Materials Science Module 2

Toughness

A mechanical characteristic that may be expressed in three contexts: 1.) the measure of a material's resistance to fracture when a crack (or other stress-concentrating defect) is present; 2.) the ability of a material to absorb energy and plastically deform before fracturing; 3.) the total area under the material's tensile engineering stress-strain curve taken to fracture

Stress raiser

A small flaw (internal or surface) or a structural discontinuity at which an applied tensile stress will be amplified and from which cracks may propagate.

On a Binary Isomorphous phase diagram, for a given a composition and temperature, be able to determine or calculate: • what phase(s) exist • for a two-phase composition, the composition of each phase • for a two-phase composition, the mass (or weight) fractional phase amount (percent mass/weight of each phase present) You do not need to be responsible for determining the volume fraction (presented at the end of this section)

A summary that may assist in differentiating between the terms: • Compositions of phases are expressed in terms of the weight percent of the components (e.g., wt% Cu, wt% Ni). For any alloy consisting of a single phase, the composition of that phase is the same as the total alloy composition. If two phases are present, the tie line must be employed, the extremes of which determine the compositions of the respective phases. • With regard to fractional phase amounts, you are looking for the percent of the material that is the α phase (based on mass/weight) or the percent of that material that is the liquid phase (again based on mass/weight). When a single phase exists, the alloy is completely (100%) that phase. For a two-phase alloy, the lever rule is used, in which a ratio of tie line segment lengths is taken.

Impact energy

Also called notch toughness, a measure of the energy absorbed during the fracture of a specimen of standard dimensions and geometry when subjected to very rapid (impact) loading. Charpy and Izod impact tests are used to measure this parameter, which is important in assessing the ductile-to-brittle transition behavior of a material

What is an annealing treatment and what is it used for?

Annealing treatment - a heat treatment used to remove the effects of strain hardening

Why do some fractures occur at stresses significantly below those predicted by theoretical calculations based on atomic bonding energies?

Because there are microscopic flaws or cracks that always exist under normal conditions at the surface and within the interior of a body of a material, they are a detriment to the fracture strength because an applied stress may be amplified or concentrated at the tip

What is anelastic behavior?

Behavior in a material when elastic deformation will continue after stress application, and upon load release, some finite time is required for complete recovery, often neglected for metals, but can have a significant magnitude for polymeric materials

How is the cross section and fracture surface of a ductile material different than that of a brittle material?

Brittle fracture surface displays V shape, ductile is more cup and cone shaped,

What is tensile strain?

Change in length over original length, measurement of deformation

Elastic deformation

Deformation that is nonpermanent - that is, totally recovered upon release of an applied stress

Plastic deformation

Deformation that is permanent or nonrecoverable after release of the applied load. It is accompanied by permanent atomic displacements

What is the difference between brittle and ductile fracture, which type of fracture is preferred and why?

Ductile fracture - slow crack propagation accompanied by significant plastic deformation, fails without warning Brittle fracture - rapid crack propagation, little or no plastic deformation, fails without warning Ductile fracture is generally more desirable because it happens more slowly and gives warning and more strain energy is required to induce ductile fracture

What happens to the dislocation density during plastic deformation? On an atomic scale?

During plastic deformation, number of dislocations increases dramatically, existing dislocations multiply, causing more dislocations, grain boundaries, internal defects, and surface irregularities like scratches and nicks, which act as stress concentrations, may serve as dislocation formation sites during deformation

What is the difference between engineering stress/engineering strain and true stress/true strain?

Engineering stress and strain use original cross-section and gauge length and true stress and strain use instantaneous cross section and length, true stress and strain are corrected for area, length, and necking and its stress-strain curve never decreases because it does not account for outside factors that cause material to fail

Fatigue

Failure, at relatively low stress levels, of structures that are subjected to fluctuating and cyclic stresses

What conditions must exist for a failure to be classified as fatigue, and what type of fracture is it most similar to; ductile or brittle?

