Fracture Mechanics i kb hUsing Workbench

v14.5

Michael BakMichael BakJuly 2013

2013 CAE Associates

Fracture Mechanics

Fracture mechanics is an important tool of engineering analysis that Fracture mechanics is an important tool of engineering analysis that makes it possible to determine whether:

a crack of given lengthin a material of known fracture toughness 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 Fracture mechanics is based on the stress distribution at the tip of a crack, derived from elasticity theory:

23sin

2sin1

2cos

2 KIxx

23sin

2sin1

2cos

2

2222

rK

r

Iyy

23sin

2sin

2cos

2

rK I

xy

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 stressthe 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: Three primary modes of fracture: Mode I: Tensile or opening mode.

Generally most critical.Mode II: Sliding or shear mode Mode II: Sliding or shear mode.

Mode III: Tearing mode.

Mixed mode fracture is also possible Mixed-mode fracture is also possible.

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Methods of Calculating K

ANSYS Mechanical and Mechanical APDL offer several different ANSYS Mechanical and Mechanical APDL offer several different methodologies to evaluate fracture:

Stress Intensity Factor (K or SIF) extraction.J-Integral (J) 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).Requires linear elements (mid side nodes not allowed).

For linear elastic materials G, J, and K are related:2

Plane stress:EKGJ

2

Plane strain: E

KGJ22 1

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Fracture Toughness

Fracture toughness K is a measured material property Fracture toughness, KIC, is a measured material property. Found using standard specimens that are loaded until the crack extends.

K i f ti f th k t d th li d l di 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 g pp gfracture using finite elements:

1. Analyze the un-cracked body in the finite y yelement analysis, extract the stress state at any location to be evaluated, and use a stand-alone crack propagation code.

Th d th fi it l t t d 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

i l d t di t ib tiincludes 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.

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This procedure becomes more difficult if crack path is not known ahead of time.

Fracture Mechanics Analysis

Creating a finite element mesh with a crack can be a challenging and time- 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.critical crack size and location.

Workbench v14.5 provides two options for quickly and efficiently including a crack in the finite element model: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.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 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 Workbench uses the CINT (contour integration) approach to perform the fracture post-processing calculations.

Conto rs are n mbered o t ard from the crack front 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.

F 3D d l h h d l l t d i bl For 3D models, hexahedral elements are desirable.

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Fracture Mechanics Analysis

The following capabilities available in Workbench will be demonstrated: 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 Obtaining fracture quantities in post-processing. Crack placement and coordinate system alignment normal to the surface.

MajorRadius

MinorRadius

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Thank you!

Thank you for attending CAE Associates webinar on fracture 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 comwww.caeai.com

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Additional Information

The following slides provide more detailed information The following slides provide more detailed information.

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3D Automated Crack Procedure

The procedure to include a crack in an 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 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 Objectand 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 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 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 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 Define the crack size and shape by major and minor radii.

Crack lies in X-Z plane Crack lies in X-Z plane. Z is major direction, X is minor direction. Y is perpendicular to crack face.

MajorRadius

MinorRadius

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3D Automated Crack Procedure

Define mesh settings for crack Define mesh settings for crack.

Can also automatically create named selections of crack nodescrack 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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crack faces.

3D Automated Crack Procedure

Mesh crack which will eventually connect to base mesh Mesh crack which will eventually connect to base mesh. Bonded contact used between buffer zone and base mesh.

R t ti t t l l i 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 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.elements in Workbench v14.5.

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3D Automated Crack Procedure

Graphics display and plot with contain crack front variation 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 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 Crack input and fracture output can be defined as parameters.

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