mechanical behavior of materials-lecture 5: fracture - macroscopic aspects
TRANSCRIPT
M.Sc. Course-Materials Engineering
Lecture 5: Fracture: Macroscopic Aspects
Text Book:Marc André Meyers and Krishan Kumar Chawla, Mechanical Behavior of Materials,
Cambridge University Press,2009
Lecturer: Asst.Prof.Dr.Ali Sabea HammoodUniversity of Kufa- Faculty of Engineering-Materials Engineering Department
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.)
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.
(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 a Circular Hole
Stress concentration at an elliptical hole for a = 3b.
Stress Concentration due to an Elliptical Hole
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.)
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.
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.
A body subjected to external forces F1, F2, . . ., Fn and with a closed contour .
Body under External Forces
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.)
Fracture Toughness: Effect of Impurities
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.)