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Mat Sci 2610 > Module 1 > Flashcards

Module 1 Flashcards

1
Q

Elastic (as a mechanical property defining deformation)

A
  • if the material eventually returns to its original dimensions when we remove the load -> it is a ELASTIC DEFORMATION
  • elastic deformations are said to be recoverable
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2
Q

Plastic (as a mechanical property defining deformation)

A
  • if the material retains some PERMANENT deformation when we remove the load -> it is a PLASTIC DEFORMATION
  • plastic deformations are not recoverable
  • almost always time dependent
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3
Q

Fracture (as a mechanical property defining deformation)

A
  • if the material separates into 2 OR MORE DIFFERENT PIECES under the applied load, its dimensions have changed dramatically, aka a fracture!!
  • fractures are not recoverable
  • can happen very fast
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4
Q

Creep

A

permanent deformation (plastic deformation) that occurs over a long period of time

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5
Q

Fatigue

A

when a crack (beginning of fracture) moves through a material in small incremental steps due to ‘low amplitude cyclic loading’

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6
Q

Stiffness

A
  • measure of a material’s ability to resist elastic deformation
  • opposite of stiffness is compliance
  • ex: rubber band is compliant, diamond is v stiff
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7
Q

Strength

A
  • measure of a material’s ability to resist permanent deformation whether it be from plastic deformation or fracture
  • opposite of strong is weak
  • words to describe it: hard = v strong, soft = not strong
  • ex: steel = strong, styrofoam = weak
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8
Q

Ductility

A
  • measure of how much a material can deform plastically before fracture
  • opposite of ductile is brittle
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9
Q

Toughness

A
  • measure of how much energy (work) it takes to fracture a material biiiiitch
  • max toughness -> materials need high ductility and high strength
  • brittle materials are not tough
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10
Q

Metals

A
  • characterized by metallic bonding
  • generally v stiff, can be made v strong
  • strength of metal depends on lattice defects, can be easily controlled
  • ductile -> usually fail in forgiving way, give warning (plastic deformation)
  • can easily be made into measured shapes
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11
Q

Ceramics

A
  • characterized by ionic (metal to nonmetal) and covalent (nonmetal to nonmetal, similar electronegativity so e- more equally shared) bonding
  • v stiff and v hard (retain these @ high temps)
  • don’t corrode easily
  • have lower specific weight (weight per unit volume) that metals
  • v brittle, fail catastrophically (fracture wo warning)
  • cannot easily be made into desired shapes
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12
Q

Polymers

A
  • made of covalently-bonded chain molecules (which may be connected by weak forces (ionic/covalent))
  • v compliant, pretty weak but can be made strong
  • can be easily made into desired shapes but they degrade @ high temps and over time
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13
Q

Composites

A
  • consist of 2+ different materials that are combined specifically to take advantage of certain features of each one
  • mechanical properties of composites cover a v wide range
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14
Q

Atomic bonding

A
  • the way that individual atoms are bound to each other

- plays key role in determining its stiffness and ductility

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15
Q

Atomic arrangements

A
  • how atoms are organized relative to each other to form phases
  • controls stiffness and ductility on large scale (0.1 to 10nm)
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16
Q

Phases

A
  • basic building blocks of the material

- at even larger scales (10nm - 10mm) defects in phases dominate in determining mechanical properties

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17
Q

Microstructure

A

defined by the features on phase scale

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18
Q

Metallic bonds

A
  • strong

- nondirectional (meaning orientation of bonds doesn’t matter)

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19
Q

Covalent bonds

A
  • nonmetal to nonmetal (nonmetal to nonmetal, similar electronegativity so e- more equally shared)
  • highly directional
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20
Q

Ionic bonds

A
  • strong

- require local charge neutrality

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21
Q

van der Waals bonds

A

weak ass bitch bonds

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22
Q

Metallic bonds II

A
  • happen when individual atoms share their valence e- w the whole ENSEMBLE of atoms (whole mat)
  • strong bonds, attribute to metal’s stiffness and strength
  • bc nondirectional, allows atoms to move around and not be tied to any particular e-
  • this allowed movement leads to metals famously high ductility
  • shared e- also contribute to metal’s conductivity and optical opacity
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23
Q

in covalent and ionically bonded materials….

