Issue 30

J. Vázquez et alii, Frattura ed Integrità Strutturale, 30 (2014) 109-117; DOI: 10.3221/IGF-ESIS.30.15 110 Figure 1 : Scheme of the experimental assembly. F ATIGUE LIFE PREDICTION MODEL he fretting fatigue life predictions model used in these analyses is based on a previous model proposed by the authors [7]. This model combines the crack initiation and crack propagation phases by analysing each phase independently. Using fracture mechanics procedures, the crack propagation phase is calculated using a curve. This curve offers the crack propagation cycles, N p ( a ), that are required to grow a crack from an initial length, a , to the final fracture crack length at which the test specimens fails. This curve is obtained by integrating the crack propagation law between a and the final crack length. Moreover, the crack initiation phase offers the number of crack initiation cycles, N i ( a ), required to nucleate/generate a crack of length equal to a . The N i ( a ) curve is obtained by considering the stress and strain fields along the prospective crack path. The total fatigue life, N t , is obtained by adding the curves, N t ( a )= N i ( a )+ N p ( a ). As a result, the total fatigue life, N t ( a ), is a function of the crack length, a , which defines when the crack initiation phase ends and the crack propagation phase begins. Depending on the value assumed for the initial crack length, a , the total fatigue life estimated is different, and the curve N t  a can be obtained by repeating the calculation process using diverse values of a . As shown in [7], close to the contact surface the fatigue life is controlled by the crack initiation process, and far from it by the crack propagation. Therefore, the value of a that produces the minimum of the curve N t ( a ) is considered the nexus between the crack initiation and the crack propagation phases [8]. For this reason, and because it is the crack initiation length that offers the most conservative prediction, the minimum value of N t is established as the fatigue life prediction. Crack propagation phase A fracture mechanics-based law reflecting a generic initial crack length, a , is used to calculate the crack propagation phase. Because the value of a can be measured on the order of microns, the proposed law also tries to model the short crack growth phase. For this reason, a modified threshold dependent on the actual crack length is introduced into the crack growth law [9]. 1/2 0 0 th n f f n I I f f f da a C K K dN a a l                                 (1) In Eq. (1), th I K   is the threshold SIF range for long cracks, f is a parameter equal to 2.5 [10], l 0 is the distance between the surface and the first microstructural barrier (a grain boundary), C and n are the Paris’ crack growth parameters and a 0 is the El Haddad’s parameter, which is defined by 2 0 1 th I FL K a             (2) in which FL   is the stress range at the fatigue limit. The factor that multiplies th I K   in Eq. (1) is based on a theoretical approximation of the Kitagawa-Takahashi diagram that considers the threshold stress to be a function of the crack length. T