DOKUZ EYLÜL UNIVERSITY MECHANICAL ENGINEERING DEPARTMENT

1. DOKUZ EYLÜL UNIVERSITYMECHANICAL ENGINEERING DEPARTMENT INTRODUCTION TO FRACTURE MECHANICS Assoc.Prof. Dr. M. Evren Toygar

2. FRACTURE MECHANICS • REFERENCES: • 1. Anderson, “Fracture Mechanics Fundamentals and Applications.” • 2. Richard W.Hertzberg, “Deformation and Fracture Mechanics Of Engineering Materials.” • 3. Dowling, "Mechanical Behavior of Materials" • 4. Broek, “Elementary Engineering Fracture Mechanics” • 5. Ağah Uğuz, “Kırılma Mekaniğine Giriş “

3. FRACTURE When material damage like micro-cracks andvoidsgrow in size and become localized, theaveragingprocedure can no longer be applied and discontinuities must be taken into account.This localization results in a macroscopic crack, whichmay grow very fast, resulting in globalfailure.

4. Fracture Mechanics Definition: It is thefield of mechanicsconcernedwiththestudy of propagation of cracks in materails. Itusesmethods of analyticalsolidmechanicstocalculatethedrivingforce on acrackandthose of experimentalsolidmechanicstocharacterizethematerial’sresistancetofracture.

5. Fracture Mechanics • In modern materials science, fracture mechanics is an important tool in improving the mechanical performance of mechanical components. • It applies the physics of stress and strain, in particular the theories of elasticity and plasticity, to the microscopic defectsfound in real materials in order to predict the macroscopic mechanical failure of bodies.

6. Fracture Mechanics In fracture mechanics attention is basically focused on a single crack. Theoretical conceptsand experimental techniques have been and are being developed, which allow answers toquestions like: • Will a crack grow under the given load ? • When a crack grows, what is its speed and direction ?

7. Fracture Mechanics • Will crack growth stop ? • What is the residual strength of a construction (part) as a function of the (initial) crack • What is the length and the load ? • What is the proper inspection frequency ? • When must the part be repaired or replaced ?

8. Fracture mechanics Fracture mechanics is a failure theory that • determines material failure by energy criteria, possibly in conjunction withstrength (or yield) criteria • considers failure to be propagating throughout the structure rather thansimultaneous throughout the entire failure zone or surface.

9. Linear elastic fracture mechanics (LEFM) A large field of fracture mechanics uses concepts and theories in which linear elastic materialbehavior is an essential assumption. This is the case for Linear Elastic Fracture Mechanics(LEFM). • is the basic theory of fracture, that deals with sharp cracks in elastic bodies. • It is applicable to any materials as long as the material is elastic except in a vanishingly • small region at the crack tip (assumption of small scale yielding), • brittle or quasibrittle fracture, stable or unstable crack growth

10. Elastic-plastic fracture mechanics • is the theory of ductile fracture, usually characterized by stable crack growth • (ductile metals) the fracture process is accompanied by formation of large • plastic zone at the crack tip

11. Why structures Fail • Negligenceduringdesign, constuction, oroperation of structure. • Application of a newdesignormaterial, whichproduces an unexpectedresult.

12. Historical Perspective • Experimentsperformedby Leonardo da Vinci severalcenturiesearlierprovidedsomeclues as totherootcause of fracture. He measuredthestrength of ironwiresandfoundthatthestrengthvariedinverslywithwirelength. • A quantitativeconnectionbetweenfracturestressandflaw size camefromthework of Griffth 1920. He applied a stressanalysis of an elliptical hole totheunstablepropagation of crack. Griffthinvokedthefirstlaw of thermodynamicstoformulate a fracturetheorybased on a simpleenergybalance.

13. Figure 1 Galileo’ s tension bar Figure 2 Da Vinci’s cable

14. Figure 3 schematic representation of ancient Rome bridge

15. During Design someimportanttitlesare: • DeformationandFracture • ExceedtheElasticDeformation • Buckling (Burkulma) • PlasticDeformation • Fracture (Kırılma) • Fatique (Yorulma) • Creep (Sünme ) • StressCorrosionCracking (Gerilme Korozyon Çatlağı )

16. Crack and stress intensity approach The unit of Ki is MPam’ dır.

17. Stresses near and tip of the crack

18. Loading types • Inall loading1/r singularitymay ocur at the tip of thecrack., K (stressintensityfactor) andfij(dimensionlessshapecorrectionfactor) depend on laodingtypeandshapegeomety. (i,j=1,3) • Therearethreeways of applying a forcetoenable a cracktopropagate: • Mode I fracture: openingmode(a tensile stress normal totheplane of thecrack). • Mode II fracture: slidingmode (a shearstressactingparalleltotheplane of thecrackandperpendiculartothecrack). • Mode III fracture: Tearingmode(a shearstressactingparalleltotheplane of thecrackandparalleltothecrackfront)

19. Cauchy stress around a crack tip

20. Stress intensity factor types in a plate including crack • Mode I and Mode II calculations of a plate subjected to tension

21. Stresses in the systems with crack • Whenthecrack at thecenter of a platethestressandsterssintensityfactorsterms can be given as :

22. P h 2a b P Center crack in an infinite plate subjected to tension • SterssIntensityFactorAprroach K :

23. Types of Stress: • Plane stress problem: in z- direction: z= xz = yz = 0 olur, • Plane strain problem: the stress in z direction becomes zero. Therefore : xz = yz = 0 and z =  (x + y).

24. Geometries of Fracture Stressintensityfactor • Center crackandfiniteplate: • infinite plate:

25. Single sided notch, subjected to stress Stres sintensity factor • if(a w) semi infinite plate β=1.12 One-sided cracked plate b) when

26. Stress intensity factor • Double-sided notch • if(a w) semi infinite plate β=1.12 b)

27. Stress intensity factors Y wrt a/w ratio

28. Eliptic Crack

29. Semi eliptic Surface crack

30. Problem 2 : AISI 4340 çelikten yapılmış ve merkezinde çatlak içeren plakanın boyutları ve malzeme özellikleri aşağıda verildiği gibidir. Bu plakada başlangıç çatlağı olarak a=1mm lik kusur mevcuttur. Plaka P=240 N lık bir çekme yüküne maruz olduğuna göre plaka ve çatlak konumu için gerilme şiddeti faktörünü hesaplayınız. (W= genişlik, B=kalınlık H=yükseklik olarak alınmaktadır.