Fatigue exists when a structure is subjected to dynamic and fluctuating stresses, these circumstances make failure at a considerably lower stress level than tensile strength possible, most similar to a brittle fracture

How does a ductile fracture progress (fig 8.2)?

First necking begins, then small cavities called microvoids form in the interior of the cross section, microvoids enlarge and come together to form an elliptical crack with long axis perpendicular to stress direction, crack grows in direction parallel to major axis by microvoids coalescing, fracture ensues by rapid propagation of crack around outer perimeter of the neck

What is the recrystallization temperature defined as?

For a particular alloy, the minimum temperature at which complete recrystallization occurs within approximately 1 h.

Plane strain fracture toughness (Kic)

For the condition of plane strain, the measure of a material's resistance to fracture when a crack is present

On the atomic level, what is occurring during recrystallization and how does temperature at which it is subjected to affect strength and ductility?

Formation of new set of strain-free and equiaxed grains that have low dislocation densities and characteristics of precold-worked condition, new grains form as small nuclei grow until they completely consume parent material, metals become softer and weaker, more ductile, as temperature increases, ductility increases and strength decreases

How does grain size in a polycrystalline material affect mechanical strength and toughness and why? Be able to calculate the percent that the material is cold worked.

Grain boundaries act as barriers to dislocation motion, so materials with smaller grains are harder and stronger because they have greater total grain boundary area to impede dislocation motion

On the atomic level, what is occurring during grain growth and what is different about the mechanism compared to recovery and recrystallization?

Grain growth - strain free grains continue to grow if metal specimen is left at elevated temperature, as grain size increases, total boundary area decreases which reduces total energy, large grains grow as small grains shrink, increasing average grain size, direction of boundary movement and atomic motion are opposite each other, grain growth does not need to be preceeded by recovery and recrystallization, it can occur in all polycrystalline materials, metals, and ceramics

Isomorphous

Having the same structure. In the phase diagram sense, isomorphicity means having the same crystal structure or complete solid solubility for all compositions

Do you remember what a solid solution is from Chapter 4 (section 3)?

Homogenous crystalline phase that contains two or more chemical species. Both substitutional and interstitial solid solutions are possible

What do the Charpy and Izod tests measure?

Impact energy or notch toughness

On an atomic level, how does introduction of an alloying element strengthen/harden a polycrystalline material? Be able to use the Figure 7.16 graphs to determine an unknown (graphs are not on the formula sheet, however will be provided if needed)

Increasing concentration of impurity results in increase in tensile and yield strengths , impurity atoms in a solid solution impose lattice strains on surrounding host atoms which restricts dislocation movement

What does the isomorphous mean in this application?

Isomorphous means there is complete liquid and solid solubility of the two components

What do the solidus and liquidus lines distinguish?

Liquidus line, above line is liquid, solidus line, below line is solid

Why is it important to know the microstructure of a material? To review, a solid solution consists of atoms of at least two different types; the solute atoms occupy either substitutional or interstitial positions in the solvent lattice, and the crystal structure of the solvent is maintained.

Many properties of materials are functions of their microstructure

What does the fracture toughness, Kc, measure?

Measures the material's resistance to brittle fracture when a crack is present

Elastic recovery

Nonpermanent deformation recovered or regained upon release of a mechanical stress

What is elastic deformation and what is happening to the material on an atomic scale?

Nonpermanent deformation, meaning material returns to its original shape when load is released, on atomic level, bonds are stretching under a small load, and they return to their initial state after load is released, elastic deformation is nonpermanent and reversible

Slip

Plastic deformation as the result of dislocation motion; also, the shear displacement of two adjacent planes of atoms

What does plastic deformation correspond to? (2nd and 3rd paragraphs, page 182)

Plastic deformation corresponds to the net movement of large numbers of atoms in response to an applied stress, and motion of large numbers of dislocations, macroscopic plastic deformation corresponds to permanent deformation that results from the movement of dislocations or slip in response to applied shear stress

What is the simple principle that virtually all strengthening techniques rely on?

