BEASY Fatigue

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BEASY Fatigue Crack Growth using Finite Element
Models
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Introduction

• What is special about BEASY?
• Differences between BEASY and Finite Element
  analysis
• Advantages of BEASY
• What can BEASY do?
• Introduction to BEASY products
• Creating BEASY models from FE source
• Performing Fatigue and Crack Growth

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What is Special about BEASY?

• BEASY is a Boundary Element Method (BEM) based
  analysis
• Most analysis code is based on the Finite Element
  Method (FEM) for example
• ANSYS
• NASTRAN
• ABAQUS
• etc

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Finite Element Analysis

• The entire model is split into elements.
• Each element is studied.
• A matrix equation is created from the combination
  of elements.
• The matrix equation is solved to give the results
  at all the node positions.

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Boundary Element Analysis

• Only the boundary of the surface is dividing into
  elements.
• The interaction of the elements is used to form a
  matrix equation.
• The matrix is solved to give the results on the
  boundary
• Internal point results are then obtained using a
  post-processing step

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Benefits of Boundary Element Methods

• Simpler model creation
• this simplifies cases where the model is changed
  during the analysis for example during crack
  growth
• Results are given with a high degree of accuracy
  on the surface of the model
• Good accuracy can be obtained with less refined
  meshes
• Meshes can be discontinuous allowing flexibility
  in mesh creation

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Mesh creation

• There is no need to match up edges of adjacent
  elements
• This greatly simplifies mesh creation and allows
  rapid localised mesh refinement

1 element
3 elements
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Limitations of BEM Analysis

• BEASY is based on small deformation theory
• BEASY is based on a linear elastic solution
• plastic zones near to the crack tip can be
  represented
• residual stresses can be applied in combination
  with the finite element model
• Large thin panel structure and not easily
  analysed with a 3D BEASY analysis due to aspect
  ratio problems
• These may be analysed using a 2D analysis or with
  the specialised stiffened panels tools
• BEASY is designed to complement rather than
  replace standard FE packages.

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Overview of BEASY Products
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BEASY Products

• BEASY Mechanical Design
• Stress, thermal and contact simulation
• BEASY Fatigue and Crack Growth
• Crack growth simulation and multi site damage
• BEASY Corrosion and CP
• Corrosion control simulation and interference
  prediction
• BEASY CRM
• Corrosion simulation, ICCP and related electric
  and magnetic fields
• BEASY ELECTROCOAT
• Simulation of electrochemical coating processes
• BEASY Acoustic Design
• Acoustic simulation

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BEASY Modelling Products

• Create BEASY Model Directly
• BEASY-IMS
• BEASY includes its own modelling and
  visualisation tools
• BEASY PATRAN
• Create and visualise BEASY models in PATRAN
• BEASY IDEAS
• Create and visualise BEASY models in IDEAS
• Create BEASY models From FE Source Files
• BEASY FE Interface
• ANSYS
• ABAQUS
• NASTRAN
• PATRAN

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BEASY Fatigue and Crack Growth
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Types of Crack Growth Modeling

• There are two main ways in which cracks in
  structures and components can be modeled
• Reference Solutions relate the model to a simple
  crack cases for which a reference solution is
  known
• Analysis Method use an advanced analytical tool
  to simulate the behaviour of cracks in the actual
  component or structure (i.e. Real Crack Growth
  Modelling)

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Problems of using Reference Solutions
Which is the correct case and equivalent loading
for this model?
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Problems of using Reference Solutions

• User has to
• Choose appropriate reference case
• Approximate or extrapolate the loading
• During crack growth
• The shape of the crack is assumed to remain the
  same
• The crack is assumed to grow in the same plane
  (i.e. straight/mode 1)
• Load redistribution is neglected as the crack
  grows
• This reduces the accuracy of the results

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Example of incorrect crack path prediction
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Incorrect Prediction of Life Data
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Benefits of Real Crack Growth Modeling

