Investigation of fretting fatigue under constant amplitude using a damage model based on dissipated energy

This study introduces an energy-based damage model for the initiation of fretting fatigue cracks, using dissipated energy per cycle as a damage indicator. Employing the UMAT subroutine, fretting fatigue life estimation and crack initiation location are conducted using the damage model based on dissipated energy, which considers the effects of all stress and strain components. In addition, Effects of loading history and sequence are introduced in the damage model using <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>n</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>i</mml:mi> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mi>e</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> parameter. The effect of bulk stress and normal force amplitudes on fretting fatigue life, stick zone width, and crack location is investigated. Results show that variations in normal force and maximum axial stress alone do not significantly affect fretting fatigue life. Despite higher normal force, bulk stress, and maximum axial stress, some cases demonstrate unexpectedly higher fretting fatigue life due to the multiaxial nature of fretting fatigue. However, fretting fatigue life decreases as dissipated energy per cycle increases, so that, a 60% increase in dissipated energy per cycle leads to a 23% decrease in fretting fatigue life, while the bulk stress ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>0</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> ), maximum axial stress <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mo stretchy="false">(</mml:mo> <mml:msub> <mml:mrow> <mml:mi>σ</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>xx</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> increases by approximately 5% and 9.5%, respectively. Reducing the normal force increases fretting fatigue life while shifting the crack initiation location away from the center of the contact surface. Specifically, a 19% reduction in normal force leads to a 0.16% increase in fretting fatigue life, while a 28% reduction results in a 3% increase. Further analysis reveals that changes in bulk stress and normal force modify the width of the stick zone and the distribution of shear stress, impacting fatigue life. Additionally, as fretting fatigue life progresses, the critical damage location remains constant, although the damage value increases.