Chapter 7: Fracture: Macroscopic Aspects
Jan 14, 2016
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.)
Tensile 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.
Griffith Criterion on Fracture
(a) Stress distribution ina large plate containing a circularhole. (b) Stress concentrationfactor Kt as a function of the radiusof a circular hole in a large plate intension.
Maximum Stress
Stress concentration atan elliptical hole for a = 3b.
Stress Distribution at Tip of Crack
Griffith Criterion
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).
Dislocation at Crack Tip
Dislocations emitted from a crack tip in copper. (Courtesy of S. M. Ohr.)
Plane Stress and Plane Strain
Linear Elastic Fracture Mechanics
Inherent material σ resistance to crack growth 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 (see Figure 7.1).
Stress Field
Crack Tip Stress Field
Crack Configuration
Some common load and crack configurations and the corresponding expressions for the stress intensity factor, K.
Plastic Zone Correction
Plastic-zone correction. The effective cracklength is (a + ry).
Dugdale–Bilby–Cottrell–Swinden model of a crack.
Plastic Zone at the Crack Tip
Variation of Fracture Toughness with Thickness
(a) Variation infracture toughness (Kc) with platethickness (B) for Al 7075-T6 andH-11 Steel. (Reprinted withpermission from J. E. Srawley andW. F. Brown, ASTM STP 381(Philadelphia: ASTM, 1965), p 133,and G. R. Irwin, in Encyclopaedia ofPhysics, Vol. VI (Heidelberg:Springer Verlag, 1958); see also J.Basic Eng., Trans. ASME, 82 (1960)417.) (b) Schematic variation offracture toughness Kc andpercentage of flat fracture P withthe plate thickness B.
Elastic Body with a Crack
(a) Elastic body containing a crack of length 2aunder load P. (b) Diagram of load P versus displacement e.
Fracture Toughness Parameters
Crack Opening Displacement
Crack Opening Displacement
A body subjected toexternal forces F1, F2, . . ., Fn andwith a closed contour .
Integral of External Forces
J Integral: Contours Around Cracks
J Integral
R Curves for Brittle and Ductile Material
Growth of a Crack-Equivalence between Equations
Fracture Toughness and Yield Stress
Variation of fracturetoughness KIc with tensile strengthand 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
Fracture Toughness for Different Alloys
Different Measures of Crack Tip Opening
Strength Distribution for a Brittle and Ductile Solid
Weibull Distribution
A Weibull Plot
A Weibull plot for asteel, a conventional alumina, and acontrolled-particle-size (CPS)alumina. Note that the slope(Weibull modulus m)→∞forsteel. For CPS alumina, m is doublethat of conventional alumina.(After E. J. Kubel, Adv. Mater. Proc.,Aug (1988) 25.)
Flexural Strengths for Ceramics
Flexural strengths(4-point bend test with inner andouter spans 20 and 40 mm,respectively, and cross section of 3× 4 mm) for three ceramics.(Courtesy of C. J. Shih.)