tensile impact was found to be markedly nonlinear. About half of the specimens underwent some plastic deformation prior to failure and specimens with similar impact energy absorption capacities exhibited large variations in ultimate stress and strain. Thus, the characterization
Table 3. Partial correlation matrix between elastic and strength properties of fresh human bone samples, controlling for percentage area of secondary osteons in !he samples (coefficient/(D.F.)/significance)
Ult. stress la.) Eng. to rupture (Li)
Tan. mod. elasticity
(E)
Ult. strain (s)
Sec. mod. elasticity
(Ei)
0.
cl
E
E
-5
10XKl (0) s = 0.001 03981 (44) S = 0.003
0.3981 W) s = oGO3 10300 (0) s = OGol
05237 (44) S = OGOl - 0.2961 (44) S = 0023
-@1282 (44) S = 0.198 0.7376 (44) S=OOOl
0.4889 (44) S=~ool - 0.3866 (44) s = oW4
0.5237 (44) s = OGOl -0.1282 (44) S = 0.198 0.4889 (44) s = 00x
- 0.2961 (4) S = 0.023 0.7376 (44) s = OGOl - 0.3866 (44) s=oxlo4
1GXlO (0) s = OGOl -0.5315 (44) S=OOOl Q8600. (44) s = OQOl
-c-5315 (44) S=OOOl 1@000 (0) S=OOol - 06380 (44) S=OOol
0~8600 (44) s = OGOl - 06380 (44) s = OGOl 1NUXl (0) s = OGOl
250
S. SAHA
and W. C. HAYES
of the impact tolerance of bone by only the total energy absorption capacity may be misleading. These results also emphasize the advantages of longitudinal impact testing in comparison to transverse impact testing where the stresses and strains cannot be accurately calculated due to unknown amounts of plastic yielding. 3. For fresh human compact bone specimens tensile impact strength was higher than the static strength by 34?& indicating the strain-rate sensitivity of bone.
4. Statistically significant correlations were obtained between: (1) ultimate strain and both impact energy capacity and modulus of elasticity: (2) modulus of elasticity and both tensile impact stress and yield stress: (3) maximum stress and impact energy capacity. The highly significant correlation between the modulus of elasticity and both yield stress and maximum stress may be helpful in attempts to estimate in riw bone strength by non-invasive methods. The results also indicate that the failure energy of bone in tensile impact can be estimated most accurately from ultimate strain. 5. Statistically significant negative correlations were shown to exist between the percentage area of secondary osteons in fresh human bone specimens and both the maximum stress in tensile impact and the impact energy absorption capacity. The correlations between elastic and strength properties were found to be independent of their dependence on microstructure. REFERENCES
Abendschein. W. and Hyatt. G. W. (1970) Ultrasonics and selected physical properties of bone. C/in. Orthop. 69, 294-301. Ascenzi. A.. Bonucci, E. and Checcucci. A. (1966). The tensile properties of single osteons studied using a microwave extensometer. Studies on the Amromy and Function c$Bonc~trnd Jo&s (Edited by Evans, F. G.), pp. 121-141. Springer. Berlin. Bird. F. and Becker. H. (1966) Dynamic experiments with beef femur. Report No. ARA 322-2. Allied Research Associates, Concord, MA. Bird. F.. Becker. H.. Healer, J. and Messer, M. (1968) Experimental determination of the mechanical properties of bone. Aerosptrce Med. Jan. 1968, 4448. Black. J. and KorostolT, E. (1973) Dynamic mechanical properties of viable human cortical bone. J. Biomechunics 6, 435-438. Bonfield. W. and Li. C. H. (1966) Deformation and fracture of bone. J. ctppl. Phys. 37, 869-875.
Bonfield W. and Li, C. H. (1967) Anisotropy of nonelastic flow in bone. J. uppl. Phys. 38, 245&2455. Brooks, D. B., Burstein, A. H. and Frankel, V. H. (1970) The biomechanics of torsional fractures: the stress concentration of a drill hole. J. Bone Jnt Sure. 52-A. 507-514. Burstein, A. H.. Currey. J. D., Frankel, q. H. and Reilly, D. T. (1972) The ultimate properties of bone tissue: the effects of yielding. J. Biomechanics 5. 35-44. Burstein. A. H. and Frankel, V. H. (1968) The viscoelastic properties of some biological materials. Ann. N.Y. Acad. Sci. 146, 158-165. Burstein. A. H.. Reilly. D. T. and Frankel, V. H. (1973) Failure characteristics of bone and bone tissue. In Per-
sprcrirrs in Biomedictrl Enginrrriryt (Edited by Kenedi. R. M.). pp. 131-134. University Park Press. Baltimore. Chamay. A. (1970) Mechanical and morphological aspects of experimental overload and fatigue in bone. J. Biomechcrnics 3, 226.
