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fe-safe/RUBBERfe-safe 2017

Legal Notices

Portions of the Endurica fatigue solver are protected under US Patent No. 6,634,236 B1.

Copyright © 2015. This document, and the software described herein, are copyrighted material, and are provided under license. Under copyright law, no parts of this document, or the associated software, may be reproduced or distributed without the expressed permission of the author.

The information in this document is subject to change without notice.

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http://www.endurica.com/

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The open source software components are grouped under the applicable licensing terms. Where required, links to common license terms are included below.

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Solution Overview

Volume 1 - fe-safe/Rubber User Guide

1 What is fe-safe/RubberTM? .............................................................................................................. 6

2 Solution Overview ........................................................................................................................... 7

3 Analysis Procedures ....................................................................................................................... 9

3.1 Before running fe-safe/RubberTM .................................................................................................................. 9

3.1.1 Preparing a Finite Element Model for fatigue analysis ............................................................................. 9

3.2 Configuring a Project in fe-safe/RubberTM .................................................................................................. 10

3.2.1 Loading the FE model ........................................................................................................................... 11

3.2.2 FEA Model Units .................................................................................................................................... 12

3.2.3 Using the EnduricaMaterials database .................................................................................................. 13

3.2.4 Material Parameters .............................................................................................................................. 17

3.2.5 Common Units System for Materials ..................................................................................................... 26

3.2.6 Configuring a Loading Definition ............................................................................................................ 27

3.2.7 Loading the plug-in ................................................................................................................................ 28

3.2.8 Configuring plug-in Algorithm and Settings ........................................................................................... 29

3.2.9 Defining Environmental Conditions ........................................................................................................ 31

3.2.10 Requesting Output ............................................................................................................................... 32

3.3 Verifying Material Model Definitions............................................................................................................ 32

3.3.1 Stress-Strain .......................................................................................................................................... 32

3.3.2 Crack Growth Rate ................................................................................................................................ 34

3.3.3 Flaw Size ............................................................................................................................................... 36

3.4 Diagnostic Techniques including additional outputs ................................................................................... 38

3.4.1 Identifying Failure Planes at a Point of Failure ...................................................................................... 39

3.4.2 Computing the loading history experienced by the failure plane(s) ....................................................... 41

3.5 Running fe-safe/RubberTM .......................................................................................................................... 45

3.5.1 fe-safe/RubberTM analysis process ........................................................................................................ 45

3.5.2 After fe-safe/RubberTM has run .............................................................................................................. 46

Solution Overview

6 fe-safe/Rubber User Guide Copyright © 2016 Dassault Systemes Simulia Corp.

Issue: 3 Date: 13.07.2016

fe-safe/RubberTM User Guide

The purpose of this guide is to describe the execution and application of the fe-safe/RubberTM fatigue life prediction software. This guide assumes the user is familiar with the basic use and concepts of the fe-safe fatigue life prediction software.

1 What is fe-safe/RubberTM?

fe-safe/RubberTM is a tool for simulating the nucleation of fatigue cracks in rubber that operates subject to complex loading histories. It calculates the number of repeated applications of a given loading history that can be tolerated before the occurrence of a specified crack. It also provides detailed information about the location of failure within a component, the plane(s) on which cracks initiate at a given location, the history of the loading experienced on the failure plane, and individual damage contributions of each cycle in a load history. The tool includes a database of pre-defined elastomeric materials, and provides for user-defined materials also.

fe-safe/RubberTM systematically handles the important factors that combine to determine the fatigue life of a rubber component. It is capable of addressing the following factors: finite straining, non-linear stress-strain behaviour, Mullins Effect, non-linear fatigue crack growth behaviour (e.g. threshold, near-fracture effects), time-dependent crack growth (frequency-dependence, ozone attack), effects of temperature on fatigue properties, strain-crystallization induced R ratio effects (both relaxing and non-relaxing strain histories), initial flaw size, size of crack at nucleation, closure of cracks experiencing compression, multiaxial stress and strain states from finite element models, and cycles of varying amplitude also from finite element models.

fe-safe/RubberTM combines the capabilities and validation depth of Endurica fatigue solver technology with the ease-of-use of the fe-safe fatigue analysis software. The Endurica fatigue solver was purpose-developed for elastomers, and has been exhaustively validated against a broad set of fatigue experiments. The solver integrates procedures such as critical plane analysis, fracture mechanics, and rainflow counting to provide a complete system capable of accounting for very complex duty cycles, including multiaxial loadings and variable amplitudes.

You can use fe-safe/RubberTM to study the effects on fatigue life of:

• Material Properties,

• Component Geometry, and

• Load History

Solution Overview

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2 Solution Overview

The general architecture of the fe-safe/RubberTM solution and its associated workflow are illustrated in Figure 2-1. The fe-safe/RubberTM solution, shown in yellow, includes both the fe-safe/RubberTM plug-in to the fe-safe fatigue analysis environment, and the Endurica materials database. The fe-safe environment, shown in light blue, provides a graphical interface through which the user specifies and executes the fatigue analysis. fe-safe reads time-domain strain and stress history from a user-created Finite Element Model source database, as well as material property information from the Endurica Materials Database. All user-created files are shown in green. Upon execution, fe-safe calls the fe-safe/RubberTM plugin to compute the fatigue life and other results. Fatigue life from the calculation for each element is written to a new Finite Element Model Output Database for visualization. Other outputs of the calculation are written as text-formatted Endurica auxiliary files. One file is provided for each output type. Third-party components used in this process are shown in dark blue. The user will develop their Finite element model in a suitable pre-processing environment, execute the analysis in a suitable FE code, and review graphical results in a Visualization Environment. A text editor and plotting software may be used to review the auxiliary files produced in the process.

Figure 2-1 General architecture of the fe-safe/RubberTM solution and its associated workflow.

FE Model Source Database

Fe-Safesoftware

/Rubberplug-inFE Code

Visualization Environment

FE Model Output

Database

Endurica Auxilliary files

Endurica Materials Database

Pre-processing Environment

Strain historyStress history

LifeOrientation

Life

Auxilliary results

Life

Material verification CED historyRainflow countDamage sphere

Text editor Plotting software

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3 Analysis Procedures

This section provides guidelines for using fe-safe/RubberTM to perform typical fatigue analysis tasks.

