Issue34

T. Itoh et alii, Frattura ed Integrità Strutturale, 34 (2015) 487-497; DOI: 10.3221/IGF-ESIS.34.54 488 principal directions of stress and strain are changed cyclically, previous studies have reported a drastic reduction in the failure life with accompanying additional cyclic hardening [1-16] depending on both the loading path and the material [6, 8, 10, 13, 16]. In addition, some studies about the fatigue property of Ti alloys have been reported [17, 18]. Meanwhile, only a paper by the authors [19] has dealt with multiaxial low cycle fatigue crack behavior of Ti-6Al-4V. To evaluate fatigue lives under multiaxial loading conditions, multiaxial fatigue models which relate fatigue lives to uniaxial fatigue properties have been established. Equivalent strains and stresses based on the theories of von Mises and Tresca, which are considered the most commonly used theory, but lead to significant overestimation of fatigue lives under non- proportional loadings from those under proportional loading. Therefore, other life evaluation models have been proposed such as critical plane approaches; i) Stress based critical plane approaches presented by Findley [20] and McDiarmid [21], ii) Strain based critical plane approach by Brown and Miller [22] and Wang and Brown [23], iii) Strain-stress based critical plane approaches by Fatemi and Socie [7, 15] and Smith, Watson and Topper [24]. Most of these models are success on life evaluation under non-proportional loadings, however, some of them have some limitation on application. Itoh et al . [8, 10, 13, 16] proposed a strain parameter taking into account the loading path and material dependencies of life, which shows good correlations with lives under non-proportional loadings for different materials [16]. The studies mentioned above treat the fatigue properties under limited multiaxial loadings of which the principal stress ratio λ range is –1≤λ (=σ II /σ I )≤0, where σ I is the principal stress whose absolute value is the maximum and σ II one of which absolute value the middle. The reason why the performable principal stress ratio range was limited to  1≤λ≤0 mainly due to the testing method to apply the axial and twist loads to hollow cylinder specimens. However, to carry out the multiaxial fatigue test beyond the principal stress ratio range, special multiaxial fatigue testing stands must be required. The authors developed a new testing machine which can apply push-pull and reversed torsion loadings and additionally inner pressure onto the hollow cylinder specimen to perform the test in  1  λ  1 under proportional and non-proportional loadings. In this study, biaxial fatigue tests of the stress ratio range 0≤λ≤1 were carried out using the hollow cylinder specimen of Ti-6Al-4V by the developed multiaxial fatigue testing machine and properties of failure life and crack mode are discussed. M ULTIAXIAL LOADING AND TESTING MACHINE Definition of stress and strain multiaxiality ultiaxial stress and strain states can be expressed by using parameters, κ and φ which are the stress and the strain ratios, as equated in Eq. (1) and Eq. (2),     (1)     (2) where  and  are axial and shear stresses and  and  are axial and shear strains in plane stress state. Besides the method above, this paper also employs principal stress ratio, λ, and the principal strain ratio,  , to define multiaxial stress and strain states, which are equated in Eq. (3) and Eq. (4), II I     (3) II I     (4) where  I and  II are put as principal stresses,  1 ,  2 or  3 (  1  2  3 ) of which absolute values takes the largest and middle ones, e.g. , if  1 =100MP,  2 =50MP and  3 =  200MP,  I =  200MPa and  II =100MPa since |  3 |  |  1 |  |  2 |. On the other hand,  I and  II are principal strains of which principal direction corresponding to those of  I and  II , M