MCHE 3310 Quiz 2

• Fatigue

progressive and localized structural damage that occurs when a material is subjected to cyclic loading

Creep and viscous flow

defined as the time-dependent and permanent deformation of materials
when subjected to a constant load or stress

Stress

force per unit area arising from applied load Tension, compression, shear, torsion or any combination

Strain

physical deformation response of a material to stress, e.g., elongation.

Young's (or Elastic) Modulus

sigma = E(epsilon)

Tangent modulus

the slope at a specific point of the - curve

Secant modulus

slope of a straight line drawn between zero and a specific point on the stress-strain curve

Shear test

For shear test, stress () and strain () are also used used.

Shear Modulus

the slope of the stressstrain curve. The larger of the slope, the higher of the strength.

Poisson's Ratio

is the ratio of lateral strain (x or y ) and axial strain (z ):

For poisson's ratio

it is general in between -1 and .5

Ductility

is a measure of the degree of plastic deformation that has been sustained at fracture

Percent elongation

The total percentage permanent increase in the length of a specimen due to a tensile test.

Percent reduction in area

The total percentage permanent decrease in the cross-sectional area of a specimen due to a tensile test.

Toughness

the energy to break a unit volume of material

Resilience

the capacity of a material to absorb energy when it is deformed elastically, and then, upon unloading, to have this energy recovered.

Modulus of resilience

Is a measure of the capacity of the material to absorb energy without danger of being permanently deformed.

True strain

The natural logarithm of the ratio of instantaneous gauge length to original gauge length of a specimen being deformed by a uniaxial force.

Hardening

An increase in σy due to plastic deformation

Hardness

Resistance to permanently indenting a surface

Factor of safety

slip

The dislocation motion

slip plane

The crystalline plane along which the dislocation line transverses

• For edge dislocation

the dislocation line (half-plane of atom) moves in the direction of the applied shear stress; the slip direction is the same as the Burgers vector direction

For screw dislocation

, the direction of the dislocation motion is perpendicular to the stress direction

Dislocation density

the total dislocation length per unit volume

Slip direction:

direction of movement on the slip plane is most closely packed with atoms - the highest linear density

Slip system

combination of slip plane and slip direction

Resolved shear stress

no matter the applied stress is pure tensile or compressive, shear component exists at all but // or ⊥ alignment to the stress direction.

Mechanisms of Strengthening in Metals

Many applications require alloys to be strong and ductile. • The ability of a metal to deform plastically depends on the ability of dislocation to move.

Principle for metal strengthening

Restricting or hindering dislocations motion renders a material harder and stronger

Four strategies to strengthen metallic materials

Grain size reduction, Solid-solution alloying, Precipitation strengthening, and Strain hardening

Strengthening by Grain Size Reduction

The size of the grains in a polycrystalline metal influence the mechanical properties (the smaller the stronger)

Solid-Solution Strengthening

Impurity atoms, either substitutional or interstitial, distort the lattice & generate lattice strains on the surrounding host atoms. Impurities tend to concentrate at dislocations (regions of tensile or compressive strains). Reduce mobility of dislocations and increase strength

Solid-Solution Strengthening example

High-purity metals are always softer and weaker than alloys composed of the same base metal

Precipitation Strengthening

Hard precipitates in a matrix are difficult to shear, which block the motion of dislocations

Strain Hardening

also called work hardening or cold working, is the phenomenon by which a ductile metal becomes harder and stronger as it is plastically deformed.

Three Stages During Heat Treatment

1. Recovery Annealing enhances atomic diffusion, which reduces the dislocation density by annihilation

2. Recrystallization • After recovery, the grains are still in a relatively high strain energy state. • Recrystallization is the formation of a new set of strain-free and equiaxed grains that have low dislocation density and are characteristic of precold-worked condition.