3.1 Before running fe-safe/RubberTM

Generally, FEA and fatigue analysis using fe-safe/RubberTM involves the following steps.

1) Determine the elastic and fatigue properties of the material(s). The properties may be selected from the Endurica Materials database, or they may be determined via experiments on the subject material(s). The fe-safe/RubberTM Theory manual provides a full description of each model.

2) Determine the time history of the nominal strain and the Cauchy stress at every potential failure location. Typically, this is accomplished via a Finite Element Analysis.

3) Determine the environmental conditions to be considered at each potential failure location. These may include temperature and ozone concentration.

4) Determine the desired exports and outputs from the fe-safe/RubberTM analysis. fe-safe/RubberTM can provide not only the fatigue life at each potential failure location, but also the failure plane(s) and local loading history. The desired results will depend on the objectives of the analysis. Analysis objectives might include: verifying material model behaviour, predicting fatigue life of a part, predicting the location where cracks first nucleate, predicting the plane of crack nucleation, identifying critical damaging events in a complex time history.

5) Configure a project in fe-safe/RubberTM to specify the requirements established in items 1-4 above.

6) Run fe-safe/RubberTM. Analysis status and progress are reported in the Message Log window.

7) Visualize, review and interpret the analysis results.

3.1.1 Preparing a Finite Element Model for fatigue analysis

In preparing a Finite Element model for use in fe-safe/Rubber, users should follow these guidelines:

• Define one repeat of the entire fatigue loading history in terms of loads or displacements applied on the FE model. The solution should be obtained with a uniform time discretization. For complex histories, make sure that the history is discretized finely enough to adequately capture any curvature in the corresponding strain-space paths, and any zero crossings.

• To work with histogram-based loads, convert the histogram into a time-domain signal prior to analysis.

• Use groups of finite elements to facilitate later specification of which elements to analyze and which to ignore. Please see the Appendices of the fe-safe User Manual for details pertaining to Interfacing to third-party FE Analysis Data format you use.

• Use membrane of elements of negligible thickness to represent the free surface of any 3D solid element meshes. This practice provides the most accurate estimate of plane stress conditions on a free surface, and is computationally efficient.

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• Request output from the FE solver for Nominal Strain (NE) and Cauchy stress (S) to be written to the FE Analysis Data format. The tensor components of stress and strain should be written with respect to the elemental or local coordinate system. Proper implementation of a local coordinate system can be checked by verifying that rigid body rotation of the model under load does not change the strain component values or the fatigue life (which should be infinite under static load and history of rigid body rotation). Please see the Appendices of the fe-safe User Manual for details pertaining to Interfacing to third-party FE Analysis Data format you use.

• Apply a consistent units system in the FE solver and record the units of stress, strain, and temperature for specification in fe-safe/RubberTM (e.g. mm-N-MPa). Note that Materials datasets in the EnduricaMaterials database are defined in a metric unit system (mm-N-MPa).

• Use the same stress-strain definition in both the FE model and the fatigue analysis. In particular, when using a material defined in the Endurica materials database, care should be taken to ensure consistent stress-strain law between the FE analysis and the fatigue analysis.

3.2 Configuring a Project in fe-safe/RubberTM

In fe-safe/RubberTM, the user specifies the details of an analysis in the fe-safe User Interface (see the fe-safe User Guide for details of the project directory).

The Project Definition file (*.stlx) contains a record of fatigue analysis configurations and material properties (see the Appendices of the fe-safe User Manual for details pertaining to Interfacing to file formats). The Project Directory can be used to re-run an analysis in the fe-safe/RubberTM User Interface (see the fe-safe User Guide for details project definition).

By default, the fe-safe/RubberTM plug-in will also export a Materials log file and a Settings log file. These working files include material parameters and settings configured for all of the groups configured for analysis.

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3.2.1 Loading the FE model

Import datasets from the FE models as per the fe-safe User Guide. Select Stress and Nominal Strain datasets at each discrete time interval of interest for fatigue load definition.

fe-safe/RubberTM supports Centroidal, Integration Point, Elemental-Nodal, or Nodal averaged position from FE formats depending on the support from the FE solver. In some cases, the selected position can be derived as shown (see the Appendices of the fe-safe User Manual for details pertaining to Interfacing to third-party FE Analysis Data format you use).

Figure 3-1 Selecting datasets to read

As discussed above in Section 3.1.1 the strain datasets that are read must be Nominal Strain (NE) due to finite straining for elastomeric materials.

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3.2.2 FEA Model Units

fe-safe/RubberTM uses stress and strain datasets in fe-safe. The user must specify Loaded FEA Model Properties, to provide the Stress Units and Strain Units based on the consistent units system applied in the FE solver.

Figure 3-2 Selecting FE models units

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3.2.3 Using the EnduricaMaterials database

The EnduricaMaterials.dbase file in the installation or user directory of fe-safe/RubberTM is opened in the Materials Databases window of the fe-safe GUI (see the fe-safe User Guide for details of material databases).

Figure 3-3 Properties of NR_GUM materials dataset

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To configure a project in fe-safe/RubberTM, a material must be selected for each group of elements in the Finite Element model to be analysed with the plugin. The materials can be:

• A material from the EnduricaMaterials database

• A material from the EnduricaMaterials database which is copied and edited by the user

• A material entered into the EnduricaMaterials database after materials characterization in a qualified test lab

The EnduricaMaterials database is a text file. It includes metadata that specify each of the material parameters that can be used by the Endurica plug-in (see the Appendices of the fe-safe User Manual for details pertaining to file format). To view the available models and parameters in the fe-safe/RubberTM User Interface, expand one of the materials included in the EnduricaMaterials database, and inspect the Properties and values as shown above in Figure 3-3.

To create a new material, copy an existing material in the EnduricaMaterials (writable copy) database. Rename the copied material and edit the parameters.

Each material specifies the stress-strain, crack growth, and other behaviours that may be included as part of the analysis. Typically, a selection of models is provided for each distinct aspect of the rubber’s behaviour. Each model is described in detail in the fe-safe/RubberTM Theory Manual. To fully describe a given elastomer, the user will select a model for each required behaviour. Optional behaviours may also be specified. Allowable combinations of the various models are summarized in Table 3-1. To select a material model, specify the model type parameter using the appropriate upper-case string.

