EFFECT OF THE DEFORMATION RATE ON THE NATURE OF COMPOUND BONE

TISSUE FRACTURE

A. E. Melnis UDC 611.08:539.04

Study of the mechanical behavior of compact bone tissue requires analysis of the mech- anisms for deformation and fracture. The nature of the breakage of anymaterial is a factor of its structural organization. This is especially true for osseous tissue which is a com- plex biocomposite. The interaction by the individual structural elements of bone on different structural levels, specifically between hydroxyapatite crystals and collagen molecules, be- tween the collagen-mineral fibers and the interfibrillar ground substance, and between the lamella in the osteons and the osteons and the interosteon ground substance account for the complexity of the multistep mechanism for the deformation and fracture of bone tissue. Fur- thermore, the presence of many pores, channels, and canals in bone tissue, which, under cer- tain conditions, may serve both as crack concentrators and factors inhibiting crack propaga- tion, additionally complicates the fracture processes of this material. The nature of bone tissue fracture also depends on a number of other factors, especially the type and orientation of stress relative to the anisotropy axes of the material, the temperature, the moisture con- tent, the rate of deformation or stressing, and the age of the individual.

Many studies have been carried out on the effect of these factors on the mechanisms for the deformation and fracture of compact bone tissue. Thus, Dempster and Coleman [i] found that in tensile testing of samples along the long bone axis, the fracture surface is uneven and at an angle of from 45 ~ to 90 ~ to this axis. For samples subjected to tension along the transverse axis, i.e., tangentially to the bone cross section, the fracture surface is more even and orthogonal to the direction of stress. A similar change in the topography of the fracture surface depending on sample orientation relative to the long bone axis was found by Kimura et al. in tensile testing [2] and in bending [3]. The fracture lines are found mainly along the stressed osteon surfaces or between the lamellae and very rarely through the Haver- sian canals [4]. An increase in temperature leads to a change in the type of fracture from brittle to viscous [5]. The moisture content has an analogous effect on the nature of frac- ture [6]: dry bone tissue undergoes brittle fracture to form a smooth fracture surface. With an increase in moisture content, the fracture becomes viscous and the specific deformation energy for fracture increases significantly, The major feature for the fracture of bone tissue in old age is related to a sharp drop in the specific deformation energy required for fracture and the formation of smoother fracture surfaces relative to young bone [7].

A study of compact bone tissue fracture by acoustic and photon emission [8] showed that marked fracture accompanied by an intense release of acoustic and photon pulses is found only in the final stressing stage. Analysis of the structure of compact bone tissue indicated that the existence of different structural levels in bone tissue, i.e., its lamellar--osteon structure, specifically accounts for the retardation of crack propagation in bone and thereby the increase in viscous fracture resistance [9]. Saha [i0] noted that the major mechanism for the fracture of compact bone tissue in shearing is fracture between the lamellae and osteons or along the fracture surface between the osteons and the ground substance. Frasca et al. [ii] examined three pronounced types of bone tissue fracture at the microscopic level: fracture along the cementation lines between the osteons and ground substance; fracture through individual osteons or groups of osteons; and fracture between the lamellae of indi- vidual osteons.

A study of the effect of the rate of deformation on the nature of compact bone tissue fracture [12] showed that fracture caused by compressive load at low deformation rates oc- curs due to detachment of lamellar structure along segments of the weaker contact of the lamellae, while at high deformation rates it occurs through the ground substance along the

Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Trans- lated from Mekhanika Kompozitnykh Materialov, No. i, pp. 118-123, January-February, 1983. Original article submitted January 4, 1982.

i00 0191-5665/83/1901-0100507.50 �9 1983 Plenum Publishing Corporation

c.

Fig. i. Idealized stress-- deformation (o : ~--s ~ ~) curves for compact bone tissue at deformation rates e11 = 10-5-10 -3 (i); 10 -2

(2); and 0.i-i.0 sec -I (3).

outer surfaces of the osteons. Robertson and Smith [13] showed that there is a change in the type of compressive fracture from brittle to viscous at a deformation rate of 2.4.10 -3 sec -~. These authors made this conclusion on the basis of the change in the form of the stress-- deformation (o1~--clz) curves and the bone tissue fracture surfaces for deformation rates above and below this critical value. A similar transition from brittle fracture with high crack propa- gation rates to viscous fracture and low rates in bending was noted by Piekarski [14].

In the present work we studied the effect of the deformation rate on the nature of human compact bone tissue fracture in tensile testing.

The processes which occur upon the deformation and fracture of a material are reflected in the appearance of the fracture surface. Study of this surface and the underlying inter- pretation of the data obtained may yield valuable information on the fracture mechanism. Thus, the study of the effect of the deformation rate on the nature of bone tissue fracture was carried out by electron microscopic analysis of the fracture surface.

