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Contents IntroductionWhat is fracture mechanics? What kind of materials fracture? Forces cause fractureModes of failureHow do cracks grow? Simulation of crack growthNotches and stress concentrationReferencesConclusion

Introduction The ways to calculate a crack, how it

begins, how it grows, and if it stops, are all part of the field called fracture mechanics. There are many, many ways to try to calculate a crack. In fact, people are still fighting about which way is the right way. The right way really depends on what kind of material and what type of structure you're talking about. Here we'll discuss a version of fracture mechanics which can be applied to large concrete structures, like dams.

What is fracture mechanics?Fracture mechanics is the study of how cracks

start, grow, and (hopefully) stop. It is important to study how cracks behave because

cracks can cause things to fail, something as small as a bone or as large as a ship. If a large structure, such as a building or a ship, cracks, this may lead to a failure which could affect many people.

To avoid in the study of fracture mechanics, people have developed computer programs which allow them to simulate how cracks might grow in different structures, such as the body of an airplane or in a concrete dam.

Fracture is another word for cracking or a crack.

What kind of materials fracture?

Many structures are made of steel and/or concrete, and both of these materials can fracture.

Civil engineers use both steel and concrete, so they must be concerned with fracture

In steel, fracture is often ductile and may be due to fatigue.

A fatigue crack is caused when a cyclic load (*) is applied

"Ductile fracture" means that the part of the material which is cracking is also deforming

concrete fracture is brittle. Brittle fracture means there is no deformation around the crack,the very grains of the material are separating

Concrete is bad in tension and therefore prone to cracking.

Ductile failure

Brittle failure

Forces cause fracture

temperature variation -- this can be a big problem in concrete. As you learned earlier in the section on concrete, when concrete is mixed it gets very hot and expands. When it tries to cool off, the concrete wants to contract. If it can't contract (because it is connected to another wall or rock) then cracks form.

Chemical reaction -- a reaction between the cement and the aggregate in the concrete which makes the concrete "grow"

Live load -- the general pulling or pushing on a material. In a dam, loads could be caused by settling or sliding of the foundation or abutments, ice, silt, waves, earthquakes.

Modes of failureMode I: the forces are perpendicular to the crack (the

crack is horizontal and the forces are vertical), pulling the crack open. This is referred to as the opening mode.

Mode II: the forces are parallel to the crack. One force is pushing the top half of the crack back and the other is pulling the bottom half of the crack forward, both along the same line. This creates a shear crack: the crack is sliding along itself.

Mode III: the forces are perpendicular to the crack (the crack is in front-back direction, the forces are pulling left and right). This causes the material to separate and slide along itself, moving out of its original plane.

Modes of failure

How do cracks grow?

How a crack grows is called "crack propagation" and this takes into account when a crack can start to grow, how far it grows, and what direction it goes in

When a crack is formed, new surfaces are also formed, along the edges where the material has split apart. The material has to have enough energy to create these new surfaces or it will not crack. If G is the energy necessary for the crack to grow and R is the material's resistance to crack growth, the condition for a crack to grow is:

G = RThe crack can grow when its stress intensity factor

reaches the fracture toughness of the material: KIc=KI

Initiation and propagation portions of fatigue life

Where are cracks likely to start in dams?

Based on the history of cracks in dams, there are some of the places where cracks are most likely to occur in dams.

cracks near the foundation and on the downstream side of a gravity dam

cracks in the arches of an arched buttress dam

cracks at the base of an arch dam

The cracks in a gravity or arch dam might look like this in a two dimensional

Simulations for crack growthHere is an image of a model with an initial cracks on

both the left hand edge and the right hand edge . The program which will analyzed this model can only handle cracks which start from the outside of the structure.

This is what the model looks like after the program has grown the crack. The tips of the cracks have moved to where you see the blue patches.

One example of a computer simulation program for cracking is a "FRacture ANalysis Code" called FRANC2D (#) which was written and developed at Cornell University (#) by the Cornell Fracture Group (#). There is also a 3d version called FRANC3D (#) which will analyze three-dimensional crack growth in structures.

Computer simulations for crack growth

Notches and stress concentration

There may be a confusion between notch and crackA notch is defined as geometric discontinuity which

has a depth and root radious.(bolt hole, screw threads)

The effect of a notch on tensile stress field is easily visualized by stress flow analogy which illustrates high density of stress around the root of the notch

So if the material is removed there will be a loss of strength and adding the material to smooth out the flow of stress

Stress concentration factor “Kt” is ratio of maximum stress at the root of notch to nominal stress.

Strength of uncracked and cracked plates

F4<F3<F1<F2

Stress concentration

crack propagation

Damage toleranceThe main two objective of damage tolerance

analysis are to determine the effect of crack on the residual strengthcrack growth behaviour as a function of timethe initial crack is assumed to exhistinspection to detect crackcrack grown determined from fracture mechanicsfailure probability after two inspection=0.001

Safe life of structureSrtucture is assumed to defect freeNo crack formation at design service lifeDesign life<service life with or without repairLife at 1.2 design loads equals to1.5 design lifeSafe life derived from s-n curve (local strain

approach)Scatter factor 3-4 applied to calculated livesFracture probability=0.001

ConclusionCracks are everywhere, it is just a matter how to

be the crack are grow largeFracture design criteria are required more often in

modern designsIts main objective is more efficient designs with

lower factor of safety Fracture mechanics approaches require that an initial crack size be known or assumed.

For components with imperfections or defects an initial crack size may be known. Alternatively, for an estimate of the total fatigue life of a defect-free material, fracture mechanics approaches can be used to determine propagation.

Strain-life approaches may then be used to determine initiation life, with the total life being the sum of these two estimates.

ReferencesJohnson, W.S., “Stress Analysis of the Cracked Lap

Shear Specimen: An ASTM Round-Robin,” Journal of Testing and Evaluation, Vol. 15, No. 6, American Society for Testing and Materials, Philadelphia, PA, 1987, pp. 303-324.

Klemczyk, M. and Belason, E.B., “Analysis of Stresses Near the Edge of a Boron/Epoxy Doubler Bonded to Aluminum,” Textron Specialty Materials, Lowell, MA, April 1995.

Rybicki, E.F. and Kanninen, M.F., “A Finite Element Calculation of Stress Intensity Factor by a Modified Crack Closure Integral,” Engineering Fracture Mechanics, Vol. 9, 1977, pp. 931-938.

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