Analysis of fatigue surface crack using the probabilistic s-version finite element model
Fatigue failure is expected to contribute to injuries and financial losses in industries. The complex interaction between the load, time and environment is a major factor that leads to failure. In addition, the material selection, geometry, processing and residual stresses produce uncertainties and...
| Summary: | Fatigue failure is expected to contribute to injuries and financial losses in industries. The complex interaction between the load, time and environment is a major factor that leads to failure. In addition, the material selection, geometry, processing and residual stresses produce uncertainties and possible failure modes in the field of engineering. The conventional approach is to allow the safety factor approach to deal with the variations and circumstances as they occur within the engineering applications. The problems may persist in the computational analysis, where a complex model, such as a three-dimensional surface crack, may require many degrees of freedom during the analysis. The involvement of uncertainties in variables brings the analysis to a higher level of complexity due to the integration of non-linear functions during a probabilistic analysis. Probabilistic methods are applicable in industries such as the maintenance of aircraft structures, airframes, biomechanical systems, nuclear systems, pipelines and automotive systems. Therefore, a plausible analysis that caters for uncertainties and fatigue conditions is demanded. The main objective of this research work was to develop a model for uncertainties in fatigue analysis. The aim was to identify a probabilistic distribution of crack growth and stress intensity factors for surface crack problems. A sensitivity analysis of all the parameters was carried out to identify the most significant parameters affecting the results. The simulation time and the number of generated samples were presented as a measurement of the sampling efficiency and sampling convergence. A finite thickness plate with surface cracks subjected to random constant amplitude loads was considered for the fracture analysis using a newly developed Probabilistic S-version Finite Element Model (ProbS-FEM). The ProbS-FEM was an expansion of the standard finite element model (FEM). The FEM was updated with a refined mesh (h-version) and an increased polynomial order (p-version), and the combination of the h-p version was known as the S-version finite element model. A probabilistic analysis was then embedded in the S-version finite element model, and it was then called the ProbS-FEM. The ProbS-FEM was used to construct a local model at the vicinity of the crack area. The local model was constructed with a denser mesh to focus the calculation of the stress intensity factor (SIF) at the crack front. The SIF was calculated based on the virtual crack closure method. The possibility of the crack growing was based on the comparison between the calculated SIF and the threshold SIF. The fatigue crack growth was calculated based on Paris’ law and Richard’s criterion. In order to obtain an effective sampling strategy, the Monte Carlo and Latin hypercube sampling were employed in the ProbS-FEM. The specimens with a notch were prepared and subjected to fatigue loading for verification of the ProbS-FEM results. The ProbS-FEM was verified for the SIF calculation, the crack growth for mode I and the mixed mode, and the prediction of fatigue life. The major contribution of this research is to the development of a probabilistic analysis for the S-version finite element model. The formulation of uncertainties in the analysis was presented with the ability to model the distribution of the surface crack growth. The ProbS-FEM was shown to resolve the problem of uncertainties in fatigue analysis. The ProbS-FEM can be further extended for a mixed mode fracture subjected to variable amplitude loadings in an uncertain environment. |
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