Issue34

T. Itoh et alii, Frattura ed Integrità Strutturale, 34 (2015) 487-497; DOI: 10.3221/IGF-ESIS.34.54 489 respectively. In proportional fatigue test, λ and  have constant values in a cycle. For tension-compression tests using the hollow cylinder specimen, relationships among σ 1 , σ 3 , σ, τ and ε 1 , ε 3 , ε, γ are shown in Eq. (5) and Eq. (6). 1 2 2 3 1 4 2 2            (5)   2 1 2 2 3 1 1 1 2 2                     (6) In Eq. (6), ν is the Poisson’s ratio. Usually, the value of Poisson’s ratio is around 0.3 in elastic regime but it is 0.5 in a fully plastic regime. Uniaxial and multiaxial stress and strain states A stress state is defined as multiaxial state if the multiple principal stresses operate and a strain state as multiaxial state when the multiple principal strains do. Using these definitions, the multiaxial stress state does not always correspond to the multiaxial strain state. For example, Fig. 1, an uniaxial tension loading is the uniaxial stress state because only one principal stress operates in tensile direction but this case becomes the multiaxial strain state because the two additional principal strains are caused by the lateral contraction as well as the tensile direction. These definitions of multiaxiality are most consistent for describing the multiaxial stress and strain states compared to using the other stress and strain components, whereas stress multiaxiality does not always correspond to strain multiaxiality. Non-proportional loading is defined as the loading where the directions of the principal stresses or strains rotate, and proportional loading when they are fixed. Applied load Principal stress Principal strain Figure 1 : Principal stress and principal strain in tension loading.   t  1   t  1  3 =-  1    t  1  1   x  y t  1  1  y  x Uniaxial loading Multiaxial loading Tension- compression Reversed torsion Tension- compression and reversed torsion Biaxial tension- compression Principal stress state Applied stress Type Principal stress directions are fixed  =  0.5  =  1  =  1  0  =  1  1   t  1 -  1   t  1 -  1    t  1   1   x  y t  1   1  y  x Uniaxial loading Multiaxial loading Principal strain state Applied strain Type Principal strain directions are fixed  =  0.5  =  1  =  1     =  1  1 Tension- compression Reversed torsion Tension- compression and reversed torsion Biaxial tension- compression (a) (b) Figure 2 : Applied stresses/strains and stress/strain multiaxiality in proportional loading. (a) Stress state, (b) Strain state. Proportional loading Figs. 2 (a) and (b) summarize the applied stresses/strains and the stress/strain multiaxiality in various proportional multiaxial testing methods under the plane stress condition. In the tension-compression test, a uniaxial stress (  ) is applied