Abstract

This article aims to investigate the characteristic microstructure-based failure mechanisms observed during the fracture cutting of age-varying bovine cortical bone. To this end, orthogonal cutting experiments are performed on cortical femoral bones harvested from three distinct bovine age groups, viz., young (∼1 month), mature (16–18 months), and old (∼30 months). Fracture cutting is induced at a depth of cut of 70 μm and a cutting velocity of 800 mm/min by using two distinct tool rake angles of +20 deg and 0 deg. The nanoindentation studies and porosity analysis show key differences between microstructural constituents, as a function of age. The high-speed camera images taken during the fracture cutting process provide insight into six dominant microstructure-specific failure mechanisms. These include primary osteonal fracture, woven fracture, and lamellar fracture observed in the plexiform region; and cement line fracture (i.e., osteon debonding), secondary osteonal fracture, and interstitial matrix fracture observed in the haversian regions. In addition to the conventionally reported specific cutting energy metric, a new metric of resultant cutting force per unit crack area and surface integrity are employed here. All cutting responses are seen to be sensitive to age-related microstructural variations and the tool rake angle. In addition to requiring more cutting force, the neutral tool rake angle also results in notable subsurface damage.

1 Introduction

The rising cost of healthcare is one of the most challenging problems faced by the United States today with critical orthopedic surgical procedures being a key contributor [17]. For example, despite the widespread clinical success of primary total knee replacement (TKR) (i.e., first-time TKR) surgeries, clinical studies have shown that about ∼20% of the patients remains unsatisfied with their surgery outcomes. Based on projections for the year 2030, this would mean that ∼600,000 patients will be unsatisfied with their surgery outcomes and would undergo revision surgeries [1,8]. The reasons for the revision surgery include fractures, infection, and instability of the bone–metal interface, all of which are related to the damage suffered by the bone during the surgery [17]. These revision surgeries place an even greater burden on the medical system, and their numbers are only expected to increase in the future [1,8].

Cortical bone microstructure and associated material properties are known to vary from patient-to-patient based on their age and health history [9,10]. These age-related bone microstructural variations are expected to influence key surgical metrics such as cutting forces and surface integrity. However, today’s state-of-the-art bone surgery techniques do not account for these factors [11,12]. Given the aforementioned state of affairs, it is imperative that the cutting of bone be revisited from a research perspective, with special attention being paid to the implications of age-related variations in the bone microstructure, on key surgery outcomes.

Common bone cutting processes such as sawing, grinding, and drilling can be fundamentally reduced to an orthogonal cutting process with established analytical protocols for force calculation [13]. As such, many orthogonal bone cutting research studies have been performed, particularly on the bovine cortical bone, since its structure and macroscopic properties are similar to the human bone [14]. However, these studies have been limited to the shear-dominated cutting regime [15,16]. An equally relevant, fracture cutting regime seen at depth of cuts >∼60 μm has received little attention particularly with respect to age-related microstructural variations [15,16]. Furthermore, while literature has shown that the forces measured during orthogonal bone cutting show a considerable amount of fluctuation, particularly at larger depths of cut [15,17], these fluctuations have not been tied to the underlying microstructure-based failure mechanisms.

Bovine cortical bone is primarily made up of two distinct components, i.e., plexiform bone and haversian bone, both of which have noticeably different microstructures and properties. Age-dependent microstructural variations within the haversian and plexiform regions can provide hitherto unexplored insights into key cutting metrics of interest. Therefore, this article aims to investigate the characteristic microstructure-based failure mechanisms observed during the fracture cutting of age-varying bovine cortical bone. To this end, three different aged bovine specimens and their respective plexiform and haversian components are first characterized for their microstructure, nanoindentation, and porosity properties. Orthogonal fracture cutting experiments are then performed by varying the tool rake angle values. The depth of cut is chosen specifically to induce fracture-dominated cutting. A high-speed camera observing the cutting process allows for both temporal insights into the failure mechanisms and their correlation to the cutting force fluctuations.

The remainder of this article is divided into the following sections. Section 2 discusses the microstructure of the age-varying plexiform and haversian bones along with their nanoindentation and porosity properties. Section 3 discusses the details of the orthogonal fracture cutting experiments. Section 4 discusses the microstructure-based failure mechanisms during fracture cutting and then discusses trends in key metrics including specific cutting energy, resultant cutting force per unit crack area, and surface integrity. Finally, Sec. 5 presents the specific conclusions that can be inferred from this work.

2 Material Characterization

This section will first discuss the specimen preparation and microstructure characterization efforts. This will be followed by a discussion of the nanoindentation and porosity measures.

2.1 Microstructure Characterization.

The three age-varying bovine femoral bones used in this study were acquired from a local butcher shop. The samples were harvested from cows of different ages, viz., ∼1 month, 16–18 months, and 30 months. These three age groups will be referred to as Young, Mature, and Old, respectively, for the remainder of this article. Mid-body (i.e., mid-diaphysis) sections of the femoral bone shaft were cut and further sectioned into pieces using a Mar-MedTM bone saw, under constant water irrigation. Samples were prepared from each femur as shown in Fig. 1 and were covered with phosphate buffered saline (PBS)-soaked gauze and frozen at −20 °C for storage. The samples were thawed at room temperature for an hour and saturated with PBS to maintain the moisture levels in the samples during experimental procedures.

