Abstract
An engineering predictive approach to determine the fatigue limit of defective material under multiaxial loading will be presented. The proposed approach is based on the affected depth model recently proposed. The affected depth model is founded on a critical depth parameter deduced from the analysis of the stress distribution in the vicinity of the defect. It is shown that the crack propagation plan is perpendicular to the direction of the maximum principal stress. Subsequently, the variation of the principal stresses during a loading cycle is studied. The finite element method is used to analyze the stress state at the instant on which the maximum principal stress reaches its maximum value. This study allows us to (i) extend the affected depth approach to multiaxial loadings and (ii) to obtain a resistance condition that leads to assess the fatigue life of a defective material submitted to combined loading. The extended approach is applied for defective medium Carbon steel under in-phase and out-of-phase combined loading. The predicted multiaxial fatigue limits are in good agreement with experimental investigations and confirm that the affected depth parameter can characterize the fatigue behavior under combined loadings.
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Abbreviations
- \({a}_{w}\) :
-
Affected depth at the fatigue limit [μm]
- \(\sqrt {area}\) :
-
Equivalent defect size of defect perpendicular to the direction of the maximum principal stress [µm]
- HCF:
-
High Cycle Fatigue
- HLP:
-
Highest Loaded Plan
- \(\sqrt{{J}_{2,a}}\) :
-
Square root of the second invariant of the stress deviator [MPa]
- P max :
-
The hydrostatic stress [MPa]
- \({R}_{\sigma }\) :
-
Load ratio:\({R}_{\sigma }=\frac{{\sigma }_{min}}{{\sigma }_{max}}\)
- \(\underline{\underline{S}}({t}_{i})\) and \(\underline{\underline{S}}({t}_{j})\) :
-
The periodic deviator stress tensor in two diverse instants (\({t}_{i}\) and \({t}_{j}\)).
- \({\alpha }_{C}\) :
-
Coefficient in Crossland criterion
- \({\beta }_{C}\) :
-
Material parameter in Crossland criterion [MPa]
- \({\sigma }_{a}\) :
-
Amplitude of the tension loading [MPa]
- \({\sigma }_{D-1}\) :
-
Fatigue limit under fully reversed tension of the defect-free material [MPa]
- \({\sigma }_{eq}^{Cr}\) :
-
Crossland equivalent stress [MPa]
- \({\tau }_{a}\) :
-
Amplitude of the torsion loading [MPa]
- \({\tau }_{D-1}\) :
-
Fatigue limit under fully reversed torsion of the defect-free material [MPa]
- \(\Delta {K}_{th}\) :
-
Threshold value of the stress intensity factor
- \({\Delta \sigma }_{0}\) :
-
Plain-specimen fatigue limit
- L :
-
Threshold of a non-propagating crack length
- CDM:
-
Critical distances model
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Hassine, W., Nasr, A. & Bouraoui, C. An Engineering Predictive Approach of Multiaxial Fatigue Life of Defective Material Based on Affected Depth. Iran J Sci Technol Trans Mech Eng 47, 1265–1273 (2023). https://doi.org/10.1007/s40997-022-00579-w
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DOI: https://doi.org/10.1007/s40997-022-00579-w