The document discusses several applications of the discontinuous Galerkin (DG) finite element method for modeling ductile fracture problems. These include: 1) using an implicit DG algorithm to accurately simulate crack propagation in the Sandia fracture challenge problem; 2) modeling multiple crack opening in ductile materials using a failure potential index to predict crack paths; 3) simulating failure mechanisms in fiber-reinforced composites under transverse loading using pressure-dependent plasticity models; and 4) micromechanical analysis of randomly distributed fiber composites using representative volume elements and pressure-dependent matrix plasticity models.

1. DG METHOD FOR MODELING DUCTILE
FRACTURE
 Sandia (second) challenge geometry
 Multiple crack opening in ductile media
 Failure of Fiber reinforced composite (FRC)
 Pressure dependent plasticity for FRC failure

2. SANDIA CHALLENGE GEOMETRY

3. SANDIA FRACTURE CHALLENGE
 Used as an assessment of the
prediction ability of the currently
available numerical technique
 Material calibration was
performed; Then challenge
geometry was modeled.
 Most of the teams used explicit
algorithm.
 Prediction with implicit algorithm
was far from the experimental
result
The Sandia Fracture Challenge: blind round robin predictions of ductile tearing, Boyce et al , 2014

4.  Locally placed DG (red marked zone) was used in
DG/CG mesh.
 Half model with a symmetry on the z direction
 Crack initiation and propagation was similar with
the experimental data

6. 0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
0 1 2 3 4 5 6 7 8 9 10
Crack path A-D-C-E
Crack path A-C-E
Grey- Structural Mechanics Lab
Blue – UT Austin Lab
Force(N)
DG simulation

7. MULTIPLE CRACK OPENING PROBLEM

8. Fuelrod
Fuel rod
Zircaloy tube
Zircaloy tube
Hydride
Zircaloy tube
Hydride/Matrix interface
MULTIPLE CRACK OPENING PROBLEM
Nilsson K-F, Jaksil N, Vokal V An elasticâplastic fracture mechanics based model assessment of hydride embrittlement in zircaloy cladding tubes. J Nucl Mater (2010)

9. MULTIPLE CRACK OPENING PROBLEM

11. Hydride debonding
 Crack initiation from hydride debonding
 Propagation following a dominant crack path
MULTIPLE CRACK OPENING PROBLEM

12. Crack branching
Failure Potential (FP) index:
where, is a function of
stress triaxiality;
Used to determine
dominant crack path that
leads to failure

13. Ligament tearing and crack coalescence Complete failure

14. Successful simulation of
debonding and matrix
failure, multiple crack
Prediction of crack
propagation direction (PF)

15. FAILURE OF FIBER REINFORCED
COMPOSITE (FRC)

16. FAILURE OF FIBER REINFORCED COMPOSITE (FRC)
Transverse tensile loading
A. Debonding of fiber/matrix interfaces
B. Kinking on debonded matrix surfaces
C. Tearing of interfiber ligaments
A
B
C
Simultaneous simulation of all these
failure modes are difficult as bulk matrix
materials are ductile and undergo large
plastic deformation (not reported yet)

17. Bi-material model
Fiber –pure elastic
Epoxy – elasto-plastic (J2)
Experimental and numerical study of the micro-mechanical
failure in composites; Danial Ashouri Vajari, Karolina
Martyniuk, Bent F Sorensen, Brian Nyvang Legarth, 2013

18.  Locally placed DG element
to reduce computational cost

19.  Kinking of debonded matrix surfaces predicted
from simulations agrees well with the
experimental results
28 µm
25 µm

23. PRESSURE DEPENDENT PLASTICITY
FOR FRC FAILURE

24. 1. Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part I – Constitutive modelling A.R. Melro a, P.P. Camanho b, F.M. Andrade Pires , S.T. Pinho
2. Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part II – Micromechanical analyses
1. Micromechanical analysis is performed on
representative volume element (RVE)
2. Fibers are randomly distributed
3. Matrix material is ductile and pressure dependent
(epoxy resin)
PRESSURE DEPENDENT PLASTICITY

25. σ2
σ3
σ1
σ1 = σ2 =σ3
Von MisesParabolic plasticity model
Yield surface in 3D stress space
Cap plasticty

26. Micromechanical analysis of polymer composites reinforced by unidirectional fibres: Part II – Micromechanical analyses
A.R. Melro , P.P. Camanho, F.M. Andrade Pires , S.T. Pinho
Pressure dependent plasticity
Matrix
Matrix
Fiber

27. Failure pattern of FRC for transverse tensile loading

28. (a)
(c) (d)
(b)
Failure
Potential
(a)
(c) (d)
(b)

30. (a) (b) (c)

31. ReactionForce(10-3N)
Displacement (µm)
0
0.2
0.4
0.6
0.8
1
0 0.1 0.2 0.3 0.4 0.5

32. Summary
 Successful demonstration of application of implicit DG FEA with
relaxation scheme for Sandia fracture challenge model
 Application of PF index for multiple crack opening problem
(debonding and matrix failure)
 Validation of PF index for failure in composite
 Application of pressure dependent plasticity model for simulating
failure of randomly distributed multiple FRC specimen (RVE).

33. Results

34. Process overview
• Mesh – ABAQUS
• Boundary condition, crack interface, material assignment are setup in
ABAQUS- read in Fortran 90 code for DG FEA input
• DG FEA analysis for model specimen is performed by in-house code
(Fortran 90/paralllel)
• Output visualization in Tecplot
• For any type of crack analysis (4 major steps)
 Material calibration (hardening , failure plastic strain are determined; both ABAQUS
and DG code )
 ONLY Plasticity analysis performed in model geometry (no crack interface)
 According to “FP”, crack path is determined and interface is set.
 Remesh and rerun until complete failure of the structure