Fracture Mechanics Conf09!09!10 14

Ansys V12 Fracture mechanics capabilities:crack meshing and propagation

Florent GallandPhD Student

David RocheSupport engineer

ANSYS, IncOctober 2009

Fracture mechanics capabilities in Ansys V12

I. Application context and difficulties:Modern issues and challenges for high technology industries.

Simulating the whole life span of the product.

II. Fracture mechanics interesting quantities:The energy release rate and the mixed mode stress intensity

factors can easily be computed by mean of the CINT command.

III. Fracture meshing :A new fracture meshing workflow for Ansys V12 was

developed. It allows for full fracture mechanics computations in Workbench.

IV. Examples :Damage tolerance sensitivity analysis, crack propagation

analysis.

Application context and difficulties

• Fracture mechanics science was born in the 20th century and for many applications, is still an open problem.

• Accident of the German train ICE in 1998:

• Accident of the flight Aloha 243 in 1988:

High need of robust automatic numerical tools for 3D fatigue crack growth

• Simulating fatigue crack growth: an opening challenge for the commercial finite element analysis softwares.

• A wide range of industrial applications are concerned by 3D fatigue crack growth simulations.

aeronautic, aerospace, military engineering, nuclear structures applications...

• Life span definition:

The initiation stage can represent a large part of

the life span

During the stable propagation stage the crack speed grows

exponentially with the crack size

The crack grows unstably until the ductile fracture

Simulation context

FRACTURE MECHANICS INTERESTING QUANTITIES

Ansys V12 enhanced fracture mechanics commands

Fracture mechanics:The global energetic approach

• The energy release rate [Griffith1921]:

• A simple crack growth criterion:

The energy release rate is the quantity of dissipated energy per unit of newly created fracture surface area

= −∂

Reference: A. A. Griffith, The phenomena of rupture and flow in solids, Philosophical Transactions of the Royal Society of London, Harrison and Sons 1921

cG G≥

Fracture mechanics: The asymptotic approach

• The 3 fracture modes:

From a kinematics point of view, 3 fracture modes can be defined

• Stress singularity at crack tip:

• The stress tensor writes then [Irwin1957]:

Fracture mechanics: The asymptotic approach

crack σ∞

singularityr

. ( . (). ). ). ( ). (I II IIIij I ij II ij III ijK r K rf f fK r O rσ θ θ θ= + + +

Reference: G. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate, Journal of applied mechanics 24, 361-364, 1921

)(ijkf θWhere the are known functions.

The scalars are called the stress intensity factors

, ,I II IIIK K K

Fracture mechanics: Ansys V12 enhanced commands

The energy release rate and the stress intensity factors are computed by energetic methods:

the J-integral and the Interaction integral

Advantages

Precise even with coarse mesh (G‐θmethod)

Robustness (path independency)

Ease of use

Drawbacks

Implementation

Reference: JR. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, Journal of applied mechanics 35, 379-386, 1968

, ,12i j kl kl ij kj k iV

J q u dVσ ε δ σ⎛ ⎞= − −⎜ ⎟⎝ ⎠∫

Simple example:Inclined crack in a 2D plate

• Problem description:– Inclined crack in a 2D plate subjected to uniformed

distributed tension load.– A linear elastic material behavior is used.

Simple example:Inclined crack in a 2D plate

• Comparison with analytical results of an inclined crack at various angles in an infinite plate yields a maximum relative error of 0.4% (100µm mesh refinement at crack tip)

‐1,00E+06

0,00E+00

1,00E+06

2,00E+06

3,00E+06

4,00E+06

5,00E+06

6,00E+06

7,00E+06

8,00E+06

0 10 20 30 40 50 60 70 80 90

Stress intensity factor (P

a*√m

Angle in degrees

Inclined crack in a 2D plate ‐ Stress intensity factors

k1 analytical

k2 analytical

k1 numerical

k2 numerical

• Problem description:– Inclined elliptical crack embedded in a 3D block subjected to

uniformed distributed tension load. The crack is inclined at 45°with respect to the loading.

– A linear elastic material behavior is used.

Simple example:embedded inclined elliptical crack

• Good agreement is found between the computed stress intensity factors and the analytical solution of Kassir and Sih.

• Crack tip mesh refinement is of a/75, and there are 120 nodes along the front.

FRACTURE MESHINGAnsys V12 enhanced workflow

Fracture meshing

• Fracture meshing has always been a complicated task:– Significant mesh refinement– Radial meshing at crack tip– Specific geometry (coincident faces)

A workflow has been developed using the Ansys V12 schematic approach, and allows for

fracture computation in workbench

Fracture meshing workflow in Ansys V12

Solve fracture mechanics test-cases and review CINT results in workbench

X-JOINT CRACK EXAMPLEWelded tubular structure

Industrial example:X-Joint tubular structure

• Problem description:– An offshore structure tubular joint. A surface crack is

introduced at the welded join.– Due to symmetry considerations, only a quarter of the

structure is simulated.