Restricting or hindering dislocation motion renders a material harder and stronger

How is plastic deformation in polycrystalline materials different than single crystals with regard to the slip planes, shape of the grain structure and strength of the material?

Single crystal - number of different slip systems capable of operating, but one is most favorable (has largest resolved shear stress), slip commences in most favorable slip system when resolved shear stress reaches some critical value, single crystal plastically deforms when resolved shear stress = critical resolved shear stress polycrystalline material - because of random crystallographic orientations of numerous grains, direction of slip varies from one grain to another, for each grain, motion occurs along slip system with most favorable orientation, plastic deformation corresponds to the comparable distortion of the individual grains by means of slip, grain boundaries usually do not come apart during slip, so each individual grain is constrained, polycrystalline metals are stronger than single crystals, meaning greater stresses required to initiate slip due to geometric constraints , even if one grain could slip, it cannot until the grains around it also slip, making these materials stronger

What is a slip system and what does this slip system depend on?

Slip system - combination of slip plane (crystallographic plane on which slip occurs most easily, also plane with high planar density) and slip direction (crystallographic direction along which slip occurs most easily, direction with high linear density, atoms are closer together and easier to break and reform), depends on crystal structure of the metal and atomic distortion that accompanies motion of a dislocation is a minimum

What are stress risers and what are some examples of things that cause them?

Stress raisers - a small flaw (internal or surface) or a structural discontinuity at which an applied tensile stress will be amplified and from which cracks may propagate, effect is more significant in brittle than ductile materials,

Resilience

The capacity of a material to absorb energy when it is elastically deformed

Recrystallization

The formation of a new set of strain-free grains within a previously cold-worked material; normally, an annealing heat treatment is necessary

Grain growth

The increase in average grain size of a polycrystalline material; for most materials, an elevated-temperature heat treatment is necessary

Hardness

The measure of a material's resistance to deformation by surface indentation or by abrasion

Fracture Toughness (Kc)

The measure of a material's resistance to fracture when a crack is present

What is Poisson's ratio and what is it dependent on?

The ratio of lateral and axial strains, measure of the amount that the material contracts in the transverse dimension when it is strained in tension in the longitudinal direction

What is Young's Modulus of Elasticity?

The ratio of stress to strain when deformation is totally elastic, also measure of the stiffness of a material

Recovery

The relief of some of the internal strain energy of a previously cold-worked metal, usually by heat treatment

Creep

The time-dependent permanent deformation that occurs under stress; for most materials it is important only at elevated temperatures

What is true stress and true strain and how does the true stress-strain diagram differ from the engineering stress-strain diagram?

True stress-strain diagram typically goes up higher than the engineering diagram and does not curve back down like engineering diagram, have to correct true stress-strain for necking because conversion equations are valid only to the point of necking

For a binary system, what happens in regards to the solute when it reaches the solubility limit and what is the solubility limit dependent on?

When solubility limit is reached, adding more solute results in formation of another distinctly different solid solution or compound, solubility limit depends on temperature

What is the difference between the fracture toughness and the plane strain fracture toughness KIc, and which one is most often cited? Calculate unknowns using equations 8.1, 8.5, 8.6, and 8.7.

When specimen thickness is much greater than the crack dimensions, Kc becomes independent of thickness, so plane strain exists, meaning when a load operates on a crack, there is no strain component perpendicular to front and back faces and we use Kic instead, Kic is most often cited

What is plastic deformation and what is happening to the material on an atomic scale?

a divergence from linear stress/strain relationship, it is permanent and nonrecoverable, bonds stretch and atoms are displaced when a load is applied, and the atoms remain displaced after unloading

What are the three types of cyclic stresses introduced in this text?

axial (tension-compression), flexural (bending), or torsional (twisting)

How does a brittle fracture progress?

