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Fracture Mechanics

From examining fallen structures, engineers found that most collapse began with cracks. These cracks may be caused by material defects, discontinuities in assembly and/or design, harsh environments and damages in service. Most microscopic cracks are arrested inside the material however it takes one run-away crack to destroy the whole structure. To analyze the relationship among stresses, cracks, and fracture toughness, Fracture Mechanics was introduced. The first milestone was set by Griffith in his famous 1920 paper that quantitatively relates the flaw size to the fracture stresses.

Nevertheless, Griffith’s method is too old for engineering applications and is only good for brittle materials. For ductile materials, the high point did not come about until Irwin developed the concept of strain energy release rate, , in 1950s. is defined as the rate of change in potential energy near the crack area for a linear elastic material. When the strain energy release rate reaches the critical value, , the crack will grow. Later on, the strain energy release rate was replaced by the stress intensity factor K with a similar approach by other researchers.

Modern trends of fracture research include dynamic and time-dependent fracture on nonlinear materials, fracture mechanics of microstructures, and models related to local, global, and geometry-dependent fractures. Linear Elastic Fracture Mechanics Principles Linear elastic fracture mechanics (LEFM) principles are used to relate the stress magnitude and distribution near the crack tip to: ? Remote stresses applied to the cracked component ? The crack size and shape ? The material properties of the cracked component

Linear elastic fracture mechanics (LEFM) is based on the application of the theory of elasticity to bodies containing cracks or defects. The assumptions used in elasticity are also intrinsic in the theory of LEFM: small displacements and general linearity between stresses and strains. Ultrahigh Molecular Weight Polyethylene (UHMWPE): An Introduction One of the main experiments to extend the service life of total joint replacements is reducing the volume of wear debris released from the articulating surface, with the goal of limiting particle-induced osteolysis (Kurtz et al, p. 1659–1688; Muratoglu and Kurtz, 2002).

To address long-term osteolyis, highly crosslinked ultrahigh molecular weight polyethylene (UHMWPE) materials have been developed. Even though the wear resistance of highly crosslinked UHMWPE observed in hip simulator studies (Kurtz et al, p. 1659–1688; Muratoglu and Kurtz, 2002; Muratoglu et al, p. 77; Jasty et al, p. 785; McKellop et al, 98; O’Connor et al, 816, researchers have also observed that certain uniaxial mechanical properties decrease following crosslinking, particularly the uniaxial elongation to failure (Muratoglu, Bragdon, O’Connor, Jasty, Harris, p. 77; Muratoglu O. K, Bragdon C.

R, O’Connor D. O, Jasty M, Harris W. H, Gul R, McGarry, p. 1463–1470). Radiation crosslinking has also been observed to decrease the static fracture and fatigue crack propagation resistance of UHMWPE (Eberhardt et al, 480; Krzypow and Rimnac, p. 2081–2087; Baker et al, 573–581; Baker, 2001). Earlier explanation of reduced uniaxial elongation, fracture resistance, and crack propagation resistance of highly crosslinked UHMWPE have contributed to apprehension among members of the orthopedic community that the technology may not be suitable for systems loaded in cyclic fatigue, such as total knee replacements.

As adhesive/abrasive wear is the primary surface damage mechanism in hips, knee inserts exhibit surface damage, by pitting or by delamination, related with fatigue damage initiation and propagation (Wrona et al, p. 92–103). Such pitting and delamination are normally observed on retrieved UHMWPE tibial components (Sauer et al, p. 1929–1935) and are thought to be related to inadequate fatigue and fracture resistance of the material, under the applied loading conditions. To calculate fatigue wear performance in vivo, fatigue studies of UHMWPE are required to understand the response of the material to cyclic loading.

Nevertheless, closing the gap between in vitro fatigue experiments and in vivo knee performance remains beyond the current state of knowledge. The fatigue behavior of polymers in general and UHMWPE specially, has been studied at length in terms of “total-life” or “flaw-tolerant” approaches (Hertzberg and Manson, 1980; Suresh, 1992. In “total life” treatment of fatigue, the lifetime of a product or material is considered to include not only the initiation of flaws during cyclic loading but also the propagation of defects to a certain failure endpoint.

