CHAPTER 8

1. CHAPTER 8

2. FRAC TURE Fracture = separation of body into two or more pieces due to application of static stress Tensile, Compressive Shear or torsional The Fundamentals Lets talk about the tensile loading of materials DUCTILE BRITTLE Modes of fracture

3. Back to the The tensile test

4. Ductile fracture in copper nucleating around inclusions

5. Cup and Cone fracture Brittle fracture

6. Transgranular vs. intergranular fracture (cleavage fracture)

7. Stress trajectories y x Professor Inglis (1913) The birth of the term ‘’stress concentration’’ Large structures

8. ~ 100 microns in diameter Bent to a strain of 7.5% i.e. 5000MPa. Normal strength of glass = 100-200MPa. Crack-free silica (glass) fiber Griffith (1920) – application of Inglis to cracks and defects HE PROVED HIS POINT!!

9. b= a = r  Kt = 1 + 2 (1/1)1/2) = 3 2b Ellipse Stress concentration factor But radius of curvature =  t = b2/a For circular hole

10. Stress concentration factor vs. Specimen Geometry/configuration So what happens if a crack intersects a hole?

11. Griffith and his Energy criterion Crack propagates when favorable, i.e. system reduces its total energy  Relaxed material behind crack = Elasticstrain energy released a Crack having surface energy (s)

12. But for v. ductile materials p >>> s Define the strain energy release rate Gc (IRWIN) Hence What about ductile materials

13. Modes of fracture

14. AND Stress intensity factor =

15. Plastic zone What about ductile materials  consider y (i.e. y means direction not yield)

19. To be plane strain Plane strain fracture toughness

21. SOLUTION Where Y = 1.12. Substitute values Design using fracture mechanics Example: Compare the critical flaw sizes in the following metals subjected to tensile stress 1500MPa and K = 1.12 a. KIc (MPa.m1/2) Al 250 Steel 50 Zirconia(ZrO2) 2 Toughened Zirconia 12 Critical flaw size (microns) 7000 280 0.45 16

24. IMPACT TESTING Tensile test vs. real life failures Impact energy measured or notch toughness

25. Also HCP How do we specify a ductile-brittle transition temperature (DBTT)?? Not all materials exhibit DBTT

28. Mean stress Range of stress Stress amplitude For Reversed cycle fatigue FATIGUE Failure under repeated cyclic loading Definitions R = -1

29. How do you practically make these fatigue measurements ?

30. e.g. Al Endurance limit or Fatigue limitvs. fatigue life e.g. steels & Ti Alloys e.g. 35-60% of TS High cycle vs. low cycle fatigue

31. STAGE II  Nf = Ni + Np Initiation Propagation How does a fatigue crack form and propagate?

32. Beachmarks Striations

35. One of failure analysis goals = prediction of fatigue life of component knowing service constraint and conducting Lab tests Ignores crack initiation and fracture times

36. Can make extrapolations To obtain log A

37. QUESTION Eqn. 8.26

38. Other effects: a) Mean stress b)stress concentrations c) Surface treatments

39. Lead pipes deforming under their own weight CREEP Time dependent and permanent deformation of materials when subjected to load or stress (significant at T = 0.4Tm)  = f (T, t, )

41. Effect of temperature and stress

43. Data extrapolation methods – e.g. prolonged exposures (years) Perform creep tests in excess of T and shorter time but at same stress level