MSE 4105 Test 1

Elastic strain

This kind of strain disappears instantly as the force causing it is removed

Hookean solids

Materials where stress is proportional to strain. Elastic does not necessarily correlate with this.

Elastic

This kind of curve is reversible and looks the same whether in unloading or loading

Plastic

This kind of deformation is permanent!

True/False

A stress-strain curve can contain both elastic and plastic portions

Viscoelastic

Time-dependent response; part of the behavior is elastic-like and part is viscous-like

Compression

In (compression/tension), true and engineering strains diverge more strongly at large deformation

True Strain

This kind of strain measures deformation continuously relative to the instantaneous length during deformation. In this way, it correctly accounts for true accumulated change and is essential for large plastic deformations.

Engineering Strain

This kind of strain measures deformation relative to a material’s original length. Best for standard design and elastic deformation where changes in length and area are small.

Shear Modulus, G

The measure of a solid material’s ability to resist shape change or twisting when a force is pushed parallel to one of its faces.
Equal to tau/gamma = shear stress / shear strain

Young’s Modulus

A mechanical property that measures the stiffness of a solid material when stretched or compressed, equivalent to stress/strain.
In single-crystals, ______ ________ is different for different crystallographic orientations, but in polycrystalline aggregates (smaller crystal grains joined together by disordered transition zones called grain boundaries), E is isotropic.

Poisson’s ratio

The negative ratio of the transvers and longitudinal strains

Isochoric

Constant volume materials

Auxetic materials

Materials with negative poisson’s ratio; they expand and become thicker when stretched, rather than thinning like ordinary material. This behavior doesn’t come from chemistry, but rather geometry. Their internal cells use special “re-entrant” or folded shapes that pop outward when pulled

Yield stress

The minimum stress required to make a material stop behaving like an elastic solid and start deforming permanently or flowing; the end of the elastic limit

Resilience, Ur

Strain energy density; the amount of internal potential energy stored in a material per unit volume when it is deformed by external forces. Equal to the area under the stress-starin curve within the elastic limit. Measure of the amount of energy that can be absorbed under elastic loading conditions and is released comletely when the loads are removed. In units of energy per unit volume

Toughness, U

Area under the entire stress vs strain curve to failure. Total energy per unit volume absorbed before fracture. In units of energy per unit volume

45 degrees

At this measure of degrees relative to the tensile axis, shear stress is at its maximum

Voigt Average

Assumes that every individual constituent or grain deforms by the exact same amount when an external force is applied, meaning internal strain is constant. Always provides the maximum mathematical upper limit for the true effective elastic moduli of a composite. Average the grain stiffnesses weighted by volume fraction.

Reuss Average

Assumes that every individual constituent or grain experiences stress by the exact same amount when an external force is applied, meaning internal stress is constant. Always provides the maximum mathematical lower limit for the true effective elastic moduli of a composite. Average the grain compliances weighted by volume fraction.

Decreases

Young’s modulus (increases/decreases) as porosity rises because porosity reduces load-bearing area and increases compliance

Compliance

The measure of how easily a material or structure deforms when a force is applied

Increases

For metals, Young’s Modulus (E) generally decreases as temperature increases

Viscoelasticity

Stress depends on strain AND how fast/long the deformation is applied.

Creep

Strain incresaes under constant stress

Stress relaxation

Stress decreases under constant strain

Spring-dashpot model

A way of thinking about how polymers elastically store energy but also slowly deform and flow.

Bauschinger effect

After plastic deformation in one direction, the material’s yield behavior shifts when the load is reversed. Prior plastic deformation changes the internal dislocation structure. The yield strength for strain in the opposite direction is less than it would be if the strain had continued in the initial direction. This can happen for two reasons: 1. dislocations and orowan loops pile up and create internal stresses that assist reverse motion. 2. Opposite sign dislocations can form and annihilate during reversal, reducing dislocation density and reverese-direction stress.

Increases

Higher strain rate generally (increases/decreases) the yield stress of typical metals.

Yield criterion

A rule for predicting when a mulitaxial stress state will cause yielding.

Solid, liquid

A (solid/liquid) responds to how much it has been deformed. A (solid/liquid) responds to how fast it is being deformed.

Increases

Fluidity (increases/decreases) with temperature

Hardness

Resistance to localized permanent deformation (indentation/ scratching / wear, depending on test)

Strain hardening

Also known as work hardening or cold working; the process where a metal or polymer becomes stronger and harder as it undergoes permanent plastic deformation. It is also called cold working because the shaping occurs below the metal’s recrystallization temperature (the temperature where crystal grains reset and heal).

Strain hardening coefficient

n, a material property that measures how much a metal strengthens and hardens when it is permanently stretched or deformed. Shows the rate at which a metal increases its strength under plastic deformation (stretching past its yield point).