In rotating cantilever beam experiments of UHMWPE, for example, specimen fracture has been used as the failure endpoint of fatigue experiments (Sauer et al, p. 1929–1935; Weightman and Light, p. 177–183; Kurtz et al, p. 1659–1688. In recent cyclic uniaxial experiments, yielding of UHMWPE has been considered to be the failure endpoint (Baker, 2001). A “total-life” approach attempts to relate the stress amplitude (S) to the total number of cycles to failure (N), resulting in the construction of so-called “S-N” curves.

The “S-N” approach has been shown to be useful for metallic materials (Suresh, 1992), however applications of this philosophy to the design of UHMWPE components has been challenging on account of the sensitivity of the predicted cycles to failure to relatively small (1 MPa) changes in cyclic stress range (Weightman and Light, p. 177–183). On the contrary with “total life,” a “flaw-tolerant” approach to predicting fatigue life assumes that the useful life of a component will be directed by propagation rather than beginning of cracks, since flaws or defects generally occur in all materials.

With use of the principles of linear elastic fracture mechanics (LEFM), fatigue crack propagation studies characterize the growth rate of a preexisting crack in a test specimen (da/dN) as a function of the range in stress intensity (K). Connelly, Rimnac, and coworkers were among the first to study fatigue in UHMWPE using fracture mechanics principles under tensile Connelly et al, p. 119-125) and mixed-mode loading conditions Elbert et al, p. 181–187). In recent times, Pruitt et al (p.

143–146), also observed the growth of fatigue cracks in UHMWPE under far-field compressive stress. Researchers have shown that compression fatigue in UHMWPE (Pruitt et al, p. 143–146), in addition to in other polymers (Pruitt, Hermann and Suresh, p. 1608–1616), is driven by residual tension at the crack tip after unloading. Using a combination of tension and compression fatigue crack propagation studies, researchers at several institutions have recognized a decreased resistance to crack growth with increased radiation crosslinking.

9–12 Nevertheless, the application of previous crack growth experiments to total knee implant designs remains undecided, and as a result fatigue crack propagation, studies have been used thus far generally to compare different candidate implant materials rather than as the basis for any particular flaw-tolerant design. Without validated theories to link crack initiation and growth experimental data to implant design, new crosslinked materials for total knee replacement have been analytically introduced based on mechanical performance in joint simulators (Wang et al, p.

17–33; Hastings et al, p. 328; Di Maio et al, p. 363). For instance, a gamma irradiated and remelted UHMWPE (4150 HP ram extruded, 50 kGy) evaluated in a knee wear tester was found to have a lower wear rate than usual UHMWPE (Hastings et al, p. 328; Di Maio et al, p. 363). More recently, Muratoglu et al (p. 149–160) have described a highly crosslinked UHMWPE processed by 95 kGy of electron beam radiation at 125°C, followed by remelting (hereafter referred to as the WIAM process). After 5 million cycles of loading in an AMTI (Advanced Mechanical Technology, Inc.

, Newton, MA) knee simulator, the wear of the highly crosslinked WIAM tibial inserts “was not detectable,” in contrast with conventional UHMWPE controls that wore at a rate of 8 2 mg per million cycles (Muratoglu et al, 2001; p. 29). In contrast, in knee simulator studies, Wang and colleagues have reported that, unlike hip simulator studies, the wear rate of tibial components was not sensitive to the radiation dose between 0 and 50 kGy. Beyond 50 kGy, the wear rate of knee inserts was observed to decrease, but to a much lesser extent than in acetabular liners (Wang et al, p.

17–33). Therefore, radiation crosslinking may be more effective in reducing the adhesive/abrasive wear of acetabular liners than that of tibial inserts. The exact reason why radiation crosslinking may be more efficient in acetabular liners compared to tibial inserts is under investigation and has been related to the difference in joint kinematics (Wang et al, p. 17–33). However, highly crosslinked UHMWPE produced by both room temperature gamma irradiation and elevated temperature electron beam irradiation have been developed for total knee arthroplasty.

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