Below is a brief listing of available behaviours, the associated models for each behaviour, and the EnduricaMaterials parameters and allowed values for each Type of material model in (parenthesis):

• Stress-Strain Behaviour

o Hyperelastic Law, (hyperelastic : Type)

Arruda Boyce (ARRUDABOYCE)

Mooney-Rivlin (MOONEYRIVLIN)

NeoHookean (NEOHOOKEAN)

Ogden (OGDEN)

Reduced Polynomial (REDUCEDPOLY)

Van der Waals (VANDERWAALS)

• Mullins (Ogden-Roxburgh) effect (mullins : *)

Optional if one or more parameter is specified

Crack Growth Behaviour (more than one type of Growth can be selected)

o Fatigue/Cyclic Crack Growth (R=0) Behaviour (fcgr : Type)

Lake-Lindley (LAKELINDLEY)

Look-up table (FCGR(T))

Thomas (THOMAS)

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o Strain Crystallization Crack Growth (R>0) Behaviour (e-cryst : Type)

Paris Law (NOCRYSTALLIZATION)

Mars-Fatemi model (MARSFATEMI)

Table Look-up (TABULAR)

o Steady (Quasi-Static or Creep) Crack Growth Behaviour (ccgr : Type)

Unused (NOCREEP)

Power Law (POWERLAW)

Look-up table (DCDTIME(T))

o Ozone Attack (ozone : Type)

Unused (NONE)

Williams (WILLIAMS)

Gent-McGrath (GENTMCGRATH)

Finally, define values for the material parameters required for the selected material models. For instance, the Hyperelastic Model (hyperelastic : Type) which is enabled by selecting a value of NeoHookean (NEOHOOKEAN) requires two parameters:

hyperelastic : NEOHOOKEAN BULK_MODULUS

hyperelastic : NEOHOOKEAN C10

Once material parameters have been specified for the first time, it is highly recommended to verify their accuracy. Verification and calibration of the initial crack size can be accomplished using the auxialliary outputs provided by fe-safe/RubberTM (see section 3.3 below) for representative elements.

For a given material, models for different aspects of the material behaviour are combined to fully specify the stress-strain and crack growth behaviours. There are few restrictions on the allowable combinations. Table 3-1shows the valid combinations.

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Hyperelastic Models R=0 Cyclic Crack Growth

R>0 Cyclic Crack Growth

Time Dependent Crack Growth

Neo

-Hoo

kean

Moo

ney-

Rivl

in

Arru

da B

oyce

Redu

ced

Poly

nom

ial

Van

der W

aals

Ogd

en

Ogd

en-R

oxbu

rgh

Thom

as

Lake

-Lin

dley

Look

-up

tabl

e

Paris

Mar

s-Fa

tem

i

Look

-up

tabl

e

Pow

er L

aw

Look

-up

tabl

e

Gent

-McG

rath

Ozo

ne A

ttac

k

Will

iam

s Ozo

ne A

ttac

k

Hype

rela

stic

Mod

els

Neo-Hookean X X X X X X X X X X X X

Mooney-Rivlin X X X X X X X X X X X X

Arruda Boyce X X X X X X X X X X X X

Reduced Polynomial X X X X X X X X X X X X

Van der Waals X X X X X X X X X X X X

Ogden X X X X X X X X X X X X

Ogden-Roxburgh X X X X X X 1 X X X X X X X X X X

R=0

Cycl

ic

Crac

k Gr

owth

Thomas X X X X X X X X 2 2 2 X X X X

Lake-Lindley X X X X X X X X 2 2 X X X X

Look-up table X X X X X X X X 2 2 X X X X

R>0

Cycl

ic

Crac

k Gr

owth

Paris X X X X X X X 2 2 2 X X X X X

Mars-Fatemi X X X X X X X 2 X X X X X

Look-up table X X X X X X X 2 2 2 X X X X X

Tim

e De

pend

ent

Crac

k Gr

owth

Power Law X X X X X X X X X X X X X X X X

Look-up table X X X X X X X X X X X X X X X X

Gent-McGrath Ozone Attack X X X X X X X X X X X X X X X X

Williams Ozone Attack X X X X X X X X X X X X X X X X

Table 3-1 Material model compatibility table

1. A hyperelastic model must be used in conjunction with the Ogden-Roxburgh (Mullins effect) model

2. Cyclic crack growth model must include specification of both R=0 and R>0 behaviour

Note: Two models are compatible for use in the same material definition if the corresponding entry in the table contains 'X'. Otherwise, the two models may not be used together.

Solution Overview


Issue: 3 Date: 08.09.2015

3.2.4 Material Parameters

Unused Parameters

These are required in any materials database for the fe-safe User Interface, but are not used by the fe-safe/RubberTM plug-in, so don’t modify these parameters:

gen:Algorithm Set to Endurica for Visual purposes only

gen:MaterialsUnits Do Not Use

text:Data_Quality Locked, unused, set to undefined

gen:PoissonsRatio Locked, unused, set to 0.5

gen:ConstAmpEnduranceLimit Locked, unused, set to 1E15

text:RevisionHistory Locked, unused, set to undefined

Table 3-2 Unused parameters

Database Parameters

These are used to track the source of materials datasets and the date and number of times a dataset has been modified within the fe-safe/RubberTM User Interface:

text:Source Can be used for source publication references, etc

text:RevisionNumber Automatically updates, number of revisions in the User Interface

text:RevisionDate Automatically updates, date of last revision in the User Interface

Table 3-3 Database parameters

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Stress-Strain Models

These models are used to configure the stress- strain response. The model and parameter values should be set to match the FE analysis.

hyperelastic:Type

Select one of six required stress-strain laws for fully relaxing cycles

ARRUDABOYCE

MOONEYRIVLIN

NEOHOOKEAN

OGDEN

REDUCEDPOLY

VANDERWAALS

Table 3-4 Stress-strain model types

Once a model is selected by using the hyperelastic:Type parameter, all of the parameters associated with the model must be entered except where noted as optional below.

Required parameters for the material model are marked with ‘x’, optional parameters are marked with ‘o’. Should an optional parameter not be used, enter Unused.