Fig. 1
Schematic illustration of the specimen preparation process
Fig. 1
Schematic illustration of the specimen preparation process
Close modal

Recall that bovine cortical bone is primarily made up of two load-carrying components, viz., plexiform bone and haversian bone. The formation of these bone types is age dependent, as both the key contributing factors of muscular activity and the distribution of mechanical stress are known to change with the bone growth and the remodeling rate. For fast-growing animals such as cows, the rapid formation of plexiform bone allows for an increase in load-bearing capacity. As such, it is expected that more plexiform bone will be found in the Young and Mature specimens due to the high growth rate experienced by cows in these age groups [18]. To characterize the size of specific haversian and plexiform components in the age-varying samples, a total of 12 micrographs (∼1950 μm × 1500 μm) taken over multiple specimens were analyzed.

2.1.1 Young Plexiform Bone.

The Young bone specimen is dominated by the plexiform bone as seen in Fig. 2, and appears to be in a developmentally disorganized stage [18] in comparison to a more established plexiform bone that contains alternating layers of woven and lamellar bone, giving it an appearance of a laminate structured composite (see Fig. 3). Contained within lamellar bone is a network of blood vessels. Most often these blood vessels can anastomose or connect and become surrounded by layers of lamellar bone that are composed of planar arrays of lamellae [19,20]. These structures are called primary osteons and produce an appearance similar to that of haversian systems or secondary osteons. As seen in Fig. 2, this bone type consists of primary osteons that are elliptically shaped with a major and minor diameter of 142 ± 25 μm and 100 ± 8 μm, respectively. These primary osteons are embedded in a mixture of lamellar and woven structures that are 113 ± 6 μm and 67 ± 11 μm thick, respectively.

Fig. 2
Microstructure of young plexiform bone (scale bar = 150 μm)
Fig. 2
Microstructure of young plexiform bone (scale bar = 150 μm)
Close modal
Fig. 3
Microstructure of mature plexiform bone (scale bar = 150 μm)
Fig. 3
Microstructure of mature plexiform bone (scale bar = 150 μm)
Close modal

2.1.2 Mature Plexiform Bone.

As bone matures, more haversian bone components can be found as primary osteons are replaced with secondary osteons due to the remodeling process [18]. The Mature bone specimen had components of both haversian and plexiform bone, and its structure was more developed and uniform compared to the Young bone. However, the amount of haversian bone was still scarce and as such could not be harvested effectively for the cutting experiments. Therefore, the fracture cutting studies on the Mature bone specimen were limited to only the plexiform component. As seen in Fig. 3, the Mature plexiform bone consists of primary osteons that are 126 ± 7 μm and 86 ± 8 μm in major and minor diameter, respectively. These primary osteons are embedded within alternate layers of lamellar bone and woven bone that are 44 ± 4 μm and 78 ± 9 μm thick, respectively.

2.1.3 Old Plexiform and Old Haversian Bones.

The radial distribution patterns of the haversian and plexiform regions seen in the Old bone specimen age group are reported by Conward and Samuel [21]. For this age group, the plexiform and haversian components were easily distinguishable and harvestable from the anterior and posterior quadrants, respectively. Similarly structured to the Mature plexiform bone specimen, the Old plexiform bone (see Fig. 4(a)) consists of primary osteons that are 80 ± 10 μm and 54 ± 9 μm in major and minor diameter, respectively. These primary osteons are embedded within alternate layers of lamellar bone and woven bone that are 61 ± 12 μm and 86 ± 19 μm thick, respectively.

Fig. 4
Microstructure of old bone: (a) plexiform bone and (b) haversian bone (scale bar = 150 μm)
Fig. 4
Microstructure of old bone: (a) plexiform bone and (b) haversian bone (scale bar = 150 μm)
Close modal

Figure 4(b) depicts the characteristic microstructure of the Old haversian bone. As seen in this figure, the haversian bone is primarily composed of unidirectional fiber-like structures called secondary osteons that are embedded in an interstitial matrix, with cement lines separating the two phases. There are important notable differences between secondary and primary osteons. Secondary osteons are “secondary” in that they have been remodeled and replaced the previously existed bone. They are also surrounded by cement lines, while primary osteons are not. Additionally, the secondary osteon is made of cylindrical arrays of lamellae instead of planar arrays [20] seen in primary osteons. Each secondary osteon has an average major and minor diameter of 198 ± 57 μm and 142 ± 35 μm, respectively, with a central vascular channel called the haversian canal that contains blood, lymph, and nerve fibers. The length of the secondary osteon was seen to be in the 3–5 mm range.

