PSI - Issue 38

Amaury Chabod et al. / Procedia Structural Integrity 38 (2022) 382–392 Amaury CHABOD / Structural Integrity Procedia 00 (2021) 000 – 000

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5.3. Damage analysis Using modal stress { } and reconstructed modal coordinates ( ) , stress time histories { }( ) are obtained thanks to modal superposition (equation (20) and Fig. 3), and then fatigue damage analysis is readily achieved. Combining unitary load cases and out-of-phase time series often conducts to multiaxial loading, which is processed in present case by critical plane obtained normal stress (nCode DesignLife Theory Guide and Heyes). Indeed, from stress tensor time history, 2D-critical plane assessment is processed to obtain normal stresses at each node, considering 18 planes around the surface normal (Fig. 8 and equation (21)). For each of these directions, rainflow algorithm counts fatigue cycles, sorted in terms of range and mean stress classes. Then, a linear damage accumulation is achieved, according to Miner’s Rule, and considering Basquin SN curve for material definition. A review of linearity assumption excludes EN analysis, as any plasticity should be avoided in current method. Goodman mean stress correction integrates the effect of non-zero mean cycles. The damage is assessed for each critical plane direction, and the most damaged direction is retained for each FE node. The dominant direction of stress in surface normal axis is also available on hot spots, as depicted in Fig. 9.

Fig. 8. Representation of normal stress vs angle in surface normal axis.

= + 2 + − 2 cos(2 ) + sin (2 )

(21)

Stress [MPa]

Angle [°]

Dominant Direction

Fig. 9. Maximum amplitude of normal stress [MPa] vs angle [°] for node #6466.

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