Mechanical failure of materials chap 4 Flashcards
What are the main types of material failure?
- Plastic yielding
- fracture
- fatigue
- creep
What is material failure?
loss of load carrying capacity
What is failure by plastic yielding?
- Yielding is defined as a form of material failure
- Yielding = onset of plastic deformation
- materials begins to deviate from a linear behavior between stress and strain
Safety factor in failure by plastic yielding
- Engineers prefer to work with materials below plastic yielding
to design against plastic yielding divide the yield strength by a safety factor and the the division will equal the acceptable work stress of the material
What is failure by fracture?
- spontaneous breaking of interatomic bonds, fast,
- happens in load bearing structures like bridges, trucks, pressure vessels, gas pipelines
- when a tensile stress is applied
- materials stores energy,
when the energy stores equals the energy required to fracture and the limit of the bond strength is reached = material fractures
Crack propagation
- when there is a defect in a material, this is an area of stress concentration
- when tensile stress is applied the crack propagates to where the bonds are still intact
Examples of failure by fracture
- Liberty ships (1946) = lack of understanding of brittle to ductile transitions
- 1250/4700 brittle fractures
- 230 of 1250 serious
- 12 fractures in which they broke into two
Energy criterion of failure
E stored = E failure
- defects reduce energy of fracture
- Elastic region in stress and strain curve moved to end of curve = energy stored in the material that can be stored to do work to create fracture
Examples of energy criterion of failure
Examples:
Pin into fully inflated balloon
Ef (intact) > Es > Ef (defect)
Pin w. partially inflated
Estored > Ef (defect)
- balloon may not pop
Pin then blow up
Estored = Ef
Modes of fracture
crack formation
crack propagtion
Brittle fracture
- catastrpphic
- ceramics, high strength metals, high strength brasses
- fracture with little or no plastic defo
- low energy stored
- Flat fracture surface morphology (cleavage fracture)
Ductile fracture
- fails are yield strength
- reveals itself
- polymers, soft metals Au and Pb
- local Plastic deformation before crack propagates
- high energy stored
- cup and cone surface morphology (dimple texture)
- slope (45 degree)
Mixed fracture
- carbon steels and engineering alloys
- bit of necking followed by brittle failure
Steps for brittle failure
- low applied force = uniform stress
- high enough applied force = cracks formed = crack tips stress concentrations with stress higher than initial constant stress
- crack propagates = failure
- stress maximum = stress at failure
- stress at fracture is a measure of a material’s ability to resist breakage of interatomic bonds
- theoretical strength = Young’s modulus divided by 10
Summary: crack spreads rapidly even without more applied stress, deemed unstable
Steps for ductile failure
- Start loading = Necking
- At crack tips = stress concentrations limited at the yield strength by local plastic deformation in front of crack tip –> creation of microvoids
- Microvoids expands and merge to advance crack tip
Summary: a lot of plastic deformation at crack site, propagates slowly so crack is deemed stable,
Brittle to Ductile transition
Material can change behaviour based on temp and sometimes these changes are irreversible
Eg steel = brittle at low temp
PVC = high temps = brittle
Ductile vs brittle failure
Ductile
- via plastic deformation
- yield strength of metals decreases as temp increases
- because energy increases –> easier to break bonds/ dislocation slips easier–> yield strength decreases
Brittle
- via cleavage of interatomic bonds
- fracture strength required for cleavage insensitive of temps - once material is brittle not much change occurs after that
Ductile Brittle Transition temperature (DBTT)
- Material with DBTT ductile at high temp and brittle at low temps
- temp at which behaviour changes = DBTT
- materials with low strength ( FCC= pure metals, Cu, Ni ) = yield strength is less than fracture strength = always fracture via ductile failure
- materials with high strength (BCC = steel alloys, HCP = Zn alloy) = yield strength is greater than fracture strength = fail in brittle manner
Charpy test
Measures DBTT
Impact vs temp curve
mgH - mgh
Stress near singularities
tips of cracks in materials= stress risers
magnitude of stress-dependent on the geometry of crack and material
For an elliptical-shaped crack = stress max = initial uniform stress multiplied by 1 +2 times (crack size divided by the crack radius of curvature ) to a half
- larger crack = higher stress concentration
- smaller radius of curvature - sharper tip = higher stress
Stress intensity factor
- stress alone not valid to predict fracture failure of materials
K = (Y)(theta)Square root(pi * a)
What is simple fracture?
separation of a body into two or more pieces in response to an imposed stress that is static
Classification of type of fracture is based on…
Ability of material to experience plastic deformation
What type of applied stresses result in fracture
- compressive
- tensile - what we focus on in this unit!!
