Tornetta Rockwood Adults 9781975137298 FINAL VERSION

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CHAPTER 1 • Biomechanics of Fractures and Fracture Fixation

TABLE 1-1. Representative Values of Material Properties for Select Tissues and Orthopedic Materials

Material

Young’s Modulus (GPa)

Yield Strength (MPa)

Ultimate Strength (MPa)

Failure Strain (%)

UHMW polyethylene (arthroplasty)

0.9

25

40

5

Ligament (in tension)

1.5

60

100

15

PMMA (bone cement)

3

74

74

2

Cortical bone (in compression)

17

200

200

1

Titanium alloy

110

800

860

10

Stainless steel

200

700

820

12

( A = 0.0001 m 2 ), 10 N loading will induce a compressive stress of σ = 10 N/0.0001 m 2 = 100,000 N/m 2 on the cylinder surface. The resulting compression by 0.1 mm represents a compressive strain of ε = 0.1 mm/10 mm = 0.01, which is typically expressed as 1%. The specimen has therefore a compressive E-modulus of E = 100,000 N/m 2 /0.01 = 10,000,000 N/m 2 . Since strain has no units, σ and E-modulus have the same units of N/m 2 or Pascal (Pa). These units are very small and are often expressed as Mega- pascals (MPa), these being 1 × 10 6 Pa, or Gigapascals (GPa), these being 1 × 10 9 Pa. Stainless steel ( E = 200 GPa) is approximately twice as stiff as titanium ( E = 110 GPa; see Table 1-1). The E-modulus describes deformation in response to loading within the linear or elastic “working” region of a material, where loads remain sufficiently small to allow complete elastic reversal of deformation after load removal. To determine the strength of a material, it must be loaded beyond its elastic region to induce failure. The load at which permanent plastic deformation begins to occur represents the yield strength of a material (Fig. 1-2). The load at which the material fractures represents its ultimate strength . The ultimate strength of titanium (860 MPa) is similar to that of stainless steel (900 MPa), demonstrating that a more elastic material does not need to be weaker than a stiffer material. Clinically, yield strength can be recognized when contouring a metal plate. With low bending forces within the elastic range, the plate springs back to its original form. Greater forces that exceed

its yield strength result in permanent deformation of the plate to the desired contour. A material such as stainless steel with a large deformation before failure is termed ductile . This is different than a material such as methylmethacrylate that tolerates very little deformation before failure and is termed brittle . The brittle nature of methylmethacrylate can be observed when it is impacted with an osteotome and it fractures rather than deforms. The ultimate strength of cortical bone is almost four times lower than that of stainless steel, suggesting that bone will fail before a stainless steel implant. This holds true for a single peak loading event, such as a fall, which may induce a periprosthetic fracture of bone near an implant rather than an implant fracture. However, repetitive loading below the ultimate strength limit induces microcracks that lead to fatigue failure . In bone, remod- eling continuously repairs these microcracks, making bone tis- sue highly resistant to fatigue failure. Unlike bone, microcracks in implant materials accumulate under repetitive loading and propagate until fatigue failure occurs. Clinically, fatigue failure becomes important in the treatment of a femoral nonunion. The surgeon must consider the number of loading cycles and stress an intramedullary nail has experienced when deciding between nail dynamization and exchanging the implant for a new nail without any loading history. Fatigue limit describes the maximal load that will not induce micro-cracks and that will not lead to fatigue failure, regardless of the number of loading cycles.

Figure 1-2.  Stress–strain curves reflecting properties of representative materials. The slope of the initial linear region of curves ( green ) represents stiffness ( E =∆σ / ∆ ε ). Steeper slops represent stiffer materials. Yield points indicate limits of the elastic “working” region. Brittle materials such as cortical bone fail abruptly, whereby the yield point coincides with failure. Ductile materials have considerable deformation between the yield point and failure point.

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