Unbounded models

Type of plasticity model that is commonly used for steels. Includes

Saturated models

Type of plasticity model that is useful when stress approaches a saturation value, such as for materials that do not maintain a constant n.

Saturation stress

The maximum limit of internal resistance or flow stress a material reaches when undergoing continuous plastic deformation or cyclic loading, beyond which the stress no longer increases.

Quenching

A type of heat-treatment process used in materials engineering where you heat the metal to a specific high temperature and cool it rapidly by plunging it into a liquid medium. It maximizes hardness, wear resistance, and tensile strength, but also leaves the metal brittle and prone to cracking, requiring tempering to restore toughness.

Annealing

A type of heat-treatment process used in materials engineering where you heat the metal to a target temperature and cool it extremely slowly. It softens the metal, relieves internal residual stresses, and improves ductility and malleability.

Covalent, BCT

Brittle fracture is most common with (covalent/ionic/metallic) bonding and (FCC/BCC/BCT) crystal structure

Void nucleation

Usually starts at 2nd phase particles. The initial process of tiny holes or cavities forming inside a material under stress or damage.

Considere Criteria of Necking

When the increase in strength of the material (work hardening) is less than the load bearing ability due to the decrease in the cross sectional area, strain is localized.

In simpler terms: Initially as a material is pulled, it stretches and its cross-sectional area decreases. however, the material also gets stronger due to work hardening. As long as the increase in strength outpaces the loss of cross-sectional area, deformation remains uniform throughout the entire gauge length. Eventually, the material reaches a critical point where the rate of work hardening can no longer compensate for the shrinking cross-sectional area. The material’s overall load-bearing capacity peaks and beyond this, the deformation concentrates in the weakest zone of the material and the material thins rapidly, forming a neck which leads to final fracture.

0.5

When deformation goes from elastic to plastic, Poisson’s ratio increases with strain and approaches [this number].

Bridgman equation

A multiplier used in tensile tests to find the true uniform flow stress of a metal after necking begins. Before necking, a tensile specimen experiences simple uniaxial stress, but after necking, the geometry of the narrow neck forces a complex multiaxial stress state to develop and the inner material experienes a hidden hydrostatic pulling force. This makes the measured axial force and apparent stress higher than the actual uniaxial yield/flow sterss of the material. So this multiplier scales down the apparent average axial stress to reveal the true equivalent uniaxial stress.

Barreling

In a compression test, this occurs because there is friction between the specimen and the plates that prevents them from smoothly spreading out easily, while meanwhile, the material in the middle can spread outward more easily.

Compressive yield strength

The specific amount of compressive stress- a squeezing or pushing force- that causes a material to stop bending elastically and begin permanent, irreversible plastic deformation.

Thermoplastics

Plastics that soften and melt when heated and solidify when cooled, meaning they can be reshaped and recycled multiple times.

Thermosets

Plastics that undergo irreversible chemical reaction during curing a form a permanent, rigid shape that will burn or char instead of melting if heated again.

Relaxation modulus

It tells how much stress remains at a given time after a fixed strain is imposed

Shear band

A narrow, microscopic zone where intense plastic deformation concentrates during the laoding of the material. Instead of spreading deformation evenly across the entire structure, the material focuses all its movement into a thin, distinct plane or band (often running at about a 45 degree angle ot the main stress axis where shear stress is highest). The chains become oriented and the volume doesn’t change substantially.

Craze

A narrow zone of highly deformed polymer containing voids. It’s not simply an open crack- the surrounding material still carries load. Associated with

Yielding criteria

Mathematical expression of the stress state needed for yielding or plastic flow. Yielding of most solids is independent of the sign of the stress state (reversing the signs of all the stresses has no effect on whether a material yields or yield strength in tension and compression are usually equal). Three kinds to know: Rankine, Tresca, and von Mises

Rankine (Maximum Normal Stress)

A yielding criterion. Plastic flow starts when the greatest principal stress reaches the flow stress (uniaxial yield stress). Limitation: it predicts plastic flow of a material under hydrostatic state of stress (stress is the same in every direction), which is incorrect.

Flow stress

The instantaneous amount of stress required to keep a material plastically deforming.

Tresca (Maximum shear stress)

A yielding criterion. Plastic flow starts when maximum shear stress in a complex state of deformation reaches a value equal to the maximum shear stress (largest difference between principal stresses)

von Mises (maximum distortion energy)

A yielding criterion. A body flows plastically when the distortional (or shear) energy in the complex state of stress is equal to the deformation energy in uniaxial stress. Basically, claims that distortion causes yielding.

Isotropic hardening

The yield surface expands symmetrically as the flow stress increases. Same center, larger surface.

Kinematic hardening

The yield surface translates in stress space. This captures directional history and connects directly to the Bauschinger effect.

Hardness

Resistance to permanent deformation at the surface; resistance to plastic deformation or cracking in compression.

