ON THE FRACTURE TOUGHNESS METACARPI*

OF EQUINE

A. ALTO Istituto di Tecnologie, Facolta di Ingegneria, Universita di Bari, 70126, Bari, Italy and M. H. POPE Departments of Orthopaedic Surgery and Mechanical Engineering, University of Vermont, Burlington, VT 05401. U.S.A. Abstract - This paper reports on the measurement of both tensile and fracture behavior of paired equine

metacarpi. Tests were performed at strain rates of IO-” set -i. Three-point bending tests were carried out on notched specimens to attain the toughness values and the same specimens were used to obtain the elastic moduli. The average fracture toughness was found to be constant from the proximal to the distal end. Both the anterolateral and anteromedial segments have fracture toughness that increases from the proximal to the distal zone. This trend is reversed in the posterior specimens. The fracture toughness was found to increase as a function of the number of discontinuities

INTRODUCTION

In the last twenty years, much has been done to improve our knowledge of the mechanical characteristics of bone substance. Evans (1957,1973) and Kraus (1968) presented a large summary of data established by various authors on mammalian bones, both dry and fresh. The mechanical properties available in the literature are, on the other hand, mostly “classical” characteristics such as ultimate strength, strain and Young’s moduli, etc. The fracture behavior and the fracture toughness of bone were more recently investigated. Bonfield and Li (1966) demonstrated that the energy absorbed from bone during fracture is decreased by the presence of surface cracks. Piekarski (1970) pointed out that at low strain rates bone displays very high resistance to crack propagation and measured the amount of energy required to propagate fracture utilizing the load-deflection curves obtained from testing notched beef bone specimens in bending. Piekarski also related the bone fracture work to the microstructure of the bone and showed that the work of fracture increased with the number of bone discontinuities (blood vessels, canaliculi, etc.). Pope and Outwater (1971) confirmed that important result and measured the fracture energy of fresh and dry anthropoid bone, both in longitudinal and in transverse direction. Pope and Murphy (1974) suggested later that the excellent fracture characteristics of bone derive from the existence of a weak osteomatric interface. Bone toughness studies as measurement of thecritical stress intensity factor for crack propagation (k,c) were conducted by Margel-Robertson (1973) * Received 16 December 1977; in reGsedform 23 June 1978.

who obtained k,, values of bovine bones of 6.48 5 2.14 MN me3 s. The study performed led to the conclusion that fracture toughness is independent of the existence of a precrack, the energy required for crack initiation being negligible compared to that for crack propagation. Bonfield and Datta (1976) measured the fracture stress of longitudinal bovine tibia compact bone sections and found fracture toughness values of 2.2-4.6 MN m-3,2 and specific fracture energy values ranging between 3.9 and 5.6 x 10zJm-‘. Melvin and Evans (1973), using bovine remora at loading rates of 0.55 and 50 mm min, found k,, of 3.21 MN rnm3” for longitudinal slow cracks and 5.05 MN m-3’r for longitudinal fast cracks. The k,c for transverse slow cracks was 5.05 MN me3 ’ and for fast transverse cracks 7.69 MN me3 ‘. Wright and Hayes (1977) found the k,, o f compact bovine bone in a longitudinal direction to be 3.61 MN rnb3 ‘. However, very few data are available on the bone toughness as critical stress intensity factor for crack propagation. Furthermore, no data at all are available on the variation of bone toughness along a long bone, although variation of other properties is well established (Piekarski, 1970; Pope and Murphy, 1974). This work refers to three-point bending fracture toughness tests carried out on notched specimens to assess the values, and thus the variation, of k,, along dry equine long bones (metacarpi). Tensile tests were also carried out measuring the ultimate strength (a), the Young’s modulus (E) and utilizing these parameters to calculate the specific surface energy (‘i) for fracture. Analysis of the fractured bone by optical microscopy enabled us to confirm some of the results obtained from the above-mentioned authors and to make some considerations on the observed fracture behavior of bone.

415

A. ALTO and M. H. POPE

416 EXPERIMENTAL WORK

For experimental tests, three pairs of equine metacarpi (2-3 yr old) were used. From each pair of antimere metacarpi, the specimens were prepared as shown, both for fracture and tensile tests (Fig. 1). Care was taken to avoid cancellous bone in the specimens. From each of the three left metacarpi, eighteen fracture test specimens were cut, six from each of three 120” segments in which a metacarpus can be divided (I: posterior segment: II: anterolateral segment; III: anteromedial segment) (Fig. 1). From each of the three right metacarpi, nine long fracture test specimens were cut (three from each segment), and after the fracture tests were performed, it was possible to obtain from the broken specimens eighteen tensile specimens (six from each segment). Care was taken to measure the dimensions of both sides of the notch (“a” and “W-a” in Fig. 1) for each specimen before the fracture test. To avoid significant errors a Leitz Durimet micrometer was used. Fracture tests were performed on a 10 tons Instron machine equipped with a 100 kg load cell. The stress intensity expression used to relate applied bending load and crack length was the one routinely used for metallic materials (ASTM 1970).

kQ=&q19(~!1‘-4.6(;y~ +21.g(s)‘z-37.6(~)7i+3g.,~~~~].

