ON THE CHALLENGING FEM APPLICATION FIELDS IN THE FRACTURE MECHANICS

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ON THE CHALLENGING FEM APPLICATION FIELDS IN THE FRACTURE MECHANICS. Institute of Physics of Materials, AS of CR, Brno, Czech Republic. Vladislav Kozák. Outline. 1. Introduction 2. Local approach -Beremin 3. GTN model 4. Cohesive-zone modelling 5. Summary. 1.Introduction FTTD.

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### ON THE CHALLENGING FEM APPLICATION FIELDS IN THE FRACTURE MECHANICS

Institute of Physics of Materials, AS of CR, Brno, Czech Republic

Outline

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

1.Introduction FTTD

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

f0

fC

GT

plast.

HMH

plasticity

D

3. Gurson-Tvergaard model(GT)

nucleation

fN = 0,004

eN = 0,3

SN = 0,1

f0 = 0,005

fC = 0,035

q1 = 1,5; q2 = 1

D = 0,2 mm

f *

fu*

fc

GT

GTN

fF

fc

f

GT x GTN model

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.

f1=0.0073

f2=0.0073

f3=0.0083

f4=0.0126

f5=0.0131

f6=0.0349

500 mm

material parameters identification

void distribution in non-affected area

void distribution in the neck area

of the round tensile bar

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)

eN = 0.3, SN = 0.1

fN = 0.004

W

a

L/2

B/2

3PB SE(B)

L = 250 mm

l = 200 mm

W = 50 mm

B = 25 mm

a = 25,25 mm

J

J0.2BL

J0.2

JI SZW

JI

0.2 mm

Da

DaSZW

FEM J=1,39syDa

The influence of q2on the values of J-integrálu at stable crack initiation

The influence of the h parameter (triaxiality parameter)

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