Clark. D. S. and Duwet
P. E. (1950) The influence of
strain rate on some tensile properties of steel.
Proc.
56C-575. Clark. D. S. and Wood. D. S. (1950) The influence of specimen dimension and shape on the results in tension impact testing. Pro
OF
s. &HA Department of Engineering and Applied Science, Yale University. New Haven. CT 06520. U.S.A. and
W. C. HAYES Department of Applied Mechanics. Stanford University. Stanford CA 94305. U.S.A. Abstract-Longitudinal specimens from human compact bone were tested in a pendulum type instrumented tensile impact tester at a strain rate of 133 set -‘. The recorded load time histories showed marked nonlinearities in the stress strain behavior of some specimens including plastic deformation and strain hardening effects, thus emphasizing that the fracture energy alone is an incomplete representation of the tensile impact behaviour of bone. Mean tensile impact strengths and impact energy capacities were 126.3 + 33.1 MN/m2 and 18790 k 7355 J/m2 for 49 fresh human specimens. Quasi-static tensile strengths for 13 fresh human samples were 34”,, less than the tensile impact strength. Statistically significant correlations were found between elastic properties. ultimate stress and impact energy capacity. Tensile impact strength also correlated negatively with the percentage area of secondary osteons in the specimen.
INTRODUCTION
safety and reduce injury levels in transportation, industrial and recreational accidents must consider the tolerance of human tissues and organs to accelerative and impact forces. Such forces are characterized by abrupt onset, short duration and high magnitude. If protective systems are to be optimally designed, tissue and organ tolerances to such forces must be accurately obtained for a variety of design parameters such as impact velocity, force magnitude and force duration and for such biological factors as age and sex. However, the current state of knowledge concerning human impact tolerance is incomplete and relatively little data is available on the tolerence limits of individual body components against localized impacts. In particular, the impact tolerence of human long bones is poorly understood. The fact that half of all injury producing automobile accidents involve injuries to the extremities (Kihlberg, 1970) emphasizes the need for data with which to better design protective systems and thus reduce the frequency and severity of fractures of the long bones. Most previous studies of the dynamic strength of bone were conducted on whole bones subjected to impact loads (Burstein and Frankel, 1968; Mather. 1968: Evans, 1970: Sammarco et ul., 1971: Kramer er ul.. 1973). These studies provide tolerance limits for individual whole bones, but little information on the dynamic behavior of bone as a material due to difficulties in calculating stresses and strains. Such Attempts
to improve
*Received
10 April
1974.
243
calculations are difficult with whole bones since: (1) the cross-section of a long bone changes shape and size along the length; (2) both compact and cancellous bone are present in varying proportions: (3) simple tension or compression tests produce combined bending and axial loading of the shaft; and (4) inelastic deformation of the bone is likely to be non-uniformly distributed over the whole cross-section (Burstein er al., 1972). Moreover, the thickness of the cortex and the shape and size of a long bone vary with age and between individuals thus making it difficult to compare results obtained by different investigators. For these reasons, this investigation followed other studies which used standardized bone specimens in well-defined loading configurations to determine the mechanical properties of bone as a material (McElhaney. 1966; Wood, 1971). The importance of tensile loading in the fracture mechanisms of bone has long been recognized. Evans and his colleagues (1951, 1952) and Evans (1957) demonstrated with brittle coatings that most bone fractures occur in tension since bone, like most brittle materials. is weak in tension. Brooks er al. (1970) also suggested that bone failure is closely associated with planes of maximum tensile stress. Therefore. it is surprising to note that while the impact tolerence of whole bones and the dynamic strength of standardized bone specimens have been investigated in modes other than tension, few attempts have been made to determine the tensile impact strength of bone at high loading rates. The objective of the present investigation was to provide data on the tensile impact strength and dynamic mechanical properties of human compact bone
244
S. SARA and
and to relate these properties to bone microstructure. Standardized tensile specimens and instrumented testing methods were used to provide accurate determinations of stress and strain throughout impact. This approach represents a significant improvement over previous impact tests of bone which only measured the total energy to fracture. PREVIOUS
INVESTIGATIONS
