Fractures- Plastic Zones Flashcards
What is wrong with assumptions with cracks so far?
Real materials cannot support infinite stresses so there cannot be infinite stresses at crack tips as previously assumed.
Irwin plastic zone correction
Assume circular plastic zone ahead of crack tip. Yield stress cannot be exceeded. Effectively throws away excess stress (problem). Uses σyy(x, 0)=K1/rt(2πry)=σys
Gives ry =(1/2π)(K1/σys)^2
r subscript y is diameter of circular plastic zone
Second Irwin plastic zone correction
Still assumes circular plastic zone ahead of crack tip. Treats plasticity as equivalent to increase in crack length. Calculate stress field using position of effective crack tip. See page 6 lecture 4 for diagram and graph. Get same equation but ry now radius of plastic zone.
How is plastic zone size determined at failure?
Use K1c and the yield stress of material
How much does ry vary for ductile and brittle materials?
A lot. For diamond is similar to bond lengths. Glass is a few interatomic distances. Steel can be mm or cm.
Dugdale-Barenblatt approach
Assumes linear plastic region not circle.
Get Δa=(π/8)(K1/σys)^2
Von Mises formula for principal stresses
(σ1-σ2)^2+(σ2-σ3)^2+ (σ3-σ1)^2=2σys
Where σ1,2=(σxx+σyy)/2 +-rt((σxx+σyy/2)^2+σxy^2)
+ for σ1 and - for σ2
Where to find formulae for Von Mises near tip stress field based on angle
Page 15 lecture 4
Where to find formula for σ1,2 based on angle
Page 16 lecture 4
Where to find formula for r(θ) for plane stress
Page 17 lecture 4
Where to find formula for r(θ) for plane strain
Page 18 lecture 4
Where to find plastic zone shapes as function of poissons ratio?
Diagrams on page 19 lecture 4
What happens when plane of crack meets outer edge of material?
In the centre, there is plane strain and the plastic zone is smaller. At the ffee surfaces there is plane stress and plastic zone is bigger.
