Issue 41

J.V. Sahadi et alii, Frattura ed Integrità Strutturale, 41 (2017) 106-113; DOI: 10.3221/IGF-ESIS.41.15 109 stress tensor, i.e. the maximum hydrostatic stress, σ h,max . This last term accounts for the mean stress effect. The criterion is given as:     a J 2 h,max , (2) where  and  are material constants determined under fully reversed tension (   1 ) and torsion (   1 ) tests with smooth specimens respectively:              1 1 3 3 ;     1 , (3) Fig. 2 (b) presents the fatigue life predictions obtained with this formulation, considering various fatigue thresholds, i.e. a test case below a line is predicted to have a longer fatigue life than the threshold of the line. On the other hand, a point above it represents a test case with shorter life. The light grey shade area corresponds to the calibrated region (tension- torsion), and is delimited by the uniaxial tension dashed lines. The darker grey shade area is delimited by the equi-biaxial line. The dashed black lines connect test cases with the same  1,peak , in order to illustrate the biaxiality effect when  2, peak is changed. It was concluded that in general the model presents good correlation with experimental data both within and outside the calibration region (tension-torsion region). Non-conservative predictions were obtained for negative values of σ 2,peak (pure shear and uniaxial load cases -- CX01, CX04, CX05 and CX10). In contrast, as σ 2,peak increases towards higher positive values, the criterion becomes proportionally more conservative (min von Mises and equi-biaxial – CX08, CX02 and CX03). (a) (b) Figure 2: (a) Fatigue life predictions with elastic strain energy density. (b) according to Crossland’s criterion. Strain-based criteria Despite the satisfactory results obtained with the stress-based criteria, it was concluded in the previous investigation that the concept of additive parameters does not properly represent the physical behaviour of materials. In this context, a further investigation was performed considering strain based critical plane approaches. This class of strain-based methods is based on the search for critical planes (one or more) where a particular damage parameter reaches its maximum magnitude. This methodology has gained great attention over the past 40 years as it mathematically describes the physical phenomenon and is capable of predicting damage and also the crack orientation (for ductile materials cracks typically nucleate along slip planes, where the maximum shear stress occurs [12,13]). In this sense, among the most widely used criteria the Fatemi-Socie [14] and Smith-Watson-Topper [15] parameters were evaluated. Based on the work of Brown and Miller [13], Fatemi and Socie [14] arrived at the conclusion that tensile normal stress in the maximum shear stress plane accelerates crack growth by separating the crack surfaces and consequently reducing frictional forces. The following damage model may be interpreted as the cyclic shear strain modified by the normal stress to include the crack closure effects described. 10 4 10 5 10 6 0.5 1 1.5 2 2.5 rsquared = 0.8677