Mechanical 2 Flashcards
Strength of paper
about 60MPa
suffixes like mega, milli, pico, etc
learn off
why easier to rip paper with crack
stress is concentrated at tip of crack, material fails there, allowing crack to grow
relationship between fracture stress and crack length
σf ∝ 1/√a
fracture toughness in tough vs brittle materials
- tough: value of constant high, good at tolerating cracks
- brittle: low, even small cracks weaken them
Fracture Toughness equation
Kc = Qσf√(πa)
Q = a constant σf = fracture stress a = crack length
Values of Q
taking a crack in a flat sheet,
if
a < W and a < H, then Q = 1.0
other values shown on graph on lecture slides 4
Total length of crack in a flat sheet
Length of crack = 2a
Brittle fracture
a material containing a crack will break at a stress σf
Ductile fracture
Failure by yielding
Sizes of cracks
- Those having large cracks will fail by brittle fracture
- Those with small cracks (a < a*) will fail by ductile fracture
Cracks and strength of material
cracks only affect strength if they are larger than a* (see diagram on lecture slides 4)
smaller cracks are harmless
Unit of fracture toughness
MPa√m
what a* means
Materials can have cracks up to this length without any loss of strength
Static properties of a material
Stiffness
Strength
Toughness
Long-Term Failure
Creep
Fatigue
Wear
Creep
Plastic strain which takes time
- Sometimes if you apply stress and hold it constant, strain will gradually increase over time
- can happen for stresses above and below σy
stages of creep test
primary, secondary, tertiart
Time to failure formula
t(subscript f) = C/σᵐ
what time to failure depends on
stress
temperature
Fatigue
A stress which was not sufficient to cause failure when applied once, can, if repeated enough times, eventually cause failure
Cyclic Loading
- tests carried out with given stress range △σ and mean stress σₛₜᵣₑₛₛ
- number of cycles to failure, N(subscript f) counted for each specimen tested
Stress-Life curve
-straight line except at high cycles, where line may become horizontal at “fatigue limit”
Wear
-Happens when two surfaces rub together
- you need a compressive force F and a shear movement d
- material removed from one or both surfaces
Wear testing
-Volume of material lost △V found by measuring/weighing test piece
Wear formula
△V = kFd
k = constant, tells you how easily material will wear away d = shear movement F = compressive force
four classes of materials
Metals
Polymers
Ceramics
Composites
Alloys
made by combining elements
Metals
strong and tough, but heavy and expensive
Polymers
- Light and cheap, can be strong
- fracture toughness poor but have high impact resistance
Ceramics
Includes cement, glass, diamond, rocks, alumina and silicon carbide
Glass
- Stiff and strong
- Low toughness
Composites
Made by combining materials from the other three classes
eg. fibre glass, carbon fibre, reinforced polymers
Three levels of structure
Nanostructure
Microstructure
Macrostructure
Nanostructure
- Also called atomic structure as atoms and molecules are around this size
- 1 nm = 10⁻⁹ m
Microstructure
1 μm = 1 micron = 10⁻⁶ m
Macrostructure
things greater than 1mm eg. aggregate particles and reinforcing bars in concrete
Levels of structure and properties
-Different properties come from diff levels of structure
Young’s Modulus and Atomic Structure
E, the elastic stiffness, comes from stiffness of atomic bonds of material
Atomic Lattices
In most metals & ceramics, atoms arranged in regular, three-dimensional lattices
3 types of lattices we studied
Body Centred Cubic (bcc)
Face Centred Cubic (fcc)
Hexagonal Close Packed (hcp)
Unit cel
smallest group of atoms which can be repeated to make the whole lattice
Simple Cubic
- atoms at cube corners
- 1 atom per unit cell (8 atoms x 1/8 volume/atom)
- atomst ouch along sides of cube
- cube side L = 2r
Body Centred Cubic
- atoms at centre and at corners
- 2 atoms per cube
- atoms touch along body diagonal
Face Centred Cubic
-atoms at corners and c centres of each face
-
Hexagonal Close Packed
-unit cell is hexagonal prism
-7 atoms on top face, 3 in middle, 7 on bottom face
-
Stacking sequences
a, b, c stacking sequence
a b a b stacking sequence
Amorphous structure
In some materials there’s no pattern: atoms packed together in random way eg. glass
Types of atomic bonds
- Strong bonds
- Weak Bonds
Strong Bonds
Ionic bonds
Covalent bonds
Metallic bonds
Weak Bonds
Hydrogen bonds
Van der Waals bonds
Metallic bond
involves non-specific sharing of outer electrons, bond is non-directional
ceramic materials bonds
-both ionic and covalent
Ionic bonds
- involve attraction of oppositely charged ions
- non-directional
Covalent bonds
- directional
- occur only at specific angles
Polymer chain molecule bonds
- covalent
- between chains are often weak bonds
Distance between atom centres
Normally equal to 2r
Potential energy
of the bond is energy needed to bring atoms to a separation a, starting at a = infinity
Force vs Separation graph
- Max force is strength of bond (not material)
- Slope near a₀ determins Young’s Modulus
Total potential energy formula
W = A/aⁿ - B/aᵐ
F = dW/da
a₀
when F=0
Fₘₐₓ
breaking strength of bond
Young’s modulus
proportional to slope of line dF/da at a = a₀
Converting dF/Da to dσ/dε
Divide force by area over which it acts to get stress, divide da by bond length a₀ to get strain
E at atomic level
fixed, as it is determined at atomic level
changing stiffness, strength, toughness
- stiffness: change to diff material
- strength & toughness: can be changed within given type of material
Strength and diff materials
- Metals and composites have good strength
- Ceramics are strongest materials
- Polymers weakest
Plastic deformation and atoms
- plastic deformation permanent
- atoms must move to make new shape, but lattice pattern and bond separation will not change
- Deformation by shear is easier
what do we need to cause plastic strain?
shear stress
plastic strain always happens by shearing
Greatest shear stress on a plane
at 45°
where yielding usually occurs
Dislocations
-Error or mistake in atomic lattice, exists in form of line in meterial
- Can move under applied stress if shear stress
- When it moves, causes plastic strain
Summary about yielding in metals
- Plastic strain happens n shear
- Shear strain much easier when you have dislocations
- Yield strength actually stress needed to make dislocations move