For metallic materials, to be sure that the measured toughness k, is the critical one, it is necessary, amongst others, that the following conditions are satisfied for each specimen :

(2)

It is thus necessary to know k, and elS of the material to design the specimen and to verify, after each test, that the result obtained from the fracture test of (k,) and the yield strength (aYS)measured on another specimen, satisfy equation 2 ; otherwise the result obtained is not valid as a measure of k,c. For bone this presents a difficulty of the variation of mechanical properties from bone to boneand from zone to zone of the same bone.

Right

I - PoJterior

metocorpus

seoment

CTi - Ant.-medlol

Fracture

Dimensions,

(1)

test

specimen

mm’

Fig. 1. Specimen cutting proceduie for each third of each pair of metacarpi and fracture test specimens.

On the fracture toughness of equine metacarpi

Fig. 2. Typical load-deflection

plot.

In the present case the specimen design was done after preliminary tensile tests to establish an average strength (0,) of the dry equine metacarpi, after the fracture tests and the tensile ones, properties were found according to equation (2). Examination of the load-deflection curves (Fig. 2) and of the fracture surfaces (by optical stereomicroscopy) showed no evidence of plastic deformation. Based on the structural symmetry of antimere bones and on their consequential similar mechanical behavior (Pope and Outwater, 1971), it can be said that twenty-seven values of k,, (nine for each quadrant), nine values of tensile strength and nine values of the Young’s modulus were obtained for each pair of bones. The hypothesis of the similar behavior of corresponding zones of antimere bones was confirmed by the fact that the values obtained from testing the specimens cut from the right metacarpi are in good agreement with the corresponding values obtained from the left. All tests were performed on dry bones at a strain rate of 0.9 x 10mJ set-i.

EXPERIMENTAL

RESULTS

Figure Z shows a typical load-deflection curve recorded during the fracture tests. The experimental results are presented in graphic form in Figs. 3-5 as average of the (corresponding) values found by testing all the three pairs of metacarpi. The highest standard deviation in most of the cases was < +21”,, The values obtained for the Young’s modulus ranged between 21 and 24 GN me2 ; considering the k,c average value of 7.5 MN mm3 ’ and utilizing the Griffith’s formula for elastic solids : 6=E’

kfC

the specific surface energy for fractures ranges between 11.7 x 10’ and 13.4 x 1O’J m-‘.

ANALYSIS OF RESULTS

The k,, results are in good agreement with the values obtained by Margel-Robertson (1973) on bo-

117

vine bones but are higher than those found by Bontield and Datta (1976) on bovine tibia. It was found that the right metacarpi had values of k,, slightly higher (about 8”,) than the left ones. All the results have good agreement amongst themselves, with the gCvalues having slightly more spread. In most cases, excepting the posterior segment, the higher the tensile strength of the bone, the lower the toughness. The trends of k,c and G, along the bone axis, for the posterior segment, are different from the trends of the anterolateral and anteromedial segments. Plotting the values of k,, averaged on both right and left metacarpi and on all the three segments along the bone axis, the toughness is almost constant. In Fig. 6 a typical crack pattern is shown: the zig-zag form of the pattern was always present in every fracture test. Each deviation from right to leit and vice versa takes place in a discontinuity. This type of pattern can affect the k,, value ofthe toughness. Figure 7 shows another very common phenomenon : when the crack reaches a discontinuity it continues to propagate in two or more different directions (bifurcating or multiple crack) : in this case along all but one of these directions it stops when it reaches a discontinuity. On observation of some specimens elast:cally loaded with very low loads it was noted that some cracks between two close discontinuities were already created. It can be thus argued that sometime forked or multiple cracks do not form at the same time as the principal zig-zag crack. This is important since the forks, like the zig-zag pattern, can affect the fracture toughness value. Observations carried out on surfaces of the specimens established that the higher the toughness value then the higher seems to be the number of discontinuities and of the forked cracks. Quantitative measures of the number of discontinuities all over the volume surrounding the fracture are needed to confirm this observation. Whilst the tests were done on dry bones, the methodology and the experience resulting from the present work can be helpful as a prelude to extending this measure of fracture toughness to wet bones. It should be noted that the k,, values on dry bones will be an underestimate of that attainable on bon6 tested in physiological saline (Melvin and Evans, 1973). The ratio of the ‘dry’ to ‘wet’ mechanical properties do not change substantially (Evans and Lebow, 1951) along the bone. It is probabie therefore that the quantitative trends of fracture properties established in this paper are valid. CONCLUSIOF;S

