TXT Ch. 8 - Deformation and Strengthening Mechanisms

A Burgers vector's direction corresponds to...

...a dislocation's slip direction.

Both the direction and magnitude of a Burgers vector depends on...

...crystal structure.

Polycrystalline metals are stronger than their single-crystal equivalents, meaning that...

...greater stresses are required to initiate slip and the attendant yielding.

For a particular crystal structure, the slip plane is the plane that...

...has the densest atomic packing, or the greatest planar density.

For a particular crystal structure, the slip direction is the direction that...

...has the highest linear density.

Grain growth occurs by the...

...migration of grain boundaries.

During the plastic deformation process, interatomic bonds must be...

...ruptured and then re-formed.

When metals are plastically deformed, some fraction of the deformation energy is retained internally. The major portion of this stored energy is as...

...strain energy associated with dislocations.

The ability of a metal to deform plastically depends on...

...the ability of the dislocations to move.

The slip system depends on the crystal structure of the metal, and is such that...

...the atomic distortion that accompanies the motion of a dislocation is a minimum.

During deformation, mechanical integrity and coherency are maintained along the grain boundaries; that is...

...the grain boundaries usually do not come apart or open up. So, each individual grain is constrained, to some degree, in the shape it may assume by its neighboring grains.

For crystalline ceramics, plastic deformation occurs by...

...the motion of dislocations.

For a single crystal specimen that is stressed in tension, each step results from...

...the movement of a large number of dislocations along the same slip plane.

On a microscopic scale, plastic deformation corresponds to...

...the net movement of large numbers of atoms in response to an applied stress.

A Burgers vector's magnitude is equal to...

...the unit slip distance.

Plastic deformation does not occur by dislocation motion for noncrystalline ceramics because...

...there is no regular atomic structure.

Why does the grain boundary act as a barrier to dislocation motion? (two reasons)

1. Because the two grains are of different orientations, a dislocation passing into a second grain must change its direction of motion. This becomes more difficult as the crystallographic misorientation increases. 2. The atomic disorder within a grain boundary region results in a discontinuity of slip planes from one grain into the other.

Why is slip still difficult in covalently bonded crystalline ceramics? (3 reasons)

1. Covalent bonds are relatively strong 2. Also limited number of slip systems 3. Dislocation structures are complex

What are the two fundamental dislocation types?

1. Edge 2. Screw

Metallic materials may experience two different kinds of deformation:

1. Elastic 2. Plastic

What are the three mechanisms that may be used to strengthen and harden single-phase metal alloys?

1. Grain size reduction 2. Solid-solution strengthening 3. Strain hardening Can be combined!

The magnitude of the resolved shear stresses depends on what three factors?

1. The applied stress 2. The orientation of the slip plane 3. The orientation of the slip direction within that slip plane

A Burgers vector can be specified by what two parameters?

1. Unit cell edge length, a 2. Crystallographic direction indices

FCC and BCC crystal structures have at least __ slip systems.

12

What are resolved shear stresses?

A component of the applied stress that causes shear on a given plane in a given direction.

What is solid-solution strengthening?

A technique to strengthen and harden metals is alloying with impurity atoms that go into either substitutional or interstitial solid solution.

Define the Burgers vector, b.

A vector, often denoted as b, that represents the magnitude and direction of the lattice distortion resulting from a dislocation in a crystal lattice.

Describe grain growth.

After recrystallization, the strain-free grains will continue to grow if the metal specimen is left at the elevated temperature; this phenomenon is called grain growth.

What kind of materials can experience grain growth?

All polycrystalline materials - metals and ceramics alike.

Where are the only places that shear components don't exist?

At the parallel and perpendicular alignments to the stress direction.

Mechanical twinning occurs in metals with which two crystal structures?

BCC and HCP crystal structures. at low temperatures, and at high rates of loading

Why does reducing the mobility of dislocations enhance the mechanical strength of a material?

Because hardness and strength are related to the ease with which plastic deformation can be made to occur. Greater mechanical forces are required to initiate plastic deformation.

Why, in general, does φ + λ ≠ 90° ?

Because it need not be the case that the tensile axis, the slip plane normal, and the slip direction all lie in the same plane.

Why do ionically bonded crystalline ceramics have few slip systems?

Because of the electrically charged nature of the ions. For slip in some directions, ions of like charge are brought into close proximity of each other; because of electrostatic repulsion, this mode of slip is very restricted.

Why does the direction of slip vary from one grain to another for polycrystalline materials?

Because of the random crystallographic orientations of the numerous grains.

Why are small-angle grain boundaries not effective in interfering with the slip process?