Arruda Boyce Model

x – Required; o – Optional

Table 3-5 Arruda Boyce parameters

Mooney Rivlin Model

hyperelastic:Type

MOONEYRIVLIN

hyperelastic:Type ARRUDABOYCE

hyperelastic:ARRUDABOYCE BULK_MODULUS Bulk Modulus K [MPa] x

hyperelastic:ARRUDABOYCE LIMIT_STRETCH λm [unitless] x

hyperelastic:ARRUDABOYCE SHEAR_MODULUS Shear Modulus G [MPa] x

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hyperelastic:MOONEYRIVLIN BULK_MODULUS Bulk Modulus K [MPa] x

hyperelastic:MOONEYRIVLIN C01 C01 [MPa] x

hyperelastic:MOONEYRIVLIN C10 C10 [MPa] x


Table 3-6 Mooney Rivlin parameters

Neo-Hookean Model

hyperelastic:Type

NEOHOOKEAN

hyperelastic:NEOHOOKEAN BULK_MODULUS Bulk Modulus K [MPa] x

hyperelastic:NEOHOOKEAN C10 C10 [MPa] x


Table 3-7 Neo-Hookean parameters

Ogden Model

hyperelastic:Type

OGDEN

hyperelastic:OGDEN ALFA1 α1 [unitless] x

hyperelastic:OGDEN ALFA2 α2 [unitless] o





hyperelastic:OGDEN D1 D1 [(MPa)-1] x

hyperelastic:OGDEN D2 D2 [(MPa)-1] o





hyperelastic:OGDEN MU1 µ1 [MPa] x

hyperelastic:OGDEN MU2 µ2 [MPa] o


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Table 3-8 Ogden parameters

Reduced Polynomial Model

hyperelastic:Type

REDUCEDPOLY

hyperelastic:RP C10 C10 [MPa] x

hyperelastic:RP C20 C20 [MPa] o





hyperelastic:RP D1 D1 [(MPa)-1] x

hyperelastic:RP D2 D2 [(MPa)-1] o






Table 3-9 Reduced Polynomial parameters

Van der Waals Model

hyperelastic:Type

VANDERWAALS

hyperelastic:VW ALPHA α parameter [unitless] x

hyperelastic:VW BETA β parameter [unitless] x

hyperelastic:VW BULK_MODULUS Bulk Modulus K [MPa] x

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hyperelastic:VW LIMIT_STRETCH λm [unitless] x

hyperelastic:VW SHEAR_MODULUS Shear Modulus G [MPa] x


Table 3-10 Van der Waals parameters

Optional Ogden-Roxburgh (Mullins effect) Model

This effect can be combined with any hyperelastic stress strain model. A hyperelastic stress-strain model must be selected for the effect to be applied. The material parameters configured for the optional effect should reflect the Mullins (Ogden-Roxburgh) response that was used in the FEA analysis. Once the effect is selected by configuring the parameters, the effect will be applied to the stress-strain law in fe-safe/RubberTM. If using the model, it is required to define all 3 parameters. See the fe-safe/RubberTM Theory Manual for details.

hyperelastic:Type ARRUDABOYCE

MOONEYRIVLIN

NEOHOOKEAN

OGDEN

REDUCEDPOLY

VANDERWAALS

mullins:beta β [unitless] o o o o o o

mullins:m m [MPa] o o o o o o

mullins:r r [unitless] o o o o o o


Table 3-11 Ogden-Roxburgh parameters

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Fatigue Crack Growth Rate (R=0) Parameters

The Fatigue Crack Growth parameters define cyclic crack growth behaviour under fully relaxing conditions. Three models are available in fe-safe/Rubber: Thomas (power law), Lake Lindley, or Table Lookup models. The models describe fatigue crack growth as a function of peak crack driving force (Tmax), for fully relaxing (e.g. R=0) cyclic loading. Find details of each material model in the fe-safe/RubberTM Theory Manual.

Description

fcgr:Type

Select one of three required fatigue crack growth rate laws for fully relaxing cycles T

HOMAS

LAKELINDLEY

FCGR(T)

fcgr:c0 Initial Crack Diameter [mm] x x x

fcgr:cf Crack Diameter at Failure [mm] x x x

fcgr:F0 Initial Power Law slope [unitless] x x

fcgr:rc Crack Growth Rate at Critical Value [mm/cyc] x x

fcgr:T0 Mechanical Fatigue Threshold [kJ/m2])* x x

fcgr:Tc Critical Crack Driving Force [kJ/m2] x x x

fcgr:TempCoef Temperature Coefficient [1/degC]) o o o

fcgr:TempRef Reference Temperature [degC] o o o

fcgr:Tt Crack Driving Force at Point of Transition [kJ/m2] x

fcgr:fcgr(T) Crack Growth Rate as a function of Tmax [mm/cyc] x


Table 3-12 Fatigue Crack Growth Rate parameters

The Table Look-up model (FCGR(T)) requires that parameter fcgr:fcgr(T) define a list of crack growth rates ri (each ri may be any positive number). Each crack growth rate is associated to a crack driving force Ti in the range T0 < Ti < Tc. The values Ti are inferred on the basis of uniform logarithmic spacing over the interval. Up to 1024 levels can be entered as long as they are equally spaced on a log scale, for instance:

Tmax (assumed) fcgr(T)

0.1 1e-9

1 1e-5

10 1e-7

100 1e-3

If temperature effects are not to be used, set to TempCoef= 0 and TempRef=25 deg C

Solution Overview


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Strain Crystallization Crack Growth (R>0) Parameters

The Strain Crystallization parameters cover cyclic crack growth behaviour under non-relaxing (R>0) conditions. Three models are available in fe-safe/Rubber: Paris Law (No Crystallization), Mars-Fatemi, or Tabular models. These models describe an equivalent crack driving force, that would give the same crack growth were the cycle fully relaxing based on maximum crack driving force and load ratio R. Using the Paris law for non-relaxing cycles (NOCRYSTALLIZATION) requires no additional material parameters other than the type parameter be selected. Find details of each material model in the fe-safe/RubberTM Theory Manual.

