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© 2009 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary© 2009 ANSYS, Inc. All rights reserved. 1 ANSYS, Inc. Proprietary
Ansys V12 Fracture mechanics capabilities:crack meshing and propagation
Florent GallandPhD Student
David RocheSupport engineer
ANSYS, IncOctober 2009
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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.
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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:
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High need of robust automatic numerical tools for 3D fatigue crack growth
Application context and difficulties
• 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...
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• Life span definition:
Application context and difficulties
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
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FRACTURE MECHANICS INTERESTING QUANTITIES
Ansys V12 enhanced fracture mechanics commands
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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
pWG
A∂
= −∂
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≥
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Fracture mechanics: The asymptotic approach
• The 3 fracture modes:
From a kinematics point of view, 3 fracture modes can be defined
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• Stress singularity at crack tip:
• The stress tensor writes then [Irwin1957]:
Fracture mechanics: The asymptotic approach
yyσ
r
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
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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⎛ ⎞= − −⎜ ⎟⎝ ⎠∫
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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.
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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
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• 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
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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.
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FRACTURE MESHINGAnsys V12 enhanced workflow
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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
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Fracture meshing workflow in Ansys V12
Solve fracture mechanics test-cases and review CINT results in workbench
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X-JOINT CRACK EXAMPLEWelded tubular structure
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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
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Industrial example:X-Joint tubular structure
• 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
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Then the crack is introduced in a submodel of the interest zone
Industrial example:X-Joint tubular structure
First an analysis of the x-joint structure is performed, without any crack
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Industrial example:X-Joint tubular structure
• 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
Paper
K1
K2
K3
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CRACKED TURBINE BLADEDamage tolerance sensitivity analysis
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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.
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Industrial example:Cracked turbine blade
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
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Then the crack is introduced in a submodel of the interest zone
Industrial example:Cracked turbine blade
First an analysis of the blade structure is performed, without any crack
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Industrial example:Cracked turbine blade
• 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
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– Response surface:
Industrial example:Cracked turbine blade
• Identify the most critical locations of the crack:
G at the free surface G in the bulk
Postprocess the variations of the energy release rate G versus the location of the crack
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– Optimization:Screening for candidates
locations giving :
Industrial example:Cracked turbine blade
• Identify the most critical locations of the crack:
For which location does the energy release rate G exceed a certain criterion Gc?
CG G>
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CRACKED HELICOPTER FLANGED PLATE
Crack propagation in an aeronautical part
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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
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Industrial example:Cracked helicopter flanged plate
• An open problem: The helicopter round-robin challenge
Objective: solve fatigue crack propagation analysis with minimal user intervention
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• Hypothesis: – Mode 1 solicitation:
planar propagation
– Paris propagation law:
– Free crack front shape:No assumption on the front
nature
Industrial example:Cracked helicopter flanged plate
. mda C Kdn
= Δ
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
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• Hypothesis: – Free crack front shape:
No assumption on the front nature.At the geometrical level, the front is now defined by a spline
Industrial example:Cracked helicopter flanged plate
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Industrial example:Cracked helicopter flanged plate
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
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J‐Script
Python
APDL
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)
Industrial example:Cracked helicopter flanged plate
• Scripting workbench: Automatic propagation loop
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Industrial example:Cracked helicopter flanged plate
• Postprocess the crack growth:
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Industrial example:Cracked helicopter flanged plate
• Postprocess the crack at the final step:
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Industrial example:Cracked helicopter flanged plate
• Ensure the solution validity all along the propagation:– Mesh quality:
– Stress intensity factors quality:
contour independency property of the interaction integral
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Industrial example:Cracked helicopter flanged plate
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
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Industrial example:Cracked helicopter flanged plate
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
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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
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