Because of the slight crystallographic misalignment across the boundary.

Why is strain hardening also called cold working?

Because the temperature at which deformation takes place is "cold" relative to the absolute melting temperature of the metal.

How do noncrystalline ceramics deform?

By viscous flow, like how liquids deform.

Define viscosity.

Characteristic property of viscous flow; a measure of a noncrystalline material's resistance to deformation. Represented by η

Define slip system.

Combination of the slip direction and slip plane.

Define lattice strains.

Compressive, tensile, and shear strains imposed on the neighboring atoms that form regions of distortion within the lattice.

What is the slip plane?

Crystallographic plane along which the dislocation line traverses. Preferred plane for dislocation to move along.

What's a major reason for the hardness and brittleness of crystalline ceramics?

Difficulty of slip/dislocation motion.

What happens specifically for high-angle grain boundaries?

Dislocations tend to pile up/back up at grain boundaries. These pileups introduce stress concentrations ahead of their slip planes, which generate new dislocations in adjacent grains.

What is a mixed dislocation?

Dislocations that have both edge and screw components.

When metals are plastically deformed, some fraction of the deformation energy is retained internally; where does the rest go?

Dissipated as heat.

Describe the spherulitic structure.

Each spherulite consists of numerous chain-folded ribbons, or lamellae that radiate outward from the center. Separating these lamellae is amorphous material. Adjacent lamellae are connected by tie chains that pass through this amorphous material.

True or False: recovery and recrystallization must happen first for grain growth to occur.

False! Grain growth is independent of recovery and recrystallization.

What third process sometimes occurs after recovery and recrystallization?

Grain growth.

What does it mean if grains are equiaxed?

Have approximately the same dimension in all directions before deformation.

For twinning, the shear deformation is ___.

Homogeneous.

Plastic deformation operations are often carried out at temperatures above the recrystallization temperature in a process termed ___.

Hot working.

Describe viscous flow in noncrystalline ceramic solids.

In response to an applied shear stress, atoms or ions slide past one another by the breaking and re-forming of interatomic bonds. Rate of deformation is proportional to applied stress.

What is an edge dislocation?

Localized lattice distortion exists along the end of an extra half-plane of atoms, which also defines the dislocation line. The direction of movement is PARALLEL to the stress direction. Ultimately, extra half-plane of atoms may emerge on the other side of the crystal, forming an edge that is one atomic distance wide.

What is a screw dislocation?

May be thought of as resulting from shear distortion; its dislocation line passes through the center of a spiral, atomic plane ramp. Direction of movement is PERPENDICULAR to the stress direction.

A parameter n is called the strain-hardening exponent. What is it a measure of?

Measure of ability of a metal to strain harden. Larger n value = greater the strain hardening for a given amount of plastic strain

What's the direction of motion for the mixed dislocation line?

Neither perpendicular nor parallel to the applied stress but lies somewhere in between.

With continued extension of a single crystal, both the ___ and ___ increase.

Number of slip lines, slip step width

What are slip lines?

On the surface of a polished single crystal, the dislocation steps appear as lines. These are called slip lines.

What's the mechanism of elastic deformation?

Onset of elastic deformation for semicrystalline polymers results from chain molecules in amorphous regions elongating in the direction of the applied tensile stress. Continued deformation occurs by changes in both amorphous and lamellar crystalline regions. Amorphous chains continue to align and become elongated. There is also bending and stretching of the strong chain covalent bonds within the lamellar crystallites, leading to a slight, reversible increase in the lamellar crystallite thickness.

Define deformation by twinning.

Plastic deformation in some metallic materials can occur by the formation of mechanical twins, or twinning. A shear force can produce atomic displacements such that on one side of a plane (the twin boundary), atoms are located in mirror-image positions of atoms on the other side.

Define slip line.

Preferred direction for deformation to travel along.

Recrystallization proceeds more rapidly in (pure metals/metal alloys). Why?

Pure metals, because the impurities in atoms reduce grain boundary mobility which hinders the recrystallization process.

Restoration of pre-cold-worked material properties results from two different processes that occur at elevated temperatures:

Recovery and recrystallization.

How does the recrystallization temperature value typically relate to the absolute melting temperature value?

Recrystallization temp. is usually between 1/3 and 1/2 of the absolute melting temp. (Depends on several factors, including amount of prior cold work and the purity of the alloy)

Virtually all strengthening techniques rely on this simple principle:

Restricting or hindering dislocation motion renders a material harder and stronger.

Most metals strain harden at what temperature?

Room temperature.

How are slip and twinning different in terms of atomic spacing?

