1. ON THE CHALLENGING FEM APPLICATION FIELDS IN THE FRACTURE MECHANICS
Institute of Physics of Materials, AS of CR, Brno, Czech Republic
ON THE CHALLENGING FEM APPLICATION FIELDS IN THE FRACTURE MECHANICS
Vladislav Kozák

2. Outline 1. Introduction 2. Local approach -Beremin 3. GTN model
4. Cohesive-zone modelling
5. Summary

3. 1.Introduction FTTD SSY stress control fracture deformation control
lower transition
upper
stress control
fracture
SSY
deformation
control
fracture
lower
bound
upper
bound
transition

4. Three different approaches to the damage modelling
no damage evaluation, elasto-plastic constitutive equation, process zone is small, K, J, C*
separation of surfaces is admitted, material outside is described conventionally, the process zone is some surface region, fracture criterion is cohesive law
softening behaviour is introduced into the constitutive model, e.g. accumulation of damage, described by additional internal variables, GTN

5. Plastic zone ahead the crack tip
region:
condition SSY
large deformation
J-integral conception K faktor conception
non defined only by one parameter
condition
elasto-plastic
conditionLSY

6. 2. Local approach - Beremin
·    Beremin model
1. averaging stresses over FPZ
2. probability of fracture
·    Extension to Fracture Mechanics
1. direct toughness prediction for SSY
2. TSM, Minami, Koppenhoefer, Ruggieri

7. Local parameters technique determination

9. 3. Gurson-Tvergaard model (GT)
nucleation
HMH
plasticity GT
plast. f0 fC D
fN = 0,004
eN = 0,3
SN = 0,1
f0 = 0,005
fC = 0,035
q1 = 1,5; q2 = 1
D = 0,2 mm

10. GT x GTN model dfnucl.=Adep q1, q2, q3 are used to adjust the model
fu * fc fF f GT
GTN
q1, q2, q3 are used to adjust the model
sm is hydrostatic stress
sYS is yield stress
f* is void fraction, fc is the critical void fraction for coalescence
fF is the final value of f, fu*=1/q1.
dfnucl.=Adep

11. material parameters identification
void distribution in non-affected area
void distribution in the neck area
of the round tensile bar
500 mm
f1=0.0073
f2=0.0073
f3=0.0083
f4=0.0126
f5=0.0131
f6=0.0349

12. the influence of the mesh size on the curve elongation-contraction

13. varying values of f0 and fN and determination of input data
f0 = 0.005, fF (fC) = q1 = 1.5, q2 = 1 (q3 = q12)
fN = 0.004
eN = 0.3, SN = 0.1

14. 3PB SE(B) L = 250 mm l = 200 mm W = 50 mm B = 25 mm a = 25,25 mm W a

15. mesh size
2.5 mm
D/2

16. J
J0.2BL
JI SZW
J0.2 JI Da
0.2 mm
DaSZW
FEM J=1,39syDa

17. The influence of q2 on the values of J-integrálu at stable crack initiation
The influence of the h parameter (triaxiality parameter)

18. 4. Cohesive-zone modelling

19. ductile

20. crack path

21. 5. Summary
The coincidence of the results of the numerical modelling and the experiment is generally the basic criterion.