Fracture Mechanics Using Workbench v14 - CAE · PDF 2 Fracture Mechanics Fracture mechanics is...

© 2013 CAE Associates

Fracture Mechanics Using Workbench

v14.5

Michael Bak July 2013

2 www.caeai.com www.caeai.com

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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θθθπ

σ

θθθπ

σ

θθθπ

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rK

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Ixy

Iyy

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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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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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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:

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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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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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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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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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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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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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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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Fracture Mechanics Using Workbench v14 - CAE · PDF 2 Fracture Mechanics Fracture mechanics is...

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