PSI - Issue 25

A. Gryguć et al. / Procedia Structural Integrity 25 (2020) 486– 495 Andrew Gryuc/ Structural Integrity Procedia 00 (2019) 000–000

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the proportionality ratio ( ε max / γ max ), or the phase angle of loading.

(c)

(a)

(b)

Figure 5 - Macroscopic fracture morphology for failed samples under bi-axial strain paths (a) proportional (0° out of phase) (b) non-proportional 45 ° out of phase and (c) non-proportional 90 ° out of phase. (For reference, (a) 0°, Δε/2 = 0.4%, Δγ/2 = 0.75%, 1201 cycles, E γ = 0.76 [MJ/m 3 ], (b) 45°, Δε/2 = 0.4%, Δγ/2 = 0.5%, 3798 cycles, E γ = 0.42 [MJ/m 3 ], (c) 90°, Δε/2 = 0.4%, Δγ/2 = 0.5%, 1492 cycles, E γ = 0.37 [MJ/m 3 ]) For reference, the axis of the sample is in the direction to the left and right of the page. 3.3. Macroscopic Cracking Behaviour Previous work by Gryguć et al. [30] and others [40]–[42] has been done highlighting the individual contributions of axial and shear components to the total strain energy density in multiaxial fatigue of a variety of wrought Mg alloys. They concluded that strain energy density (SED) is a good parameter to correlate multiaxial fatigue loading, and the effect of non-proportional loading was found to be detrimental on fatigue life only if the rotation of the principal axis causes the axial proportion of total SED to increase. Figure 6 illustrates the relationship between total strain energy density and fatigue life for various strain paths; (a) pure axial, (b) pure shear, and (c) multiaxial (0° proportional and non-proportional 45 ° & 90 ° ). For reference, the typical cracking behaviour is illustrated for each of the various strain paths focusing on the early crack growth response. It was observed that under pure axial loading Figure 6 (a), forged AZ80 Mg, exhibits transverse cracking along the planes of maximum principal stress which is orthogonal to the load (i.e. the plane of maximum normal stress, an orientation referred to as 0 ° ) for the entire range of strain amplitudes that were investigated. Under pure shear loading Figure 6 (b), it can be observed that there is a transition in cracking behaviour between 20 000 – 40 000 cycles from longitudinal cracking (LCF, < 20 000 cycles) to helical cracking (HCF, > 40 000 cycles). This threshold of change in cracking behaviour corresponds with a pure shear cyclic SED of 0.6 [MJ/m 3 ], such that above this threshold, longitudinal cracking is observed (i.e. shear dominated, along the plane of maximum shear stress, an orientation referred to as 90 ° ), and below this threshold helical cracking prevails (i.e. along the plane of maximum normal stress, an orientation referred to as 45 ° ). Bemfica et al. [36] investigated the axial torsional fatigue and cyclic deformation response of 304L stainless steel and observed that under pure shear loading, there was a similar shift in cracking mode between 10 4 – 10 5 cycles, such that in the HCF (>10 5 cycles) the material exhibited a helical cracking behaviour, which is similar to what can be observed in the presented study highlighted in Figure 6(b). This dependence on shear SED (or more generally, the level of cyclic plasticity in shear) in early crack growth mode in pure shear loading plays an important role in the combined effects observed in the multiaxial cracking behaviour. The multiaxial response is highlighted in Figure 6 (c) and includes results from both proportional and non proportional load paths. Important to note is the detrimental effect of non-proportion loading on the fatigue life previously discussed results in life ranges that are within the regime of 10 2 - 10 4 which can all be considered to be low cycle fatigue. However, the contributions of each individual axial and shear component towards total SED reside in regimes which are both higher and lower than the aforementioned “kink” threshold in pure axial loading and transition threshold in cracking behaviour in pure shear loading, thus enabling exploration of the various modes of cracking and their synergistic effects in multiaxial loading. As illustrated in Figure 6 (c)(i) mixed cracking is observed when the shear strain contribution is above the transition threshold of 0.6 [MJ/m 3 ], and transverse cracking Figure 6 (c)(ii) when