Lecture-17 - Fracture Mechanics.pdf

7/27/2019 Lecture-17 - Fracture Mechanics.pdf

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Stress Analysis

Dr. Muhammad Abid

Assistant Professor - FME

CHAPTER

7FractureMechanics



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FRACTURE MECHANICS

• Fracture Mechanics is concerned with the initiation and propagation of crack or cracks

in the material until the extent of crack is such that the applied loading can no longer be

sustained by component or structure.”

• Failure by fracture is typically thought to be limited by the ultimate strength of the

material SU .

• In-spite of rigorous inspection, most components or structures contain some cracks /

flaws during manufacturing.

• These cracks may accelerate fracture of a part at a stress somewhat lower than the

Ultimate Strength, or more surprisingly, may fracture at a stress lower than the Yield

Strength of the material.

• Fractures in this manner resemble the rapid failure of the brittle material and are called

as Brittle Fractures.

• However, this type of failure can even occur in ductile materials.

• Fracture mechanics intimately and uniquely intertwined with the finite combinations of;

• Material behavior • Service environment

• Loading conditions

• Crack conditions and

• Part geometry

• Crack propagation tendency is related to stress field at crack tip region.

http://localhost/var/www/apps/Mechanics%20of%20Materials-McGrawHill/SOM-Chattha/Beer/Power%20Point%20Presentations/contents.ppt




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Fracture mechanics involves,

• Analytical predictions vs. experimental results

• Correlation is made by calculating fracture parameters.

Simplest parameter which describes the severity of stress field at the crack tip is

called as “Crack Tip Stress Field Intensity Factor” (K)

DIFFERENT THEORIES FOR FRACTURE MECHANICS

• C. E. Inglis, presented the first exact solution for a crack for an elliptical hole in a

linear elastic plate, loaded uniformly at an infinite distance from the crack.

• A. A. Griffith, put forward the original concept of L.E.F.M but restricted to Brittle

materials (glass) for an Elliptical Flaw in a plate developed by Inglis.

• Irwin, developed the technique for metals. Irwin defined stress intensity factor “K”

as,

• K = ( a)1/2 („a’ is the half -length of crack)

• In more general form

• K = Y

( a)1/2 („Y‟ is geometry factor)

FRACTURE MECHANICS

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ba

y 21max

max y

• For an infinite plate loaded by an applied uni-axial stress „σ‟

the maximum stress occurs at (±a,0) and is as;

• When a =b then ellipse becomes circle, then above equation

gives stress concentration factor of 3.

• This agrees with the well known result for an infinite plate

with a circular hole with d/w = 0, predicting;

• This result is also similar to the Contact Stress problem

where the contact area is assumed to be zero, showing stress

to be infinite and the material would fail under any load nomatter how small.

• An infinitely sharp crack is physically impossible.

• For any plastic deformation, the stress will be finite at the

crack tip.

Elliptical hole in

a flat plate

loaded in tension

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The Plastic Zone Correction

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FRACTURE MECHANICS

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Example-1

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Example-1 (Continued)

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Example-2

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Example-2 (Continued

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Example-3

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Stress AnalysisFatigue Analysis (Fatigue Strength and Endurance Limit)



Lecture-17 - Fracture Mechanics.pdf

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