Slip = occurs in distinct atomic spacing multiples Twinning = atomic displacement is less than the interatomic separation

How are slip and twinning different in terms of shear deformation?

Slip = the crystallographic orientation above and below the slip plane is the same both before and after the deformation Twinning = there is a reorientation across the twin plane

For a single crystal specimen that is stressed in tension, what does the deformation look like?

Slip occurs along a number of equivalent and most favorably oriented planes and directions at various positions along the specimen length. Slip deformation forms as small steps on the surface of the single crystal that are parallel to one another, and loop around the circumference of the specimen.

What happens during recovery?

Some of the stored internal strain energy is relieved by virtue of dislocation motion, as a result of enhanced atomic diffusion at the elevated temperature. Some reduction in the number of dislocations, and dislocation configurations are produced having low strain energies. Physical properties return to pre-cold worked states.

Many semicrystalline polymers in bulk will have what kind of structure?

Spherulitic structure

Material ___ and ___ are measures of a material's resistance to plastic deformation.

Strength; hardness.

The mechanical properties at room temperature are usually (inferior/superior) to those of course-grained ones.

Superior. i.e. higher strength and toughness

Driving force behind recrystallization?

The difference in internal energy between the strained and unstrained material.

Explain strain hardening in terms of dislocations.

The dislocation density in a metal increases with deformation or cold work because of dislocation multiplication or the formation of new dislocations. So, the average distance of separation between dislocations decreases, and the dislocation-dislocation strain interactions are on average repulsive. Net result = dislocation motion is hindered by the presence of other dislocations.

What is recrystallization?

The formation of a new set of strain-free and equiaxed grains that have low dislocation densities and and are characteristic of the pre-cold-worked condition. New grains form as very small nuclei and grow until they completely consume the parent material via short-range diffusion. Mechanical properties that were changed as a result of cold working are restored to their pre-cold worked values.

The strain fields that exist around dislocations are influential in determining ___ and ___.

The mobility of the dislocations, as well as their ability to multiply.

Define dislocation density.

The number of dislocations in a material. Expressed as the total dislocation length per unit volume, or the number of dislocations that intersect a unit area of a random section.

Define strain hardening/cold working.

The phenomenon by which a ductile metal becomes harder and stronger as it is plastically deformed.

Define slip.

The process by which plastic deformation is produced by dislocation motion.

What is the driving force behind grain growth?

The reduction in energy as a result of increasing grain sizes.

Define recrystallization temperature.

The temperature at which recrystallization just reaches completion in one hour.

In terms of slip systems, why are HCP metals usually quite brittle?

They have few active slip systems.

How can the effects of cold working/strain hardening be undone?

Through an annealing heat treatment.

The extent of recrystallization is dependent on both ___ and ___.

Time and temperature.

As grains increase in size during grain growth, what happens to grain boundaries and their associated energies?

Total grain boundary area decreases, yielding a reduction in the total energy.

Grain size reduction improves not only the strength, but also the ___ of alloys.

Toughness.

True or False: several slip systems may exist for a particular crystal structure.

True!

What's a third name for strain hardening/cold working?

Work hardening.

For grain growth, the equation showing the dependence of grain size on time?

dⁿ - d₀ⁿ = K*t d = grain diameter d₀ = initial grain diameter at t=0 n = time-independent constant, generally ≥2 K = time-independent constant t = time

Equation for viscosity, η?

η = τ/(dv/dy) = (F/A) / (dv/dy)

When φ = λ = 45°, what's an alternative equation for the yield strength of a single crystal?

σ_y = 2 * τ_CRSS

Hall-Petch Equation?

σ_y = σ₀ + k_y / √d σ_y = yield strength σ₀, k_y = constants for a particular material d = average grain diameter

Equation for the yield strength of a single crystal, based on the critical resolved shear stress?

σ_y = τ_CRSS / (cosφ * cosλ)_max

What else does τ_R_max represent?

τ_CRSS, or the critical resolved shear stress.

Equation for resolved shear stress τ_R?

τ_R = σ * cosφ * cosλ τ_R = resolved shear stress σ = applied stress φ = angle between the normal to the slip plane and the applied stress direction λ = angle between the slip and stress directions

Equation for the maximum resolved shear stress τ_R_max?

τ_R_max = σ * (cosφ * cosλ)_max

What are the φ and λ values associated with the minimum stress necessary to introduce yielding?

φ = λ = 45°

Equation for percent cold work?

%CW = [ (A₀ - A_d) / A₀] x 100 A₀ = original cross-sectional area A_d = cross-sectional area after deformation