Recent reviews of the mechanical properties of bone (Evans, 1957, 1973: Kraus, 1968: Currey, 1970: Swanson. 1971: Herrmann and Liebowitz. 1972: Reilly and Burstein. 1974) emphasize that few data are available on the dynamic behavior of small bone specimens. Some workers have reported the use of Charpy impact tests to study dynamic fracture of bone (Tsuda. 1957: Hert er (II., 1965: Bonfield and Li. 1966: Swanson. 1971). However, the large scatter evidenced in these results makes it difficult to draw meaningful conclusions. Moreover, because of uncertainties concerning plastic deformation in such experiments, bending tests cannot be used to calculate maximum stresses and strains during impact (Burstein rr al.. 1972). Compared to the number of transverse impact tests, few attempts have been made to study the longitudinal impact properties of bone. Bird and Becker (1966) and their associates (Bird et al., 1968) performed compressive impact tests on specimens from fresh beef femurs in order to establish a relationship between failure mode and impactor velocity. They found that the modulus of elasticity decreased and the ultimate stress increased with stress rate. They also noted that whole bones were more impact resistant than were small specimens. McElhaney and Byars (1965) and McElhaney (1966) performed constant velocity compressive tests at strain rates of from OGOl to 1500 see-’ on specimens from embalmed human and fresh beef femurs. For human bone, the ultimate compressive stress increased from 21% ksi at the lowest strain rate to 46.0 ksi at the highest. The energy absorption capacity and maximum strain first increased to a maximum and then decreased with increases in strain rate. The only detailed study on the dynamic response of bone in tension was conducted by Wood (1971) in tests of cranial bone specimens at strain rates ranging from 0005 to 150 set- I. While the breaking stress and modulus of elasticity increased with strain rate, the breaking strain decreased. The energy absorption capacity was independent of strain rate. Black and Korostoff (1973) also studied the frequency response of the elastic modulus of excised human compact bone specimens in tension. Elastic moduli were found to increase with loading frequency in the range of 354353.6 Hz. Previous investigations of the influence of bone microstructure on mechanical properties have concentrated mainly on the effects of the size and num-
W. C. HAYES
ber of osteons in specimens tested quasi-statically. Evans and Bang (1967) demonstrated negative correlations between ultimate tensile strength and the percentage area of osteons in the specimen break area for embalmed human compact bone. Evans and Vincentelli (1974) found a positive correlation between bone compressive strength and percentage osteon area. Evans and Riolo (1970) also found a positive correlation between the fatigue life and percentage of osteon area in bone. Recently. Burstein and co-workers have focused considerable interest on the importance of plastic deformation in the mechanical behavior of bone. Using tensile tests on bovine bone at relatively low strain rates. Burstein et t/l. (1972) demonstrated the existence of significant regions of plastic deformation in bone. They later demonstrated that this deformation is truly plastic by conducting quasi-static tensile loading and unloading tests on bovine bone and showing irreversible and successively additive deformations beyond yield (Burstein et d.. 1973). Using standard histological techniques the authors were unable to determine the exact mechanisms for plastic flow but assumed that they included osteon pull out. microcracking and void coalescence. Similar plastic deformation has also been observed in specimens of human compact bone tested at low strain rates (O.OS/sec)in both tension and compression (Reilly et al., 1974). In a recent paper. Currey and Brear (1974) have examined the microstructural changes that are associated with tensile yield in bone.
MATERIALS
AND METHODS
The initial stages of this investigation utilized bone specimens from fresh adult beef femurs and tibias. These results are reported elsewhere (Saha and Hayes, 1974). Subsequently, human compact bone specimens were obtained from both femurs of an embalmed adult human skeleton and from the right femur of a 38 yr old male autopsy specimen with no history of bone disease. All compact bone specimens were removed from the femoral diaphysis and were longitudinally oriented as it was not possible to obtain sufficiently long test specimens from the circumferential or radial directions. The dimensions of the tensile specimens were chosen acccording to the ATSM specifications for the tensile impact testing of plastics (D-1822-61T, Type L). The standard specimen used in this investigation is shown in Fig. 1. To prepare tensile test specimens, each femur was sectioned into five segments along its length and each segment was divided into quadrants. Parallel sided strips of the required thickness were removed from each quadrant using a diamond saw thin sectioning machine. The finished necked shape was produced in a standard mill. All machining operations were performed using copious irrigation to minimize thermal
(Facing p. 244)
Tensile
impact
properties
ENERDI SCALE
PENDULUM HEAD
Q”ARTZ LOAD TEST CELL SPECIMEN
Fig. 2. Schematic
diagram
of the tensile
impact
test set-up.