Description

e-cryst:Type Select one of three required fatigue crack growth rate laws for non-relaxing cycles N

OCRYSTALLIZATION

MARSFATEMI

TABULAR

e-cryst:Fexp Power Law exponent 2

e-cryst:F1 Power Law coefficient 1 1



e-cryst:x(R) Crystallization as a function of load ratio R x


Table 3-13 Strain Crystallization Crack Growth parameters

The Mars-Fatemi model (MARSFATEMI) includes two optional methods:

1. Polynomial – requires parameters marked with 1 above

2. Exponential - requires parameters marked with 2 above

Note: Do not specify parameters for both options.

The Tabular model (TABULAR) model requires parameter e-cryst:x(R) define a crystallization function x at equally-spaced (on a log scale) intermediate levels of load ratio (R) (which may be any number between 0 and 1, typically increasing). Up to 1024 levels can be entered as long as they are equally spaced on a log scale, for instance:

R (assumed) fcgr(T)

0.1 0.0

0.2 0.156

…

0.9 0.995

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1.0 1.0

Steady (Quasi-Static or Creep) Crack Growth Behaviour Parameters

The Steady or Creep Crack Growth parameters cover static crack growth behaviour due to viscoelasticity. Two models are available in fe-safe/RubberTM: Power Law or Table Lookup models. The Creep Crack Growth Rate type parameter can also be set to No Creep so that the model will not be applied. These models describe a time rate of viscoelastic rupture as a function of crack driving force. Find details of each material model in the fe-safe/RubberTM Theory Manual.


Table 3-14 Viscoelastic creep crack growth rate parameters

The Table Look-up model (DCDTIME(T)) model requires that parameter ccgr:ccgr(T) define a list of crack growth rates ri (which may be any positive number) at equally-spaced (on a log scale) intermediate levels of static crack driving force (T). Up to 1024 levels can be entered as long as they are equally spaced on a log scale, for instance:

T (assumed) fcgr(T)

100 1e-9

1000 2e-9

10000 5e-9

100000 1e-8

If temperature effects are not to be used, set to TempCoefQS=0 and TempRefQS=25 deg C.

Description

ccgr:Type Select one of the three required creep crack growth rate type parameters for static loading N

OCREEP

POWERLAW

DCDTIME(T)

ccgr:FQS Slope of the Power Law curve [unitless] x

ccgr:RQS Time Rate of crack growth (rq) at TQS [mm/sec] x

ccgr:TempCoefQS Temperature coefficient (Cq) [1/deg C] o o

ccgr:TempRefQS Reference Temperature (θq0) [deg C] o o

ccgr:TMINQS Minimum Crack Driving Force (T0q) [kJ/m2] x x

ccgr:TMAXQS Maximum Crack Driving Force (Tc) [kJ/m2] x

ccgr:TQS Reference Crack Driving Force (Tq) [kJ/m2]

ccgr:ccgr(T) Time Rate of crack growth as a function of T [mm/sec] x

Solution Overview


Issue: 3 Date: 08.09.2015

Ozone Effect Parameters

The Ozone Effect or Attack parameters cover static crack growth behaviour due to environmental or chemical attack. Two models are available in fe-safe/Rubber: Williams or Gent-McGrath models. The Ozone Effect type parameter can also be set to None so that the model will not be applied. These models describe a time rate of rupture as a function of crack driving force. Find details of each material model in the fe-safe/RubberTM Theory Manual.


Table 3-15 Chemical attack static crack growth rate parameters

Description

ozone:Type Select one of three required ozone crack growth rate type parameters for chemical attack N

ONE

WILLIAMS

GENTMCGRATH

ozone:Fv Coefficient/exponent of temperature effect [unitless] x

ozone:Gv Threshold of Exponential temperature effect [deg C] x

ozone:Kv Ozone attack constant Kv [mm/sec] x

ozone:Kz Ozone attack constant Kz [ mm/sec]/][Mol03/MolAir)] x

ozone:rz Time Rate of crack growth above ozone Threshold Tz [ mm/sec] x

ozone:Tg Temperature at Glass Transition [deg C] x

ozone:Tz Ozone effect crack growth Threshold (Tz) [kJ/m2] x x

Analysis Procedures


Issue: 3 Date: 13.07.2016

3.2.5 Common Units System for Materials

The default unit convention of the fe-safe/RubberTM materials database is SI (mm, N). Using Material Default Units in the fe-safe User Interface is not appropriate.

When entering materials parameters, if sources are in English Units the user must convert to metric units before entering the parameters into the fe-safe/RubberTM materials database.

Table 3-16 gives typical quantities from English to SI.

Table 3-16 Typical units for Rubber fatigue material parameters

Quantity SI Units (mm, N) English Units (in, lbf)

Conversion Factor (English to SI)

Pressure, Stress, Modulus, Energy Density

MPa psi=lbf/in2 6.895e-3 MPa/psi

Bulk Compliance 1/ MPa 1/psi=in2 / lbf 145.0377 psi/MPa

Mullins r, beta Unitless Unitless none

Mullins m MPa psi=lbf/in2 6.895e-3 MPa/psi

Flaw size mm in 25.4 mm/in

Fatigue crack growth rate

mm/cyc in/cyc 25.4 (mm/in)

Crack Driving Force (Tear Energy, Energy Release Rate)

kJ/m2 inlbf / in2 5.710 e-3 (lbf/N)(m/in)

Temperature deg C deg F (5/9)*(deg F-32)

Temperature Coefficient

1/degC 1/degF (9/5)(1/deg F)/(1-32(1/deg F))

Quasistatic crack growth rate

mm/s in/s 25.4 (mm/in)

Ozone attack constant Kz

(mm/s) / (Moles O3 / Mole Air)

(in/s) / (Moles O3 / Mole Air)

25.4 (mm/in)

Ozone attack constant Kv

mm/s in/s 25.4 (mm/in)

Solution Overview


Issue: 3 Date: 08.09.2015

3.2.6 Configuring a Loading Definition

To configure loading definitions in fe-safe/RubberTM there must be a sequence of stress results and strain results from a Finite Element Solution opened in fe-safe. The stress and strain results should be obtained at uniformly-timed intervals as part of the FE model solution process. The user configures the loading definition in the Loading Settings window using datasets which have been loaded into the Current FE Models window, from FE models (see the fe-safe User Guide for details on defining fatigue loadings). This is done by configuring a dataset sequence of paired stresses and strains in one Elastic-Plastic block:

Figure 3-4 Specifying the sequence of stresses and strains

The Loading Settings window in fe-safe requires stresses and strains for all fe-safe/RubberTM loading definitions.

