The fundamentals of fatigue strength of structures are presented. Crack initiation phase, crack propagation phase and fracture as a final consequence, are considered as a part of the total fatigue life of a structure subjected to cyclic loading. Damage tolerance analysis as the base for fracture control is discussed

Student responsibilities:

Grading and evaluation of student work over the course of instruction and at a final exam:

seminar paper: 50% oral exam: 50%

Methods of monitoring quality that ensure acquisition of exit competences:

Consultations with the lecturer and the assistant and student demonstrator allow the students additional explanations of the subject and help with the seminar assignment. After the lecture the students are invited to access available anonymous online evaluation of the course and the lecturer. Upon completion of the exam through voluntary conversations students are interviewed about the level of fulfillment of their expectations regarding the course and are invited to suggest possible improvement of lectures and lecture materials.

Upon successful completion of the course, students will be able to (learning outcomes):

Upon successful completion of the course, students will be able to: explain theoretical background needed for modeling and analysis of crack initiation compare different models for crack propagation simulation select criteria for fracture onset assessment; calculate stress intensity factors and J-integral by using finite element method for structural parts; predict fatigue life of a structure (number of cycles to fracture) by integrating the Paris equation; determine a critical load and crack length associated with fracture onset in structures;

Lectures

1. Introduction. Objectives of fatigue strength analysis of structures.

2. Damage tolerance and fracture mechanics. Effects of cracks and notches. Plastic collapse.

3. Linear elastic fracture mechanics. Stress at a crack tip. The stress intensity factor, K.

4. Numerical methods for calculation of K. The energy release rate and the energy criterion for fracture onset.

5. Elastic-plastic fracture mechanics. The energy criterion for plastic fracture. Fracture mechanics parameters: J-integral and crack tip opening displacement, CTOD.

6. Numerical calculation of the J-integral parameter. Fracture analysis, and fracture onset conditions.

7. Plane strain and plain stress fracture toughness, transitional toughness. R-curve. Toughness in terms of J. Estimates of toughness.

8. A cumulative damage hypothesis approach to fatigue problems. Miners rule, linear damage accumulation assumption.

9. Thermal stresses and thermal fatigue. Low Cycle Fatigue of gas turbine parts. Design S-N curves.

10. Fracture mechanics approach and fatigue crack growth analysis concept. Behavior under cyclic loading. Constant amplitude crack growth in a structure. Measurement of the rate function. Fitting the da/dN data.

11. Rate equations. Paris" equation. Fatigue life prediction.

12. Crack growth analysis for variable amplitude loading. Cycle counting methods. Stress history generation. Clipping. Truncation.

13. Multiple cracks, changing geometry. Other loading modes: mixed mode loading.

14. Fracture control. Fracture control options. Determining the inspection intervals. Fracture arrest. Stable fracture, unstable fracture.

15. Aircraft damage tolerance requirements.

Exercises

1. Examples of fatigue caused fracture.

2. Calculation of stress concentration factors for different notch shapes. Plastic collapse.

3. Westergaard stress function.

4. Calculation of K for various specimen shapes.

5. Corelation between J and CTOD.

6. Finite element calculation examples.

7. Comparison of calculated CTOD values with experimentally obtained data.

8. Accumulated damage calculation examples for several loading blocks.

9. LCF analysis examples for gas turbine parts. Temperature dependent SN-curves.

10. Determination of rate diagrams using experimental a-N data obtained from a constant stress range loading case.

11. Paris" constants determination using rate diagrams.

12. Rain flow counting method. Examples based on strain measurements of actual aircraft structures.

13. Residual lifetime and strength of parts damaged by multiple cracks.

14. Inspection intervals - examples. Crack arresters.

15. Numerical examples.

Compulsory literature:

Broek, D., The practical use of fracture mechanics, Kluwer academic publishers (1989).

Kanninen, F., Popelar, C.H., Advanced fracture mechanics, Oxford University Press (1985).

Bozic,Z., Dinamička čvrstoća tankostjenih konstrukcija, FSB, Zagreb (in Croatian), 2011. http: //www.fsb.unizg.hr/zbozic/

ship structures, Information from Germanisher Lloyd Group (1997).

Recommended literature:

Knot, J.F., Fundamentals of fracture mechanics, Butterworths, (1973).

Broek, D., Elementary engineering fracture mechanics, 4th Edition, Nijhoff (1985).

Božić, Ž. Selected papers