damage. Specimens were equilibrated in Ringer’s SOlution and stored at from - 10 to -20-C. For testing specimens were thawed and kept submerged in Ringer‘s solution at room temperature. Impact testing was accomplished within 3 min of removal from the solution and exposed surfaces were continually saturated to minimize surface drying. These preparation. storage and testing procedures have been shown by other workers to optimally preserve the mechanical properties of bone (McElhaney er trl.. 1964: Sedlin and Hirsch. 1966). A schematic diagram of the experimental apparatus used for tensile impact testing is shown in Fig. 2. An instrumented pendulum type tensile impact tester (Modified Custom Scientific Instruments model CS-137) at a striking velocity of 11.3 ft,isec (3-44 m:secl was used throughout. The bone specimens were gripped at one end using fixed, serrated jaws and at the other end by a freely movable end clamp. A 500 lb (22365N) capacity quartz load cell (Kistler Model 910) with a signal rise time of Sp/sec and a natural frequency of 100 kc was used to monitor load during testing. The load cell output was amplified and recorded on a storage oscilloscope (Tektronix model 564) as a load-time curve. Triggering was accomplished internally by using a vertical plug-in with a built-in delay line (Tektronix mode1 3A6) in the oscilloscope. With this arrangement it was possible to use internal triggering without any loss of the initial portion of the load-time curve. ENERGY ABSORBED
DURING
CATASTROPHIC
of human
compact
hone
Combining all the losses during impact due to air resistance, friction and the kinetic energy imparted to the clamp. the velocity of the pendulum head was reduced by less than 4’,, during impact. Therefore. it is reasonable to assume a constant velocity impact and to calculate total specimen deformation on the basis of an average velocity of 133.9 inset. Thus. the Inad-time cur\es also represent dynamic stress-strain curses. The dynamic mechanical properties cl\lculuted from the load-time curves are shown in Fig. 3. The proportional limit. (T;. was defined as the maximum stress the samples sustained without an appreciable deviation from linearity. Strain was calculated on the bases of an effective length of one inch. a value verified by strain gaged specimens (Saha. 1973; Saha and Hayes. 1974). A secant modulus of elasticity. Ei. was also calculated from the stress-strain data at the proportional limit. indicating the slope of the straight line joining the point of yield stress to the origin. The total energy absorption capacity was obtained by measuring the area under the load-time curve with a planimeter. In all cases the values agreed with scale reading of the pendulum impact tester after corrections were made for windage and friction losses and for clamp kinetic energy. The use of instrumented testing methods also allowed the separation of the total energy to fracture into: (1) Energy absorbed during elastic deformation: (2) Energy absorbed during plastic deformation: and (3) Energy absorbed during tearing (Fig. 3). The’total impact energy. U. was considered the sum of the energy absorbed during elastic and plastic deformation. The total numbers of human compact bone specimens tested at a strain rate of 133 set were 58 fresh and 42 embalmed. Thirteen additional fresh human specimens were tested quasi-statically in tension using a speciallv designed loading rig at a cross-head speed of OGOl2 in:sec (0.031 mm’secl. The same load cell used for tensile impact testing was used to monitor load during quasi-static testing. After mechanical testing. the specimens were imbedded in cold metallurgical mound, polished on a series of rotating metallurgical wheels and photopmphed at 50x magnification in a reflected-light metallurgical microscope. The percentage of the total area occupied by osteons was measured with a planimeter by tracing osteon outlines on transparent paper and joining the outlines. This method resulted in osteon area measurements repeatable to within five percmt. RESULTS
AND DISCCSSION
PROPAGATION STRAIN
(TIME)
’
Fig. 3. Idealized stress-strain (or load-time) curve in tenslle impact showing the energy absorbed during elastic, plastic and tearing phases.
