Fractures- Crack Closure Flashcards
Stress intensity factor ratio
R=Kmin/Kmax=σmin/σMax
What does R mean for crack growth?
Crack growth is faster for higher R. Means in part of stress range growth doesn’t necessarily occur. So ΔKeff<=ΔK
Why does crack closure happen?
Plastically deformed material in the plastic zone has an increased equilibrium size. No constraint along the crack surfaces. The plastically deformed material can expand into the open crack and the crack closes sooner than otherwise expected. Means crack closure can occur whilst applied stress is still tensile.
Graph of stress cycles with locations of σmax, σmin and σop
Peaks are at σmax. Troughs are at σmin. A little bit above this is σop (opening stress). Crack is open (and growth can occur) above this and crack is closed (no growth) below.
What is ΔK for no crack closure?
Kmax-Kmin
What is ΔKeff with crack closure?
ΔKeff=Kmax-Kop
More accurately ΔKeff=Kmax-Kmin,eff but Kmin,eff is unmeasurable
Graphs of K vs stress for crack closure and no crack closure
No crack closure: straight diagonal line up from (σmin, Kmin) to (σmax, Kmax). Line has height ΔK and width Δ σ
With crack closure: straight diagonal line up from (σop, Kop ) to (σmax, Kmax). Height of this part is ΔKeff. There is a shallower curve down to Kmin,eff from Kop between σop and σmin.
What does crack closure mean for the Paris equation?
da/dn=A(ΔKeff)^m
=A(Kmax-Kop)^m
=A(UΔK)^m
Where U is ΔKeff/ΔK
At what R is crack closure minimal?
High values of R
Typical graph for ΔKeff/ΔK vs R
Curve up from about 0.3 to 1 between R=-1 and 1
What changes about graph of da/dn vs ΔK1 when crack closure is considered?
When no crack closure, different values of R gives different lines (diagonal ish upward) that are spaced out a bit (more positive R line is further left). When crack closure, ΔKeff is used and the lines for different R are very close to each other (basically overlap).
Describe an example of overloads
Single overload in otherwise uniform cyclical loading pattern
What happens when there is a single overload?
Initially crack grows more quickly due to higher maximum stress. But higher max stress means higher max stress intensity factor. This means larger plastic zone ahead of crack tip by ry proportional to (K1/σys)^2. Material in plastic zone permanently deformed and its equilibrium size is larger.
What does the plastic zone mean for surrounding material?
Most stages of fatigue plastic zone is relatively small and surrounding material can constrain it. Means residual stresses present which are compressive in the plastic zone and at least equal to yield stress. There are tensile residual stresses just beyond plastic zone shown on diagrams from lecture 8 slide 17
Describe residual stresses and plastic zone immediately following overload
If σoverload=2σmax, roverload=4ry. Plastic zone starts from crack tip. Compressive residual stresses out from the width of the new larger plastic zone. Tensile residual stresses start from edge of new plastic zone. Residual compressive stresses at crack tip much higher than before overload. See slide 18 for diagram.
