Part 1 Flashcards
What is the difference between a total life approach and a defect-tolerant approach?
Total life approach considers 1.initiation of crack 2.crack growth and 3.failure after Nf cycles
Defect-tolerant approach considers already flawed specimens; focuses on crack growth (to failure) only
What is HCF and what characterizes it?
HCF -High Cycle Fatigue:
low stress high number of cycles low plasticity:(expect SSY) -Small scale yielding (can apply hooke’s law) -Dimensioning against stress life
What is LCF and what characterizes it?
LCF - Low Cycle Fatigue: high stress low number of cycles high plasticity (expect LSY): -Large scale yielding (can apply Ramberg-Osgood) -Dimensioning against strain life
Explain safe-life
Safe Life:
do experiments on components with typical load conditions to find the safe life cycle Nx which does not give failure. Change the part after Nx is reached even if it is needed or not.
Explain fail-safe
Fail-safe:
even if a part of the structure fails the structure should be able to operate safely until crack is detected
also known as redundancy
periodical inspections
What is RFC?
Retirement for cause
inspect and replace if needed
not like safe life
What is ”Leak-before-break”?
1) an example of the Fail-safe approach
2) widely used in structural design of pipes and vessels
the pipe leaks before it breaks
- the fatigue flaw can easily be detected and repaired
- crack length a< ac (critical length)
- (can still be used)
What is the influence from hydrostatic pressure on plasticity in metals?
No influence
Since the plasticity in metals only depends on the shear stresses the hydrostatic pressure has no influence on the plasticity. This because in hydrostatic pressure sigma1=sigma2=sigma3and when this occurs the shear stresses equals zero.
What are the flow surfaces according to von Mises?
von Mises
-right circular cylinder
What are the flow surfaces according to Tresca?
Tresca
-regular hexagonal prism
If the flow surface is given by the function f(σij), what are the implications f(σij)>0,
f(σij)=0 and f(σij)<0?
f(σij)=0
yielding occurs
f(σij)<0
material is elastic
When are Maxwell and Kelvin-Voigt models useful?
Models for handling viscoelastic behaviour ; fit’ the creep response of metals and polymers with greater degrees of precision.
Describe Maxwell
series arrangement of dashpot and linear spring
Describe Kelvin-Voigt
parallel arrangement of dashpot and linear spring
Define resolved shear stress
The shear stress acting on the slip plane
Why is the resolved shear stress important?
The slip plane with the highest resolved shear stress will slide first (determines whether a plane will slip)
What is Schmid´s law?
Stating that slip will occur if the resolved shear stress in the slip direction reaches Tc
What is the Schmid-factor?
T = sigma * m
m is the Schmid factor; m= cos(phi) *cos(lambda)
What is meant by hardening of a metal?
- hinder dislocations in the metal
- ex. plastic deformation (strained past yield point)
- generates dislocation
- hinder each other - increases stress fields
What is meant by softening of a metal?
- more ductile
- often when heating a material
- dislocations can move easily
What is the critical plane approach?
Refers to the analysis of stresses and strains as they are experienced by a particular plane in a material, as well as the identification of which plane is likely to experience the most extreme damage
( stays fixed relative to the loading axis.)
How is a S-N-curve constructed?
Plotting the stress amplitude sigma_a to number of cycles to failure N_f
This is done by experimental data, fatigue testing in plane bending, rotating bending etc.
Define fatigue limit.
Below the fatigue limit, the specimen can be used indefinitely without causing failure. This stress amplitude is called the fatigue limit or the endurance limit.
How is the fatigue limit defined if the S-N curve do not approach a constant value?
If no constant value is approached in the curve, the fatigue limit is defined as the stress amplitude which the specimen can support for at least 10^7 fatigue cycles.
Which is the Basquin equation and when does it apply?
When the total life is observed, one can choose either Wöhler or Basquin. Both of these assume sigma_a= constant
It applies for a fully-reversed (R= -1), constant-amplitude fatigue test, to relate the stress amplitude, to the number of load reversals to failure. Basquin assumes sigma_m= 0
(Applies for total fatigue life at hcf)
Define the diagram in which the Basquin equation is a straight line. What is the slope of the line?
log(sigma_a) - log(Nf)
slope = A_B= b
Define R
Load ratio: R =sigma_min/ sigma_max
Describe thre different R ratios
R= -1 for fully reversed loading, R=0 for zero-tension fatigue, and R=1 for a static load.
How is a mean stress ≠ 0 , i.e. R ≠ −1 compensated for?
When the mean stress is not zero, the S-N curve will change. Life will be shorten if the mean stress m increases (it will open the possibility for cracks).
What are Soderberg, Gerber, Goodman and Haigh-diagrams?
Soderberg. goodman, gerber and Haigh compensates for Wöhler diagrams
What is the Palmgren-Miner rule? Which objections can be raised against?