Typical load-time curves for human compact bone specimens in tensile impact are shown in Fig. 4. The observed failure modes ranged from nearly brittle fracture as in Fig. 4(a) to fracture with plastic deformation as in Fig. 4(b). Some specimens also indicated
246
S. SAHA and
(b)
(a)
(d
Fig. 4. Characteristic load-time or stress-strain curves for fresh human bone in tensile impact: (a) elastic failure: specimen from proximal femur, medial quadrant: V. Scale = 501b or 6017 psi/div. H. Scale = 20~ set or 0.002658 in/in/div. (b) plastic deformation; specimen from distal femur. anterior quadrant; V. Scale = 25 lb or 3161 psi/div. H. Scale = 20 !1 set or 0.002658 in/in/div. (c) strain hardening; specimen from distal femur. medial quadrant: V. Scale = 25 lb or 2941 psi/div. H. Scale = 20 p set or 0.002658 in/in/div. strain hardening effects as shown in Fig. 4(c). Specimens with markedly nonlinear stress-strain relations exhibited an initial elastic region followed by a smooth transition to a plastic region which usually included some strain hardening. Similar stress-strain relations were reported by Reilly er c/l. (1974) in quasistatic tensile tests of human compact bone. In the present investigation. bone specimens with similar impact energy absorption capacities (as measured by the area under the stress-strain curves) often exhibited large differences in ultimate stress and strain. Since the energy to fracture is a function of the applied force times the distance through which the force operates. equal tensile impact energies may result from a large force associated with a small elongation and from a small force associated with a large elongation. The results presented here suggest that the failure characteristics of bone are not adequately described by the failure energy alone since significant deviations from linearity often occur. The use of the total energy to fracture as a tolerance limit for bone is thus an oversimplification which may preclude optimum use of tolerance data in the design of protective systems. Means and standard deviations for the tensile impact properties for 49 fresh and 42 embalmed human compact bone specimens are presented in Table 1. Of the total of 58 fresh human bone samples tested. nine specimens had cavities in their structure which were visible to the naked eye and subsequent examin-
W. C. HAW
ation of their microstructure indicated that they were partially cancellous in character. Thus their mechanical properties were not included in the values shown in Table 1. The data show that the ultimate tensile strength of fresh human bone specimens is higher than that of embalmed specimens. These results are in agreement with data on the effect of embalming in beef bone (McElhaney et trl.. 1964) but contradict the results reported by Evans (1973) on wet-tested human cortical bone. The fact that the embalmed specimens were from an older person in this study may the the reason for this difference. Table 1 also shows that the modulus of elasticity (with a coefficient of variation of 23.706) is the most consistent of the mechanical properties of bone. Wood (1969). in this study of the dynamic tensile behavior of cranial bone, also observed that the modulus of elasticity was the least variable of the mechanical properties. Of the 49 fresh human bone samples tested, 19 showed a decrease in the initial slope of the stress strain curve (E in Fig. 3) beyond the proportional limit (ai) which indicated the onset of some plastic deformation. The yield stress. Ui. was 9.79 + 2.72 ksi (67.5 + 18.8 MN/m’) for these 19 fresh human bone specimens. This agreed with our previous result of plastic deformation of beef bone samples in tensile impact (Saha and Hayes. 1974). Other investigators have also noted plastic deformation of bone in static tension (Ascenzi et trl.. 1966: Bonfield and Li, 1966, 1967; Burstein ef al.. 1973; Reilly et al., 1974). shear (Bonfield and Li, 1967). bending (Burstein rt trl.. 1972) and dynamic compression (McElhaney, 1966: Bird et al., 1968). While the mechanism leading to this plastic deformation has not been definitely established, most workers assume that it represents a combination of microcrack formation. osteon pullout, and void coalescence (Chamay, 1970: Reilly et al., 1974: Currey and Brear, 1974). Data on the biological effects of plastic deformation in bone is not available. Such information would be helpful in determining whether the tolerance limits for bone should be based on the prevention of plastic deformation or whether some plastic deformation may be allowed. Sttrtic. rs trttsilr
iriprcf
strmgtk
The mean yield stress. oi. for 13 specimens of fresh human compact bone tested in quasi-static tension
was Il.13 ~fr2.25 ksi (76.74 f 15.51 MN/m*).
Simi-
Table 1. Means and standard deviations of the mechanical properties of human bone specimens in tensile impact (values in S.I. units are shown within parentheses)
Condition
No. of samples
Ultimate stress 0, in ksi (MN/m’)
Impact energy U in in. lb/in’
(Jim’)
Maximum strain (:‘/,)
Fresh
49
18.32 i 4.80 (1263 + 33.1)
107.3 + 42 (18790 + 7355)
1.15 + 030
Embalmed
42
14.3 * 3.7 (98.6 + 25.5)
81.7 + 31.5 (14308 f 5517)
0.982 k 0.225
Modulus of elasticity in IO’ psi (GN/m’) Secant, E, Tangent. E 2.11 f 0.50 (145 k 3.4)
1.80 f 0.42 (12.4 f 2.9) 1.76 k 023 (12.1 + 1.6)
Tensile impact properties of human compact bone larly. the ultimate stress. uu. was 13.72 + 1.47 ksi (94.60 & 1013 MN,m’). The static tensile strength of each fresh human bone sample was compared with the impact strength of another sample of the same region. i.e. from the same quadrant, longitudinal segment and approximate radial distance from the center of the shaft. The percentage of increase in strength was calculated for each pair using the formula
.a .
