Non-symmetrical fatigue life of nodular graphite cast iron under non-proportional multi-axial cyclic loading

Abstract

Non-proportional axial-torsional loading fatigue tests on nodular cast iron revealed a non-symmetrical behavior of the fatigue life relatively to the phase shift angle δ = 90° between axial and torsion loads. This behavior was in agreement with fatigue crack orientation investigated using optical and electron microscopy. Elasto-plastic finite element model (FEM) were used to assess the crack orientation behavior and it could explain this non-symmetrical behavior by the non-symmetrical values of both σI and σI / σII ratio relatively to δ = 90°. FEM revealed that for the δ < 90° loads, principal stress was applied essentially at critical planes of low angle ϕn, thus occurrence of tensile cracks mode was higher for δ < 90° than for δ > 90° load, which reduces the fatigue life. σI / σII ratio strongly influenced the dominant crack mode. When the applied loads were torsion σI / σII = 1, cracks were observed to occur, equally, in modes I and II. Presence of the nonpropagating failure (mode II) significantly increased the fatigue life. Conversely, for high phase shift, where σI / σII >> 1, crack mode I dominated and crack driving force remained high during the whole fatigue cycle, inducing a lower fatigue limit.

Cracking behavior in nodular graphite cast iron under non-proportional cyclic loading

“…Generally, cracks continued growing in a specific plane without distinct kinks for axial torsion and small-phase angle loads, whereas they grew into several directions for the close to 90° phase-shift loads. The crack orientation behavior was well explained in previous study [16]. For axial load, cracks initiated at the interface matrix/nodules and propagated globally, perpendicular to the specimen axis (ϕ = 0°) (cf.…”

“…The curves for torsion represented the lower limit values, and those for the highest phase angle (90°) represented the upper one. A plateau was distinguished at a high number of cycles for torsion load, with signs of crack propagation halting and mode II cracking [16], which would explain the highest value of fatigue life in torsion load (> 4.10 -6 cycles). The average crack growth rate on the whole of fatigue life (calculated by Ls / Nr, Ls being the apparent length of crack) is reported in Figure 4b.…”

“…According to previous studies, The number of loading cycles to failure (Nr) decreases nearly linearly in the interval δ = 0°-90°, and the behavior is quite symmetrical for out-of-phase angle of 90° (δ90) [11]. Inversely, Kachit et al [16] found that the curve is non-symmetrical for δ90 because more planes underwent maximum principal stress (tensile cracks mode) for δ < 90° than for δ > 90° loads. Due to the domination of Mode I cracks, it was found that the distribution of crack orientation increased while the phase-shift angle approaching 90°.…”

“…Figure 5). The presence of a Mode II crack for torsion load [16] explains the large difference of fatigue life between these two modes (cf. Figure 1a).…”

“…Crack growth and mode depend on loading condition [16 -19] and material ductility [20]. The effect of loading condition on crack mode was widely studied in EN-GJS-400-18, undergoing nonproportional fatigue at different phase angles δ [16]. The fatigue cracks were initiated and propagated in Mode I and/or Mode II.…”