2.2 Nanoindentation.

A Hysitron TI 900 TriboIndenter was used to perform nanoindentation tests on the bone samples used in the cutting experiments. To prepare the samples for the nanoindentation tests, they were first polished using 600 and 1500 grit sandpaper, followed by 5 μm and 1 μm alumina slurry on a wet polishing pad. Afterward, the specimens were placed in an ultrasonic bath for 15 min to remove embedded alumina powder and surface debris, and then placed back into saline solution. Within each bone sample, a series of five to ten indents were carried out on all identified microstructures, viz., primary osteon, woven bone, lamellar bone, secondary osteon, cement line, and interstitial matrix. The spacing between consecutive indents was at least three to five times the indentation width so that residual plastic deformation zones would not overlap.

For the nanoindentation tests, a Berkovich indenter was used to apply a 2000 μN load-controlled indent using a trapezoidal function with a 5 s load, 5 s hold, and 5 s. unload cycle. The 5 s hold period was used to allow for the stabilization of any creep in the samples. The elastic modulus was calculated from the slope of the upper portion of the unloading curve as per the protocols laid out by Hoffler et al. [22]. The hardness value was measured by dividing the load by the area of contact of the indenter.

In bovines and humans, the bone mineral density increases significantly with age, resulting in corresponding increases in elastic properties, toughness, and risk of fracture [23,24]. The elastic modulus and hardness results from our study are shown in Figs. 5(a) and 5(b), respectively, with the data being categorized by age and the key microstructural components. There is a clear observation that the moduli and hardness values increase with age for each microstructure components. Furthermore, there are some noticeable differences between mechanical properties when comparing the microstructures themselves within the age groups.

Fig. 5
Nanoindentation data: (a) elastic modulus and (b) hardness
Fig. 5
Nanoindentation data: (a) elastic modulus and (b) hardness
Close modal

Generally, the mechanical properties within the plexiform bone are highest for woven bone, followed by the primary osteon, and lastly the lamellar bone. This trend is attributed to differences in mineralization [25] and has also been observed in past nanoindentation studies [26]. In haversian bone, the interstitial matrix has superior mechanical properties, followed by the secondary osteon, and lastly the cement line. This is similar to the finding of Refs. [27,28] who reported a higher modulus and hardness value for the interstitial matrix in comparison to the secondary osteon. The cement line properties are in line with that of the authors of Refs. [2931] who reported the modulus and hardness values to be ∼30% lower than the surrounding microstructures.

2.3 Porosity Measure.

Porosity is one of the main factors contributing to the mechanical properties of bone. A micro-computed tomography scan can be expected to provide an accurate assessment of the sample porosity values [32]. However, in this work, relative porosity trends associated with different age groups are of particular interest. Therefore, the technique proposed by Manilay et al. [18] was used as it relies on two-dimensional image analysis of the micrographs to estimate a porosity measure of interest. A total of 12 micrographs (∼1950 μm × 1500 μm) taken over multiple specimens were processed by ImageJ software [33]. The porosity measure associated with the young and mature plexiform bone was ∼25%, whereas, for the old plexiform and haversian bones, this measure was found to be ∼14% and ∼12%, respectively. As bone ages, there is an increase in mineralization, which accounts for an increase in stiffness and strength, yet there is also a reduction in porosity that results in a decrease of toughness and critical stress intensity factor, thereby increasing the risk of fracture [18,34,35]. These findings agree with our nanoindentation results (refer to Sec. 2.2) and are also in line with the findings of Singleton et al. [36].

3 Fracture Cutting Experiments

Figure 6 depicts the experimental setup used to perform the orthogonal fracture cutting experiments for this study. The cutting experiments were conducted on a three-axis hybrid micro-machining center (MikrotoolsTM DT-110, Singapore). A stationary tool mount was designed for orthogonal cutting with an embedded Kistler 9256C1 dynamometer. The tool remained stationary, while the cutting operation was performed by imparting velocity to the workpiece. A Phantom v.7.3 high-speed camera was integrated into the experimental setup to observe the cutting process (see inset in Fig. 6).

Fig. 6
Schematic of orthogonal cutting setup
Fig. 6
Schematic of orthogonal cutting setup
Close modal

The orthogonal cutting experiments were performed on all four bone specimens, viz., Young plexiform, Mature plexiform, Old plexiform, and Old haversian. As seen in Figs. 2 and 3, plexiform bone has an inherent directionality associated with the orientation of its woven/lamellar structures. For the plexiform bone specimens, all cuts were made at an orientation parallel (i.e., at 0 deg) to its woven/lamellar structures. The orthogonal cutting tools were made of high-precision ground tungsten carbide with an edge radius of 1 μm, clearance angle of 10 deg, and two separate rake angles of 0 deg and 20 deg. The width of the cutting edge (∼7 mm) was considerably larger than the specimen width (400 ± 100 μm) to satisfy the conditions of plane strain in the Merchant theory for orthogonal cutting [37]. The cutting operations were performed at a depth of cut of 70 μm with an average bone specimen length of 10 mm, fed at a constant velocity of 800 mm/min. The cutting velocity of 800 mm/min was chosen based on the range of velocities used in prior orthogonal bone cutting studies [13,17,38] and the limits of the three-axis micro-machining center. The depth of cut of 70 μm was chosen based on the findings of prior studies [13,16,17,38,39] and our preliminary experiments that confirmed it to be suitable for fracture-dominated cutting. For each experimental condition, two replicate experiments were performed. The cutting force data were collected by sampling at 30 kHz using a high-speed data acquisition card (National Instruments), while the high-speed camera images were collected at 5000 frames/s.

