ES exam 2

What loading type is shown?

Tension

What loading type is shown?

Compression

What loading type is shown?

Shear

Stress definition, equation, and units

distribution of internal forces, (o = F/A), Pascal (N/m^2) or Psi (pound force per square inch)

Strain definition, equation, and units

deformation within the body, (delta L/L), dimensionless

What are the assumptions in “engineering stress” and “engineering strain” calculations

take original cross-sectional area and don’t consider shrinkage/bulging

What type of testing is done to find the mechanical properties of materials

tensile test

Elastic deformation is

non-permanent and reversable

If the elastic modulus (E), is large, the material is ______,__ and deforms _____

stiff, less

How does the elastic modulus(E) compare for the three main materials?

Ceramics>metals>composites

Describe hooke’s law as it applies to elastic modulus

o = Ee, relates stress to strain for linear elastic deformation

What’s the use of Poisson’s ratio and how is it calculated?

ratio between axial and transverse deformation, v =-ex/ez

Explain the difference between elastic and plastic deformations

elastic is temporary since any deformation goes back to 1, while plastic is permanent and non-reversible

deflection is dependent on

material, geometric, and loading parameters

yield strength

stress value that marks the transition form elastic to plastic deformation

tensile strength

highest point of stress/strain curve, max stress before failure

ductility and ways of calculating it

amount of plastic deformation before failure, %EL = how much it can elongate, % RA = how much radius can shrink

What’s the difference between resilience and toughness

resilience is ability of material to absorb energy during elastic deformation while toughness is amount of energy absorbed during fracture (brittle = small toughness, ductile = large toughness)

What’s the difference between true and engineering stress-strain?

engineering= original lo and Ao, true= instaneous lo and Ao

hardness

measure of resistance to surface plastic deformation

Rockwell hardness

standard force leads to measured depth, can measure large scale of hardness

Brinell Hardness

single scale (HB), can be related to tensile strength

Why do we need design/safety factors

because of design uncertainties, allowances must be made to protect against failure, so you assume material is weaker than it actually is

Plastic deformation from atomic perspective

Plastic deformation occurs by motion of dislocations (edge, screw, mixed) in process called slip, Applied shear stress can cause extra half-plane of atoms (and edge dislocation line) to move, and Atomic bonds broken and reformed along slip plane as  dislocation moves

what does slip system consist of?

slip plane (crystallographic plane on which slip occurs most easily, high planar density), and direction (crystallographic direction along which slip occurs most easily, high linear density)

Slip occurs when Ƭ*R*

exceeds critical resolved shear stress, highest shear yeild’s first

before rolling, grains are

\-grains equiaxed and randomly oriented, isotropic

after rolling, grains are

elongated in rolling direction, anisotropic

if dislocations can’t move

plastic deformation can’t occur

the easier it is to move dislocations,

the less strength and hardness the material has and vice versa

mechanisms for strengthening/hardening materials

decrease dislocation mobility, Grain size reduction, Solid solution strengthening, Strain hardening(cold working)

reducing grain size

increases grain boundary area, creates more barriers to dislocation motion, which in turn increases yield strength, tensile strength, and hardness

solid solution strengthening

smaller impurity pulls in neighbors (tensile strain) while large impurity pushes neighbors (compressive strain), both cancel tensile dislocation strain so higher shear stress required are to cause disl. motion

strain hardening (cold work)

deformation reduces cross sectional area, which increases strength and lowers ductility, dislocation density increases

heat treatment nullifies

effects of cold work (annealing)

three annealing stages

Recovery(reduction in disl. density and disl), Recrystallization(new smaller grains are formed), Grain Growth

Metals having small grains are

relatively strong and tough at low temperatures

Hot working is deformation _____*TR*

above

Cold working is deformation _____*TR*

below

fracture

separation into 2+ pieces in response to a static stress, accompanied by propagation of crack

ductile fracture

generally slower and accompanied by significant plastic deformation- fails with warning (1 piece)

brittle fracture

shatters like glass, multiple pieces, no plastic deformation/warning

what fracture is this

brittle

what fracture is this

ductile

microscopic flaws (cracks) always

exist in materials, magnitude of applied tensile stress amplified at the tips of these cracks