A
  • atoms either share or donate/accept e- in specfic orbitals
  • atoms not free to move
  • since these bonds are typically strong, materials are stiff and strong -> AKA CERAMICS
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24
Q

Ceramic bondage info

A
  • covalent: highly directional
  • ionic: needs local charge neutrality
  • both “ “ contribute to making ceramics extremely brittle
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25
Q

Crystal

A
  • 3D periodic array of atoms in space
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26
Q

Amorphous material

A
  • has no discernable long-range order

- a structurally hot mess

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27
Q

Molecular materials

A
  • defined when basic units composing materials are molecules not atoms
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28
Q

Defects

A
  • “mistakes” in the crystal structure
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29
Q

Vacnacies

A
  • example of a defect

- when an atom is missing in the periodic structure

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30
Q

Interstituals

A
  • example of a defect

- when extra atoms are inbetween periodic atomic positions

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31
Q

Dislocations

A
  • defect

- line defects which move to produce plastic deformation

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32
Q

Grain boundaries

A
  • defect

- boundaries between regions have the same crystal structure but different orientations so they don’t quite fit right

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33
Q

Phase (more in depth)

A
  • region of material possessing a unique crystal structure and properties that vary continuously (in the mathematical sense) w position within the grain
  • composition doesn’t have that to be constant within a phase
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34
Q

Morphology

A

refers to the spatial arrangement and distribution of defects or phases

Note: 2 steels can have the same amount of phases but different morphologies and their properties will be very different

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35
Q

Structure insensitive

A
  • means property not really influenced by by changes in the microstructure
  • ex: elastic properties
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36
Q

Structure sensitive

A
  • very sensitive to microstructure

- ex: plastic deformation and fracture

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37
Q

Stress

A
  • Force (F) per Area (A)

- F/A

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38
Q

Normal stress (sigma)

A
  • Normal stress is measured as perpendicular to the area being stressed
  • Normal stress (signma) = Normal force (Fn) / Area (A)
  • Sigma = Fn/A
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39
Q

Shear stress (tau)

A
  • Shear stress is measured as parallel to the area being stressed
  • Shear stress (tau) = Shear force (Fs) / Area (A)
  • Tau = Fs/A
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40
Q

Shear force (Fs)

A

Fs = Force*cos(theta)

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41
Q

Normal force (Fn)

A

Fn = Force*sin(theta)

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42
Q

Normal stress equation

A

Sigma = (Fn/A) = (Fsin^2(theta))/A = sigma_a*sin^2(theta)

43
Q

Shear stress equation

A

Tau = Fs/A = Fsin(theta)cos(theta)/A0 = (sigma_a*sin(2theta))/2

44
Q

We know the state of stress at a point if for ANY plane passing through that we can compute normal (sigma) and shear (tau) stress

A

we can do this only if we know BOTH the normal and shear stresses on 3 mutually perpendicular planes (think coordinate system of a cube) at a point
- there is a normal and stress for every direction (sigma x, y, z, tau x, y, z)

45
Q

Hydrostatic pressure

A

equal pressure coming from all directions (think deep sea)

46
Q

Given all normal stresses (sigma x, sigma y, sigma z) find the maximum shear stress (tau max) on any plane through the point…

A

tau max = (sigma principle max (greatest value) - sigma principle min (lowest value)) / 2

47
Q

sigma max =

A

= sigma principle max

48
Q

Strain

A
  • measure of deformation independent of sample size
49
Q

Normal strain (epsilon)

A

epsilon = change in length (delta L) / original length (L)

  • length changing strain
  • aka engineering strain
50
Q

Shear strain (gamma)

A
  • strain about an angle
51
Q

True strain

A

epsilon t = ln(delta L / L)
- at small strains (epsilon < 0.1) nominal/engineering strain is the same as true strain but at larger strain values u must use the true strain!!

52
Q

Isotropy

A

a material is said to be isotropic in some property if the value of a property at a point is INDEPENDENT OF THE DIRECTION in the material

  • ex: if a material is elastically isotropic its stiffness is the same regardless of which direction it is pulled
  • opposite = anisotropic
53
Q

Homogeneous

A

a material is said to be homogeneous if its are INDEPENDENT OF POSITION in the material
- a material composed of 2 or more different phases is called INhomogeneous

54
Q

Elastic modulus

A

when we apply a stress to a material in the linear elastic regime, we get a strain response…
- the ELASTIC MODULUS that relates the elastic strain to stress

55
Q

Young’s modulus (E)

A

ratio of the normal stress (sigma) to the normal strain (epsilon)
E = stress/strain

56
Q

Poisson’s ratio (v)

A

v = - epsilon2 / epsilon3 = - epsilon1 / epsilon3

57
Q

Shear modulus (G)

A

ratio of shear stress (tau) to shear strain (gamma)

G = tau/gamma

58
Q

Bulk modulus (K)

A

gives the elastic (also known as dilatation) of the material to a hydrostatic pressure P