Table 1 summarizes the cutting conditions used in this study. It should be noted that in this work, the cutting was done in the “across” direction (as identified in Ref. [21]), to ensure that the tool width would separately encounter each of the microstructural constituents of interest, while also providing the high-speed camera with a clear view of the microstructure-specific failure mechanisms. This line of sight is critical to synchronize the failure mode-specific cutting force data with its associated high-speed camera image/s. This “across” direction is unlike the transverse/perpendicular or longitudinal/parallel directions reported in Ref. [39] where the tool width would simultaneously cut through multiple microstructural constituents encountered in the cross section. Fracture cutting in those directions will be more complex and is an open interest area to the research community.

Table 1

Cutting conditions

Material
  • Young plexiform bonea (∼1 month)

  • Mature plexiform bonea (∼16–18 months)

  • Old plexiform bonea (∼30 months)

  • Old haversian bone (∼30 months)

  • Sample thickness (400 ± 100 μm)

Tool
  • High-precision ground tungsten carbide

  • 1 μm edge radius

  • 10 deg clearance angle

  • 0 deg and 20 deg rake angle

Cutting velocity800 mm/min
Depth of cut70 μm (fracture cutting mode)
Material
  • Young plexiform bonea (∼1 month)

  • Mature plexiform bonea (∼16–18 months)

  • Old plexiform bonea (∼30 months)

  • Old haversian bone (∼30 months)

  • Sample thickness (400 ± 100 μm)

Tool
  • High-precision ground tungsten carbide

  • 1 μm edge radius

  • 10 deg clearance angle

  • 0 deg and 20 deg rake angle

Cutting velocity800 mm/min
Depth of cut70 μm (fracture cutting mode)
a

All plexiform bone samples were machined parallel (i.e., 0 deg) to the lamellar/woven bone structures.

4 Cutting Results and Discussion

4.1 Microstructure-Based Failure Mechanisms.

A total of six distinct fracture-based mechanisms were observed between the plexiform and haversian bones across the diverse age groups. These mechanisms will be presented in this section along with their correlation to cutting force fluctuations.

4.1.1 Plexiform Bone.

Three distinct failure mechanisms were observed during fracture cutting of plexiform bone, viz., (i) primary osteonal fracture, (iii) lamellar fracture, and (iii) woven fracture. Given that plexiform bone is seen in all age groups, all three of these mechanisms were observed in Young, Mature, and Old bones. Figure 7 depicts these mechanisms for the Young and Mature plexiform bone. Given the similarities in the microstructure between the Mature and Old plexiform bone, the high-speed images of old plexiform bone have been excluded in Fig. 7 for brevity.

Fig. 7
High-speed images of failure mechanisms observed in age-varying plexiform bone: temporally evolving images showing (a and b) primary osteonal fracture, (c and d) lamellar fracture, and (e and f) woven fracture (note: scale bar = 70 μm, arrows indicate crack opening)
Fig. 7
High-speed images of failure mechanisms observed in age-varying plexiform bone: temporally evolving images showing (a and b) primary osteonal fracture, (c and d) lamellar fracture, and (e and f) woven fracture (note: scale bar = 70 μm, arrows indicate crack opening)
Close modal

Primary osteonal fracture is observed when the tool engages with a primary osteon present in the plexiform region and a crack propagates through the contained blood vessel, thereby resulting in fracture of the osteon. These stages are depicted in the temporally evolving images seen in Figs. 7(a(i, ii)) and 7(b(i, ii)) for the Young and Mature age groups, respectively. The images show an in-plane crack propagation through the primary osteons. Considering the planar arrangement of lamellae within the primary osteons, this mode of crack propagation is expected as per the observations of Ref. [20]. The dominance of this mode of failure is seen to reduce with an increase in age given the slight reduction in both the size and occurrence of these structures within the plexiform bone.

In the plexiform bone, there are alternating layers of woven and lamellar bones, with the softer lamellar bone being sandwiched between the harder woven bone. Lamellar fracture is observed when machining parallel to these layered structures. The failure occurs similar to the mode seen for primary osteonal fracture, i.e., by the splitting or disjoining of the blood vessels contained within the lamellar bone. This is depicted in the images seen in Figs. 7(c) and 7(d) for the Young and Mature age group, respectively, where the crack is seen to propagate significantly ahead of the tool tip through the softer lamellar bone, thereby resulting in larger crack lengths. Woven fracture is a discrete fracture that occurs in the harder and more brittle woven bone. This discrete fracture mode is depicted in Figs. 7(e) and 7(f) for the Young and Mature age groups, respectively.

4.1.2 Haversian Bone.

Three distinct failure mechanisms were observed during fracture cutting of haversian bone, viz., (i) cement line fracture, (iii) secondary osteonal fracture, and (iii) interstitial matrix fracture. Figure 8 depicts these mechanisms for the Old haversian bone. These mechanisms are not seen in the Young bone given the absence of haversian regions in that age group. It is also likely that some of these mechanisms may also be prevalent in the relatively small haversian regions seen in the Mature age group sample. However, this cannot be confirmed from the current work given the difficulty in harvesting these samples for the orthogonal cutting study.