by rapid crack propagation, take place by successive and repeated breaking of atomic bonds

On a microscopic level, what two steps occur during the fracture process?

crack formation and propagation

What is the definition of creep and under which two circumstances does creep occur?

creep - time dependent permanent deformation that occurs under stress, for most materials it is important only at elevated temperatures, occurs at elevated temperatures and when exposed to static mechanical stress

What are three things that can affect the microstructure of an alloy?

depends on the temperature, the heating time at temperature, and rate of cooling to room temperature

For less critical static situations and when a tough material is used, what is the design stress?

design stress is σd = N'σc

What is dislocation density and what are some of the causes for these dislocations?

dislocation density - length of dislocations per unit volume or number of dislocations in a material, causes are solidification, plastic deformation, and rapid cooling (Strain)

How does the grain size affect strength and ductility?

ductility increases with grain size, strength decreases with grain size

What are edge and screw dislocations and what are they caused by (chapter 4)?

edge dislocation - crystalline defect caused by an extra half plane within a crystal, motion is parallel to applied shear stress screw dislocation - crystalline defect created when normally parallel planes join to form a helical ramp, motion is perpendicular to applied shear stress

What is the definition of fatigue limit, fatigue strength, and fatigue life? Be able to determine an unknown from figures 8.21 and 8.22.

fatigue limit - for fatigue, the maximum stress amplitude level below which a material can endure an essentially infinite number of stress cycles and not fail fatigue strength - the maximum stress level that a material can sustain without failing, for some specified number of cycles fatigue life (Nf) - the total number of stress cycles that cause a fatigue failure at some specified stress amplitude

What is hardness and in what general way do the Rockwell, Brinell hardness tests and the Knoop and Vickers microindentation hardness tests measure hardness?

hardness is a measure of resistance to surface plastic deformation, dent or scratches. large hardness = high resistance to deformation and better wear properties, a load is applied to an indenter and either the area or depth of the indentation is related to a hardness on a scale that depends on the method, the indenter material and geometry, and the load applied

What are three things that can be done that will improve the fatigue resistance to structural components

improve fatigue life by 1. reducing magnitude of mean stress 2. surface treatments - imposing compressive surface stresses increases surface hardness and suppresses surface cracks from growing 3. design changes - remove stress concentrators by rounding corners to reduce stress concentration

How does temperature and applied stress each influence the instantaneous strain and the rupture lifetime?

increasing temperature or stress causes 1. instantaneous strain at the time of stress application to increase 2. the steady-state creep rate increases 3. the rupture lifetime decreases

What happens to a material if it has a ductile to brittle transformation?

it transitions from ductile to brittle behavior with a decrease in temperature, exhibited in some low-strength steel BCC alloys,

What are lattice strains and how do they affect the atoms in the lattice?

lattice strain - slight displacement of atoms relative to their normal lattice positions, normally imposed by crystalline defects such as dislocations and interstitial and impurity atoms, causes atoms to experience a compressive strain relative to atoms positioned in perfect crystal and far removed from dislocation, atoms below the strain experience a tensile strain, for screw dislocation, lattice strains are pure shear only

What are two ways that ductility can be quantitively be determined, not using the stress-strain diagram? Be able to use the stress strain diagrams to determine the items in the first question above. Be able to calculate an unknown using percent elongation, reduction of area, and/or modulus of resilience for linear elastic behavior.

percent elongation and percent reduction in area, it is dependent on temperature, prior deformation, impurities, and heat treatment

Know what a phase is and whether the microstructure (see the next section) is a single phase or multiple phases.

phase - a homogenous portion of a system that has uniform physical and chemical characteristics

For a single crystal that has a tensile force applied to it, what are the resolved shear stresses and what is the critical resolved shear stress.? Be able to calculate an unknown using the three equations 7.2, 7.4, 7.5

phi is angle between vector normal to plane and vertical y, lambda is angle between vertical y and slip direction, at minimum stress necessary to induce yielding, when phi and lambda are both 45