The loading block containing the stress and strain pairs will be labelled as an Elastic-Plastic block regardless of the stress-strain law used in the FE solution (e.g. fe-safe does not distinguish the Hyperelastic law configured in the FE solution). This is only a naming convention, stresses and strains actually follow the stress-strain law the user implemented in FE. The block must contain datasets defining at least two instants of time.

Multiple Blocks and Repeats cannot be used with fe-safe/RubberTM. Scale-and-combine loading is not appropriate since it applies only to results from Elastic FE solutions.

For analyses requiring time-dependent crack growth models, it is required to use the loading settings to specify the total time duration of the given histories using the Length in Seconds option as shown in Figure 3-5.

Analysis Procedures


Issue: 3 Date: 13.07.2016

Figure 3-5 Length in seconds applied

The Loading Definition (LDF) file can be used to define complex sequences or reference loading definitions for remote analysis, as described in the fe-safe User Guide. For instance the loading configured in Figure 3-5 can be saved as a text file and edited outside of the fe-safe/RubberTM User Interface as an LDF file for later modification and reuse:

# .ldf file created by fe-safe compliant product [mswin] INIT END # Block number 1 BLOCK dt=1 ds=1, de=2 ds=3, de=4 ds=5, de=6 ds=7, de=8 ds=9, de=10 ds=11, de=12 END

To exit the Loading Settings window select the Analysis Settings tab.

3.2.7 Loading the Plug-in

To enable the Endurica fatigue solver technology, first load the plug-in to the fe-safe/RubberTM environment. Loading the plug-in can be accomplished by selecting Tools >> Load Plugin from the top right of the fe-safe User Interface and browsing to the Endurica1.dll library file from the installation directory under /plugins. A dialogue will be displayed to indicate that the plug-in was loaded as shown in Figure 3-6:

Solution Overview


Issue: 3 Date: 08.09.2015

Figure 3-6 Plug-in loaded

3.2.8 Configuring Plug-in Algorithm and Settings

To select from the plug-in algorithms, select the "Algorithm" column in the "Fatigue From FEA" dialog box. A new window will open named "Group Algorithm Selection." In this window, select "Analyse using a plug-in algorithm" and choose from the algorithms under the "Plug-in Algorithm" drop-down menu, as shown in Figure 3-7:

Figure 3-7 Analysis algorithm selection

The Algorithm selections in the plug-in are:

• Bulk (not recommended): only to be used for groups of 3D elements when the strain components are known with an accuracy of at least 5 significant digits. Only the strain datasets in the Loading Settings window will be used for fatigue life calculation.

• Bulk with Pressure: to be used for groups of 3D elements when the accuracy of the strain components is not known, or when the strain components may not accurately reflect the appropriate volume change. Stress datasets in addition to strain datasets in the Loading Settings window will be used for fatigue life calculation.

• Surface: to be used for groups of 2D elements on the surface of a finite element mesh, where an accurate plane stress condition is enforced. Only the strain datasets in the Loading Settings window will be used for fatigue life calculation.

Analysis Procedures


Issue: 3 Date: 13.07.2016

Cracks often nucleate on a free surface of a 3-dimensional part. When computing the strain history for this free surface in the FE solver, it is highly recommended to ensure an accurate representation of the plane stress condition by covering the free surfaces of the model with 2D plane stress membrane elements. Fulfilling plane stress conditions at free surfaces, and applying local coordinate systems in the plane of the surface are required for fe-safe/RubberTM, which is why membrane elements on the free surfaces of any 3D models are recommended.

To access the optional Settings for the plug-in algorithm, click on the Settings button as shown in Figure 3-7, and the Edit Plug-in Settings dialogue will appear as shown in Figure 3-8.

Figure 3-8 Plug-in settings

Setting 1: Threshold flag is set to 0 by default, and can be set to 1 in order to eliminate nodes from analysis. Specifying this optional parameter requests that critical plane analysis only be performed on those histories in which the product (strain energy density) x (flaw size) x 2 x pi > the mechanical threshold (fcgr: T0). This option when set to 1 can significantly increase execution speed, by avoiding calculations that will yield essentially infinite life.

Settings 10 and 11 define the discretization of the half-sphere of trial critical planes, as illustrated in Figure 3-9. Each point on this half-sphere represents a unit vector which is the normal to a particular material plane. For each item (node, element, etc) in the project, the discretization governs how many individual fatigue calculations will be made. Finer discretization will give longer run times, and better resolution of the critical plane. Coarser discretization will give shorter run times, and less accurate resolution of the critical plane. The half-sphere is discretized in terms of the two spherical coordinate system variables phi and theta:

Solution Overview


Issue: 3 Date: 08.09.2015

• N[phi] defines the number of angles used to discretize the half sphere along the phi direction. Phi ranges from 0 to 90 degrees. The default discretization of 5 provides for normal vectors every 18 degrees from phi=0 to 90.

• N[theta] defines the number of angles used to discretize the half sphere along the theta direction. Theta ranges from 0 to 360 degrees. The default discretization of 16 provides for normal vectors every 22.5 degrees from theta=0 to 360.

The default settings thus give a total of 5x16=80 directions searched per item.

Note: The coordinate system the unit vectors are generated in for each item is the same as that used to describe the strain history components, a local coordinate system on the element (see section Requesting Output3.2.10 below).

Figure 3-9 Half sphere discretization for critical plane search

3.2.9 Defining Environmental Conditions

Environmental conditions such as material Temperature and Ozone concentration in the surrounding atmosphere may affect crack growth behaviour. These effects can be modelled in fe-safe/RubberTM.

To access the optional Settings for the plug-in algorithm, click on the Settings button as shown in Figure 3-7, and the Edit Plug-in Settings dialogue will appear as shown in Figure 3-8 above. Settings 8 and 9 can be used to set the Temperature or Ozone concentration for the entire mesh being analysed with the plug-in. fe-safe/RubberTM assumes that temperature and ozone concentration are constant in time.