Fig. 8
High-speed images of failure mechanisms observed in old haversian bone: (a) cement line fracture, (b) secondary osteonal fracture, and (c) interstitial matrix fracture (note: scale bar = 70 μm, arrows indicate crack opening)
Fig. 8
High-speed images of failure mechanisms observed in old haversian bone: (a) cement line fracture, (b) secondary osteonal fracture, and (c) interstitial matrix fracture (note: scale bar = 70 μm, arrows indicate crack opening)
Close modal

Cement line fracture (see Fig. 8(a)) occurs when the crack engages with the cement line and progressively proceeds along the periphery of the secondary osteon. This mode of failure ultimately results in a partial or complete osteon debonding. This is seen in regions where the cement line is likely weaker allowing for circumferential crack propagation.

In regions where the local strength of the cement line may be higher than its surrounding regions, it can resist the circumferential crack propagation. In such cases, the crack passes through the cement line and engages with the circumferential lamellae of the secondary osteon to result in secondary osteonal fracture (see Fig. 8(b)) that typically involves partial removal of the secondary osteon. The circumferential lamellae of the secondary osteon have been observed to be beneficial for crack arrestation [20]. As such this failure mode is expected to result in a higher expenditure of energy compared to that seen for the primary osteons that have planar lamellae (Sec. 4.1.1).

Controversial literature regarding the mineralization of the cement line has described it as both a highly mineralized material (suggesting a brittle and stiff nature) and poorly mineralized material [31,40]. Furthermore, modeling studies have shown that a lower elastic modulus typically results in secondary osteonal fracture [41], while stiffer cement lines increase the chance of crack propagation around the osteons, i.e., cement line fracture. Both modes of failure have been observed here and reported in the experimental literature [4244], which imply that the mechanical properties of cement lines may vary with the location and age [41]. When the crack initiates in local regions dominated by the interstitial matrix, there is a discrete fracture of this phase. This is shown in Fig. 8(c) and is termed as interstitial matrix fracture. It is principally similar to the characteristics of the woven fracture seen in the plexiform bones.

4.1.3 Cutting Force Fluctuations.

Figures 9(a)9(c) show representative cutting force signatures seen for Young plexiform, Mature plexiform, and Old haversian bone, respectively. The discontinuous fracture process gives rise to cutting force fluctuations with a buildup of the force leading up to the fracture event followed by a subsequent drop in the magnitude after the fracture event [16,17]. Portions of the signals have been labeled to indicate some of the distinct fracture events as identified by the synchronized high-speed images. The time between successive force peaks in a cutting force signal corresponds to the time between successive fracture events (Fig. 9). This is similar to the situation for discontinuous chip formation in metals.

Fig. 9
Representative cutting force signals seen in age-varying bone: (a) young plexiform bone, (b) mature plexiform bone, (c) old haversian bone, and (d) old plexiform bone (note: (i) The 0.15 s cutting force signal is a snippet of the overall signal. Its beginning here at 0 s does not imply the start of the orthogonal cut. (ii) Boxed areas are portions of the signal corresponding to specific failure mechanisms)
Fig. 9
Representative cutting force signals seen in age-varying bone: (a) young plexiform bone, (b) mature plexiform bone, (c) old haversian bone, and (d) old plexiform bone (note: (i) The 0.15 s cutting force signal is a snippet of the overall signal. Its beginning here at 0 s does not imply the start of the orthogonal cut. (ii) Boxed areas are portions of the signal corresponding to specific failure mechanisms)
Close modal

The synchronization of the cutting force and the high-speed images in Fig. 9 is achieved as per the following protocol. First, both the cutting force and high-speed imaging data streams are turned on before the execution of the cut. At this stage, the cutting force continues to record a zero value, while the camera frames are all stationary. The orthogonal cutting motion program is then executed on the machine tool. As with any orthogonal cutting experiment, the first contact of the cutting tool with the workpiece provides a distinct spike in the force signal. This entry spike is used as the identifying feature to synchronize the cutting force and the camera images. The synchronization is further fine-tuned by clearly identifying drop in force magnitudes that follow the opening of the crack as seen in the high-speed images.

When comparing the Young and Mature plexiform force signatures (refer Figs. 9(a) and 9(b)), one observes longer time periods of no tool–material engagement for the Mature age group. This is because in the Mature bone, the plexiform structures are more developed, structured, and longer in length than in the Young bone (refer to Figs. 2 and 3). As such, when the structures break off ahead of the tool, it takes longer to reengage the material.

The Old haversian bone is harder and brittle compared to the Young and Mature age groups [18]. It also lacks lamellar structures compared to the plexiform region and instead has a higher fraction of secondary osteons compared to the surrounding interstitial matrix. As seen in Fig. 9(c), these factors lead to this signal being differentiated from the Young and Mature age groups by a more consistent material engagement with the tool marked with high-frequency components. The force signal of Old plexiform bone seen in Fig. 9(d) displays the characteristics of both the plexiform type as well as the Old age group, in that (i) there is significant time between fracture events due to breakage of the lamellar structures ahead of the tool; and (ii) the signal shows also an overlay of the high-frequency components caused by age-increased brittleness.

