PSI - Issue 25

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

490

5

3.2. Multiaxiality & Proportionality Effects Previous work by Gryguć et al, explored the effect of load multiaxiality on the cyclic behaviour of various forms of wrought Mg alloys [28][30]. Figure 4 illustrates the effect of proportionality on the number of cycles to failure for multiaxial loading with axial components above and below the “kink” threshold. It can be observed, that in general, non-proportional loading that is 90 ° out of phase results in the lowest fatigue life for a given multiaxial strain amplitude, and approximately a 50% reduction in life compared with proportional loading. Conversely, at a 45 ° phase angle, the proportionality effect is dependent on the level of axial strain amplitude. At 45 ° phase angle, at axial strain amplitudes which are below the kink, the life is insensitive to the presence of non-proportional loading. However, at axial strain amplitudes above the kink, an 18% increase in life was observed, which represents a change which is approximately 3 times smaller in magnitude than that which occurred at 90 ° phase angle. It is well known that for ductile materials, increasing the level of non-proportionality (i.e. increasing phase angle) has a detrimental effect on fatigue life, however semi-ductile materials are insensitive to this change [34], [36]–[39] The multiaxial response observed in the presented study for forged AZ80 Mg agrees well with the fact that the material can generally be considered to be ductile with a failure elongation of ε FAIL = 15.3% in tension and γ FAIL = 18.1 % in shear [28].

10.000

3.230 Number of Cycles to Failure [N f ] 100 1.000

3.798

1.492

375

374

212

Δε/2 = 0.4% Δγ/2 = 0.5% Δε/2 = 0.7% Δγ/2 = 0.5%

Proportional 0° Non-Proportional 45° Non-Proportional 90°

Figure 4 - Number of cycles to failure for three different multiaxial strain paths. Two different strain amplitudes were shown, one with high axial strain (above the “kink” in the ε -N curve) and one with low axial strain amplitude (below the “kink”), the shear strain component remains constant. The effect of the non-proportionality and phase angle of loading is illustrated via the various strain paths which are presented. Based the strain controlled cyclic response of AZ80, the multiaxiality effect is most pronounced when the axial strain amplitude is above the “kink” threshold and twinning-detwinning is the salient deformation mechanism. How the multiaxiality effect also influences the macroscopic crack path is critical in understanding the directional nature of fatigue damage phenomenon in wrought AZ80 Mg. Jiang et al. proposed a criterion based on the critical plane approach for predicting the macroscopic directionality early crack growth in extruded AZ31B Mg [34]. Their criterion incorporates the effects of both tensile and shear cracking, and they postulate that a material exhibits “mixed” cracking behaviour if early fatigue cracking is observed on the maximum normal plane for pure axial loading and the plane of maximum shear for pure torsional loading. They determined that since transverse cracks (max normal) were observed in axial loading and longitudinal cracks (max shear) were observed in torsional loading the material should exhibit mixed mode cracking behaviour in multiaxial loading. Their criterion has provisions to account for the dependence of the cracking behaviour on the loading amplitude or the fatigue life. Figure 5 illustrates the macroscopic crack orientations for tubular specimens following low-cycle multiaxial fatigue loading with different levels of loading proportionality and phase angle. It should be noted that all specimens illustrated in Figure 5 have axial strain amplitudes which are below the kink threshold and thus the shear response should be invariant of the level of non proportionality, for reference the component of shear SED (E γ ) is also given. All three of these samples show evidence of transverse crack orientations similar to those which were observed by Jiang in pure axial loading of extruded AZ31B Mg [34]. This provides qualitative evidence of the dominance of the axial cracking mode (max normal stress) in the early crack growth behaviour of forged AZ80 Mg under low-cycle multiaxial fatigue. This observation is invariant of