Suggests that big amplitudes followed by small ones behaves the same as the opposite order.
Coaxing -extends fatigue limit if small amplitudes come first
big amplitudes first → might just require small amplitude before it breaks
tensile overloads applied to notched and cracked metallic materials reduce the rate of fatigue crack growth and that the application of compressive overloads generally has the opposite trend
How can residual stresses be enforced?
Residual stresses are generated in a component as a consequence of thermal, chemical or mechanical treatments
Name some ways to achieve residual stresses
shot-peening, quenching, phase transformations, fabrication techniques
Why are residual stresses helpful?
compressive stress field can reduce crack growth
Define Kt
theoretical elastic stress concentration factor. relates local stress of the notch to the far field loading
Define Kf
= unnotched bar endurance limit/notched bar endurance limit
Define q
q notch sensitivity factor (effect from the notch)
What are the implications of q=1 and q=0?
q =0 no notch effect
q= 1 full notch effect
How is Kf used at HCF?
The stress life approach is used for HCF ahead of stress concentrations by modifying the endurance limit of the unnotched specimen .
Why is Kf only applied to stress range?
HCF: Dimensioning against stress life with LEFM Hooke’s law.
Divide by Kf (conservative results)
How is a multi axial stress state treated?
von Mises or Tresca
What is proportional and non- proportional loading?
Proportional loading: if the stress tensor varies in constant proportion to one another during changes/fluctuations in the loads.
sigma_2/sigma_1=lambda_1
How is the critical plane-approach applied at non-proportional loading?
Non-proportional → orientation of critical plane will vary –>
- identify orientation of the plane (based on some crietria such as mas normal stress
- esitmate number of cycles to initiate a fatigue crack
When should the Coffin-Manson relation be applied?
Relating plastic strain amplitude to number of cycles to failure. (Strain life approach)
How is σ m ≠ 0 compensated for?
Morrow (modified Basquin)
The Neuber rule reads: Kf=(K_sigma*K_epsilon)^0.5. What is the rational for this?
In the elastic case, the stress and strain concentration factors increase equally. But for the plasticity, these concentration factors take different values (at the tip of the notch).
What is the Neuber hyperbola?
It is used with the Ramberg- Osgood curve to intersect a limiting value point (max,max).
How is the Neuber hyperbola used?
Limits the stress and strain allowed at the notch!
How can an effective strain be determined?
Using von Mises distortional energy theory or the Tresca yield theory.
What is the Griffith fracture theory?
the decrease in potential energy of the system must equal the increase in surface energy
Define the energy release rate G.
G is the crack driving force, also known as the energy release rate.
It is defined as:
G = - dWp/dA =dWs/dA
where Wp is the total mechanical potential energy of the cracked plate, Ws is surface energy, and A = 2aB
The fracture criterion is G=Gc. What holds for dG/da?
dG/DA > 0 –> unstable (load control)
dG/dA< 0 –> stable (displacement control)
Define mode I, II and III. Which is most common?
Mode I - force applied perpendicular to the crack surface
most common
Mode II - force applied parallel to the crack surface, perpendicular to the crack front
earthquake
Mode III - force applied parallel to the crack surface, parallel to the crack front
torsion (seldom)
Define the stress intensity factors.
the stress intensity factor is a measure of the intensity of the near-tip fields under linear elastic conditions.
Why is, always, KI >=0?
Because it’s dependant on the external load.
What is the T-stress?
Contains the non-singular stress sigma_xx=T, it is constant in the x-direction. It can introduce significant errors in certain fatigue situations.
What is K-dominance?
The region of K-dominance is known as an annular zone ahead of the crack tip, within which the stress intensity factor provides a unique measure of the intensity of stress, strain or deformation.
What is the fracture toughness KIc?
Fracture will occur if KI reaches KIc. It has been measured under plane strain conditions at a particular temperature.
State the Paris Law
The growth of a crack under cyclic loading should be governed by the ‘law’
da/dN=C dK^m
What is the J-integral measuring?
The J-integral measures the energy that flows in the crack tip
How is Crack Tip Opening Displacement, CTOD, defined?
distance between the crack faces varies as the crack tip is approached. Therefore, 2 45 degree lines are drawn from crack tip to crack faces. The CTOD is the vertical distance in between these interception points.
How can CTOD be used as a fracture criteria?
The crack tip opening displacement provides a measure of the size of the region at the crack tip where finite strain deformation is dominant.
What is J-dominance?
When we have a crack in SSY (small scale yielding) then there is an annular zone called K-dominance. A smaller zone called J-dominance is present. If we increase the load we go from SSY to Elastic-Plastic condition, then the K-dominance disappears and J-dominance grows and take its place.
Which is, according to ASTM, the limit for the use of LEFM? How is this limit
defined?
all measures > 25 * plastic zone
How is a hydrostatic stress state in the vicinity of a crack tip compensated for?
J-Q theory
