FRACTURE MECHANICSMENG 486

BY

DR. O. PHILLIPS AGBOOLA

Failures?

The failure of engineering materials is almost always an undesirable event for several reasons; these include human lives that are put in jeopardy, economic losses, and the interference with the availability of products and services.

Even though the causes of failure and the behavior of materials may be known, prevention of failures is difficult to guarantee.

The usual causes are improper materials selection and processing and inadequate design of the component or its misuse.

It is the responsibility of the engineer to anticipate and plan for possible failure and, in the event that failure does occur, to assess its cause and then take appropriate preventive measures against future incidents.

Fundamentals of Fracture Mechanics

Simple fracture is the separation of a body into two or more pieces in response to an imposed stress that is static (i.e., constant or slowly changing with time) and at temperatures that are low relative to the melting temperature of the material.

The applied stress may be tensile, compressive, shear, or torsional; the present discussion will be confined to fractures that result from uniaxial tensile loads.

For engineering materials, two fracture modes are possible: ductile and brittle. Classification is based on the ability of a material to experience plastic deformation.

Ductile materials typically exhibit substantial plastic deformation with high energy absorption before fracture. On the other hand, there is normally little or no plastic deformation with low energy absorption accompanying a brittle fracture.

“Ductile” and “brittle” are relative terms; whether a particular fracture is one mode or the other depends on the situation.

Furthermore, ductility is a function of temperature of the material, the strain rate, and the stress state.

Any fracture process involves two steps —crack formation and propagation—in response to an imposed stress

An applied tensile stress is amplified at the tip of a small incision or notch

Early structural concepts

Some of the structures in earlier days have endured for ages. Materials used were brittle type like bricks, stones, mortar: poor to carry tensile loads. Avoided fracture possibilities by selecting appropriate geometric shapes like arches, domes The structure were designed to carry load by compression

New structural concepts

Availability of metals lead to change in structural concepts: allowed tension in structure. (this invited additional problems like fracture) Designs based on strength allowed a factor of safety ranging from 2 to 10, but still structures failed by sudden brittle fracture Eg. 1919 rupture of Molasses tank in Boston spilling 2 million gallons of molasses

* When ever there is new material or new design concepts produces unexpected results leading to catastrophic failure

Hogging Bending Moment

1943, Liberty ship: a cargo ship

Prior to II world war liberty ships were riveted (very slow process) having no fracture problems

During war, to accelerate ship building, England sought help from USA. USA companies offered to build ship faster, by welding joints.They maintained same geometric shape, ship hull turned out to be a single envelope of steel. Ships were sailing across Atlantic and Artic ocean. (cold temperatures). During which two ships fractured suddenly in to two halves ( brittle fracture). Out of 2700 ships built, 400 ships suffered fractures of various degree.

Analysis

Unequal distribution of cargo and ballast was causing hogging bending moment Wave motion also caused hogging BM, resulting in tensile stress on the deck.Welds were produced by semi skilled work force, which contained crack like flaws

*Negligence during construction or operation some times results in catastrophic failures

Flaw

Analysis (contd.)

cracks were found to initiate at square hatch which induced stress concentration due tensile stress The high strength steel used for the ship had poor toughness (Charpy impact test). Heat Affected Zone (HAZ) will have low ductility, behaving like a hardened material. Due to rapid cooling, tensile residual stress are induced. This is equivalent to crack like defect.

3

Riveted joints act as crack arrester

welded joints produce continuous crack

Conclusion on liberty ship failure

Steel-BCC crystal.They can fracture by extended slip in some preferred planes producing plasticity orFracture by cleavage under different plane under tensile stress without plastic deformation, at a stress level below yield strengthCleavage fracture are predominant at lower temperatures ( at lower temperature yield strength is higher than fracture strength)

The combined effect of low ductile steel, freezing temperature, presence of crack like defect (residual tensile stress), crack like defect in the weld lead to sudden brittle fracture, which initiated at the hatch on the deck due to tensile service load, crack propagated at fast rate (crack velocity = velocity of sound) through the entire cross section of the hull breaking ship into two halves.

Points to be noted• At service load tensile stress is induced in the deck due to which crack is initiates/grows.•Presence of microcrack leading to stress concentration

Conventional Design Method

•Conventional method ensures safety of structure based on strength characteristics• often structure may have a FS varying from 2 to 10•Design does not safeguard against possible failure by fracture (brittle, ductile, fatigue, dynamic)

Applied Stress

< YieldStrength

Safe DesignAccept

YieldStrength

Unsafe Design

>

Structure ora structural component

F

f

Design based on Strength of Material Approach

Applied Stress

< FractureToughness

Safe DesignAccept

FractureToughness

Unsafe Design

>

Structure ora structural component

Fracture parameter

Flawsize

F

f

Design based on Fracture Mechanics Approach

Fracture Mechanics Design approach

•Fracture mechanics approaches require that an initial crack size be known or assumed. For components with imperfections or defects (such as welding porosities, inclusions and casting defects, etc.) an initial crack size may be known. •Fracture Mechanics ensures safety against fracture failure• Evaluation of fracture parameter may be required•In presence of visible crack for ductile or fatigue loading condition, FM can predict safety and life of the structure

Ductile Fracture

Intragranular(Transgranular)

Intergranular

Rupture by Necking Rupture by Shear

Ductile fracture is preceded by extensive plastic deformation Ductile fracture is caused due to growth and coalescence of voids (at the sites of inclusion) Ductile fracture is a slow process , gives enough precaution before catastrophic failure Ductile fracture usually follows transgranular path If the density of inclusion are more along grain boundary, crack grows along boundaries leading to fibrous or ductile intergranular fracture If inclusions are not present, voids are formed at severely deformed regions leading to localized slip bands and macroscopic instability resulting in necking or shear fracture

Plasticity retards crack growth and it provides a factor of safety against over loading or oversight in design.

Voids formed (at particle sites) during plastic deformation and ductile fracture

Voids formed (at non-particle sites) during plastic deformation and ductile fracture

Cleavagefracture

Intergranularbrittle fracture

Brittle fracture

Fast crack growth without excessive or no plastic deformation. Fracture stress will be lower than yield strengthBrittle fracture may be transgranular (cleavage) or intergranularBrittle fracture are mostly predominant in metals with bcc crystal at cryogenic temperature or at high strain rate. Micro cracks initiated by fatigue loading may lead to brittle fracture HAZ induces high tensile residual stressHAZ also reduces the ductilityShrinkage tears in weld may also cause brittle fracture

What are the general characteristics of brittle fracture? •Very little general plasticity - broken pieces can be fitted together with no obvious plastic deformation; •Rapid crack propagation (one third the speed of sound), eg 1 km/s for steel; •Low energy absorption; •Low failure load relative to load for general yield; •Usually fractures are flat and perpendicular to the maximum principal stress; •Fracture always initiates at a flaw or a site of stress concentration. Examples •Mild steel at low temperature; •high strength Fe, Al and Ti alloys; •glass; perspex •ceramics •concrete •carrots (particularly fresh ones)