What is an enginering stress strain diagram and how can the proportional limit, yield strength at a 0.2% offset, tensile strength, ductility, resilience and toughness be determined from this diagram?

plot of stress vs strain, proportional limit is end of linear portion, 0.2% offset, start line at 0.002 and draw line parallel to linear portion until it intersects line, yield strength is stress required to produce a very slight yet specified amount of plastic strain, tensile strength is maximum strength value, low ductility have steeper linear portions, high have flatter linear portions, resilience is area under stress strain curve to yielding (approximately (1/2)σyεy, toughness is amount of energy absorbed and it is approximated by total area under stress strain curve with units of energy per volume, brittle fracture is small toughness, ductile fracture is large toughness

Be able to calculate an unknown using the Poisson's ratio equation (eq. 6.8) and possibly in combination with eqns. 6.1, 6.2, 6.5

poisson's ratio = εx/εz, εx = ∆d/d0, εz=∆l/l0

What happens once a material that has been stressed within the plastic region is unloaded?

some fraction of the total deformation is recovered as elastic strain, essentially curve traces a near straight line path down from the point of unloading and slope is virtually identical to modulus of elasticity, or parallel to initial elastic portion of the curve, magnitude of elastic strain corresponds to strain recovery, there is elastic strain recovery associated with fracture, yield strength after releasing load and upon reloading is higher than initial

On the atomic level, what is occurring during recovery and how are the material properties changed?

some of the internal strain energy is relieved by dislocation motion because of enhanced atomic diffusion at elevated temperature, reduction in number of dislocations, properties such as electrical and thermal conductivities recover their precold-worked states

What is strain hardening, what are two other terms that may be used for this phenomenon, and on the atomic level, how is the material strengthened? Be able to use the Figure 7.19 graphs to determine an unknown

strain hardening - phenomenon by which a ductile metal becomes harder and stronger as it plastically deformed, sometimes called work hardening or cold working because temperature at which deformation takes place is cold relative to absolute melting temperature of metal, most metals strain harden at room temp, on atomic level, dislocation density increases with deformation or cold work because of dislocation multiplication, average distance of separation between dislocations decreases, because dislocation strain interactions are repulsive, motion of dislocation is hindered by other dislocations

What is tensile stress and why is it more important to know the stress in an object as opposed to just knowing the force applied to the object?

stress caused when tension is applied, important to know because it can be used to ascertain several mechanical properties of materials that are important to design

How is plastic deformation related to the ability of dislocations to move and how is the mechanical strength affected by the mobility of dislocations?

the ability of a metal to deform plastically depends on the ability of dislocations to move, hardness and strength are both related to ease of plastic deformation, reducing mobility of dislocations enhances mechanical strength

What is a microstructure?

the structural features of an alloy (grain and phase structure) subject to observation under a microscope

What two factors significantly affect the size of the grains?

time and temperature

What is the difference between a transgranular and an intergranular fracture?

transgranular - fracture cracks pass through grains because of successive and repeated breaking of atomic bonds along crystallographic planes called cleavage intergranular - crack propagation along grain boundaries, usually occurs as a result of processes that weaken or embrittle grain boundary regions

For critical applications, what other approaches should be taken to ensure safety?

utilize materials that have adequate toughness and also offer redundancy in the structural design, provided there are regular inspections to detect flaws and safely remove or repair components when necessary, use σw

What is Hooke's law and what are the constraints of this law?

σ=Eε, Hooke's law is not valid beyond the elastic limit of a material, only valid for elastic deformation

Be able to calculate an unknown using the engineering tensile stress and strain equations (eqns. 6.1, 6.2).

σ=F/A, ε=∆l/l

Be able to calculate an unknown using Hooks law, along with the tensile stress and strain equations (eqns. 6.1, 6.2, 6.5).

σ=F/A, ε=∆l/l, σ=Eε