The average fracture toughness of dry bone along the equine metacarpi seems to be almost constant going from the proximal to the distal zones. This behavior is mainly due to the fact that while the anterolateral and anteromedial segments have fracture

118

A.

I

Pro.mlaiI h,,d

ALTO

!

and M. H.

Mt.3

POPE

tsrai

tnlrd

,n,r*

I

Fig. 3. klc values obtained on right (a) and left (b) metacarpi for different circumferential and longitudinal positions.

MN/m2

K&",,2

I

Cl3 Proxtmal

tkwd

I I I Mid third

I

I DIetal lhltd

Fig. 4. Average of the values of 6, as a function of longitudinal position.

----_

-* i t T-+ .L

-.

Fig. 6. Crd

propdytion

rhraugh

the bms rk,, L ,S11% m-’ ‘I t 1 31.

A. .ALTO and $1. H. POPE

c-

i

___1 c--

Fig. 7. Multiple

crack

propagation

( x 100).

On the fracture toughness of equine metacarpi

a-

2

3:

3

Prollmal

tn,rcl

wJS,eriCr

I

Ml0

I

5

tnlrd

Olstal

421

j / I-l-:

Fig. 5. k,, values obtained on right metacarpi for different circumferential positions.

toughness slightly decreasing from the proximal to the distal zones, the posterior one has lower toughness in the proximal zone but higher in the distal one. Crack propagation in three point bending fracture tests is a zig-zag pattern from one discontinuity to another; the higher the measured fracture toughness the higher seems to be the number of discontinuities present near the crack and the bifurcations of the same crack.

Acknowledgements - Tbe authors would like to acknowledge the help of Dott. Ing. F. Sforza (Istituto di Tecnologie Bari) in running the tests.

REFERENCES

ASTM, (1970) Fracture toughness testing, 141, STP 410. American Society for Testing and Materials, Philadelphia. Amtmann, E. (1968) The distribution of breaking strength in the human femur shaft. J. Biomech. 1, 271-277. Bonfield, W. and Datta, P. K. (1976) Fracture toughness of compact bone. J. Biomech. 9, 131-134. Bonfield, W. and Li, C. H. (1966) Deformation and fracture of bone. J. appl. Phys. 37, 869-875.

Evans, F. G. (1957) Stress and Strain in Bones. Thomas. Springbeld. Evans, F. G. (1973) Factors affecting the mechanical properties of hone. Bull. ?i.Y. Acad. hied. 49, 751-764. Evans, F. G. and Lebow. M. (1951) Regional differences in some of the physical properties oftbe human femur. J. appl. Physiol. 3, 563-572. Kraus, H. (1968) On tbe mechanical properties and behavior of human compact bone. Adc. biomed. Engng med. Phys. 2, 169-204.

Margel-Robertson, D. R. (1973) Studies of fracture in bone. Doctoral dissertation, Stanford University. Marotti. G. (1961) Number and arrangements of osteons in corresponding regions of bomotropic long bones. Notlrre. Land. 191, 1400-1401. Melvin, J. E. and Evans. F. G. (1973) Crack propagation in hone. Biomech. Symp. ASME 2 87-88. Piekanki, K. (1970) Fracture of bone. J. appl. Phys. 41, 215-223. Pope, M. H. and Murphy, M. C. (1974) Fracture energy of bone in a shear mode. Med. biol. Engng 12, 763-767. Pope, M. H. and Outwater, J. (197 I) The fracturecbaracteristics of bone substance. J. Biomech. 5, 457-465. Pope, M. H. and Outwater, J. 0. (1974) Mechanical properties of bone as a function of position and orientation. J. Biomech. 7, 61-66. Wright, T. M. and Hayes, W. C. (1977) Fracture mechanics parameters for compact bone-effects of density and specimen thickness. 1. Biomech. 10,419-430.

On the fracture toughness of equine metacarpi.

ON THE FRACTURE TOUGHNESS METACARPI* OF EQUINE A. ALTO Istituto di Tecnologie, Facolta di Ingegneria, Universita di Bari, 70126, Bari, Italy and M...
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