4.2 Conventionally Reported Specific Cutting Energy.

The specific cutting energy is defined as the energy consumed per unit volume of material removed. As such, the magnitude of specific cutting energy values also provides a measure of the temperature rise seen during the cutting process, which is critical for bone cutting applications. During the orthogonal cutting process (Fig. 10(a)), the resultant cutting force (R) has two components, viz., the cutting force (Fc) in the direction parallel to the cutting velocity, and the thrust force (Ft) in the direction perpendicular to the cutting velocity. For shear-based orthogonal cutting processes, the conventionally reported specific cutting energy is equal to the average value of the cutting force divided by its uncut chip cross-sectional area, i.e., specimen thickness (w) multiplied by the depth of cut (to) as shown in Fig. 10(a) [45,46]. While this metric is not appropriate for fracture-dominated cutting, it has been used by past bone cutting researchers [13,14,16,17,47] to report their findings associated with fracture-dominated cutting. Therefore, this conventionally reported metric is first presented here to benchmark the findings from this age study.

Fig. 10
Force analysis metrics used for fracture cutting bovine bone: (a) cement line fracture example and (b) conventionally reported specific cutting energy values (note: boxed areas are ranges of past literature reported values)
Fig. 10
Force analysis metrics used for fracture cutting bovine bone: (a) cement line fracture example and (b) conventionally reported specific cutting energy values (note: boxed areas are ranges of past literature reported values)
Close modal

The specific cutting energy results from the cutting experiments can be found in Fig. 10(b) for each bone age type, i.e., Young plexiform, Mature plexiform, Old plexiform, and Old haversian. A comparison with literature-reported values of specific cutting energy could only be made for the old haversian bone from studies that used similar cutting parameters, viz., cutting orientation, depth of cut, and tool rake angles [13,16,39]. The range of these literature values is shown as the dotted rectangular box associated with the Old haversian bone data. As can be seen, the current values are within 10% of the reported values.

The trends of the average specific cutting energy values are as expected with a reduction being seen with a more positive rake tool. Old haversian bone requires the highest specific cutting energy for both tool rake angles, likely due to the fact that (i) it is generally composed of a high volume fraction of secondary osteons ∼70% [4850]; (ii) the force required for secondary osteonal fracture is high [16]; and (iii) it is also the least porous bone (refer to Sec. 2.3).

4.3 Resultant Cutting Force Per Unit Crack Area.

In fracture-dominated cutting, the crack propagates ahead of the tool tip implying that the crack velocity will differ from the tool velocity, which has implications for the cutting power calculation. Furthermore, the crack propagation also leads to unpredicted failure paths that can change the effective material removal rate. Therefore, instead of the conventionally reported specific cutting energy metric, here a new metric tailored to microstructure-based fracture events is proposed, viz., the resultant cutting force per unit crack area (RCF/UCA). For the 2D orthogonal case discussed here, the crack area is obtained as a product of the crack length (lc) and the width (w). The crack length is calculated digitally using both information from the high-speed camera images (Fig. 10(a)) as well as the subsequent morphology of the cut surface when examined under a microscope.

Figures 11(a) and 11(b) present the values associated with this new metric (RCF/UCA) for each of the six modes of failures reported in this article. These values allow for a comparison between different microstructure-based failure mechanisms while taking into account both the resultant force experienced by the tool and the surface morphology generated when cutting. In addition, this metric is useful for the validation of microstructure-based finite element models for bone cutting such as those reported by Potukuchi [51]. Given the nature of this calculation, the variation seen in the averages reported in Figs. 11(a) and 11(b) then is a complex function of (i) age-related microstructure and property variations; (ii) the stress state of the sample influenced by the tool geometries and cutting conditions; and (iii) the variation in the crack lengths observed within the instances of the specific failure mode. It should be noted that the crack length variation is unique to this metric and does not influence the metric reported in Fig. 10(b). Sections 4.3.1 and 4.3.2 present the trends observed in this metric across the three age groups while using a positive and neutral rake tool.

Fig. 11
Resultant cutting force per unit crack area (RCF/UCA) metric trends: (a) 20 deg rake tool and (b) 0 deg rake tool
Fig. 11
Resultant cutting force per unit crack area (RCF/UCA) metric trends: (a) 20 deg rake tool and (b) 0 deg rake tool
Close modal

4.3.1 Positive 20 deg Rake Angle Tool.

In the plexiform bone, it is observed that when using a rake angle tool of 20 deg, the (RCF/UCA) values among the different failure modes slightly decreases with an increase in age. This is expected as fracture toughness in bone reduces with an increase in age [35]. Additionally, as the plexiform bone ages, the size of primary osteons decrease (refer to Sec. 2.1), which can be attributed to the remodeling process [52]. This phenomenon can ultimately result in shorter crack lengths with age, in addition to a reduction in resultant force magnitude, which leads to lower (RCF/UCA) values.