(delta V)/V = - (1/K)P

59
Q

when E and v are, G and K can be computed simply by

A 
G = E / (2 * (1+v))
K = E / (3 * (1-2v))
60
Q

We can find the relationships among stress and strain along the principal axes for biaxial or triaxial loading using the principle of SUPERPOSITION

A

by SUPERPOSITION we can write for the 3D stress state

epsilon x = epsilon x (of sigma x) + epsilon x (of sigma y) + epsilon x (of sigma z)
~or~
epsilon x = (1/E)[sigma x - v(sigma y + sigma z)]
(works for all epsilon x y z)

61
Q

Stiffness (revisited)

A
  • quantified by the elastic moduli

- units are Pascals (Pa)

62
Q

Strength (revisited)

A
  • determined by the stress at which permanent deformation begins
  • this is the yield stress (onset of plastic deformation)
  • (or if material fractured) this is the fracture stress
  • units are Pascals (Pa)
63
Q

Ductility

A
  • defined as the plastic strain to fracture

- unitless

64
Q

Toughness

A
  • defined as the energy (work) per unit volume required to fracture a material
  • *** toughness can thus be found as the area under the stress -strain curve for a material tested to fracture
  • units are N/m^3 or Pa
65
Q

most materials are elastically anisotropic even if they are homogeneous

A

in an anisotropic solid, E, v, and G vary with direction in the material

66
Q

in practice, all atoms tend toward a configuration where the outer electron shell is filled

A

…

67
Q

Electropositive

A

atoms with 1 or 2 “extra” electrons in their outer shells tend to “give up” the extra electrons

68
Q

Electronegative

A

atoms “missing” 1 or 2 electrons in their outer shells tend to “accept” extra electrons

69
Q

Secondary, weak bonds

A
  • weak bonds that form between atoms that do not donate, accept, or share electrons
  • in this case atoms are attracted to each other by local polarities or charge fluctuations
  • materials containing secondary bonds are generally weak and have very low density
70
Q

Metallic bonds form between atoms with only a few electrons in their outer shells. These atoms give up their extra electrons, becoming ions. The extra electrons are then shared by all of the metal ions in the solid.

A

Metallic bonds are very strong but relatively non-directional so metal atoms can have some freedom to move around relative to one another and tend to find closely packed configurations. This makes metals relatively heavy per unit volume and is also the reason why metals can be ductile.

71
Q

Covalent bonds form between atoms that can share electrons to fill the outer shell s and p states. Only two atoms can share any one electron in a covalent bond

A

Covalent bonds are very strong, but are quite directional since atoms share electrons only at certain positions. As a result, the atomic configurations can be relatively open, making these materials lighter per unit volume than metals. The strong directional covalent bonds also make these materials quite brittle

72
Q

Ionic bonds form between strongly electropositive and strongly electronegative elements. e.g. Li and F. Ionic bonding occurs when atoms form ions (by accepting or donating electrons) which then bond by electrostatic attraction.

A

Ionic bonds are strong, but the ions must be arranged so as to preserve local charge neutrality. Ionic solids thus typically also have lower densities than metals and are brittle.

73
Q

Secondary bonds are weak bonds that form between atoms that do not donate, accept, or share electrons

A

In this case, atoms are attracted to each other by local polarities or charge fluctuations. Materials containing secondary bonds are generally weak and have very low density.

74
Q

how can you approximate the potential energy curve?

A

φ (a)= −c/a^n + b/a^m

75
Q

In general binding energies are highest for covalent solids and somewhat smaller for ionic and metallic solids.

A

because of the atomic nature of solids that elastic properties are typically anisotropic

76
Q

In most applications, it is also necessary to limit elastic deflections to tolerable values

A

The elastic deflections for a given set of bonds are proportional to 1/E, so that higher values of E permit higher loads with comparable or less deflection. there are many applications where it is desired to have as high a natural (or resonant) frequency of vibration, f_res, of a structure as possible.
- f_res ∝ E ρ
where ρ is the density of the solid (high values of E help here also)

77
Q

How does one go about selecting a material with a high E?

A

One should pick a material with strong bonds and small a_0

78
Q

Polycrystalline Materials

A
  • most solids when viewed at high enough magnification appear to be made of many tiny parts called “grains”
  • each individual grain is actually a single crystal of material
  • grains have different orientation therefore reflecting light differently under magnification
  • if a material is composed of grains it is called POLYCRYSTALLINE
  • properties of polycrystalline materials depend on the properties of the individual grains
79
Q

crystallography

A

the study of crystals

80
Q

2 parts that crystals consist of

A

lattice and basis

81
Q

lattice definition

A

3D array of mathematical points, EACH OF WHICH MUST HAVE IDENTICAL SURROUNDINGS
- not an actual physical manifest, but the concept of lattice structure (points) is vital

82
Q

basis definition

A

the identical group of atoms which surround each point in the lattice to actually make up the crystal

83
Q

the structure of a crystal can be theoretically thought of as…

A

a real group of atoms (basis) attached to each point of a mathematical lattice

84
Q

how to construct a lattice tho??