.
C”.____-ll”,FKl)- 01,,.!.>,I‘, ‘1oagrincrease = _ x 100 rs” (\l&lCI and the ultimate stress in tensile impact was 34.4 & 30.1”,, higher than the static strength for 13 fresh compact human bone specimens. This difference. using a paired r-test, is significantly different from zero at the P < OQOl level. Wood (1971) also found an increase in ultimate stress of approx. 409, for cranial bone specimens tested at strain rates of 0.01 and 100 set-‘. An increase in maximum stress with increasing strain rates has also been observed for bone in compression (McElhaney and Byars. 1965: Bird et r/l.. 1968). This increased bone strength in tensile impact is in agreement with similar observations for engineering materials. Clark and Duwez (1950) compared the static tensile strength with the dynamic strength of steel at a strain rate of 190 set-’ and showed increases in ultimate strength of 30-450,,. Clark and Wood (1950) also showed that the ultimate strength of some metals and alloys was greater under dynamic conditions than under static conditions. Similar observations, indicating an increase in ultimate stress with higher strain rates. have been reported for other engineering materials (Ely. 1960). For embalmed human compact bone in static tension. Evans and Lebow (1951. 1952) obtained an energy absorption capacity of 83.6 in. lb/in.3 The tensile impact energy of 81.7 in. lb/in3 obtained in this investigation (Table 1. expressed per unit volume). agrees with the value obtained by Evans and Lebow. The present results do not exhibit the increase in energy absorption capacity that was observed by Mather (1968) and Burstein and Franked (1968) in their comparison of static and dynamic properties. Hc,\\c‘\cr. the rc5ults are similar to Wood’s (1971) hndlngs of no Increase in the energy absorption capacity of cranial bone when tested in dynamic tension. McElhaney and Byars (1965) further reported a critical strain rate of 1 set-’ at which the energy absorption capacity was a maximum for bone in compression. Experiments over a wide range of strain rates are presently underway to determine if such a critical strain rate exists for bone in tension. On the basis of tests of 242 specimens from the human femur in static tension. Evans and Lebow (1951 j obtained percentage elongations of from 1.15 to 1.27”,, which is slightly higher than the 0.98’- -+ 0.3’5” -0. obtained in tensile impact for embalmed bone in this investigation. This is to be expected. however. since with higher strain rates. the
. . /.
* . /
. l *
.‘* . .* . . .. ’ . / I l
J.
I
*
i 0.5
I.0
2.0
I.5
Max. Strain
2.5
1%)
Fig. 5. Relationship between the impact energy absorption capacity and maximum strain of fresh human compact bone specimens in tensile impact. material has less chance to deform plastically before failure. These results also agree with Wood (1969) who observed a decrease in breaking strain with increases in strain rate. Correltrtions
between
eltrstic
properties
ctnd strength
Pearson’s product moment correlation coefficients were used to determine correlations between elastic properties and bone strength. The correlation matrix for 49 fresh human samples tested in tensile impact is shown in Table 2. An extremely high positive correlation (P < OQOl) was noted between impact energy absorption capacity. U. and ultimate strain. E. This relationship is shown graphically in Fig. 5. Using a HP 9805 A calculator. the linear regression equation (Fig. 5) was obtained as (coefficient of determination 1.’ = 0.7180) I! = -48.87
+ 14@0 E
(1)
where the energy absorption capacity U is given in in. lb/in* and c is the percentage of ultimate strain. This indicates that the failure energy of bone in tensile impact can best be estimated from ultimate strain. Evans and Lebow (1951, 1952) also reported a strong correlation between maximum strain and energy absorption in static tensile testing of human femoral specimens. In most cases, the correlation coefficient between U and E is higher than the coefficient between U and ultimate stress 0,. This suggests that it may be more appropriate to base the tolerance limits of bone on maximum strain rather than on maximum stress. as is customary. Table 2 also shows that statistically significant positive correlations exist for: (1)
