3.15b). Viscoelastic materials also display hysteresis, which is the tendency for materials to exhibit different mechanical behaviour based on whether a load is being applied or removed (Figure 3.15c). When a viscoelastic material is loaded and unloaded, the unloading curve is different from the loading curve. The difference between the two curves represents the amount of energy that is dissipated or lost during loading. A key factor in these phenomena is the movement and redistribution of fluid through pores in the viscoelastic biologic tissue [42].
An important characteristic of viscoelastic materials such as bone is strain rate sensitivity, which means that the stress–strain behaviour of the material depends on the rate at which it is loaded (Figure 3.16). Strain rate is the speed or velocity at which a change in dimension (deformation) of a material occurs. The unit quantity for strain rate is inverse time, typically seconds (denoted s−1 or 1/s). As strain rate increases, the stiffness and ultimate strength of the bone increase. The energy absorbing capacity of bone also increases with increasing strain rate until a critical velocity is reached, beyond which this capacity decreases. The critical strain rate is reported to occur at approximately 10−1 to 100/s and represents a transition in the behaviour of the bone from pseudo‐ductile to brittle [29, 30, 82]. Once the critical velocity is reached, the bone becomes increasingly brittle, resulting in lower strain to failure, lower energy absorbing capacity and reduced fracture toughness [26, 82, 83].
The relationship between gait and strain rate is roughly linear such that the highest strains are experienced at the fastest gaits [84]. Strain rates experienced by horses at walk to canter gaits (2–10 m/s) in vivo are in the range of 1.3–8.3 × 10−2/s [81]. At a gallop, horses regularly achieve a velocity of 1.5 × 10−1/s [84], and in the dorsal aspect of the third metacarpal bone of Thoroughbred racehorses strain rates as high as 3 × 10−1/s can be estimated for racing speeds (16–18 m/s) [69, 79]. These are within the range at which bones undergo brittle deformation; however, the relationship between strain rate and catastrophic fracture risk is not straightforward. Whether or not a fracture will occur likely depends on the interaction of strain rate with several other factors including the direction of loading, number of load cycles, magnitude of strain and the presence of pre‐existing fatigue microdamage [80].
Figure 3.15 Behaviour of viscoelastic materials. (a) Creep is an increase in strain under constant stress over time. (b) Stress relaxation is a decrease in stress under constant strain over time. (c) Hysteresis refers to the loss of energy with cyclic loading.
Figure 3.16 The mechanical behaviour of bone is strongly dependent on strain rate. High strain rates lead to higher yield strength and stiffness in cortical bone, but also increased brittleness and reduced fracture toughness. However, strain rates measured on the dorsal metacarpus of Thoroughbred racehorses are intermediate (i.e. between low and high strain rates), ranging from ~10−2/s at a walk to ~10−1/s at a gallop [69, 79, 80]; and physiological strains are less than 0.6%. Thus, strain‐rate‐related effects in vivo are likely lower than those observed in ex vivo studies. Very high strain rates (~103/s) are expected for impact speeds as might occur in a violent collision.
Source: Modified from Davies et al. [81].
Monotonic and Repetitive Stress Fractures
Fractures can occur as a result of a single extreme load or smaller repeated loads. A monotonic fracture occurs when a single extreme load deforms the bone beyond its ultimate limit, resulting in complete and sudden failure [85]. Examples include a fall over a fence during jump racing or cross country, or an accident during recovery from general anaesthesia [85, 86]. Stress fractures are the result of repetitive loads, caused by a few repetitions of a high load or by multiple repetitions of lower loads. The vast majority of bone injuries in racehorses are due to repeated high‐intensity loading, which results in weakening of the bone and subsequent failure [85,87–89].
Experimentally, loading conditions are simulated by monotonic (single cycle to failure or quasi‐static tests) and cyclic loading. Materials that fail from repeated cyclic loading are typically viewed as failing secondary to fatigue [90]. The ‘fatigue life’ refers to the number of load cycles that can be sustained at a given load before catastrophic failure occurs [87]. The in vitro fatigue life of bone is related to the magnitude of the applied load as well as the geometry and material properties of the loaded structure [85, 87]. The fatigue life can be deduced from the S–N curve that depicts the relationship between the applied stress (S) and the number of loading cycles before failure (N) (Figure 3.17). At high loads, a relatively low number of cycles will induce failure, whereas at lower loads the bone endures a greater number of cycles before failure. The fatigue limit of a material is the stress level at which the material can endure an infinite number of loading cycles without failure. The fatigue limit can be determined from the stress plateau in the S–N curve. When loaded below the stress plateau, the material has infinite fatigue life. Bone does not exhibit a fatigue limit [10,91–93]; however, an endurance limit has been characterized for bone, which is defined as the stress amplitude at which the material can sustain a defined number of cycles [94, 95].
Figure 3.17 An idealized S–N curve for cortical bone illustrates the relationship between load magnitude (stress) and cycles to failure. Larger loads have a disproportionately larger effect on reducing fatigue life than smaller loads.
Source: Modified from Kawcak et al. [89].
Cyclic loading of bone results in formation of cracks at micro‐ and ultrastructural levels [96]. Most cracks stop enlarging after reaching a certain length because cracks interact with microstructural features that retard their propagation [97]. This observation is supported by studies that have demonstrated an increase in crack density but not length, with continued loading [2, 98, 99]. However, excessive accumulation of microdamage reduces bone stiffness and ultimate strength, increasing the risk of catastrophic fracture [85, 92, 100].
Paradoxically, the process of microcrack formation can also increase resistance to crack propagation (toughness) and catastrophic failure [85]. Energy is released when the bone material yields, marking the onset of plastic deformation. If the amount of energy released is less than the energy required to form the initial crack, the damage will arrest. Otherwise, the crack will continue to spread, and more cracks will form [99, 101]. The stable (subcritical) cracking that precedes outright fracture is best characterized by the rising resistance curve (R‐curve), where fracture resistance
