Issue 38

S. Suman et alii, Frattura ed Integrità Strutturale, 38 (2016) 224-230; DOI: 10.3221/IGF-ESIS.38.30 225 I NTRODUCTION atigue is one of the most prolific phenomena responsible for the failure of machine parts. Very often, the fatigue related damage stays undiagnosed, and by the time a visible fatigue crack is detected, the structure is left with a very small number of cycles required to propagate this crack until catastrophic fracture. Therefore, it is very important to understand this phenomenon, and consider it during the very early stages of the design process. Although it is very convenient to assume uniaxial loading conditions and perfect machine parts with no defects or irregularities, in practice this is seldom the case, and many cyclic loading conditions create some multiaxial stress states. Thus, the modeling of fatigue phenomena and the development of suitable damage methodologies is very challenging for engineers and researchers in the fatigue and fracture community. Extensive review of several multiaxial fatigue theories [1-18] leads to three broad categorizations of fatigue analysis methodologies, namely equivalent stress-based, energy-based and critical plane-based models. Efforts have been made by several researchers [1-4] to represent the multiaxial stress state by an equivalent uniaxial stress value using von Mises or Tresca type equations. However, this approach fails to adequately account for many complexities like LCF-HCF interactions and the effects of non-proportional loading. Equivalent stress-based parameters often result in highly conservative fatigue life predictions with large factors of safety. Unlike equivalent-stress based models, energy-based fatigue theories compute the damage by estimating the strain energy within each fatigue cycle [5-9]. Critical plane-based fatigue theories [10-17] support the observation that the fatigue damage computation should be based upon the estimation of location and orientation of the crack. This approach is more convincing because it allows designers to determine the exact orientation of the fatigue crack plane to accurately make any design changes in the parts. Findley [10] was one of the earliest researchers to put forth the concept of the critical plane approach; however; the Findley model [10] is stress-based and thus often produces significant errors within the LCF regime. Other researchers [7-9] have proposed energy based-critical plane fatigue models, but it is difficult to exactly estimate the total energy of fatigue cycles that have mean stresses [11]. Brown & Miller [15] developed a strain-based fatigue model, and Fatemi & Socie [16] developed a critical plane model that included a normal stress term for non-proportional loading. The extra hardening and softening caused by multiple normal stress subcycles on the critical plane was addressed by Erickson et al. [17]. The critical-plane concept for the prediction of fatigue life of steel and titanium alloys has further been explored in this paper through a series of additional uniaxial and multiaxial fatigue tests under a wide variety of load paths. Special attention has been given to the need of a strain term, and a parameter to model the interaction of shear stress and normal stress on the critical plane. The Erickson et al. [17], Findley [10] and Fatemi-Socie [16] damage parameters have also been assessed for their complexity and ability to accurately estimate the fatigue damage, and a comparatively simpler formulation has been proposed. M ATERIAL AND METHODS everal material data sets were used to evaluate the accuracy of the new damage parameter, including a titanium alloy (Ti-6Al-4V) and nickel-based steel alloys (718 steel and Rene 104). These alloys have been used extensively in gas turbine engines for military and commercial applications, and also have many applications in the automotive and electronics industries. These data sets included both uniaxial and biaxial (axial/torsion) data subjected to a wide variety of cyclic load paths. Much of data were generated as part of a US Air Force program on High Cycle Fatigue, while other data sets were generated by industrial sources or taken from the literature [18]. Additional details about the materials can be found in Erickson et al [17]. Tests were conducted using both solid and tubular specimens with highly polished inner and outer surfaces. The majority of the tests were conducted in strain control on servo-hydraulic tension/torsion load frames. Some of the long-life tests were switched to load control after cyclic stabilization had occurred in order to accelerate the tests. An elastic-plastic stress strain analysis was performed using FEM to calculate the stresses on the outer surface of the specimens, using measured strains as input. This analysis utilized cyclically stabilized stress-strain curves for each material, which were generated from the half-life hysteresis loops recorded from the uniaxial fatigue tests. Separate curves were generated for both R = -1 and R = 0 loading conditions. A wide variety of cyclic load paths were used in generating the fatigue data sets, including uniaxial, torsion, and combined axial/torsion. The biaxial tests included both proportional and non-proportional load paths, as illustrated schematically in Fig. 1. When both axial and shear stresses (strains) remain linearly proportional to one another throughout the cycle, the F S