248
S. SAHA and
Table 2. Correlation
Ult. tensile
Impact
matrix
elastic and strength
stress @,I
energy
(U)
Tan mod of elasticity
Ult. strain
between
(E)
(E)
Sec. mod. elasticity
(&)
Yield stress (ci)
properties
2.0
HAYES
for fresh human
bone (coefficient;(cases)~significancek
0”
u
E
E
-5
0,
1GOOO (0) S=O.oOl 0.6926 (49) S = oNl1 05303 (49) s = O+Ol 0.1660 (49) S = 0127 05458 (49) S=OOOl 04734 (19) s = 0.020
06926 (49) S=OOOl 1WOO (0) S=OOOl - 0.0549 (49) s = 0354 08473 (49) S=OOOl - 0.0673 (49) S = 0323 04142 (19) s = 0039
0.5303 (49) S = OQOl - 0.0549 (49) s = 0.354 1.0000 (0) s = OGOl -0.4144 (49) s = oGO2 0.8701 (50) s = OQOl 0.7589 (19) S=OOOl
0.1660 (49) S = 0.127 0.8473 (49) s = 0.001 -0.4144 (49) s = oGO2 1+)000 (0) s = OQOl - 0.4738 (49) s = 0.001 01568 (19) s = 0.261
05458 (49) S = 0~001 - 0.0673 (49) s = 0323 0.8701 (501 s = oNl1 -0.4738 (49) s = OGOl 1GOOO (0) s = 0001 0.7774 (19) s = 0001
04734 (19) S = 0.020 04142 (19) s = 0.039 0.7589 (19) s = OXKll 0.1568 (19) S = 0.261 0.7774 (19) S=OOOl 1WOO (0) s = 0001
25-
I.5
W. C.
25
3.0
Mod. 01 ElaSticv?y (IO’pri)
Fig. 6. Relationship between the ultimate stress and the modulus of elasticity of fresh human compact bone specimens in tensile impact.
proportional limit, bi. and maximum stress, bU, with both moduli of elasticity, E and Ei; and (2) energy absorption capacity, U, and maximum stress ati. Figure 6 shows the relationship between the maximum stress (a,) and tangent modulus of elasticity (E) for fresh human bone specimens. The linear regression equation describing this relationship is given by (coefficient of determination r2 = 028).
*
where U is given in in. lb/in’ and 0” in lo3 psi. A parabolic relation U = 91.28 - 5524 a, + 0.3245 au2 fitted the data slightly better (coefficient by determination. r2 = 05483). The highly significant correlations between initial modulus of elasticity Ei and both proportional limit ui and maximum stress u, is significant. Since the in ~iuo strength of living bone cannot be determined by destructive testing, methods are being developed whereby the modulus of elasticity may be measured in citlo ultrasonically (Abendschein and Hyatt, 1970). Thus, with the correlations suggested here it may be possible to develop improved estimates for bone strength from non-invasive tests.
r
250
l
. ..
.
a,, = 7.73 + 5.0 E.
(2)
.
U = -9.94 + 6.354 a,
. . .
l
(3)
where a, is given in 10’ psi and E in lo6 psi. Both equations (2 and 3) have been shown graphically in Fig. 6. The relationship between the energy absorption capacity. U, and the maximum stress, 0, for fresh human bone specimens is,shown in Fig. 7. The linear regression equation is given by (coefficient of determination rz = @509) (4)
’
.
Although a linear relationship is simple to use, but a parabolic equation fitted the data better (coefficient of determination rz = 0.41) a, = -24.22 + 35.1 E - 7 E2,
.
$
Ip “I,.
. .
/
.
.
l* . . . . *l*
/
.I
I$
2p
Q
P
strmaUdPSi)
Fig. 7. Relationship between the impact energy absorption capacity and ultimate stress of fresh human compact bone specimens in tensile impact.
Tensile
0
IO
20
40
30
50
60
impact
70
properties
00
90
S. Osteons (YJ
Fig. 8. Relation between the tensile impact strength of fresh human bone and the percentage area of secondary osteons in the specimen. Co~~lurior~s hrtwrrn
impact
properties
and
rnicrostruc-
IUJY Correlation coefficients were also calculated between tensile impact properties and percentage area of secondary osteons in the fresh human bone specimens. Highly significant negative correlations (P < O+Ml) between the percentage area of secondary osteons and both the tensile impact strength and the impact energy absorption capacity were obtained Saha. 1974). The relation between the tensile impact strength and percentage osteon area is shown graphically in Fig. 8. The regression equation describing this relation is CT,= 30.88 - 0.269 X.
