Workshop 9

Use of English for professional trainingСегодня: пятница,

6 мая 2016 г.

Associated Professor of National Research Tomsk Polytechnic University, Kuprekova E.I.

Mechanical Failure

Part 1. Matching GamesTask: Read the cards. Then decide whether the definitions fits to the word or not. Prove your answer.

Ductility ratio of the lateral and axial strains

Plastic Deformation Poisson's ratio for isotropic materials

Shear Modulus a measure of the degree of plastic deformation that has sustained at fracture

Proportional limit Reversible

True Stress gradual elastic-plastic transition. The initial departure from linearity of the stress-strain curve

Brittle The slope of the linear elastic region of the shear stress-strain curve

Poisson's ratio the load F divided by the instantaneous unit time which deformation is occuring

Slip metal that experiences very little or no plastic deformation fracture

0.25 permanent

Elastic Deformation motion of dislocation in non crystalline solids occurs by a viscous mechanism

Part 2. How do Materials Break?

Ship-cyclic loading from waves Computer chip-cyclic thermal loadingHip implant-cyclic

loading from walking

Fracture: separation of a body into pieces due to stress, at temperatures below the melting point.

So, Failure sometimes takes place!!!.Why does it occur?

What actually happens during fracture?How can we prevent it?

Engineer should anticipate & plan for possible failure, and iffailure does occur find out why and prevent re-occurrence.

Fracture mechanismsDepending on the ability of material to undergo plastic deformation before the fracture two fracture modes are ductile or brittle

Ductile fracture - most metals (not too cold): Extensive plastic deformation ahead of crack Crack is “stable”: resists further extension unless applied stress is increased

Brittle fracture - ceramics, ice, cold metals: Relatively little plastic deformation Crack is “unstable”: propagates rapidly withoutincrease in applied stressCatastrophic Usually strain is < 5%.

Ductile fracture is preferred in most applications

Brittle vs. Ductile FractureDuctile materials - extensive plastic deformation and energy absorption (“toughness”) before fractureBrittle materials - little plastic deformation and low energy absorption before fracture

A. Very ductile, soft metals (Pb, Au) at room temperature, polymers,

glasses at high temperature.

B. Moderately ductile fracture,

typical for ductile metals

C. Brittle fracture, cold metals,

ceramics.

Rapture cup & cone fracture Brittle fracture

Evolution to failure (Moderately Ductile)

Ductile Fracture

Typical Cup-and-Cone fracture in ductile Al

Scanning Electron Microscopy: Fractographicstudies at high resolution.

Spherical “dimples”

correspond to micro-

cavities that initiate crack

formation.

Brittle Fracture (Limited Dislocation Mobility

No appreciable plastic deformation Crack propagation is very fast Crack propagates nearly perpendicular to thedirection of the applied stress Crack often propagates by cleavage - breakingof atomic bonds along specific crystallographic planes (cleavage planes).

Brittle FractureA. Transgranular fracture: Fracture cracks pass through

grains. Fracture surface have faceted texture because of different orientation of cleavage planes in grains.

B. Intergranular fracture: Fracture crack propagation is along grain boundaries (grain boundaries are weakened or embrittled by impurities segregation etc.)

Part 3. Student’s work

1. When do atomic bonds break?

Task 1. Give short answers to the questions.

2 . What is the Lennard-Jones potential?

3. Give a short explanation of

members in the Lennard-Jones

potential.

4. Explain how to calculate the force between a pair of atoms?

Stress Concentration

Fracture strength of a brittle solid is related to the cohesive forces between atoms. One can estimate that the theoretical cohesive strength of a brittle material should be ~ E/10. But experimental fracture strength is normally E/100 - E/10,000.

This much lower fracture strength is explained by the effect of stress concentration at microscopic flaws. The applied stress is

amplified at the tips of micro-cracks, voids, notches, surface scratches, corners, etc. that

are called stress raisers. The magnitude of this amplification depends on micro-crack

orientations, geometry and dimensions.

Stress Concentration

t

x xx x

0

0

x x x

0

f

Assume an elliptical crack of length, 2a, the local stress is:

2/1

0 21t

m

a

Maximum stress occurs at the tip

Where ρt is the radius of the crack tip and a is the length of a surface crack or half the length of an internal crack.

а2

а

where σo is the nominal applied stress

For a long and thin crack oriented perpendicular to the applied stress the maximum stress near the crack tip is:

t

m

a

02stress concentration factor is

t

mt

aK

2

0

Flaws are Stress Concentrators!

Engineering fracture design

Griffith Theory of Brittle Fracture

Griffith proposed that there is a population of defects in all brittlematerials of various sizes, shapes and orientations. When anapplied stress creates a concentrated stress at one of thesedefects which is higher than the cohesive strength then thedefect or crack propagates and fracture occurs.

During crack propagation elastic strain energy is released

• Fracture creates new surfaces which raises the surface energy

• Griffith performed balance between two energies and derived a critical stress σc for propagation of an elliptical crack.

Griffith Theory of Brittle Fracture

If the change in elastic strain energy due to crack extension is higher than the energy required to create new crack surfaces,

crack propagation will occur

a

Е Sс

2

(Griffith Equation)

where,E = elastic modulusγs = specific surface energy (energy to break bonds/unit area)a = one half of the length of an elliptical internal crack (2a)

Ductile behavior

• In………… materials, energy of fracture involves both generation of new surfaces (γs) and plastic deformation (γp ) particularly at the crack tip• therefore Griffith equation becomes:

a

Е pS

с

2

for highly ductile materials where γp >> γs:

a

Е p

с

2

Critical strain energy release rate:

pScG 2E

aGc

2

crack extension occurs whenE

aGc

2

Ductile-to-Brittle transitionAs temperature decreases a ductile material can become brittle -

ductile-to-brittle transition Alloying usually increases the ductile-to-brittle transition temperature. FCC metals remain ductile down to very low temperatures. For ceramics, this type of transition occurs at much higher temperatures than for metals. The ductile-to-brittle transition can be measured by impact testing: the impact energy needed for fracture drops suddenly over a relatively narrow temperature range – temperature of the ductile-to-brittle transition.

In metals DBTT is around 0.1-0.2Tm while in ceramics it is about 0.5-0.7 Tm

Summary

1. What are the different types of fracture?

2. What is the fracture criterion of Griffith and how it is modified when considering the existence of a plastic zone near a moving crack?

3. What is the role of localized plastic deformation in the process of destruction of metallic material by the movement of the crack?

4. What structural factors affect the susceptibility of materials to brittle fracture?