3. Grain Growth • At longer times, average grain size increases.

Metals having small grains

relatively strong and tough at low temperatures

Metals having large grains

good creep resistance at relatively high temperatures

Ductile fracture

• substantial plastic deformation in the vicinity of an advancing crack

• high energy absorption

• slow process - "stable" - it resists any further extension unless the stress is increased

• appreciable gross deformation at the fracture surface

• warning sign

• metals, some polymers

Brittle fracture

• no or little plastic deformation

• less energy absorption

• occur suddenly, catastrophically without any warning

• "unstable" - once starts, continues spontaneously

• ceramics, some polymers

Crack Propagation

Cracks having sharp tips propagate easier than cracks having blunt tips • A plastic material deforms at a crack tip, which "blunts" the crack.

Crack propagates if

crack-tip stress (σm) exceeds a critical stress (σc )

Fracture Toughness

is a measure of a material's resistance to brittle fracture when a crack is present. It is defined as the amount of energy per volume that a material can absorb before rupturing.

Plane strain

when the specimen thickness is much greater than the crack dimension, there is no strain component perpendicular to the front and back faces.

Ductile-to-brittle transition

The Charpy and Izod tests are primarily used to determine whether a material experience a ductile-to-brittle transition with decreasing temperature and the related temperature range.

Fatigue

is the progressive and localized structural damage that occurs in structures subjected to dynamic and fluctuating stress.

rotating-bending beam

which alternating tension and compression stresses of equal magnitude to a specimen as it simultaneously bent and rotated.

Fatigue: The S-N Curve

Fatigue Crack Surface

The process of fatigue failure involves three steps: -- crack initiation - a small crack is formed -- crack propagation - crack advances incrementally with each stress cycle -- final failure - occurs rapidly once the advancing crack has reached a critical size

Improving Fatigue Life

Since fatigue cracks always initiate (nucleate) on the surface, the fatigue life can be improved by modifying the surface of the component • Impose residual compressive stresses within a thin outer surface layer (to suppress surface tensile stress of external origin, therefore to reduce cracks formation) Remove stress concentrators

Creep

the time-dependent and permanent deformation of materials when subjected to a constant load or stress.

Creep Failure

Failure: along grain boundaries.

Diffusion

Mass Transport by Atomic Motion

Interdiffusion

atoms of one metal diffuse into another

Self Diffusion

in pure metals, atoms also migrate; but all atoms exchanging positions are of the same type.

Vacancy Diffusion

atoms exchange with vacancies

What does the rate of vacancy diffusion depend on?

number of vacancies and activation energy to exchange

Interstital Diffusion

Smaller atoms, eg. H, C, N, O can diffuse into or between interstitial positions

Which is faster, interstitial or vacancy diffusion?

interstitial diffusion

Flux

defined as the mass (or number of atoms) diffusing through and perpendicular to a unit cross-sectional area of solid per unit of time

Steady State Diffusion

rate of diffusion which is independent of time

Activation energy

the energy required to produce the diffusive motion of one mole of atoms

Non steady state diffusion

the diffusion flux and the concentration gradient at some particular point in a solid vary with time

Hardness Testing Techniques

Brinell, Vickers microhardness, Knoop microhardness, Rockwell and superficial Rockwell

Strengthening by Grain Size Reduction

Smaller grain size results in more grain boundaries and therefore more barriers to slip. grain boundary acts like a "barrier" to dislocation motion.

Solid Solution Strengthening

Impurity atoms, either substitutional or interstitial, distort the lattice &generate lattice strains on the surrounding host atoms. These strains can act as barriers to dislocation motion

Precipitation Strengthening

Hard precipitates in a matrix are difficult to shear, which block the motion of dislocations

Reversed Stress Cycle

The stress alternates from amaximum tensile stress (+) toa maximum compressivestress (-) of equal magnitude

Repeated Stress Cycle

Maximum and minimum stresses are asymmetrical relative to the zero-stress level

random stress cycle

stress cycle that has no pattern and is very sporadic

transgranular

through grains

intergranular

between grains