Surfaces of fractured moist samples (moisture content W = 10.5%) were studied at differ- ent deformation rates under tension. The experimental method and results obtained in the deformation-rate range 10-5-1 sec -~ were given in our previous work [15]. The material was studied using an IEM-100C electron microscope with an ASID-4D scanning attachment at 40 kV operating voltage at the accelerating electrode. Prior to examination, the bone tissue sur- face was coated with a 60-80-nm-thick layer of gold in an IEE-4c vacuum unit. The exposures were taken at magnifications of i000 and 5000x.

Deformation diagrams are very important for understanding the mechanisms for the deforma- tion and fracture of bone tissue. Detailed analysis of the o::--e1~ curves for moist bone tissue (W = 10.5%) obtained in our previous work [15] showed that these curves in the deforma- tion-rate range 10-5-1 sec -~ may be seen as idealized curves of the three different types

(Fig. i). While the curve consists of two linear segments at low deformation rates (e,~ from l0 -5 to 10 -3 sec-:), a third segment arises leading to an increase in the maximum ultimate deformation in the final stage of deformations on the curve for e~ = 10 -2 sec -* (curve 2). A further increase in the deformation rate to 0.i-i.0 sec -~ leads to coalescence of the sec- ond and third deformation segments with virtually unchanged ultimate deformation. Such a change in the o~--s11 curve with change in the deformation rate is apparently the result of different mechanisms for bone tissue deformation and fracture at different deformation rates. Thus, the samples studied under the microscope were divided into three groups: samples fractured at deformation rates E~I = 10-2-10 -3 sec-:, 10 -2 sec -~, and 0.i-i.0 sec -~.

Electron microscopy gave microphotographs of the surface of bone samples fractured at different deformation rates (Fig. 2). We should note that analysis of the fracture surface is complicated, since the nature of fracture changes, relative not only to the deformation rate, but also to structural nonuniformities in bone tissue. The presence of a branched net- work of canals, pores, lacunae, and other cavities accounts for the pronounced variability of the appearance of the fracture surface. Thus, a rather large number of fractograms at dif- ferent E:~ was obtained in order to make general conclusions concerning the nature of bone tissue fracture relative to deformation rate. 0nly some of these fractograms are given -- those which have the most characteristic featues for compact bone tissue fracture in the given range of deformation rates. In addition, we studied the same structural elements, namely the

i01

Fig. 2. Microphotographs of the compact bone fracture surface at deformation rates ~11 = 0.i-i.0 (a) and 0.01 sec -I (b).

surface of fractured osteons and the zones of their contact with interosteon ground substance, for different $i~. The osteon fracture surface for slow deformation ($~i from 10 -5 to 10 -3 sec -~) is very uneven, with marked penetration into the inner layer of the osteon. Detach- ment was also found along the most complex planes of the individual lamellae of the osteons. At rapid deformation (~ = 0.i-i.0 sec-~), the osteon fracture surface is more even, with marked roughness (see Fig. 2a). Fracture in this case occurs, as a rule, with the formation of many fine bone chips. The topography of the fracture surface changes at the contact boundary between the osteon and the ground substance from a relatively even surface of the interosteon substance to an uneven one, with coarsening of the relief. The appearance of the

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Fig. 3. Microphotographs of the fracture surface of compact bone demineralized after sample fracture at deformation rates e~ = 10-5-10 -3 (a), 0.01 (b), and 0.i-i.0 sec -I (c).

surface relief in this case is very variable and goes from even, with the formation of rela- tively fine elements, to a relief with marked uneven segments (see Fig. 2b).

For a more detailed examination of the fracture surface, some of the samples after frac- ture were subjected to demineralization (the mineral component of the bone tissue was re- moved). The fracture surface of demineralized bone tissue at deformation rates e1~ = i0 -s- 10 -3 sec -: is quite uneven and has penetrations due to longitudinal displacement of the oste- ons and lamellae relative to the ground substance.(Fig~ 3a)~ Figure 3b clearly shows lamellae extruding on the bone tissue fracture surface at e11 = 0.01 sec -I. However, we should note

that demineralization of the bone tissue after fracture, while retaining the relief of the fracture surface with large osteon and lamellar elements, nevertheless significantly smooths

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Fig. 4. Microphotographs of the fracture surface of compact bone tissue deproteinized after sample fracture at deformation rates ~11 = 10-5-10 -3 (a, b) and 0.i-i.0 sec -I (c).

the fine unevenness of the fracture surface. Thus, the rough fracture surface formed at more rapid deformation (~11 = 0.i-i.0 sec -I) acquires the specific appearance of demineralized bone tissue upon demineralization, with characteristic platelike elements. At high magnifi- cation, this surface is very smooth without any structural pattern (Fig. 3c). Such a change in the fracture surface may apparently be attributed not only to the demineralization of the bone tissue, but also to significant shrinkage of the collagen matrix as a consequence of drying.