In addition, lamellar bone generally has the least (RCF/UCA) value because of its longer crack length due to its microstructure arrangement (refer to Fig. 7). Woven bone shows more distinct differences across age likely because of its isotropic mechanical characteristics [53]. With no vascular channels as stress concentrators and increased mineralization [25,54], woven bone results in shorter crack lengths during fracture cutting and thus has higher (RCF/UCA) values.

In the old haversian bone, secondary osteonal fracture has the highest value for RCF/UCA. Liao and Axinte [16] reported a high resistance to fracture due to the strength and toughness enhancement of secondary osteons. Carter and Spengler [55] and Martin and Burr [56] have suggested that the structure of secondary osteons may serve to arrest the propagation of microcracks. A more detailed explanation may be the stiffening mechanism observed in the work of Katsamenis et al. [57]. Between the concentric layers of lamellae are interfaces known as thin lamellae. Though these thin lamellae are softer, when loaded, they help stiffen the secondary osteon and aid in arresting cracking propagation. All of these previous findings support an expected high value of resultant force magnitude over relatively smaller crack areas. This would explain the high (RCF/UCA) values observed here.

The findings of Li et al. [41] suggest that a stiffer cement line results in crack propagation around the secondary osteon. As such, this is a reasonable explanation for the resultant force magnitude for the cement line fracture being comparable to that of the interstitial matrix fracture. However, the crack length around the osteon is generally higher than that seen for the interstitial matrix fracture, which explains the lowest (RCF/UCA) value for the cement line. The interstitial matrix fractures in a manner similar to the woven bone due its homogenous structure. As such its relative (RCF/UCA) value follows the trend seen for the nanoindentation hardness measurements (refer to Sec. 2.2).

4.3.2 Neutral 0 deg Rake Angle Tool.

Figure 11(b) shows the (RCF/UCA) values when using a rake angle tool of 0 deg. The trends of the data are similar to that of the 20 deg rake angle tool, except that the values are generally higher. This is expected as more negative rake angle tools will increase cutting forces during the machining process. In addition, there are more noteworthy phenomena with the 0 deg rake angle tool that provide insight into effects of tool geometry on the fracture process. Similar to the carbon fiber failure modes observed in the composite machining work of Calzada et al. [58], machining with a 0 deg rake tool is observed to cause the lamellar structures to buckle during lamellar fracture (see Fig. 12(b)) as opposed to bending/peeling with a more positive rake tool (see Fig. 12(a)). Furthermore, the compressive force generated by the 0 deg rake angle tool prevents the removal of entire secondary osteons during cement line fracture, whereas the tensile forces induced by a positive rake angle tool result in the secondary osteon pullout. For the young bones, this stress state imposed by the 0 deg rake tool combined with their developmentally disorganized microstructure (Fig. 2) implies that there are more variations in the crack lengths as well as the associated cutting force magnitudes. This explains the relatively larger variations seen both in Figs. 10(b) and 11(b) for the Young plexiform bones.

Fig. 12
Lamellar fracture seen in mature plexiform bone: (a) 20 deg rake and (b) 0 deg rake (scale bar = 100 μm)
Fig. 12
Lamellar fracture seen in mature plexiform bone: (a) 20 deg rake and (b) 0 deg rake (scale bar = 100 μm)
Close modal

4.4 Surface Integrity.

The control and prediction of machined bone surface quality are critical for orthopedic procedures. There are some instances where maximum surface roughness is desired, e.g., in cases where bone cement is used to achieve mechanical interlocking of a device [14]. There are other scenarios where surface roughness should be minimized, e.g., when maximum bone-to-implant contact is required [14]. Thus, it is critical to examine the surface integrity metrics associated with the age-varying fracture cutting cases.

Figure 13(a) shows a sample image of the surface left behind while cutting old haversian bone with a neutral rake tool. As seen, in this case, the surface shows evidence of both near-surface craters as well as subsurface cracks. Therefore, the surface integrity metrics used here include lengths to quantify both near-surface and sub-surface damage in the samples. The damage metric H, used to quantify near-surface damage, is an average of distances H1, H2, … Hn measured from intended depth-of-cut line to the near-surface damage craters (Fig. 13(a)). The damage metric L, used to quantify subsurface damage, is an average of distances L1, L2, … Ln measured from intended depth-of-cut line to the farthest propagation of a subsurface crack (Fig. 13(a)). These distance metrics are averaged over the entire 10 mm length of the sample. The results from all surface integrity measurements can be found in Fig. 13(b). It should be noted that the evidence of subsurface damage was only found for the 0 deg rake angle tool experiments.