To account for temperature effects, the user must specify the Temperature Sensitivity Coefficient (TempCoef, TempCoefQS) and Reference Temperature Coefficient (TempRef, TempRefQS) in the crack growth material models, of the materials dataset. Please see Section 3.2.3 above. Units of Temperature in setting 8 are degrees C. If these effects are not to be used, set to TempCoef=TempCoefQS=0 and TempRef=TempRefQS=20).

NPHI

NTHETA

Analysis Procedures


Issue: 3 Date: 13.07.2016

To account for ozone concentration, the user must specify the values required for the selected Ozone Attack crack growth model (Williams or Gent McGrath), in the materials dataset. Please see section 3.2.3 above. Units of Ozone concentration in Setting 9 are molar fraction, as discussed in the fe-safe/RubberTM Theory Manual.

3.2.10 Requesting Output

LogLife contours will be exported to the Output File by default as discussed in the fe-safe User Guide, along with a Results Log file pertaining to the fe-safe configurations.

Optional Settings for the plug-in algorithm provide the user the ability to generate additional diagnostic output in ASCII format for all nodes analysed while running a job using fe-safe/RubberTM.

Large amounts of text output can be produced if the number of elements analysed is large, and if plug-in settings are configured to export additional log files. The List of Items feature of the fe-safe User Interface can be used to limit analysis for additional exports and outputs requested using the optional Settings. Please see the fe-safe User Guide for details on the diagnostic techniques available in the fe-safe user interface.

To access the optional Settings for the plug-in algorithm, click on the Settings button as shown in Figure 3-7 above, and the Edit Plug-in Settings dialogue will appear as shown in Figure 3-8

General types of output that are available include:

• Material Model Verification Methods (Settings 5-7): material model verification (stress-strain curves, fatigue crack growth curves, effect of initial flaw size on fatigue life). See section 3.3 below.

• Exports and Outputs (Settings 2-4): final and intermediate quantities from the fatigue analysis (rainflow count, cracking plane orientation, CED history on cracking plane). See section 3.4 below.

3.3 Verifying Material Model Definitions

Before conducting a fatigue analysis with newly obtained material parameters, the user should verify that the material parameters specified in the materials dataset describe the intended behaviour. fe-safe/RubberTM provides output options to facilitate this important task. Verification settings are set to NO by default.

3.3.1 Stress-Strain

The stress-strain models can be verified by configuring the value of the following output request:

Solution Overview


Issue: 3 Date: 08.09.2015

Setting 6: Verify stress/strain (YES)

This produces a verify-stress-strain log file. If for example C:/temp/example.odb is the name of the output file, the log file C:/temp/example_MATVERIFYSTRESS.log will be created. Inspect the text file to see that two tables of stress-strain data are generated for each of the elements analysed:

• A loading curve for each of the following modes of deformation: simple tension (StressST), planar tension (StressPT), equibiaxial tension (StressEB), versus (Strain).

• A Hydrostatic stress-strain curve containing Volumetric Strain (VolumeStrain) and Pressure (Pressure). The range of strain to be evaluated can be specified by the user.

For instance:

ITEM= 2748, SUBITEM= 1, MATERIAL=NR_GUM2 Loading Curve Strain, StressST,StressPT,StressEB -0.50000E+00 -0.70000E+00 -0.15000E+01 -0.63000E+01 -0.42105E+00 -0.48090E+00 -0.91486E+00 -0.29591E+01 -0.34211E+00 -0.33050E+00 -0.57078E+00 -0.14912E+01 -0.26316E+00 -0.22100E+00 -0.35256E+00 -0.77342E+00 -0.18421E+00 -0.13736E+00 -0.20522E+00 -0.39037E+00 -0.10526E+00 -0.70880E-01 -0.10027E+00 -0.16983E+00 -0.26316E-01 -0.16220E-01 -0.21922E-01 -0.33791E-01 0.52632E-01 0.30026E-01 0.39051E-01 0.55770E-01 0.13158E+00 0.70123E-01 0.88285E-01 0.11852E+00 0.21053E+00 0.10562E+00 0.12936E+00 0.16516E+00 0.28947E+00 0.13761E+00 0.16461E+00 0.20179E+00 0.36842E+00 0.16688E+00 0.19563E+00 0.23200E+00 0.44737E+00 0.19400E+00 0.22351E+00 0.25799E+00 0.52632E+00 0.21941E+00 0.24902E+00 0.28112E+00 0.60526E+00 0.24344E+00 0.27270E+00 0.30229E+00 0.68421E+00 0.26633E+00 0.29498E+00 0.32208E+00 0.76316E+00 0.28830E+00 0.31614E+00 0.34089E+00 0.84211E+00 0.30948E+00 0.33643E+00 0.35899E+00 0.92105E+00 0.33002E+00 0.35600E+00 0.37657E+00 0.10000E+01 0.35000E+00 0.37500E+00 0.39375E+00 Hydrostatic stress-strain curve VolumeStrain, Pressure -0.50000E-01 -0.14496E+03 -0.44737E-01 -0.13018E+03 -0.39474E-01 -0.11528E+03 -0.34211E-01 -0.10028E+03 -0.28947E-01 -0.85158E+02 -0.23684E-01 -0.69926E+02 -0.18421E-01 -0.54582E+02 -0.13158E-01 -0.39127E+02 -0.78947E-02 -0.23559E+02 -0.26316E-02 -0.78809E+01 0.26316E-02 0.79086E+01 0.78947E-02 0.23809E+02 0.13158E-01 0.39819E+02 0.18421E-01 0.55940E+02 0.23684E-01 0.72170E+02 0.28947E-01 0.88510E+02 0.34211E-01 0.10496E+03 0.39474E-01 0.12152E+03 0.44737E-01 0.13818E+03 0.50000E-01 0.15496E+03

This data can be used to plot curves and check that they match expectations (perhaps experimental measurements), similar to those below:

Analysis Procedures


Issue: 3 Date: 13.07.2016

Figure 3-10 Verification curve for hydrostatic stress-strain behavior

Figure 3-11 Verification curves for simple, planar, and equibiaxial stress-strain behavior

3.3.2 Crack Growth Rate

The crack growth models can be verified via the following output requests:

Setting 6: Verify FCG rate law (YES)

-150

0

150

-0.05 0 0.05

Pres

sure

(MPa

)

Volume Strain

Material = NRGUM2

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

-0.75 0 0.75

Engi

neer

ing

Stre

ss (M

Pa)

Engineering Strain

StressSTStressPTStressEB

Material = NRGUM2

Solution Overview


Issue: 3 Date: 08.09.2015

This produces a verify-fcg-rate-law log file. For example for the output file C:/temp/example.odb the log file C:/temp/exampleVERIFYFCGR.log will be created. Inspect the text file to see that one table of fatigue crack growth data is generated for each of the elements analysed, this includes five columns:

• Energy Release Rate (EnergyReleaseRate)

• Load Ratio (RRatio)

• Crack Growth Rate (CGR)

• Quasi-Static Crack Growth Rate (QSCGR)

• Total Fatigue Crack Growth Rate (TotalFCGR)

The data in the log are based on all material models configured for the material shown.