Deproteinization of the bone samples, on the other hand, led to a great contrast of the fracture surface and to a clearer structural organization of the bone tissue. Micropho- tographs of the fracture surface in the deformation-rate range from 10 -5 to 10 -3 sec -I clearly show lamellar structure of the osteon, which is the major independent bone tissue element

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(Fig. 4a). The propagating crack along the external osteon contour indicates fraction of the bone tissue along the separation surface of the osteon and ground substance. Figure 4b at higher magnification shows a segment of the fracture surface of this osteon. The extruding lamellar fragment and pronounced penetrations in the adjacent lamellae indicate a different nature of their fracture, due to a different direction of the reinforcing collagen-mineral fibers. The fracture for el: = 0.i-i.0 sec-: is more even with significant roughness (Fig. 4c). Observations at high magnification showed that the fracture surface relief in this deformation-rate range consists of extruding bundles of collagen-mineral fibers or individual such fibers.

Thus, analysis of the microphotographs of the fracture surfaces gives the general pattern for the structural changes which occur in bone tissue upon tensile testing of bone samples in the deformation-rate range from I0 -s to 1 sec-: The change in the appearance of the fracture surfaces indicates a wide spectrum of fracture processes which take place in the different structural elements of bone tissue. The microphotographs given and the deformation curves presented by Robertson [13] for moist bone tissue show that transformation from viscous to brittle fracture in this deformation rate range does not occur, in contrast to the findings of Frasca et al. [ii] in compression and by McElhaney [12] for bending. The critical deforma- tion rate at which this transition is found apparently depends on the type of stress. While it is only 2.4.10 -3 sec -~ in compression [ii], this value for tensile testing is, in all likelihood, significantly greater and beyond the range of deformation rates examined.

In the range of e1~ from 10 -3 to 1 sec-:, the fracture is largely viscous in nature. This is indicated by the formation of fracture surfaces which are specific for bone tissue with extrudin~ individual elements. Larger osteon and lamellar elements are found at slower deformation (e~1 from 10 -5 to 10 -3 sec-1), and finer individual collagen--mineral fibers or fiber bundles are found at higher deformation rates (~:I = 0.I-i.0 sec-1). There is extrusion of osteons, lamellae, and collagen--mineral fibers at ~11 = 10 -2 sec -I.

While cracks at low deformation rates (from i0 -s to 10 -3 sec -:) pass, as a rule, along the external contour of the Haversian systems, crack propagation for the higher deformation rates more often is not related to specific geometric features of the bone tissue micro- structure.

Returning to the idealized deformation curves for bone tissue given in Fig. i, we should note that the curve type is largely a function of the interaction of the structural elements on all the levels of the structural organization of the medium, as in the case of synthetic composites. An increase in the deformation rate leads to a more pronounced deformation of the collagen--mineral fibers and their orientation relative to the long axis of the sample. This apparently also accounts for the increase in the ultimate deformation relative to low values of ~i and the appearance of a third segment on the deformation curve for ~I = 10 -2 sec -I A further increase in the deformation presumably would enhance the effect of the processes which occur at the lower levels of bone tissue structure (fibrillar and molecular levels), which, in turn, would lead to coalescence of the second and third segments of the deformation curve.

We should, however, note that the fractograms obtained for the fracture surfaces give us a notion of the nature of fracture largely for the three highest structural levels of bone tissue. Some concepts concerning the mechanisms for deformation and fracture of bone tissue at the molecular level may be found in the work of Krauya et al. [16], who used x-ray dif- fraction to study the microdeformation of the mineral component of bone tissue, namely the hydroxyapatite crystals. These crystals are deformed nonproportionally to deformation of the sample, while fracture occurs at the separation surface between the crystal and collagen ma- trix. A unique model for the deformation of bone tissue on this structural level was given by Burstein et al. [17]. Considering bone tissue as a two-phase composite, the inflection in the o:i--c:i curve was explained by the elastic behavior of collagen and the plastic deformation of the mineral crystal s . Without denying the real contribution of processes which take place on the molecular level to the mechanisms for the deformation and fracture of bone tissue, such an explanation should, nevertheless, be considered doubtful, because, in the opinion of most workers, the deformation of hydroxyapatite crystals is elastic.

CONCLUSIONS

An electron microscopic study showed that the major type of fracture of moist bone tissue is viscous fracture with the extrusion of elements on various structural levels. Larger ele-

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ments are found at lower deformation rates, and finer elements are found at higher $:~. The longitudinal shear deformation between the osteons and interosteon ground substance, between the individual lamellae in the osteons, between the collagen--mineral fibers and interfibrillar ground substance, and between hydroxyapatite crystals and collagen molecules largely accounts for the viscoelastic properties of bone tissue. Processes occurring on some structural level of bone tissue predominate at certain specific deformation rates.

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