An epidemiological crack percolation model with application to probabilities of failure for gas turbines / by: Mathis Harder, M.Sc. Wuppertal, Januar 2024
Inhalt
- 1 Introduction
- 2 Basics on Mechanics and Fatigue of Metals
- 2.1 Polycrystalline Structure of Metals
- 2.2 Strain and Stress
- 2.3 Plastic deformation
- 2.4 Schmid factors
- 2.5 Fatigue
- 2.5.1 Load During Fatigue Testing
- 2.5.2 Stage I: Crack Initiation
- 2.5.3 Stage II: Crack Propagation
- 2.5.4 Stage III: Fracture
- 2.5.5 Wöhler Curves
- 2.5.6 Damage Accumulation
- 2.6 Stress Intensity Factor
- 2.7 LCF Experiments
- 3 Mathematic Foundation
- 3.1 Boundary Value Problem
- 3.1.1 Weak Solutions
- 3.1.2 Linear Elasticity as a Boundary Value Problem
- 3.1.3 Finite Element Method
- 3.2 Rotations
- 3.3 Crack Initiation Process
- 4 Epidemiological Percolation Model Uniaxial Stress
- 4.1 Single Grain Crack Initiation Times
- 4.2 Percolation Model
- 4.3 Uniaxial Infection Function
- 4.3.1 Geometry and Boundary Conditions
- 4.3.2 Numerical Results
- 4.3.3 Gradient Boosting Trees
- 4.3.4 The Surrogate Model
- 4.4 Failure Criteria
- 4.5 Results and Experimental Validation
- 5 Microstructual Models
- 5.1 Grain Orientations
- 5.1.1 Feed Forward Neural Networks
- 5.1.2 Density Estimation as Supervised Function Approximation
- 5.1.3 Sampling new Angles
- 5.2 Percolation with Grain Boundary
- 6 Multiaxial Percolation
- 6.1 Adjustments to the Percolation Model
- 6.2 Multiaxial Infection Function
- 6.2.1 Decomposition of the Stress
- 6.2.2 Geometry
- 6.2.3 Boundary Conditions
- 6.2.4 The Surrogate Models
- 6.2.5 Integration into the Percolation Model
- 6.3 Fitting the Model
- 6.4 Experimental Validation
- 6.5 Comparison of the Different Orientation Distributions
- 7 Application to a Turbine Blade
- 7.1 Linear Hazards
- 7.2 Blisk-Geometry and Surfaces Stress
- 7.3 Surrogate Model for the local cumulative Hazard rate
- 7.4 FEM Postprocessor
- 8 Conclusion and Outlook
- 9 References