• Accurate Prediction of
• Stress Intensity Factors
• Crack Path
• Crack Shape
• Number of cycles to failure
• Including the effects of
• Load Redistribution
• Multiple site damage. (i.e. Multiple cracks)
• Changes in loading due to changes in deformation.
  (e.g. non-linear contact)
• Increased Confidence in Results

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Additional advantages of BEASY analysis

• Analysis of fatigue cracks at corrosion pits.
• The irregular geometry of the corrosion pit can
  be modelled with BEM.
• Loading from residual stress fields can be
  applied directly from finite element stress
  fields
• Multiple geometry configurations can be easily
  simulated and an optimum design obtained.
• Studies can be performed investigating the
  effects of
• Crack size
• Crack orientation
• Initiation site positions
• Fatigue loading properties

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Simple Crack Growth Model
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Crack Representation mesh on a lug with a crack

• BEASY requires that only the boundary of the
  model is generated
• The crack is added using a wizard.
• The picture shows an example mesh after a crack
  has been added

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Mesh on an edge crack

• The modelling of the crack geometry allows cracks
  in BEASY to be defined naturally, making it
  simple to use

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Fracture Results

• After the solution, the stress distribution is
  given over the model
• This picture shows the distribution around crack
  tip
• The next slide shows the same model with the
  crack growing

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Automatic Crack Growth
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Automatic Crack Growth

• Stress intensity factors can be displayed
  graphically
• These values can also be exported to MS-EXCEL

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Accuracy of BEASY compared to reference solutions

• Stress intensity factors can be displayed
  graphically
• These values can be processed in MS-EXCEL

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Model Creation Tools

• BEASY models can be built directly using the
  BEASY-IMS user interface or using a customised
  tools in PATRAN or I-DEAS.
• BEASY models can also be created from selected
  elements from existing Finite Element models
• This process will be described here

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BEASY Model Generation Wizard
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Generating BEASY models from FE source data

• The BEASY model generation wizard allows a BEASY
  model to be created from finite element source
  data
• Source data can currently be from
• ANSYS rst file
• ABAQUS fil or odb files
• NASTRAN op2 file
• PATRAN taken directly from database
• Full models or sub models can be created

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BEASY FEM Crack Modelling
Perform analysis of complete un-cracked structure
Use prediction software to identify likely crack
initiation sites
Automatically create the BEASY model and boundary
conditions form the FEM model
Decide size and shape of crack to initiate
Perform crack growth analysis
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Crack Growth Prediction Using FEM Data
FEM Model
BEASY Crack Growth simulation
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Accurate Crack Growth Modelling Using FEM Data

• The aim is to provide an easy and fast approach
  to crack growth simulation to the FEM user
  community
• BEASY users already have these benefits but they
  have up till now been required to build a new
  BEASY model
• The new approach uses existing FEM models and
  BEASY technology to offer significant benefits to
  users

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Crack Growth In A FEM Environment

• FEM models are very good at representing global
  behaviour
• Load transfer
• Deformation
• General stress levels
• Difficult to model small details and features
• Cracks

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Crack Growth In A FEM Environment

• BEM captures local behaviour
• Cracks
• Fatigue stresses
• Small geometry details (fillets, holes etc)
• Impact of residual stresses

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Crack Growth In A FEM Environment

• By combining the technologies we can
• Reduce the cost of crack growth modelling
• Obtain answers faster
• Obtain more accurate predictions
• Reuse existing model data

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Example of a model created from an ANSYS rst file

• The picture shows a ANSYS model.
• A sub-model will be created from this model
• The sub-model area is denoted by the box
• The sub-model will be fully loaded
• A crack can then be added to the sub-model

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Start the BEASY model generation wizard
Select the option to create a model from an FE
source
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Selection of the model in the wizard
Select the source file, source type and define
the output file to be created.
modele_cril.rst
cril_large_submodel
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Definition of the area of the model
Define the area of the model to be used in the
BEASY sub-model
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Define the Material Properties
Define the material properties for this model
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Create the initial BEASY model
The initial model is now ready to be created.
The initial model will not have boundary
conditions added.
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Definition of the loading in the model
A number of simple steps are required to
configure the loading in the model. A loaded
BEASY model is then created.
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BEASY Model Created by the Wizard
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BEASY Fracture Wizard
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Crack Wizard
The complex process of meshing the crack and
selecting compatible load and material data is
automated
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BEASY Fracture Wizard

