J. Albinmousa, Frattura ed Integrità Strutturale, 37 (2016) 94-100; DOI: 10.3221/IGF-ESIS.37.13 94 Focussed on Multiaxial Fatigue and Fracture Investigation on parametric representation of proportional and nonproportional multiaxial fatigue responses J. Albinmousa Mechanical Engineering Department, King Fahd University of Petroleum & Minerals, Dhahran 31261, Saudi Arabia binmousa@kfupm.edu.sa A BSTRACT . This study aims to investigate fatigue damage resulting from multiaxial fatigue, proportional and/or nonproportional, loading by analyzing stresses and strains over a full domain around a representative stress-strain element. Plain stress-strain transformation of multiaxial hysteresis was performed by varying orientation of plane for 0≤φ≤2π. Parametric representations for both normal and shear stresses and strains were obtained by plotting them in polar figures. These figures show that depending on the applied loading stresses and strains represent definitive known parametric curves. Parametric representation of fatigue damage parameter such as Fatemi-Socie suggests that fatigue damage shall be calculated as the sum of the damage values on all planes. The proposed technique has been shown to improve fatigue life prediction compared to that obtained from the critical plane method. K EYWORDS . Critical plane; Fatigue damage; Multiaxial fatigue; Parametric representation. I NTRODUCTION atigue cracks initiate and grow at certain planes, i.e., persistent slip bands (PSBs). This established fact can be clearly observed in deformed single crystals [1-3]. Fatigue damage is associated with crack formation and critical plane concept originated based on this observation. Critical plane concept is widely used as the basis for formulating fatigue damage models. Therefore, fatigue damage is calculated at specific planes that are usually experience maximum value of either normal or shear strain or stress [4-7]. In some models, the critical plane is defined as the plane at which the value of the damage parameter is maximum [8]. On smooth specimen level, critical planes models have been shown to provide reasonable fatigue life predictions for different testing scenarios that include mean stress or strain, constant and variable amplitude loading, proportional and nonproportional loading conditions as well as complex loading paths [9]. However, Socie et al. [10] conducted a comparative numerical analysis on multiaxial fatigue benchmark experiment performed on simple notched SAE shaft [11]. Five software packages were used to compute the fatigue lives for 75 bending-torsion notched shafts. Socie et al. [10] showed that cumulative probability distribution for in-phase loading test on smooth tubular specimen indicates that there is 99% chance for fatigue life to be predicted within a factor of 2. Conversely, there is 99% chance for fatigue life to be predicted within a factor of 10 when it comes to notched shaft. Socie et al. [10] emphasized on the consideration of complex geometries and loading conditions for evaluating fatigue models. On the other hand, it is often found that models that are based on completely different critical plane assumptions such as normal or shear still give very similar fatigue life predictions [9, 12, 13]. Such observation raises two important questions. First, what is the “critical” plane? The second question is: if two criteria are based on two different critical plane assumptions predict similar fatigue lives then which one of them is correct? These arguments suggest that further development is required to improve not only fatigue life but also fatigue crack path predictions. F

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