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

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

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

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

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

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

Local parameters technique determination

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

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

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

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

varying values of f0 and fN and determination of input data f0 = 0.005, fF (fC) = 0.035 q1 = 1.5, q2 = 1 (q3 = q12) fN = 0.004 eN = 0.3, SN = 0.1

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

mesh size 2.5 mm D/2

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

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

4. Cohesive-zone modelling

ductile

crack path

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