Types of Fatigue Outline • Fatigue F ti - Review R i • Fatigue crack initiation and propagation • Fatigue fracture mechanics • Fatigue fractography • Crack propagation rate • Example • Factors affecting fatigue - Design factors - Surface S f effects ff - Environmental effects
Occurs under dynamic stresses 90% of metal failures occur in fatigue! Occurs in all kinds of materials Usually breaks ………………….; no, or very little little, observable plastic deformation (some micro-deformation).
…
…….
low cycle fatigue
- high loads → short Nf (104-105 cycles) high g cycle y fatigue f g – low loads → long Nf (>105)
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/1
Dr. M. Medraj
•
• Fatigue data is normally shown as ……….. values. • It is very useful to evaluate the probabilities of fatigue failure at certain stress level. This is more accurate than “average” values.
MECH 321 lecture 11/3
Three steps: Th t – …………….. – …………….. – final fi l ffailure il (when ( h area decreases d sufficiently)
•
Fatigue life:
•
Nf = Ni + Np – Ni is the number of cycles to initiate fracture – Np is the number of cycles to propagate to failure high cycle fatigue (…… stress levels): – most of the life is spent in crack initiation and Ni is high low cycle fatigue (…….. stress levels): – propagation step predominates and Np>Ni
•
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/2
Crack Initiation and Propagation
Variability in Fatigue Data
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Dr. M. Medraj
Figure g 6.48 Schematic rep. p of
a fatigue fracture surface in a steel shaft. When the crack length exceeds a ………. value at the applied stress, catastrophic rupture occurs. “The science and Engineering of Materials 4th edition by D.R. Materials” DR Askeland and P.P. Phule.
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/4
Fracture Mechanisms
Fracture Mechanisms
Cracks C k th thatt cause fatigue f ti failure f il almost l t always l initiate/nucleate i iti t / l t att component surface at some stress concentration: scratches, dents, fillets, keyways, threads, weld beads/spatter…..
• Fatigue crack propagation mechanism (stage II) by repetitive crack tip plastic blunting and sharpening; • Double notch at crack tip, extends along shear planes
On very smooth surfaces, SLIP steps can act as stress raisers. • •
• •
•
zero tensile load or maximum comp. load
stage I propagation crack tends to grow initially along crystallographic planes of high shear stress: high stresses and notches tend to shorten this stage. It may only propagate over a few grains. Length of stage I is controlled by presence of stress raisers such as: – ……………. – ……………. – ……………. stage II - crack growth rate increases (perpendicular to tensile stress direction)
• leading to sharp notches again maximum tensile load
zero tensile load or maximum comp. load MECH 321 lecture 11/5
Dr. M. Medraj
Fractography of Fatigue • • • •
small compressive load
small tensile load.
• And then again and again……. Sometimes S i this hi process leaves l markings on the fracture surface; …………… and/or …………... Indicate position of crack tip at some point in time.
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/6
Fractography of Fatigue
beachmarks are macroscopic evidence of fatigue and can be observed with the naked eye → classical fatigue fracture surface (clam-shell markings) always concentric with the fracture origin caused by interrupted loading, e.g. machine being switched on and off duringg stage g II ppropagation p g Origin ee.g. g Beachmarks may represent an 8hr daily shift: for a shaft operating p g at 3000 rpm, total number of cycles per day is ……………
These marks DO NOT i di t the indicate th crackk growth th per stress cycle.
• under tensile loading and then blunts due to deformation • Compression closes crack and shear occurs in opposite sense
Mech. Eng. Dept. - Concordia University
Dr. M. Medraj
small tensile load
H However, f i fatigue striations i i are microscopic i i andd require i a scanning i electron microscope (SEM) to observe them • each beachmark is composed of thousands of striations • results from incremental advance of the fatigue crack during stage II • propagation region of crack is usually relatively smooth and often discoloured in relation to the final fracture
- Each of these microscopic striations is usually caused by one stress cycle. - If the stress increases, the spacing usually increases.
Final failure
- Can count striations/mm to get ESTIMATE of crack growth rate. Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/7
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/8
Fractography of Fatigue
Fractography of Fatigue
• Beachmarks and striations will not appear on that region over which the rapid failure occurs. • Rather, Rather the rapid failure may be either ductile or brittle; - evidence of plastic deformation will ill be b presentt for f ductile d til failure f il andd absent for brittle failure.
Figure 6.47 Fatigue fracture surface. (a) At low magnifications, the beach mark ppattern indicates fatigue g as the fracture mechanism. The arrows show the direction of growth of the crack front, whose origin is at the bottom of the photograph. (b) At very high magnifications, closely spaced striations formed during fatigue are observed (x 1000). From “The science and Engineering of Materials” 4thh edition by D.R. Askeland and P.P. Phule.
• This region of failure may be noted in the following figure.
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/9
Fatigue Crack Propagation rate • Results R lt off fatigue f ti studies t di have h shown h that th t the life of a structural component may be related to the rate of crack growth. • During stage II propagation, cracks may grow from a barely perceivable size to some critical length. • Experimental techniques are available that are employed to monitor crack length during the cyclic stressing. • Data are recorded and then plotted as crack length a versus the number of cycles N.