A

PRIMITIVE TRANSLATION VECTORS

  • translate an initial point an integer combination of a set of primitive translation vectors
  • primitive translation vectors are a set of vectors that can be combined as integer multiples to describe EVERY lattice point
85
Q

in a 3D lattice, ALL points must be described as end points of the vector …

A

r = l(a1)+m(a2)+n(a3)

where a1, a2, and a3 are the independent primitive lattice translation vectors and l, m, and n are (positive and negative) integers

86
Q

symmetry operation

A

any operation that leaves the lattice unchanged

- (lattice translations are symmetry operations)

87
Q

rotation (as a symmetry operation)

A
  • view a lattice along a certain direction or axis
  • Now rotate the lattice through a full circle about that axis. If during that rotation, the lattice coincides with itself N-times, we call that axis an n-fold rotational symmetry axis, or we say that the lattice has n-fold rotational symmetry about that axis… yuh
88
Q

unit cell

A
  • small element of the lattice which can be translated to generate the entire lattice
  • unit cells can be thought of as parallelopipeds that can be stacked up together to fill space (without leaving gaps)
89
Q

primitive unit cell

A

a unit cell which contains only one lattice point but will not necessarily contain all symmetry elements of the infinite lattice

90
Q

conventional unit cell

A
  • smallest parallelopiped which contains all the symmetry elements of the infinite lattice
  • might be more than one lattice point
  • think hexagonal setup for complex 3D (at least sometimes)
91
Q

lattice parameters

A

the lengths of the sides of a conventional unit cell

92
Q

Bravais lattices

A
  • 3D lattices which fulfill the requirements that all points have identical surroundings
  • only 14, each has a different symmetry
93
Q

Simple cubic (SC)

A
  • know how to draw this
  • |a1| = |a2| = |a3| = a
  • all angles between edges = 90
  • points at corners
94
Q

Face Centered Cubic (FCC)

A
  • know how to draw this
  • |a1| = |a2| = |a3| = a
  • all angles < 90
  • points at the center of faces
95
Q

Body Centered Cubic (BCC)

A
  • know how to draw this
  • |a1| = |a2| = |a3| = a
  • all angles < 90
  • point at center of cube
96
Q

Hexagonal

A
  • know how to draw this
  • |a1| = |a2| = a
  • |a3| = c (straight up) ~= a
  • hexagonal face angles - 120
97
Q

Other Bravais lattices to at least remember exist

A
  • tetragonal
  • body centered tetragonal
  • orthorhombic
  • base centered orthorhombic
  • face centered orthorhombic
  • body centered orthorhombic
  • monoclinic
  • base centered monoclinic
  • rhombohedral
  • triclinic
98
Q

FCC and HCP and Close Packed (what the CP stands for) Planes

A
  • in many metals where atomic bonding is relatively non-directional, atoms tend to group together so as to form close-packed planes
  • a close-packed plane can be constructed by packing spheres, which we use to model the non-directionally-bonded atoms, together in a plane (think ping pong ball demo)
99
Q

Stacking closed packed planes

A

Once we have one close-packed plane, we can add another close-packed plane of top of it by placing a second layer of spheres on top of the first one. We can see that the spheres in the second layer will want to rest in the triangular indentations in the first layer and that they can go either in the upward pointing triangles or the downward pointing triangles (but not both!)

100
Q

Stacking closed packed planes pt 2 (structure/labelling)

A

We label the in plane positions of the first layer as “A” sites, of the upwardpointing triangles as “B” sites, and of the downward pointing triangles as “C” sites. Thus, for a given A layer, we have two options for the second layer, B or C.
- Now imagine adding a third layer. If the second layer is on B sites, then the available sites for the third layer will be either A sites or C sites

101
Q

FCC stacking structure

A

ABCABC (or CBACBA)

102
Q

HCP stacking structure

A

ABABAB or ACACAC

103
Q

Miller Indices

A

notation has been developed to refer to specific directions and planes in a crystal structure

104
Q

Procedure for determining the Miller indices of a DIRECTION is

A
  1. ) Find the coefficients l, m, and n of the lattice translation vector (r = l(a1)+m(a2)+n(a3)) parallel to the direction of interest
  2. ) Reduce these numbers to the smallest integers having the same ratio
  3. ) Enclose them in square brackets
    - to indicate negative value put a bar (-) OVER the number in question

Mat Sci 2610 (1 decks)

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