1. Doç.Dr.M.Evren Toygar, DEÜ
Elastic - Plastic Fracture Mechanics
Application of LEFM ve EPFM with respect to Fracture Behaviour
LEFM: 1) For high strength materials at Plane Strain Case
2 ) For high strength materials at Plane Stress Case
EPFM: 1) For high strength materials at Plane Stress Case
2) For Ductile Materials at Plane Stress Case or Plane Strain Case
3) Ductile materials that have plasticity
Plastic Failure: Fully plastic Deformation of ductile materials
Doç.Dr.M.Evren Toygar, DEÜ

2. Doç.Dr.M.Evren Toygar, DEÜ
LEFM and EPFM
In LEFM, K is the stress intensity factor that identifies stress and displacement at the tip of the crack. K indentifies not only stress and strain magnitudes but also resistance of materials and the crack tip behaviours due to loading. K value depends on both stress and crack length.
The stress statements near the crack tip for plane strain case when the crack a exists
Doç.Dr.M.Evren Toygar, DEÜ

3. Doç.Dr.M.Evren Toygar, DEÜ
LEKM
For =0
Tekillik bölgesi
According to Irwin: if the plastic zone size less than the size of singularity then, LEFM is valid.
If not, Dugdale yield model for plane sterss case is:
ASTM: a, B, W-a , namely , specimen dimension.
Doç.Dr.M.Evren Toygar, DEÜ

4. Doç.Dr.M.Evren Toygar, DEÜ
EPFM
Two parameters used in EPFM :
crack opening displacement (Çatlak ucu deplasmanı) (COD) veya crack tip opening displacement (çatlak ucu açılma miktarı) (CTOD).
J-integral.
All two parameters give the fracture toughness measurement results independent of geometry. y
Sharp crack x
Blunt crack
Doç.Dr.M.Evren Toygar, DEÜ ds

5. CRACK TIP OPENING DISPLACEMENT- CTOD
WELLS, has obtained the relations between CTOD and stress intensity factors with approximate analysis.
IRWIN has obtained the effective crack length a + rp due to plasticity at the tip of the crack.
Doç.Dr.M.Evren Toygar, DEÜ

6. Doç.Dr.M.Evren Toygar, DEÜ
EPFM
According to Wells: In LEFM conditons, at structural steel to do KIC measurement, the thickness of specimen has to be large and the plastic deformation makes the crack tip as blunt.
Sharp crack ;
Blunt crack
Irwin’s effective crack length, a + rp and plane stress case:
Doç.Dr.M.Evren Toygar, DEÜ

7. CTOD Plane Strain Energy Release Rate
Equation can be obtained when the small-scale
yield occurs. Here CTOD is related with G (strain energy release rate).
Wells : is valid for large –scale yield and it is related with J integral
Dugdale yields strip model: is the opening amount at the tip of the crack
Crack tip opening displacement with respect to yield strip model
Doç.Dr.M.Evren Toygar, DEÜ

8. CTOD Plane Strain Energy Release Rate
Infinite plate with a crack
Taylor series expansion,
If and can be
Obtained as:
Doç.Dr.M.Evren Toygar, DEÜ

9. CTOD Plane Strain Energy Release Rate
Generally:
Dugdale Model:
Dugdale : examined the plastic zone size for thick plate at plane stress case
Doç.Dr.M.Evren Toygar, DEÜ

10. Doç.Dr.M.Evren Toygar, DEÜ
CTOD
Blunted crack
Sharp crack
Blunted crack
Original displacement at he crack tip
Displacement at 900 line intersection, suggested by Rice
CTOD Measurement by using bending specimen
deplasman Vp ' '
Doç.Dr.M.Evren Toygar, DEÜ '

11. SENB Specimen Elastic-plastic analyses
V,P
Here, has the value 0.44 for SENT specimen
ASTM E standards:
At experiments both CT and SENT specimens can be used.
cross sectional area: for rectangle W=2B; or for square W=B can be taken
the following equation KI can be used
CTOD Equation
Doç.Dr.M.Evren Toygar, DEÜ

12. Doç.Dr.M.Evren Toygar, DEÜ
J-kontur Integral y x ds
Define the path around the crack ( ) tanımlayalım. J-integral :
Here w is the strain energy density and ,
Ti is the component of the perpendicular traction vector.
Doç.Dr.M.Evren Toygar, DEÜ

13. Doç.Dr.M.Evren Toygar, DEÜ
J- Integral
Linear Elastic Behavior :
J Integral : G (is the strain energy release rate for the unit crack extansion)
:Plane stress case
:Plane strain case
Doç.Dr.M.Evren Toygar, DEÜ

14. Doç.Dr.M.Evren Toygar, DEÜ
J- Integral
2) J Integral for both Elastic and Plastic Behaviour :
: the path at the crack around
w : is the strain energy density
T : is the perpendicular traction vector
n : normal to the surface
u : displacement vector
ds: is the inctement of the length along the path
Doç.Dr.M.Evren Toygar, DEÜ

15. Doç.Dr.M.Evren Toygar, DEÜ
J- Integral
J = Jelastic+ J plastic
For the edge notch specimen when the plane strain case
Doç.Dr.M.Evren Toygar, DEÜ