Issue34

T. Itoh et alii, Frattura ed Integrità Strutturale, 34 (2015) 487-497; DOI: 10.3221/IGF-ESIS.34.54 490 to the specimen in Fig. 2 (a) and a uniaxial strain (  ) is applied to the specimen but the multiple principal strains arise in the specimen thickness direction in Fig. 2 (b). The lateral strain is  is applied to the specimen. In the reversed torsion test, the applied stress/strain is only the shear stress/stress (  /  ) but the two principal stresses/strains with the opposite sign are caused in this case. So, the reversed torsion test also becomes a multiaxial test. The combined tension-torsion and the biaxial tension-compression loadings also enable the fatigue test in multiaxial strain states. The former test only covers the stress/strain biaxiality for  1  0/  1  but the latter test does  1  ,  1. Non-proportional loading Fig. 3 shows the tension-compression and reversed torsion testing and the biaxial tension-compression testing with phase shift in applied strains. In the tension-torsion test with the phase shift, the direction of the principal strains rotates with time and this loading is non-proportional loading. The phase shift in applied strain in the biaxial tension-compression test causes no rotation of the principal strains but it causes the switch of the principal strain directions. The authors consider that this loading should be classified to a proportional loading because no large additional hardening and little reduction of fatigue life was confirmed in this type of test using type 304 steel cruciform specimens at 823 K [12]. However, another research [25] stated that this loading should be a type of non-proportional tests showing a fair reduction of fatigue lives in experiments. More detailed experimental studies and evidences are needed to have a definite conclusion on the classification of this type of loading.     t  1  1   1   1  =  1  0    y  y t  1  1  y  y  x  x Biaxial / Multiaxial loading Tension - compression and cyclic torsion Biaxial tension - compression Principal stress/strain state Applied stress/stain Type Principal stress/strain directions rotate continuously. Principal stress/strain directions are fixed but they interchange. Rotated Fixed Changed  =  1  1  =  1     =  1  1  1   1  x  x   Shape of specimen Cylinder Cruciform Cubic Type Ⅰ A Type Ⅰ B Type Ⅱ Type Ⅲ Axial load Shear load Internal pressure External pressure Axial load Shear load load load load Figure 3 : Definition of non-proportional loading. Figure 4 : Type of specimens. Types of multiaxial fatigue tests Fig. 4 shows four types of common used multiaxial fatigue testing methods classified by types of loading and specimen. Type IA is the tension-compression and reversed torsion test using the hollow cylinder specimen, which is most widely used testing. Type IB is similar to Type IA from the point of using the hollow cylinder specimen but Type IB is applied with the internal and external pressures in addition to the tension-compression and reversed torsion loadings. Type II is the biaxial tension-compression testing using the cruciform specimen. Type III is the tri-axial tension-compression testing using a cubic specimen. Principal stain and stress ratio ranges which can be performed in each type of test are summarized here. Type IA have been used widely multiaxial fatigue studies ， but the principal stress/strain ratio range performable by this testing is  1<λ  0/  1<  ν. Types IB and II can perform the multiaxial fatigue test under full ranged principal stress/strain ratio range of  1<λ,  1. Type III also does the test under the same multiaxial strain state and tri-axial tension-compression loading, too. However, Types II and III have no change in principal directions of stress and strain since the directions always fixed into the direction of applied loading. Only type IB can perform the multiaxial fatigue test in the full ranged principal stress/strain ratio range with non-proportional loading. Multiaxial fatigue testing machine for tension-torsion and inner pressure Fig. 5 (a) shows a schematic view of the testing machine used in this study of which type is corresponds to Type IB. To generate the inner pressure with tension and torsion loadings, additional hydraulic actuators is installed into the common