Presentation on theme: "Chapter 7 Fracture: Macroscopic Aspects. Goofy Duck Analog for Modes of Crack Loading “Goofy duck” analog for three modes of crack loading. (a) Crack/beak."— Presentation transcript:
Chapter 7 Fracture: Macroscopic Aspects
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.)
Theoretical Tensile Strength
Theoretical Cleavage Strength
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.
Inglis: Stress Concentration
(a)Stress distribution in a large plate containing a circular hole. (b) Stress concentration factor K t as a function of the radius of a circular hole in a large plate in tension. Stress Concentration due to a Circular Hole
Stress concentration at an elliptical hole for a = 3b. Stress Concentration due to an Elliptical Hole
Griffith Criterion of Crack Propagation
Crack in Thin and Thick Plates Crack in (a) thin (t 1 ) and (b) thick (t 2 ) plates. Note the plane-stress state in (a) and the plane-strain state in (b).
Dislocation Emission at Crack Tip Dislocations emitted from a crack tip in copper. TEM. (Courtesy of S. M. Ohr.)
Plane Stress and Plane Strain
Linear Elastic Fracture Mechanics Inherent material resistance to crack growth, K R and its relationship to the applied stress σ and crack size a.
Three Modes of Fracture The three modes of fracture. (a) Mode I: opening mode. (b) Mode II: sliding mode. (c) Mode III: tearing mode.
Stress Field at a Crack Tip
Crack Tip Stress Field
Some Crack and Loading Configurations
Plastic Zone Correction Plastic-zone correction. The effective crack length is (a + r y ).
Dugdale–Bilby–Cottrell–Swinden Model of a Crack.
Plastic Zone at Crack Tip Plane Stress and Plane Strain
Variation of Fracture Toughness with Thickness (a) Variation infracture toughness (K c ) 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). (b) Schematic variation of fracture toughness K c and percentage of flat fracture P with the plate thickness B.
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.
Crack Extension Force
Crack Opening Displacement
A body subjected to external forces F1, F2,..., Fn and with a closed contour. Body under External Forces
R Curves for Brittle and Ductile Material
Different Parameters for Fracture Toughness
Fracture Toughness vs. Yield Stress
Variation of fracture toughness K Ic 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.) Fracture Toughness: Effect of Impurities
Plane Strain Fracture Toughness
Fracture Toughness vs. Yield Strength for Different Alloys
Measures of Crack Tip Opening Displacement
Strength Distribution for a Brittle and Ductile Solid
Typical Values of Weibull Modulus
Weibull Plots for Steel and Two Alumina samples Weibull plots 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.)
Probability of Failure for Three Ceramics Probability of failure of flexural strength (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.)