Issue 47

M. Peron et alii, Frattura ed Integrità Strutturale, 47 (2019) 425-436; DOI: 10.3221/IGF-ESIS.47.33 426 perfectly to the patient specific site of interest and have to resemble the mechanical properties of the bone to avoid bone resorption due to the stress-shielding phenomenon [9–11]. Moreover, load-bearing implants have to be characterized by sufficient strength since they are intermittently stressed due to weight and activity. For example, prostheses implanted to the lower extremities of the body have to withstand loads several times heavier than body weight [12–14]. In addition, the biologically-attractive implant design of these implants might cause challenging mechanical conditions leading to tensile and fatigue failure. For example, implant porosity is widely reported to enhance osseointegration and it is used to tailor the mechanical properties of the prosthesis to fit the biological site of interest [15]. However, such features lead to stress concentrators that reduces the strength of the components [16]. Moreover, a high surface roughness has been reported to favor the cell adhesion and growth, but at the same time is known to lead to crack initiation [17–20]. These competing requirements are aggravated due to the corrosive environment in the human body, leading to effects such as corrosion fatigue and stress corrosion cracking [21,22]. Sivakumar and Rajeswari reported the failure due to the stress corrosion cracking phenomenon of a 316L stainless steel used for fixing a femoral fracture in a 27 years old man [23]. Yokoyama et al. reported that the failure of a titanium occlusal screw failed after three years of implantation was due to the fatigue crack nucleation at the root of the thread [24]. Moreover, Chao and Lopez reported that corrosion fatigue was responsible of the failure of almost 90% of Ti-6Al-4V hip prosthesis [25]. In this challenging scenario, a robust and reliable design tool for the prediction of implant tensile and fatigue strength is highly claimed, especially in the presence of stress concentrators. Considering the developments obtained in the engineering field, many researchers and clinicians have tried to assess implant behavior of notched components using linear elastic fracture mechanics (LEFM) theory and, in particular, the notch stress intensity factors (NSIFs) [26]. Concerning the tensile assessment, the NSIF approach predict the failure of a component comparing the NSIF at which the implant is subjected with a reference strength value obtained by testing samples weakened by the same notch geometry. Concerning fatigue, instead, the NSIF approach predicts the fatigue life of notched components comparing the NSIF at which the implant is subjected with a reference fatigue curve determined from samples characterized by the same notch geometry [27,28]. However, the reliable applicability of the NSIF approach requires to accurately evaluate the stress field ahead of the geometrical discontinuities, and the time-consuming stress field analyses has thus limited its development. In addition, the NSIF-based criteria are dependent on the geometry and this represent another drawback of this approach. Their unit depends in fact on the notch opening angle: the exponent β in their unit MPa(m) β is in fact equal to 1-λ 1 , where λ 1 is the geometrical dependent Williams’ eigenvalue [29]. The geometry dependence implies the necessity of ad hoc experimental data to use the NSIF method, representing thus a complexity in its use. The theory of critical distance (TCD), that represents a set of methodologies, allows to overcome the geometry-dependence limitation. Based on the definition of a material parameter (the critical distance L), the TCD states that failure of notched components subjected either to static or cyclic loadings occurs when the stress averaged over a line (line method, LM) or calculated at a certain distance from the notch root (point method, PM) equals the inherent material strength, σ 0 , or the plane specimen fatigue limit, Δσ 0 , depending on whether tensile or fatigue assessment is considered. The applicability of the TCD to predict the strength of bio-materials has been assessed by Kasiri and Taylor [30]. They applied the LM to predict the fracture behavior of bones, weakened by different holes, and subjected to various loading scenario, but, although the general trend was well predicted, the results underestimated the fracture stress by 20–30%. In fact, it is generally acknowledged by proponents of critical distance methods that the point and line method are limitation of a more accurate approach that average stresses over a certain volume (or area in 2D problems) in the vicinity of the hot-spot. Taylor [31] thus formalized the so-called area method (AM), where the range of the maximum principal stress is averaged over a semi- circular area. Although the accuracy of the results increases considering the AM, stress fields ahead of the notch still need to be accurately determined, resulting in high-performance hardware demand. However, although the accuracy of the results increases considering the AM, stress fields ahead of the notch still need to be accurately determined, resulting in high-performance hardware demand. This has been overcome by the strain energy density (SED) approach, according to which failure occurs when the strain energy W (or strain energy range W  for fatigue loadings) averaged in a control volume of radius, R C , ahead of the notch or crack tip reaches its critical value W C (or ΔW C for fatigue), independently from the notch geometry [32–34]. Moreover, the strain energy range can either be obtained analytically, deriving the stress fields ahead of the geometrical discontinuity, or by means of FE analyses with a coarse mesh, being mesh-insensitive [35,36]. This tool has been widely reported to accurately predict the tensile and fatigue behavior of different notched materials [37–41] and for real component such as steel rollers [42], and its improvements with respect of the TCD methodologies has been reported in details in [43] for Ti-6Al-4V. In addition, it has recently been utilized to predict the fracture and fatigue behavior of plastics [44–46], including the biocompatible biopolymer polyetheretherketone (PEEK) [47,48]. In particular, SED approach has been reported to provide better assessment of the PEEK fatigue life compared to NSIF and TCD approaches [48]. PEEK is considered an emerging material due to its yielding behavior and its superior