Kt

stress concentration factor, suggests avoiding sharp corners for safe design

stress concentration is higher for ___ cracks and lower for ___ cracks

sharp, blunted

crack propagation (and fracture) occurs when

*σm(*stress at crack tip*)* > *σc*(critical stress) for crack with lowest *σc*

Kc

fracture toughness

Kic

plane strain fracture toughness, high for ductile, low for brittle

Y

shape factor

what is the technique to quantify fracture toughness

Charpy impact test

fatigue failure

failure under lengthy period of repeated stress (stress varies with time), even though applied stress is less than yield strength, responsible for 90% of engineering fails

as T increases, impact energy

increases

Some BCC metals exhibit Ductile-to-Brittle Transition as

temperatures increase

Sfat

fatigue limit, no fatigue if *S(*stress amplitude) < *S*fat (theoretically safe forever)

two types of fatigue behavior

some materials have asymptotic fatigue limit while others don’t safe below curve of S vs N for both

fatigue life Nf

total # of stress cycles to cause fatigue failure at specified stress amplitude

three techniques for improving fatigue life

reducting mean stress Om, surface treatments (shot peening and carburizing), and design changes (removing stress concentrators-sharp corners)

shot peening

surface compressive stress due to plastic deformation of outer surface layer

carburizing

surface compressive stress due to carbon atoms diffusing into outer surface layer

explain creep deformation

Measure deformation (strain) vs. time at constant stress, Occurs at elevated temperature for most metals, *T* > 0.4 *Tm* (in K)

three stages of creep

Primary Creep (slope (creep rate) decreases with time), Secondary Creep (steady-state, constant slope (Δe /Δt), Tertiary Creep (slope increases with time, acceleration of rate)

with increasing temp and stress,

steady state creep rate increases and rupture lifetime decreases

how to predict time to rupture in creep without spending years in labs

increase temp for a lower time, use larson miller parameter m

components (phase diagram)

elements/compounds present

phase

physically and chemically distinct material regions

solution

solid, liquid, or gas, single phase

mixture

more than one phase

solubility limit

max conc. for which only a single phase solution exists

What 2 main factors affect the number of phases

changing temp and conc

phases are a function of

temp and conc(independent variables) and pressure (1 atm)

binary systems

just 2 components

isomorphous

complete solubility of one component in another (phase field extends from 0 to 100%)

Tie line

connects phases in equilibrium with each other (isotherm)

Binary Eutectic systems

2 components, has special comp. with a min melting temp, limited solubility

Hypoeutectic

below eutectic comp (α particles)

Hypereutectic

above eutectic comp (β particles)

eutectic

liquid phase to 2 solid phases

eutectoid

1 solid phase to 2 other solid phases

peritectic

1 liquid and 1 solid phase to a second solid phase

Fe3C

intermetallic compound cementite, hard

α

ferrite, soft

Pearlite

alt. layers of α and Fe3C layers

 **γ**

austenite- red hot steel

Hypoeutectoid steel

proeutectoid ferrite in gran boundaries

Hypereutectoid steel

proeutectoid cementite in grain boundaries

affects eutectoid temp and conc

alloying with other elements

nucleation

nuclei (seeds) act as template for crystal growth (addition of atoms to nucleus must be faster than loss), and once nucleated, growth continues until equilibrium is reached

as temp increases, driving force to nucleate

increases

kinetics

study of reaction rates of phase transformations

coarse pearlite

formed at higher temp, thick layers so relatively soft (low strength and ductile)

fine pearlite

formed at low temp, multiple thin layers so relatively hard (moderate strength and brittle)

Bainite

elongated Fe3C particles in α-ferrite matrix, diffusion controlled (moderate strength)

Spheroidite 

formed by heating bainite/pearlite at temp just below eutectoid for long times produces spherical Fe3C particles, so very soft and ductile

Martensite

single phase, has body-centered tetragonal structure, diffusion less transformation, very hard (high strength and brittle)

as carbon content increases

tensile and yield strength increase while ductility decreases

tempered martensite

heat treating martensite makes it less brittle, producing extremely small Fe3C particles surrounded by ferrite (high strength and ductile)

slow cooling austenite produces

pearlite( ferrite and cementite layers plus proeutectoid phase)

moderately cooling austenite produces

bainite