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We find that after only 500 μm of cracking, the driving force for crack propagation was more than five times higher in the transverse direction than in the longitudinal direction owing to major crack deflections/twists, principally at cement sheaths

The true toughness of human cortical bone measured with realistically short cracks

NATURE MATERIALS, no. 8 (2008): 672.0-677

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摘要

Bone is more difficult to break than to split. Although this is well known, and many studies exist on the behaviour of long cracks in bone, there is a need for data on the orientation-dependent crack-growth resistance behaviour of human cortical bone that accurately assesses its toughness at appropriate size scales. Here, we use in situ m...更多

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简介
  • Bone is a complex hierarchical composite of collagen and hydroxyapatite that is imbued with mechanisms to resist fracture at different size scales[1].
重点内容
  • Bone is a complex hierarchical composite of collagen and hydroxyapatite that is imbued with mechanisms to resist fracture at different size scales[1]
  • Our approach is threefold: we use nonlinear-elastic fracture mechanics, with crack-deflection mechanics, to properly quantify the toughness properties, we have examined both crack-initiation and crackgrowth (R-curve) toughnesses for realistically short crack sizes and we have compared behaviour with the more commonly evaluated longitudinal orientation
  • There have been numerous previous evaluations of the toughness of mammalian cortical bone (Table 1)[2,8,9,10,11,12,13,14,15,16,17,18,19,20], none has focused on evaluating the important crack-growth properties for the short crack sizes associated with the cortical shell in the transverse orientation
  • Most previous measurements have involved single-value characterizations of the toughness[8,9,10,11,12,13,14,15,16,17,18,19,20], for example, the fracture toughness Kc, which do not necessarily include any contribution from the crack-growth toughness; such measurements have, with few exceptions[2,19,20], been based on linear-elastic fracture mechanics[8,9,10,11,12,13,14,15,16,17,18,19], which minimizes any contribution from plastic deformation, or have involved large crack sizes (∼several millimetres) in the longitudinal orientations
  • We use nonlinear-elastic fracture mechanics testing of human cortical bone under hydrated conditions in situ in an environmental scanning electron microscope (ESEM) to permit resistance-curve measurements for growing short cracks, less than ∼1,000 μm in size, in both the transverse and longitudinal orientations, with simultaneous high-resolution imaging of crack paths to discern the dominant sources of toughness and to show how they confer crack-growth resistance
  • We believe that the approach used here is necessary for a full understanding of the fracture properties of human cortical bone: we have examined realistic short cracks in both the longitudinal and transverse orientations, used an R-curve analysis to capture both crack initiation and growth behaviour, accounted for the inelasticity and mixed-mode loading using the J-integral and simultaneously characterized the development of the extrinsic toughening mechanisms in cortical bone
结果
  • The authors use nonlinear-elastic fracture mechanics testing of human cortical bone under hydrated conditions in situ in an ESEM to permit resistance-curve measurements for growing short cracks, less than ∼1,000 μm in size, in both the transverse and longitudinal orientations, with simultaneous high-resolution imaging of crack paths to discern the dominant sources of toughness and to show how they confer crack-growth resistance.
  • Corresponding fracture in the longitudinal orientation requires far lower driving forces, stress intensities between 1 and 2 MPa m1/2 (J ∼ 0.05–0.2 kJ m−2) to initially extend the crack the first ∼500 μm, consistent with the highly linear crack profiles and smooth fracture surfaces (Fig. 2f,j); with continued crack extension into the millimetre range, toughness values approach 5 MPa m1/2 (J ∼ 1.2 kJ m−2), consistent with Kc values measured in most previous studies.
  • FRACTURE TOUGHNESS/ R-CURVE MEASUREMENTS In situ testing of samples soaked in HBSS was carried out for stable crack extensions less than ∼600 μm for the longitudinal orientation and ∼150 μm in the transverse orientation in a Hitachi S-4300SE/N ESEM (Hitachi America) at 25 ◦C using a Gatan Microtest 2kN three-point bending stage (Gatan); images of the crack path were obtained simultaneously in backscattering mode at 15 kV and a pressure of 35 Pa. In addition, the authors tested samples ex situ in HBSS at 25 ◦C on an EnduraTec Elf 3200 testing machine (BOSE) and an MTS 810 (MTS Corporation) to determine the R-curve for larger crack extensions ( a ∼ 150–7,000 μm).
  • Where Apl is the area under the plastic region of the load versus load-point displacement curve, B is the specimen thickness and b is the uncracked ligament (W − a); the corresponding elastic component given by Jel = K2/E was small and typically only 5–10% of Jpl. because it is unusual to express the toughness of biological materials such as bone in terms of J, equivalent stress intensities were computed from the standard J–K equivalence relationship:
结论
  • The authors believe that the approach used here is necessary for a full understanding of the fracture properties of human cortical bone: the authors have examined realistic short cracks in both the longitudinal and transverse orientations, used an R-curve analysis to capture both crack initiation and growth behaviour, accounted for the inelasticity and mixed-mode loading using the J-integral and simultaneously characterized the development of the extrinsic toughening mechanisms in cortical bone.
总结
  • Bone is a complex hierarchical composite of collagen and hydroxyapatite that is imbued with mechanisms to resist fracture at different size scales[1].
  • The authors use nonlinear-elastic fracture mechanics testing of human cortical bone under hydrated conditions in situ in an ESEM to permit resistance-curve measurements for growing short cracks, less than ∼1,000 μm in size, in both the transverse and longitudinal orientations, with simultaneous high-resolution imaging of crack paths to discern the dominant sources of toughness and to show how they confer crack-growth resistance.
  • Corresponding fracture in the longitudinal orientation requires far lower driving forces, stress intensities between 1 and 2 MPa m1/2 (J ∼ 0.05–0.2 kJ m−2) to initially extend the crack the first ∼500 μm, consistent with the highly linear crack profiles and smooth fracture surfaces (Fig. 2f,j); with continued crack extension into the millimetre range, toughness values approach 5 MPa m1/2 (J ∼ 1.2 kJ m−2), consistent with Kc values measured in most previous studies.
  • FRACTURE TOUGHNESS/ R-CURVE MEASUREMENTS In situ testing of samples soaked in HBSS was carried out for stable crack extensions less than ∼600 μm for the longitudinal orientation and ∼150 μm in the transverse orientation in a Hitachi S-4300SE/N ESEM (Hitachi America) at 25 ◦C using a Gatan Microtest 2kN three-point bending stage (Gatan); images of the crack path were obtained simultaneously in backscattering mode at 15 kV and a pressure of 35 Pa. In addition, the authors tested samples ex situ in HBSS at 25 ◦C on an EnduraTec Elf 3200 testing machine (BOSE) and an MTS 810 (MTS Corporation) to determine the R-curve for larger crack extensions ( a ∼ 150–7,000 μm).
  • Where Apl is the area under the plastic region of the load versus load-point displacement curve, B is the specimen thickness and b is the uncracked ligament (W − a); the corresponding elastic component given by Jel = K2/E was small and typically only 5–10% of Jpl. because it is unusual to express the toughness of biological materials such as bone in terms of J, equivalent stress intensities were computed from the standard J–K equivalence relationship:
  • The authors believe that the approach used here is necessary for a full understanding of the fracture properties of human cortical bone: the authors have examined realistic short cracks in both the longitudinal and transverse orientations, used an R-curve analysis to capture both crack initiation and growth behaviour, accounted for the inelasticity and mixed-mode loading using the J-integral and simultaneously characterized the development of the extrinsic toughening mechanisms in cortical bone.
表格
  • Table1: Single-value toughness measurements of mammalian cortical bone in the longitudinal and transverse orientations[<a class="ref-link" id="c2" href="#r2">2</a>,<a class="ref-link" id="c8" href="#r8">8</a>,<a class="ref-link" id="c9" href="#r9">9</a>,<a class="ref-link" id="c10" href="#r10">10</a>,<a class="ref-link" id="c11" href="#r11">11</a>,<a class="ref-link" id="c12" href="#r12">12</a>,<a class="ref-link" id="c13" href="#r13">13</a>,<a class="ref-link" id="c14" href="#r14">14</a>,<a class="ref-link" id="c15" href="#r15">15</a>,<a class="ref-link" id="c16" href="#r16">16</a>,<a class="ref-link" id="c17" href="#r17">17</a>,<a class="ref-link" id="c18" href="#r18">18</a>,<a class="ref-link" id="c19" href="#r19">19</a>,<a class="ref-link" id="c20" href="#r20">20</a>]. SENT: single-edged notched tension; SENB: single-edged notched bend; C(T): compact tension
Download tables as Excel
基金
  • This work was supported by the Director, Office of Science, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, of the US Department of Energy under contract no
  • Computed X-ray tomography was carried out at LBNL’s Advanced Light Source, which is supported under the same contract
研究对象与分析
37–41-year-old: 3
Our focus is on the transverse orientation because this is often the more clinically relevant direction[1,30]; however, cracks growing in this orientation invariably deflect along the longitudinal direction such that both orientations act in concert to provide resistance to fracture. Using test samples from the midsection of the frozen caderveric humeral cortical bone of three 37–41-year-old donors, both singleedged notched bend and compact-tension samples were sectioned and notched from locations longitudinal or transverse to the bone long axis. The notch orientation was such that the nominal crackgrowth direction was either along the proximal–distal direction of the humerus, in the longitudinal–radial plane, that is, parallel to the long axis of the osteons (longitudinal), or transverse to the long axis of the humerus (transverse), as in Fig. 1

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