(5)
where 0, is given in ksi, and X is the percentage area of secondary osteons in the specimen. This result is similar to the observation by Currey (1959) of a significant negative correlation between static tensile strength and percentage area of Haversian systems in beef bone specimens.
of human
compact
249
bone
In light of these relationships between bone microstructure and mechanical properties it is possible to question if the correlations between elastic and strength properties are due to a dependence on the percentage area of secondary osteons or are instead an inherent property of bone irrespective of the histe logical structure. To answer this question. partial correlation coefficients were calculated between elastic and strength properties. controlling for the area of the secondary osteons (Table 3). Table 3 shows that statistically significant correlation coefficients do change slightly from the values shown in Table 2 but the values and the levels of significance for these correlations are not changed appreciably. Thus. the significant correlations between mechanical properties shown in Table 2 can be assumed to be inherent properties of compact bone, irrespective of the percentage area of secondary osteons. Therefore. attempts to use the modulus of elasticity to obtain bone strength by non-invasive methods may regard the relationship between modulus of elasticity and strength as independent of bone microstructure. SUMMARY
AND CONCLUSIONS
I. Standardized longitudinal specimens from human femoral diaphyses were tested in tensile impact at a strain rate of 133 set-‘. Dynamic mechanical properties were determined from the load-time histories of 49 fresh and 42 embalmed human compact bone specimens. For the fresh human bone specimens. the maximum stress, ultimate strain and impact absorption energy capacity were respectively 18.32 + 4.80 ksi. 1.15 k @309, and 107.3 + 42 in. lb/ in’. 2. Stress-strain behavior during tensile impact was found to be markedly nonlinear. About half of the specimens underwent some plastic deformation prior to failure and specimens with similar impact energy absorption capacities exhibited large variations in ultimate stress and strain. Thus, the characterization
Table 3. Partial correlation matrix between elastic and strength properties of fresh human bone samples, controlling for percentage area of secondary osteons in !he samples (coefficient/(D.F.)/significance)
Ult. stress la.) Eng. to rupture (Li)
Tan. mod. elasticity
(E)
Ult. strain (s)
Sec. mod. elasticity
(Ei)
0.
cl
E
E
-5
10XKl (0) s = 0.001 03981 (44) S = 0.003
0.3981 W) s = oGO3 10300 (0) s = OGol
05237 (44) S = OGOl - 0.2961 (44) S = 0023
-@1282 (44) S = 0.198 0.7376 (44) S=OOOl
0.4889 (44) S=~ool - 0.3866 (44) s = oW4
0.5237 (44) s = OGOl -0.1282 (44) S = 0.198 0.4889 (44) s = 00x
- 0.2961 (4) S = 0.023 0.7376 (44) s = OGOl - 0.3866 (44) s=oxlo4
1GXlO (0) s = OGOl -0.5315 (44) S=OOOl Q8600. (44) s = OQOl
-c-5315 (44) S=OOOl 1@000 (0) S=OOol - 06380 (44) S=OOol
0~8600 (44) s = OGOl - 06380 (44) s = OGOl 1NUXl (0) s = OGOl
250
S. SAHA
and W. C. HAYES
of the impact tolerance of bone by only the total energy absorption capacity may be misleading. These results also emphasize the advantages of longitudinal impact testing in comparison to transverse impact testing where the stresses and strains cannot be accurately calculated due to unknown amounts of plastic yielding. 3. For fresh human compact bone specimens tensile impact strength was higher than the static strength by 34?& indicating the strain-rate sensitivity of bone.
4. Statistically significant correlations were obtained between: (1) ultimate strain and both impact energy capacity and modulus of elasticity: (2) modulus of elasticity and both tensile impact stress and yield stress: (3) maximum stress and impact energy capacity. The highly significant correlation between the modulus of elasticity and both yield stress and maximum stress may be helpful in attempts to estimate in riw bone strength by non-invasive methods. The results also indicate that the failure energy of bone in tensile impact can be estimated most accurately from ultimate strain. 5. Statistically significant negative correlations were shown to exist between the percentage area of secondary osteons in fresh human bone specimens and both the maximum stress in tensile impact and the impact energy absorption capacity. The correlations between elastic and strength properties were found to be independent of their dependence on microstructure. REFERENCES
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