• This is a tool to create BEASY fracture models
• Select a crack from a library
• Add fatigue properties
• Define a load spectrum file
• The wizard also enables post-processing and
  further analysis tasks

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BEASY Fatigue and Crack Growth Main Functions

• The wizard allows a user to
• Add a crack from a library into a standard BEASY
  model

Note this library can be customised by users
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BEASY Fatigue and Crack Growth Main Functions

• The wizard allows a user to
• Growth the crack for a required distance, number
  of cycles or growth increments

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BEASY Fatigue and Crack Growth Main Functions

• The wizard allows a user to
• Select fatigue properties from the NASGRO database

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BEASY Fatigue and Crack Growth Main Functions

• The wizard allows a user to
• Compute the crack life for each growth increment

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BEASY Fatigue and Crack Growth Main Functions

• The wizard allows a user to
• Select fatigue properties from the NASGRO database

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Defining a crack

• Cracks can be added by
• Selecting from the crack library
• Defining the crack mesh
• Cracks can be added to the crack library
• Results at the crack tip and along the crack
  front include
• Stress Intensity Factors
• Ki, Kii and Kiii
• Crack growth direction
• Crack growth rate

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Fatigue Fracture Components - Overview
Base Model Crack Definition
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Fracture model creation
The crack is added to the model using the crack
library in the fracture wizard
Base Model Crack Definition
As the crack grows new crack definition files are
generated representing the crack at each stage of
the analysis
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Example of adding a crack to a model

• A simple cylinder model has been generated,
  without a crack considered in the modelling.
• The cylinder has been given a very simple
  uniaxial loading.
• The model has been meshed with the same size mesh
  over the entire model, with no consideration
  given to where the crack will be placed.

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Adding the Crack

• Simply choose the crack from the BEASY crack
  library.
• Decide the size, location and orientation.
• The crack is automatically added by BEASY and the
  model automatically remeshed to include the
  crack.

Sample edge crack from the library
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Adding a Crack
The crack is automatically added to the model and
the surface remeshed

• The library crack that was selected for this
  model had a straight edge
• However the surface that the crack is going to be
  attached to is not straight.
• This is taken care of by BEASY with the edge
  where the crack intersects the geometry surface
  being trimmed back to the required size.

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Fatigue Fracture Components
Stress intensity factors are computed using the
BEASY solver
Base Model Crack Definition
The stress displacements are obtained for the
model with the crack and the SIF values are
computed
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Calculations of stress intensity factors

• The model with the crack is analysed
• The calculation uses the Dual Boundary Element
  Method to perform a powerful and accurate
  calculation of the stress/displacement solution
• The stress intensity factors are evaluated
• in 2D the J-integral method is used
• in 3D the crack opening displacement method is
  used

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Fatigue Fracture Components
Base Model Crack Definition
The crack growth model controls the rate of crack
growth
The required model can be selected using the
fracture wizard
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Material Data Selection in the wizard
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Nasgro Fatigue database in the fracture wizard
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Fatigue Fracture Components
The loading can be simply cycling or controlled
by a load spectrum file where combinations of
loading cycles are defined
Base Model Crack Definition
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Choose The loading
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Fatigue Fracture Components
Base Model Crack Definition
Once all the components have been included the
crack growth direction and step size can be
computed
This direction uses either the minimum strain
energy density or the maximum principle stress
direction
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Predicted new crack front positions

• The new crack front positions are predicted
  this is based on
• the stress intensity values at the crack front
• the defined load spectrum
• The crack growth model
• The new crack front is automatically predicted

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Automatic Crack Growth

• Growing cracks to predict product performance and
  life is simple
• Simply
• Add a crack to a model solve
• Define the loading history
• Select the crack growth model
• BEASY will automatically compute
• The crack growth direction
• The rate of growth of the crack
• Also
• Automatically generate elements to represent the
  crack growth
• Automatically re mesh the model as the crack grows