Reference: Chong Rhee and Salama, Mixed-mode stress intensity factor solutions of a warped surface flaw by three-dimensional finite element analysis, Engineering fracture mechanics 28, Elsevier 1987

• To make the crack meshing easier (intense refinement at the vicinity of the front) a submodelling approach is used:

First an analysis of the x-joint structure is performed, without any crack

Then the crack is introduced in a submodel of the interest zone

First an analysis of the x-joint structure is performed, without any crack

• Computed stress intensity factors are in fairly good agreement with the paper from Chong Rhee and Salama

Reference: Chong Rhee and Salama, Mixed-mode stress intensity factor solutions of a warped surface flaw by three-dimensional finite element analysis, Engineering fracture mechanics 28, Elsevier 1987

CRACKED TURBINE BLADEDamage tolerance sensitivity analysis

Industrial example:Cracked turbine blade

• Objective: Identify the most critical locations of a crack– A turbine blade is submitted to a pressure and a rotational

velocity. – A submodel geometry is set up in the zone of interest.

Then the crack is introduced in a submodel of the

interest zone

First an analysis of the blade structure is performed, without any crack

Finally, a response surface and an optimization are computed to determine the most critical

locations of the crack

First an analysis of the blade structure is performed, without any crack

• Identify the most critical locations of the crack:

Parameterize the position of the crack

Create a Design of Experiments

Automatic solving for several positions of the crack

– Response surface:

G at the free surface G in the bulk

Postprocess the variations of the energy release rate G versus the location of the crack

– Optimization:Screening for candidates

locations giving :

For which location does the energy release rate G exceed a certain criterion Gc?

CRACKED HELICOPTER FLANGED PLATE

Crack propagation in an aeronautical part

Industrial example:Cracked helicopter flanged plate

• An open problem: The helicopter round-robin challenge

• Initiated in 2002 by the American helicopter community to benchmark the fatigue crack growth simulation methods.

- Complicated 3D part- Complicated variable loading- High number of cycles

• An open problem: The helicopter round-robin challenge

Objective: solve fatigue crack propagation analysis with minimal user intervention

• Hypothesis: – Mode 1 solicitation:

planar propagation

– Paris propagation law:

– Free crack front shape:No assumption on the front

nature

. mda C Kdn

Reference: P.C Paris et al., A rational analytic theory of fatigue, The trend in engineering 13, 528-34, 1961S. Pommier, Principaux mécanismes physiques de fissuration par fatigue en mode 1, ENS Cachan, 2009

New crack front

Initialfront

( . )K MPa mΔthK cK

Stage A Stage B Stage C

• Hypothesis: – Free crack front shape:

No assumption on the front nature.At the geometrical level, the front is now defined by a spline

First an analysis of the whole structure is performed,

without any crack

Draw the initial crack in a submodel of the interest zone and initialize the 3D curve with that geometry

Solve the problem, compute the new crack front position, send back parameters to workbench

J‐Script

Python

Design Modeler

• Refresh the 3D curves

• Update the geometry

Mechanical

• Mesh the model

• Set up the boundary conditions

Mechanical APDL

• Solve the model

• Compute the crack advance (Paris law)

• Scripting workbench: Automatic propagation loop

• Postprocess the crack growth:

• Postprocess the crack at the final step:

• Ensure the solution validity all along the propagation:– Mesh quality:

– Stress intensity factors quality:

contour independency property of the interaction integral

Reference: J.C. Newman et al., Crack growth predictions in a complex helicopter component under spectrum loading, Fatigue & Fracture of Engineering Materials & Structures 29 (11), 949-958, Blackwell Publishing Ltd 2006

• Postprocess the crack front evolutions:The obtained front shapes are in fairly good agreement

with experimental results

Reference: J.C. Newman et al., Crack growth predictions in a complex helicopter component under spectrum loading, Fatigue & Fracture of Engineering Materials & Structures 29 (11), 949-958, Blackwell Publishing Ltd 2006

• Postprocess the crack front evolutions:The obtained front shapes are in fairly good agreement

with experimental results

Concluding remarks

• Direct computation of the mixed mode stress intensity factor is possible in Ansys V12

• Fracture mechanics problem can be solved entirely in workbench, thanks to a new workflow

• It gives the opportunity of using all the workbench project page features. Solve problems with:– Contact– Confined plasticity, thermal loading– Submodelling– Parametric update– Design of experiment

Performing fatigue crack growth analysis on realistic 3D industrial parts is now possible

THANKS FOR YOURATTENTION

Fracture Mechanics Conf09!09!10 14

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