Brinell scale

A test of hardness. Pressing a hard steel or tungsten carbide ball into the metal under a heavy load to measure the size of the impression.

Vickers scale

A test of hardness. Using a diamond shape indenter and measuring the optical diagonal of the indentation for high precision.

Rockwell

A test of hardness. Measuring the depth of penetration of an indenter under a large load compared to a preload.

Point defects

A type of defect that is a zero-dimensional imperfection in a crystal lattice where an atom is missing, out of place, or replaced by a different atom. Includes vacancies, interstitials, and substitutional atoms.

Vacancy

A type of point defect where an atom is missing from its position in the lattice

Interstitial

A type of point defect where an extra atom is squeezed into a space between the regular lattice sites

Substitutional

A type of point defect where a foreign atom replaces one of the original atoms in the crystal structure.

Frenkel defect

Type of point defect where an ion leaves its normal spot and moves into an interstitial space, creating a vacancy-interstitial pair

Schottky defect

Type of point defect where there are pairs of missing cations and anions in ionic solids that keep the crystal electrically neutral

Irradiation

The process of exposing a material to energetic particles or radiation which displaces atoms from their lattice sites and alters the material’s physical and mechanical properties. Leaves point defects.

Line defects

One-dimensional imperfections in a crystalline material where atoms are misaligned along a specific line.

Screw defects

A type of line defect where the atomic planes are shifted in a spiral or helical ramp around the defect line. The burgers vector (describes the magnitude and direction of the lattice translation associated with the dislocation) is parallel to the dislocation line.

Edge dislocation

A type of line defect where an extra half-plane of atoms terminates inside the cyrstal. The burgers vector is perpendicular to the dislocation line.

Dislocation density (rho)

The total length of dislocation line per unit volume of material. Cold work significantly increases ___________ _________ and an increase in ________ _______ leads to increased strength and hardness but also reduced ductility as the dislocations hinder each other’s movement. Proportional to shear strength.

Peirels Nabarro Stress

The minimum shear stress required to move a dislocation through a crystal lattice. Represents the internal resistance a crystal offers to dislocation glide. It is lowest along close-packed directions (smallest interatomic spacing, b) and close-packed planes (smaller interplanar spacing, a)

Burgers vector

A measurement that defines the magnitude (size) and direction of the lattice distortion or atomic displacement caused by a dislocation in a crystal structure. Tells you how far and in what direction the atoms are pushed out of place when a defect occurs.

Schmid Law

States that plastic deformation (slip) in a crystalline material begins when the resolved shear stress on a slip system reaches a critical threshold value.

Critical Resolved Shear Stress

The minimum shear stress required to begin plastic deformation or slip. Depends on temperature, strain rate, and material.

Line tension (T)

The change in the energy of the dislocation with its change in length. Acts to straighten the dislocation line, minimizing length and energy

Peach-Koehler Equation

An applied stress creates a force per unit length on a dislocation. In simple shear, the driving force magnitude is F/L = tau * b. The force acts in the direction that moves the dislocation through the crystal; it is not simply the smae direction as the applied tensile load. This relation connects continuum stress to dislocation motion; larger applied stress or larger b gives a larger driving force. It is especially useful when thinking about dislocation bowing, glide, and interactions with obstacles.

Frank’s rule

If two locations, with Burgers vectors b1 and b2, combine, the new dislocation will have a burgers vector, b3, which will be the sum of the burgers vectors of the two dislocations from which it formed. The line (tangent) vector of the new dislocation, 13, will be the intersection fo the slip planes of the two original dislocations. The plane in which the new dislocation may slip will be the plane containing both its burger vector, b3, and its line vector, l3. For such a dislocation reaction to occur, it must be energetically favorable. Dislocations will combine if b3² < b1² + b2².

Unit dislocation

Dislocation with the shortest burger’s vector

Perfect dislocations

Type of dislocation which does not change the crystal structure, as atoms are displaced by a whole lattice vector

Partial dislocations

Type of dislocation where planar stacking is changed by the passage of dislocations with less than whole lattice vector displacement

Shockley partial dislocations

A pair of dislocations which can lead to the presence of stacking faults. The partials are separated by a ribbon of stacking fault; the local ABCABC stacking is disrupted between them.

Sessile

Means the resulting defect cannot easily glide on the original slip planes under ordinary conditions

Frank-Reed source

A pinned dislocation segment that, under sufficient shear stress, bows out and repeatedly generates expanding dislocation loops, multiplying the number of dislocations in the crystal.

Kink

A step in the dislocation line that remains inside the active slip plane. Because it stays within the plane, it is highly mobile and can easily glide to help the material deform under lower stress.

Jog

A step in the dislocation line that moves outside of the active slip plane. Because it is out of the plane, a jog cannot move easily by slimple gliding; it requires a much sloewr, temperature-dependent process called “climb”. This impedes movement and contributes to work-hardening.