Issue 33

J.M. Ayllon et alii, Frattura ed Integrità Strutturale, 33 (2015) 415-426; DOI: 10.3221/IGF-ESIS.33.46 416 due to the geometry or to defects in the material such as inclusions [3]. In these methods, if the initial crack is large enough, the propagation is analysed by LEFM by applying a propagation law for long cracks. If the crack is considered to be initiated from a microstructural defect, various models take into account the behaviour of short cracks [4-7]. However, models regarding short crack growth are not sufficiently developed, and some of them do not work properly under certain conditions or with certain materials, so that there is currently no method that can be applied successfully in any circumstance. To avoid these problems, the defect is considered to be long enough so it is correct to apply the LEFM or some modification of it. The problem here is that predictions may be too conservative, with the addition that it is not possible to quantify the error. Another group of methods considers the fatigue process as the combination of an initiation and a propagation phase, analysing life as the sum of the durations of both phases [8,9]. In most of these methods, the duration of the initiation phase is determined by local strain methods, through the ε-N curves, and the propagation based on fracture mechanics methods. In this paper, to characterise the fatigue life of a dental implant, two life prediction models for notched elements subjected to multiaxial stress states are used. As it will be shown, one of them analyses separately the initiation and propagation phases, and combines these results to obtain the total life of the specimen. The other life prediction model used is based on the Theory of the Critical Distance (TCD) and considers that, in presence of notches, the crack propagation phase is negligible compared to the total life of the specimen. Therefore, it analyses the initiation phase and initial propagation of micro/mezzo cracks using a combination of the TCD and a critical plane damage model. T HEORETICAL MODELS oth life prediction models used in this paper are described in this section. Variable initiation length model (VIL) This paper uses a model for the prediction of life already proposed by the authors [10]. It bears the characteristic of combining the initiation and propagation stages without having to predefine the crack length at which the initiation ends and propagation begins. However, each phase is analysed separately. The initiation phase is analysed by determining the number of cycles required to generate a crack. This number is calculated from the stresses along the path followed by the crack and from a fatigue curve ε-N, which will be detailed later. The result is a curve, a – Ni, representing the cycles required to cause a crack of length a. In the propagation phase, the number of cycles needed to propagate a crack from any length a up to failure, is calculated using fracture mechanics. To do this, the growth law is integrated from each crack length, a, until failure, yielding the curve (a – Np). The sum of these two curves would provide the total life depending on what value is taken for the crack length separating the initiation and propagation phases. It has been shown [10] that the initiation process dominates near surface, and the propagation process does so farther from it, so that the link between the two is found in the minimum of the total life curve described above. For this reason, and because it is the most conservative value, the minimum of the curve is taken as the total life of the specimen. Variable initiation length model (VIL). Initiation phase The analysis of the initiation phase uses the idea of McClung et al. [11] for notches, where they obtain an initiation curve by subtracting the propagation cycles from the total number of cycles until fracture. The first step consists in obtaining a fatigue curve,   | t a N , in smooth unnotched specimens, which provides the number of cycles required to generate a crack of length a t , as a function of the applied strain. For each level of strain, ε j , the number of cycles of this curve,  j t a N , is obtained by subtracting the number of cycles to grow the crack from a t to failure from the total number of cycles. Each curve,   | t a N , for different values of a t will be called initiation curve. In case of application of the model in a simple fatigue test, the number of cycles required to generate a crack of length, a t , could be calculated using the appropriate curve,   | t a N . In the case of a component with a multiaxial state and stress gradient, the same process may be applied, but with some modifications. Firstly, this requires a multiaxial fatigue criterion; in this case, Fatemi-Socie [12] will be used. Subsequently, the Fatemi-Socie parameter ( FS ) is calculated for each strain B