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© 2013 CAE Associates
Fracture Mechanics Using Workbench
v14.5
Michael Bak July 2013
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Fracture Mechanics
Fracture mechanics is an important tool of engineering analysis that makes it possible to determine whether:
— a crack of given length — in a material of known fracture toughness — will propagate to fracture at a given stress level.
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Theoretical Background
Fracture mechanics is based on the stress distribution at the tip of a crack, derived from elasticity theory:
Although the stress approaches infinity at the tip of the crack (as r → 0), the fracture behavior can be determined from the value of K, the stress intensity factor.
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Theoretical Background
Three primary modes of fracture: — Mode I: Tensile or opening mode.
• Generally most critical. — Mode II: Sliding or shear mode. — Mode III: Tearing mode.
Mixed-mode fracture is also possible.
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Methods of Calculating K
ANSYS Mechanical and Mechanical APDL offer several different methodologies to evaluate fracture:
— Stress Intensity Factor (K or SIF) extraction. — J-Integral (J). — Energy release rate (G) using Virtual Crack Closure Technique (VCCT).
• Typically used for delamination. • Requires linear elements (mid-side nodes not allowed).
For linear elastic materials G, J, and K are related:
— Plane stress:
— Plane strain:
EKGJ
2
==
( )E
KGJ22 1 ν−
==
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Fracture Toughness
Fracture toughness, KIC, is a measured material property. — Found using standard specimens that are loaded until the crack extends.
K is a function of the crack geometry and the applied loading:
— If K > KIC: The crack will propagate.
Can also combine fracture with fatigue to determine cycles of repeated loading until crack will propagate to failure.
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Analysis Approaches
There are two general approaches to modeling fracture using finite elements:
1. Analyze the un-cracked body in the finite
element analysis, extract the stress state at any location to be evaluated, and use a stand-alone crack propagation code.
• These codes use the finite element stresses and a library of crack geometries to determine K.
• Can predict cycles to failure based on cyclic loading information.
2. Include the crack in the finite element model.
• This is considered the most accurate approach – includes stress redistribution.
• For crack propagation would need to evaluate the initial crack, then extend the crack and re-analyze to obtain K versus crack length.
• This procedure becomes more difficult if crack path is not known ahead of time.
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Fracture Mechanics Analysis
Creating a finite element mesh with a crack can be a challenging and time-consuming effort.
— In addition, it is often of interest to model various crack sizes to determine the critical crack size and location.
Workbench v14.5 provides two options for quickly and efficiently including a crack in the finite element model:
— Pre-meshed crack that can be imported. • Using geometry from DesignModeler or mesh from FE Modeler.
— Automatic crack creation within Mechanical.
Crack definition input can be assigned as parameters in Workbench. — Can parametrically model the effect of different size and locations of cracks.
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Fracture Mechanics Analysis
Workbench uses the CINT (contour integration) approach to perform the fracture post-processing calculations.
Contours are numbered outward from the crack front. — No limit on the number of contours – user-controlled. — Radial/ring mesh is not required but usually results in more accurate solution. — For 3D models, hexahedral elements are desirable.
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Fracture Mechanics Analysis
The following capabilities available in Workbench will be demonstrated: — Creating cracks in 2D analyses using mesh connections. — Automatically creating flat semi-elliptical cracks in 3D analyses. — Obtaining fracture quantities in post-processing. — Crack placement and coordinate system alignment normal to the surface.
Major Radius
Minor Radius
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Thank you!
Thank you for attending CAE Associates webinar on fracture. You will receive via email a survey to fill out and return. We welcome any
comments or additional questions on the content.
A transcript of this presentation can be downloaded from our website:
www.caeai.com
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Additional Information
The following slides provide more detailed information.
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3D Automated Crack Procedure
The procedure to include a crack in an existing model in Workbench v14.5 includes the following steps:
— Create base mesh (no cracks) – must use quadratic tetrahedrons in the region where the crack will be modeled.
— Create a crack coordinate system using the hit point method to automatically create a local coordinate system normal to the surface.
— Insert the Fracture branch into the Outline Tree, and insert a Crack Object.
— Define the crack geometry and mesh via the Details of the Crack Object.
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3D Automated Crack Procedure
Automatically define the location of the crack using the hit point coordinate approach.
— Toggle on the Hit Point Coordinate button in the Graphics Toolbar.
— Select a point on a surface.
— Right-click the Graphics window and select Create Coordinate System Aligned with Hit Point.
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3D Automated Crack Procedure
The Crack Shape is currently set to Semi-Elliptical. — Indicate the body where the crack will be scoped. — Indicate the local crack coordinate system. — Define the crack size and shape by major and minor
radii.
Crack lies in X-Z plane. — Z is major direction, X is minor direction. — Y is perpendicular to crack face.
Major Radius
Minor Radius
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3D Automated Crack Procedure
Define mesh settings for crack.
Can also automatically create named selections of crack nodes.
— For example, can create top and bottom crack face nodes which can be used to apply pressure on the crack faces.
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3D Automated Crack Procedure
Mesh crack which will eventually connect to base mesh. — Bonded contact used between buffer zone and base mesh.
Run static structural analysis.
Insert Fracture Tool under Solution, and Insert either J-Integral or SIFS
Results. — VCCT is not available with the automated Crack Object since it requires linear
elements in Workbench v14.5.
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3D Automated Crack Procedure
Insert Fracture Tool under Solution, and Insert either J-Integral or SIFS Results.
— VCCT is not available with the automated Crack Object since it requires linear elements in Workbench v14.5.
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3D Automated Crack Procedure
Graphics display and plot with contain crack front variation. — Can export results to text or XLS file.
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Using Parameters With Crack Object
Crack input and fracture output can be defined as parameters.
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Using Parameters With Crack Object
Crack input and fracture output can be defined as parameters.
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