Fig. 13
Surface integrity metrics: (a) surface of old haversian bone machined with 0 deg rake tool and (b) near-surface and subsurface damage trends (note: 200 rake tool did not show evidence of subsurface damage)
Fig. 13
Surface integrity metrics: (a) surface of old haversian bone machined with 0 deg rake tool and (b) near-surface and subsurface damage trends (note: 200 rake tool did not show evidence of subsurface damage)
Close modal

It is also important to note that during fracture cutting of bone, the surface damage is directly related to the size scale of the microstructures and their orientation with respect to the cutting velocity. Therefore, as seen in Fig. 13(b), the surface integrity metrics have a wide range in their values. It is observed that there is not much difference in near-surface damage caused by the 20 deg and 0 deg rake tool for the plexiform bone structures in Young, Mature, and Old bone. These values are all in the range of the thickness values for the lamellar/woven structures (refer Sec. 2). Old haversian bone has the highest near-surface and subsurface damage, which is likely a result of its age-increased brittleness/fracture and microstructure arrangement that has more interfaces for deeper subsurface crack propagation. For example, as seen in Fig. 8(a), the tensile force caused by the 20 deg rake tool can initiate fracture along the cement line and cause larger craters due to secondary osteon removal. On the other hand, the structures within plexiform bones have longer characteristic lengths that break off cleanly ahead of the tool.

4.5 Discussion.

The findings reported in Secs. 2 and 4 have highlighted the effects of age-varying bovine bone microstructures and their material property differences on fracture cutting responses of interest. For the Young, Mature, and Old age groups tested in this article, nanoindentation and porosity analysis results have shown that as age increases, elastic moduli and hardness values for the key microstructural components increase, while overall bone porosity decreases.

The conventionally reported specific cutting energy measure is not appropriate for fracture cutting, as it does not correctly account for crack tip velocity as well as the noncutting regions seen in Fig. 9. The resultant cutting force per unit crack area (RCF/UCA) metric appears to be more effective in capturing material property influences on cutting forces, as it accounts for the crack length variations associated with each microstructure-specific failure modes. With an increase in age, the plexiform bone shows a decrease in (RCF/UCA) values across its dominant failure mechanisms. This could be attributed to increased mineralization/stiffness and a decrease in porosity, which in turn reduces subsequent fracture toughness [36]. Additionally, specific failure mechanisms within Old haversian bone, such as secondary osteonal fracture and cement line fracture, highlight how the relative stiffness properties and energy dissipation mechanisms of key microstructural constituents can impact the fracture events during cutting. For instance, the lowest stiffness value of the cement line (Fig. 5) is also correlated with cement line fracture having the lowest (RCF/UCA) value among the three dominant mechanisms seen in the Old haversian bone (Fig. 11). Secondary osteonal fracture on the other hand has the highest (RCF/UCA) value due to its relatively higher stiffness as well as its concentric lamellar structures that allow for an efficient crack energy dissipation mechanism. The surface integrity results show evidence that the size scale of microstructures coupled with the dominant failure mechanisms influences the extent of surface and subsurface damage.

These early-stage results on fracture cutting of age-varying bovine cortical bone hold promise for the overall vision of developing age-/patient-specific bone cutting protocols. Translational efforts toward clinical adoption will require such fracture cutting studies to be extended to all dominant directions prevalent in human bone cutting. In these follow-up studies, fracture events involving multiple microstructural phases could be monitored using acoustic emission sensors [59]. While there have been some attempts in bone cutting literature to design elliptical tool motion paths to suppress crack propagation [39], these studies should be extended to age-varying microstructures. In the absence of a line of sight provided by high-speed cameras, these studies will also require the development of novel tool-mounted sensing modalities that are sensitive to microstructural variations.

5 Conclusions

The following specific conclusions can be drawn from this work:

  1. The overall fracture cutting responses of bovine cortical bone are affected by age. The material properties of the microstructural constituents change with age and thereby dictate the failure mechanisms encountered during cutting.

  2. The synchronization of high-speed images with their associated cutting force signals reveals six distinct microstructure-specific failure mechanisms present during fracture cutting of bovine bone. For the plexiform bone, these include primary osteonal fracture, lamellar fracture, and woven fracture. For the haversian bone, these include cement line fracture, secondary osteonal fracture, and interstitial matrix fracture.

  3. The resultant cutting force per unit crack area is used as the metric to effectively compare each of the six failure mechanisms encountered during fracture cutting of bovine bone. For the failure mechanisms observed in the plexiform bone (i.e., primary osteonal fracture, woven fracture, and lamellar fracture), this metric is seen to decrease with age while cutting with a 20 deg rake tool. When using the same tool on an old haversian bone, this metric indicates that the cement line fracture and secondary osteonal fracture require the lowest and highest force, respectively, to propagate a crack. The data also suggest that irrespective of age, reducing the positive rake angle of the tool results in more force being required to propagate cracks within both the plexiform and haversian microstructures. This effect of tool rake angle is in-line with conventional understanding.

  4. Neutral rake tools may also produce subsurface damage in addition to near-surface damage. The histological effects of this type of damage need to further be examined.

Acknowledgment

The authors acknowledge funding support from the United States National Science Foundation CAREER award (CMMI 13-51275), as well as internal funding from Rensselaer Polytechnic Institute. Dr. Srikrishna Sasidhar Potukuchi (Rensselaer PhD 2021) is acknowledged for his insightful discussions related to the experimental data sets.

Conflict of Interest

There are no conflicts of interest.

Data Availability Statement

The authors attest that all data for this study are included in the paper.

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