From fracture mechanics:
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Dr. M. Medraj
MECH 321 lecture 11/10
Fatigue Crack Propagation rate rapid crack growth just prior to final fast fracture da = A((Δ ΔK ) m dN and then taking logs of both sides :
Initial crack length
⎛ da ⎞ log ⎜ ⎟ = m log ΔK + log A ⎝ dN ⎠ gives straight line of slope m and intercept, logA
(1) initially, growth rate is small, but increases with increasing ……………….. (2) growth rate increases with increasing applied stress level and for a specific crack length.
ΔK = Kmax-Kmin (stress intensity not KIc). If σmin is compressive, it closes the crack so σmin and Kmin are taken as being zero.
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/11
- crack grew even though Kmax < Kc - m is typically from 1 to 6 - crack grows faster if • Δσ increases • crack gets longer • loading freq. increases.
At low stress levels and/or small crack si es pre sizes, pre-existing e isting cracks will ill not grow with cyclic loading. Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/12
Fatigue Crack Propagation Rate
Fatigue Crack Propagation Rate
Logarithm crack growth rate versus logarithm stress intensity factor range for a Ni–Mo–V steel.
One goal of failure analysis is to predict fatigue life of a component, given its service conditions. We are able now to develop analytical expression for Failure by integrating in the linear region: da which when integrated gives : A(ΔK ) m Limits are initial flaw length, ao which can Nf ac da be determined by NDT, and critical crack Nf = dN = m l length h ac, which h h can bbe determined d d from f 0 a0 A( ΔK ) fracture mechanics
• So, So a straight-line straight line segment will result when log(da/dN)-versus-log K data are plotted • the slope and intercept correspond to the values of m and log A, respectively. • A & m are material constants
dN =
∫
∫
Substitution for ΔK gives : N f =
∫
ac
a0
da A(YΔσ πa )
m
=
Aπ
1 (Δσ ) m
m2
∫Y ac
a0
da am 2
m
• this results when assuming that ΔK and Δσ are constant (which often are not) • Also ignores the time needed to initiate the crack. ⇒ This analysis is only an estimate. Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/13
Mech. Eng. Dept. - Concordia University
Dr. M. Medraj
Example
MECH 321 lecture 11/14
Factors Affecting Fatigue Life
A relatively l ti l large l sheet h t off steel t l is i to t be b exposedd to t cyclic li tensile t il andd compressive stresses of magnitudes 100 MPa and 50 MPa, respectively. Prior to testing, it has been determined that the length of the largest surface crack is 2.0 mm. Estimate the fatigue life of this sheet if its plane strain fracture toughness is 25 MPa√m and the values of m and A are 3.0 and 1.0 x 10-12, respectively, for Δσ in MPa and a in m. Assume that the parameter Y is independent of crack length and has a value of 1.0.
• Important factors are: – mean stress level – geometrical design – surface condition – metallurgical structure – environment Mean Stress (σm) •
in stress reversal, σm= 0
• σm > 0, then S-N curve moves to lower values • Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/15
fatigue life …………. Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/16
Effect of Mean Stress
Geometrical Effects Design D i F Factors • component design is important • notches or stress raisers act as crack initiation sites for fatigue: – grooves, scratches, keyways, threads corrosion pits etc. threads, etc
• sharp corners and radii, any discontinuities – all increase the stress concentration
• rounded fillets where gradual changes of diameter occur in shafts • Scratches and machining marks reduce the fatigue life • Surface polishing …………. the fatigue properties Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/17
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/18
Geometrical Effects
Geometrical Effects
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/19
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/20
Effect of Welding
Effect of Surface Conditions
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/21
Surface Treatments
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/22
Effect of Welding and Shot Peening
• shot peening localized micro-plastic deformation using i small ll steel t l balls b ll (shot) ( h t) impacting i ti on surface. f • It increases the fatigue properties significantly (aircraft components etc) also increases yield strength, h hardness h d andd fatigue f i life. lif • work hardening occurs in the surface – …………… surface hardness – introduces a residual ………..……... stress Surface burnishing Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/23
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/24
Surface Treatments
Effect Shot Peening on Mean Stress
Case Hardening: • Surface hardening g through g carburizing or nitriding increases surface strength and hardness • iron carbide or nitrides (hard) form in the surface layer to ~1mm depth or greater • increase i in i hardness h d i increases th the resistance to fatigue. • compressive stress in case hardening also generated due to difference in volume of case layer
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/25
Dr. M. Medraj
Effect of Materials Composition
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/26
Effect of Grain Size
MECH 321 lecture 11/27
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/28
Environmental Effects
Environmental Effects
Thermal Fatigue • created at high temperature by fluctuating thermal stresses (σt ) • restraint in thermal expansion/contraction during uneven heating/cooling σt = E αl ΔT • αl is the linear thermal expansion coefficient • E is the modulus of elasticity • ΔT is the temperature difference, αl ΔT is the thermal strain εt • can be minimized by careful design – elimination of restraint and temperature gradients (use expansion gaps) – consideration of physical properties, (materials CTE, k) Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/29
Next time:
Creep
Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/31
Corrosion Fatigue • simultaneous i lt effect ff t off cyclic li stress t andd chemical h i l attack tt k • formation of pits leading to stress concentration on surface and nucleation of fatigue cracks • corrosion can enhance crack growth rate • prevention is by: – protective coatings (painting, galvanizing) – selection of more corrosion resistant material – reducing the corrosive environment –………………………………………… –………………………………………… Dr. M. Medraj
Mech. Eng. Dept. - Concordia University
MECH 321 lecture 11/30
