Issue 38

S. Suman et alii, Frattura ed Integrità Strutturale, 38 (2016) 224-230; DOI: 10.3221/IGF-ESIS.38.30 227 w w w 2 1 3 max min min min max 2 max max y max k σ k σ τ σ DP τ 1 1 k σ 1 τ σ σ                              (3) For each model, the stress and strain values on the surface of the specimen were taken from the finite element analysis and considered as the values on the zero degree plane. These values were rotated in 1-degree increments onto all possible planes to identify the critical (maximum shear) plane. The material constants required by each model were optimized using a least- squares process to minimize the error between predicted and experimental lives for each data set. A double power-law type of formulation was assumed to relate the DP value to the fatigue life, N, as shown in Eq. 4. b d DP AN CN   (4) The initial model evaluations were performed using a large set of uniaxial and biaxial Ti-6Al-4V fatigue data. The resulting correlations of the data set using each model are shown in Fig. 2. (a) Findley [10] (b) Fatemi & Socie [16] (c) Erickson et al. [17] Figure 2 : Correlation of Ti-6Al-4V fatigue data using three different models. It can be observed that the best correlation of all the uniaxial, proportional and non-proportional fatigue data has been achieved by computing the damage with the Erickson et al. model. The Findley parameter and Fatemi & Socie parameter provided good correlation for most of the uniaxial and proportional test data; however, both of these parameters failed to collapse some of the non-proportional fatigue data along the best-fit curve. It is to be noted that the Fatemi & Socie parameter has a shear strain term which allows it to better account for the plasticity in the short-life (LCF) regime, relative to the Findley parameter. Similarly, Erickson et al.’s model accounts for the strain-hardening effects, as well as the damage caused by multiple normal-stress “subcycles” on the critical plane, by summing the damage caused by these subcycles. This parameter was clearly superior in its ability to correlate the non-proportional test data. Development of New Damage Parameter While all three damage parameters possess both normal and shear components to model the fatigue damage, the Erickson et al. [17] formulation (Eq. 3) contains extra terms in an effort to account for additional subtleties that may arise in non- proportional load paths. The first term, comprised of maximum and minimum values of shear stress, can account for the effect of mean shear stresses. The second term is designed to model the effect of the normal stress on the critical plane, while the third term has been introduced to capture the additional damage from multiple normal-stress subcycles on the critical plane. Despite the fact that this parameter captures many factors that contribute towards the nucleation of a fatigue crack, this model is very complex and has altogether six material dependent constants. The optimization of these constants requires extensive computations and a large volume of data. In an effort to better understand the effects of normal-stress subcycles on the critical (maximum shear) plane, a series of specialized tests were designed to vary the number and timing of these subcycles, relative to the major shear cycle. The tests were designed in such a way that after rotating the stresses onto the critical plane, they produced identical shear stress cycles and one or more normal stress subcycles. These tests were performed on a different material, DA 718, for which a significant amount of uniaxial and proportional fatigue data was also available.