Issue 41

M.V.C Sá et alii, Frattura ed Integrità Strutturale, 41 (2017) 90-97; DOI: 10.3221/IGF-ESIS.41.13 93 fatigue curve at least four stress amplitude levels were tested covering life ranges from 10 4 up to 2x10 7 cycles. These tests were then controlled by prescribed loads. L - N f curves To obtain the L  – N f and L  – N f curves (and respective equations) it is necessary to compute the stress field around the notch root. To this aim, a Finite Element Analysis (FEA) was considered. A three dimensional structural element with eight nodes was adopted. Each node had three degrees of freedom. The material behaviour was assumed to be linear elastic. A prescribed stress was applied in the normal direction to simulate the push-pull tests and later a prescribed torsion was applied to model the torsion tests. For a specific failure life, N f,i , it is possible to obtain from the experimental curves the respective values of stress amplitude that the unnotched and the notched specimens can withstand,  UN (N f,i ) and  N (N f,i ) , respectively. Then, from the FEA, the distance where  UN (N f,i ) occurs for the notched specimen loaded by a nominal stress  N (N f,i ) can be found. Therefore, conducting successive increments in the life cycles, N f,i+1 , the L  – N f is raised. Fig. 2 shows an scheme of this procedure. The L  – N f curve is obtained following these same steps, but using as a reference the τ- N curve. Figure 2: Schematic view of the procedure to obtain the L  – N f curve. Aplication of PM (TDC) and MWCM for life estimation in multiaxial fatigue The calibration of the Modified Wholer Curve Model (MWCM) can be achieved using the σ-N and τ-N curves for unnotched specimens. Once calibrated, the amplitude of shear stress at the critical plane,  a , at an initial distance from the notch root,  i , is the input information for the MWCM and the respective life, N(  i ) , is the output. If L  (  i ) =  i , then N f =N(  i ).If not, the next increment at the distance  i should be sought until convergence is reached. Fig. 3 shows the application of this methodology. This procedure can be repeated but using L  – N f in conjunction with the MWCM to estimate the life. To assess the accuracy of the methodology presented above to estimate life of components containing geometrical discontinuities and subjected to complex loadings a set of 15 proportional multiaxial fatigue tests were carried on the notched specimens of Al7050-T7451 shown in Fig. 1. These tests were conducted in a MTS 809 servohydraulic test rig and involved a combination of push-pull and torsion, hence normal load amplitude and torsion amplitude were prescribed to control the tests. The input signals were sinusoidal, synchronous and in phase, without superimposed mean components. R ESULTS Tests n Figs. 4(a) and (b) are presented the results of the fatigue uniaxial tests performed under fully reversed push-pull and alternated torsion. These graphs contain then the σ-N and τ-N curves for the plain and for the notched specimens. In the case of the notched specimens these nominal stresses were computed in terms of the gross sectional area of the specimen. I