Transcript Chapter7
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 Stress Concentration due to a Circular Hole (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. Stress Concentration due to an Elliptical Hole Stress concentration at an elliptical hole for a = 3b. Griffith Criterion of Crack Propagation Crack in Thin and Thick Plates Crack in (a) thin (t1) and (b) thick (t2) 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, KR 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 + ry). 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 (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). (b) Schematic variation of fracture toughness Kc 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 Crack Opening Displacement Body under External Forces A body subjected to external forces F1, F2, . . ., Fn and with a closed contour . J Integral J Integral R Curves for Brittle and Ductile Material Different Parameters for Fracture Toughness Fracture Toughness vs. Yield Stress 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.) 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 Weibull Distribution 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.)