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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effectively results in multiaxial cyclic responses that do not depend on the level of non-proportionality in the loading, as can be observed in the marginal differences in the peak stresses and cyclic energies for each particular strain path. However, when considering axial strain amplitudes above this kink, twinning is active, and it has a pronounced effect upon the shear response as illustrated in Figure 3. Despite having shear strains which are identical to the previous case, the presence of twinning-detwinning in the axial direction has the effect of augmenting the cyclic shear stresses. A secondary effect is the initial increase in plastic SED in non-proportional loading at 45 ° phase angle, followed by a decrease in plastic SED when the phase angle is increased to 90 ° . Once again, the axial response is unaffected to this change in non-proportionality as was the case at the lower stain amplitude. Thus, it can be postulated that in the axial direction, both the dislocation slip and twinning-detwinning mechanisms (below and above the kink respectively) are insensitive to the level of non-proportionality in multiaxial loading. In contrast to this, the shear deformation mode is sensitive to the presence of the axial loading when twinning-detwinning is the salient deformation mechanism above the kink, but is not sensitive below it.

100 150 200

70

(a)

(b)

50

30

-200 -150 -100 -50 0 50

10

-0,4% -0,2% 0,0% 0,2% 0,4%

-10 -0,6% -0,4% -0,2% 0,0% 0,2% 0,4% 0,6%

-30

C (Proportional 0°) D (Non-Proportional 45°) E (Non-Proportional 90°)

C (Proportional 0°) D (Non-Proportional 45°) E (Non-Proportional 90°)

-50

Engineering Axial Stress [MPa]

-70 Engineering Shear Stress [MPa]

Engineering Axial Strain [%]

Engineering Shear Strain [%]

Figure 2 - Stabilized cyclic hysteresis loops for (a) axial and (b) shear, for various multiaxial strain paths with strain amplitudes of Δε/2 = 0.4% Δγ/2 = 0.5%. Please note the axial strain amplitude of 0.4% shown here is below the aforementioned “kink” in the ε -N curve.

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(b)

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0

-10 -0,6% -0,4% -0,2% 0,0% 0,2% 0,4% 0,6%

-0,7% -0,5% -0,3% -0,1% 0,1% 0,3% 0,5% 0,7%

-100

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C (Proportional 0°) D (Non-Proportional 45°) E (Non-Proportional 90°)

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C (Proportional 0°) D (Non-Proportional 45°) E (Non-Proportional 90°)

-50

-300 Engineering Axial Stress [MPa]

-70 Engineering Shear Stress [MPa]

Engineering Axial Strain [%]

Engineering Shear Strain [%]

Figure 3 - Stabilized cyclic hysteresis loops for (a) axial and (b) shear, for various multiaxial strain paths with strain amplitudes of Δε/2 = 0.7% Δγ/2 = 0.5%. Please note the axial strain amplitude of 0.7% shown here is above the aforementioned “kink” in the ε -N curve”.