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Automatic Crack Growth Prediction
Cylinder Example Mesh after 5 Steps This
procedure can be repeated until the crack grows
the required distance.
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Fatigue Fracture Components
Base Model Crack Definition
The process repeats until the crack is grown as
required
At each stage of the analysis the life is
calculated and the data can be viewed using
post-processing tools
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Accurate Predictions Of Stress Intensity Data
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Accurate Predictions Of Stress Intensity Data
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Crack Wizard

• The BEASY crack wizard simplifies and automates
  all the tasks required to model cracks and their
  growth
• Crack initiation
• Crack meshing
• Crack library
• Crack growth models
• Materials database
• Remeshing for crack growth
• Loading data (multiaxial)
• Plotting of life data in EXCEL

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Examples of Crack Growth Models
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Crack Growth Pattern During Testing
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2D Model - Crack Growth Results For 10 Steps
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Detailed View Of Crack Growth From Bolt Holes
ADVANCING CRACKS
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Multiple Site Damage (MSD)
Reproduced from paper titled Multiple Site Damage
(MSD) crack growth numerical evaluations and
experimental tests by C. Calì, R. Citarella, M.
Perrella, Department of Mechanical Engineering,
University of Salerno
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Experimental Setup
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Experimental Results
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Multiple Site Damage (MSD)
N774,000 cycles
N1,070,000 cycles
Reproduced from paper titled Multiple Site Damage
(MSD) crack growth numerical evaluations and
experimental tests by C. Calì, R. Citarella, M.
Perrella, Department of Mechanical Engineering,
University of Salerno
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Crack 1 Size Prediction
BEASY
BEASY
Reproduced from paper titled Multiple Site Damage
(MSD) crack growth numerical evaluations and
experimental tests by C. Calì, R. Citarella, M.
Perrella, Department of Mechanical Engineering,
University of Salerno
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3D Comparison
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Experimental Comparison -Part Through Crack
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Prediction Of SIF Along The Crack Front As Crack
Grows
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Part Through Crack Propagation
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Through Crack Propagation
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Predicted And Experimental Crack Growth Rates
Through crack
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Accurate Predictions Of Stress Intensity Data
Through-Crack in Circumferential Direction
FIXED
Life Prediction
TRACTION
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Accurate Predictions Of Stress Intensity Data
Deformed Shape of Tube Subject to Bending Moment
Open Crack in Tube Wall (crack advanced from
0.1 to 0.94 inches
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Accurate Predictions Of Stress Intensity Data
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Accurate Predictions Of Stress Intensity Data
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Crack Growth in Gear with Contact Loading
Node to Surface Contact
Crack Located in Root of Gear Tooth
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Crack Growth in Gear with Contact Loading
Initial Crack Located in Root of Gear Tooth
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Crack Growth in Gear with Contact Loading
Crack Surface After 10 Increments
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Crack Growth in Gear with Contact Loading
Another View Notice cupping of crack as it
grows
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Crack Growth in Gear with Contact Loading
Initial Crack a 0.15 inch
Step 5 amax 0.51 inch
Step 10 amax 0.94 inch
Cross Sectional Views Showing Progressive Crack
Growth
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Predicting Failure
Predicted Stress Intensity Factors on the crack
front
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Cracks In Built Up Structures
Extr L-T LA HHA M2EC31AB1 CRACK GROWTH LAW
- NASGRO3
Axial Load on Panel
Rivets Prestressed Using Contact Interference
Condition
Panel and Stiffener Fixed
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Examples of a complex loaded model
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Detailed Analysis
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Summary

• BEASY provides a tool to grow a crack in a two or
  three dimensional model
• The process of adding the crack is automated with
  the fracture wizard
• Fatigue properties and loading spectra can be
  defined
• The full fatigue history is computed
• The BEASY model generation tool allows BEASY
  models to be created from existing Finite Element
  models