Chapter 7: Fracture: Macroscopic Aspects

1. Chapter 7:Fracture: Macroscopic Aspects

2. Goofy Duck Analog for Modes of Crack Loading “Goofy duck” analog for three modes of crack loading. (a) Crack/beak closed. (b) Opening mode. (c) Sliding mode. (d) Tearing mode. (Courtesy of M. H. Meyers.)

3. Tensile Strength

5. Stress Concentration “Lines of force” in a bar with a side notch. The direction and density of the lines indicate the direction and magnitude of stress in the bar under a uniform stress σ away from the notch. There is a concentration of the lines of force at the tip of the notch.

6. Griffith Criterion on Fracture

7. Maximum Stress (a) Stress distribution in a large plate containing a circular hole. (b) Stress concentration factor Kt as a function of the radius of a circular hole in a large plate in tension.

8. Stress Distribution at Tip of Crack Stress concentration at an elliptical hole for a = 3b.

9. Griffith Criterion

10. Crack Propagation Crack in (a) thin (t1) and (b) thick (t2) plates. Note the plane-stress state in (a) and the plane-strain state in (b).

11. Dislocation at Crack Tip Dislocations emitted from a crack tip in copper. (Courtesy of S. M. Ohr.)

12. Plane Stress and Plane Strain

13. Linear Elastic Fracture Mechanics Inherent material σ resistance to crack growth and its relationship to the applied stress σ and crack size a.

14. Three Modes of Fracture The three modes of fracture. (a) Mode I: opening mode. (b) Mode II: sliding mode. (c) Mode III: tearing mode (see Figure 7.1).

15. Stress Field

16. Crack Tip Stress Field

17. Crack Configuration Some common load and crack configurations and the corresponding expressions for the stress intensity factor, K.

18. Plastic Zone Correction Plastic-zone correction. The effective crack length is (a + ry).

19. Dugdale–Bilby–Cottrell–Swinden model of a crack.

20. Plastic Zone at the Crack Tip

21. Variation of Fracture Toughness with Thickness (a) Variation in fracture toughness (Kc) with plate thickness (B) for Al 7075-T6 and H-11 Steel. (Reprinted with permission from J. E. Srawley and W. F. Brown, ASTM STP 381 (Philadelphia: ASTM, 1965), p 133, and G. R. Irwin, in Encyclopaedia of Physics, Vol. VI (Heidelberg: Springer Verlag, 1958); see also J. Basic Eng., Trans. ASME, 82 (1960) 417.) (b) Schematic variation of fracture toughness Kc and percentage of flat fracture P with the plate thickness B.

22. Elastic Body with a Crack (a) Elastic body containing a crack of length 2a under load P. (b) Diagram of load P versus displacement e.

23. Fracture Toughness Parameters

24. Crack Opening Displacement

25. Crack Opening Displacement

26. Integral of External Forces A body subjected to external forces F1, F2, . . ., Fn and with a closed contour .

27. J Integral: Contours Around Cracks

28. J Integral

29. R Curves for Brittle and Ductile Material

30. Growth of a Crack-Equivalence between Equations

31. Fracture Toughness and Yield Stress

32. Fracture Toughness: Effect of Impurities Variation of fracture toughness KIc with tensile strength and sulfur content in a steel. (Adapted from A. J. Birkle, R. P. Wei, and G. E. Pellissier, Trans. ASM, 59 (1966) 981.)

34. Fracture Toughness for Different Alloys

35. Different Measures of Crack Tip Opening

36. Strength Distribution for a Brittle and Ductile Solid

37. Weibull Distribution

39. A Weibull Plot A Weibull plot for a steel, a conventional alumina, and a controlled-particle-size (CPS) alumina. Note that the slope (Weibull modulus m)→∞for steel. For CPS alumina, m is double that of conventional alumina. (After E. J. Kubel, Adv. Mater. Proc., Aug (1988) 25.)

40. Flexural Strengths for Ceramics Flexural strengths (4-point bend test with inner and outer spans 20 and 40 mm, respectively, and cross section of 3 × 4 mm) for three ceramics. (Courtesy of C. J. Shih.)