- shear
- torsion
Fracture toughness
Increase load K increases when K is at a critical value = Kc = fracture toughness
Mechanical criterion for brittle fracture
K >= Kc
Three modes of fracture propagation
- Plain strain fracture or Normal tensile mode Kic
- Sliding mode Kiic
- Tearing mode Kiiic
Comparing Kc
Metals - high
Ceramics - Mid
Polymers - Low
Designing with Kc
- designing against brittle fracture and yielding
- K <= Kc
- Maximum crack size tolerance
Designing against fracture
- determined by applied stress and pre-existing cracks captured in stress intensity factor (K)
- K = (Y)(theta)Square root(pi * a)
- Kic = fracture toughness = given value
- Failure criterion K= Kic or (Y)(theta)Square root(pi * a) = Kic
L15 What is fatigue
- failure by a material after cyclic stresses
- cycles of fluctuating stress
- 90% of failures
- striations
Characteristics of fatigue
- occurs at lower stresses than the tensile yield strength for static loads
- occurs after a lengthy period of time of repeated stresses and strain cycling
- brittle manner even in ductile materials
- Catastrophic - sudden and without warning
Low cycle fatigue failure
< 10^4 -10^5
- high loads - elastic and plastic deformations
- limited lifetime of important components
High cycle fatigue failure
> (greater)10^4 - 10^5 cycles
low loads - elastic deformation
common - despite designing the material below yield strength continual unloading and loading can lead to failure
How fatigue occurs
- Crack initiation
- at surface
- flaw/ scratch
- defects on surface - Crack growth
- incremental growth of crack after every cycle
- beach mark - mm - macroscopic - each band is a display of growth over multiple cycles
- striations - microscopic - advance of a crack after a loading cycle - Final failure
- area is insufficient to hold the load
- can be brittle or ductile
- surface texture points to origin of crack
What do beach marks look like
What do striations look like
Applied stress may be
- Axial (tension/compression)
- Flexural (bending)
- Torsional (twisting)
cyclic with fluctuating stress modes
Reversed cycle
- fixed frequency
- amplitude is symmetrical about mean stress zero
- Stress max = - stress min
stress mean = 0
range of stress = - 1
Repeated cycle
- sinusoidal time dependency
- fixed frequency
- max and min are asymmetric
Random
non-sinusodial
- frequency and amplitude are random
Cyclic stress parameters (Stress)
Mean stress = 1/2(stress max + stress min)
Range of stress = stress max - stress min
Stress amplitude = 1/2 range of stress
Stress ratio = stress min/ stress max
SN curves
- used to predict fatigue life
- ## displays stress amplitude versus no of cycles to fatigue failure
Materials with fatigue limit
Materials with fatigue limit = ferrous metals + Ti alloys - Stress level below which material will never fail by fatigue - above which stress increases and no of cycles to failure decreases
- for materials with fatigue limit = fatigue strength = stress at which material will survive 10^7 fatigue cycles
Materials without fatigue limit
- non- ferrous metals
- Al, Cu, Mg
Fatigue life (no of cycles to failure at a particular stress) increases and lowered stress amplitude
Factors that affect fatigue failure
draw diagrams
a) Mean stress - as mean stress increases fatigue life decreases
Materials with lowest mean stress - highest possible stress amplitude
b) Stress raisers decrease fatigue life
- notches
- grooves
- holes
- shaper discontinuity = more severe stress concentration
Improving fatigue life
- Lower mean stress
- reduce stress raisers
- impose surface residual compressive stresses by shot peening
- improve surface harness - rough, fine grinding, honing, polishing (most expensive)