For instance:

ITEM= 2745, SUBITEM= 1, MATERIAL=MY_RUBBER

EnergyReleaseRate, RRatio, CGR, QSCGR, TotalFCGR

0.20000E-01 0.00000E+00 0.10000E-17 0.00000E+00 0.10000E-17

0.28251E-01 0.00000E+00 0.10000E-17 0.00000E+00 0.10000E-17

…

0.14159E+02 0.00000E+00 0.10000E+19 0.71174E+00 0.10000E+19

0.20000E+02 0.00000E+00 0.10000E+19 0.28335E+01 0.10000E+19

0.20000E-01 0.20000E+00 0.10000E-17 0.00000E+00 0.10000E-17

0.28251E-01 0.20000E+00 0.10000E-17 0.00000E+00 0.10000E-17

…

0.14159E+02 0.20000E+00 0.10000E+19 0.14759E+01 0.10000E+19

0.20000E+02 0.20000E+00 0.10000E+19 0.58755E+01 0.10000E+19

0.20000E-01 0.40000E+00 0.10000E-17 0.00000E+00 0.10000E-17

0.28251E-01 0.40000E+00 0.10000E-17 0.00000E+00 0.10000E-17

…

0.14159E+02 0.40000E+00 0.10000E+19 0.27342E+01 0.10000E+19

0.20000E+02 0.40000E+00 0.10000E+19 0.10885E+02 0.10000E+19

0.20000E-01 0.60000E+00 0.10000E-17 0.00000E+00 0.10000E-17

0.28251E-01 0.60000E+00 0.10000E-17 0.00000E+00 0.10000E-17

…

0.10024E+02 0.60000E+00 0.10000E+19 0.11717E+01 0.10000E+19

0.14159E+02 0.60000E+00 0.10000E+19 0.46644E+01 0.10000E+19

0.20000E+02 0.60000E+00 0.10000E+19 0.18569E+02 0.10000E+19

0.20000E-01 0.80000E+00 0.10000E-17 0.00000E+00 0.10000E-17

…

0.14159E+02 0.80000E+00 0.10000E+19 0.74715E+01 0.10000E+19

0.20000E+02 0.80000E+00 0.10000E+19 0.29745E+02 0.10000E+19

0.20000E-01 0.10000E+01 0.10000E-17 0.00000E+00 0.10000E-17

0.28251E-01 0.10000E+01 0.10000E-17 0.00000E+00 0.10000E-17

…

0.14159E+02 0.10000E+01 0.10000E+19 0.11388E+02 0.10000E+19

0.20000E+02 0.10000E+01 0.10000E+19 0.45335E+02 0.10000E+19

This data can be used to generate curves, similar to those below:

Analysis Procedures


Issue: 3 Date: 13.07.2016

Figure 3-12 Verification curves for a material exhibiting creep crack growth

Figure 3-13 Verfication curves for a material exhibiting fatigue crack growth

Temperature and ozone concentration to be evaluated can be specified by the user using optional Settings 8 and 9 as discussed in Section 3.2.9 above. Re-run the post-processing analysis with a new Output File name to be sure of not overwriting the original log, in order to get the verification data for the new environmental settings.

3.3.3 Flaw Size

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-01 1.E+00 1.E+01 1.E+02

Qua

sist

atic

Gro

wth

Rat

e, m

m/s

ec

EnergyReleaseRate, kJ/m2

R=0

R=0.2

R=0.4

R=0.6

R=0.8

R=1

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-01 1.E+00 1.E+01 1.E+02

Fatig

ue G

row

th R

ate,

mm

/cyc

EnergyReleaseRate, kJ/m2

R=0

R=0.2

R=0.4

R=0.6

R=0.8

R=1

Solution Overview


Issue: 3 Date: 08.09.2015

The predicted fatigue life depends strongly on the specified size of initial flaws (those that exist before the application of any load history). Thus, accurate prediction of the fatigue life depends on accurate knowledge of the flaw size. Flaw size may be determined by factors both intrinsic and extrinsic to the material itself. These factors may include compound recipe (polymer microstructure, filler particle size and distribution), and manufacturing processes (degree of mixing, surface imperfections introduced during moulding). It is therefore good practice to calibrate the flaw size on the basis of known fatigue test results on a part similar to the one that is to be analyzed (same compound, same manufacturing processes, etc.). This calibration can be performed by simulating the known test condition over a range of flaw sizes. The flaw size that gives a prediction in agreement with the known result can then be selected and used in subsequent analysis.

Setting 6: Calibrate flaw size (YES)

This produces a flawsize calibration log file. For example, for the output file C:/temp/example.odb the log file C:/temp/example CALIBRATE_FLAWSIZE.log will be created. Inspect the text file to see that one table showing how the fatigue life depends on the assumed flaw size is generated for each of the elements analysed, this includes two columns:

• Initial Flaw size (first column)

• Fatigue life (second column

For instance:

ITEM= 2827, SUBITEM= 1, MATERIAL=MY_RUBBER 0.10000E-05 0.22001E+17 0.17378E-05 0.22001E+17 0.30200E-05 0.22001E+17 0.52481E-05 0.22001E+17 0.91201E-05 0.22001E+17 0.15849E-04 0.22001E+17 0.27542E-04 0.22000E+17 0.47863E-04 0.22000E+17 0.83176E-04 0.21999E+17 0.14454E-03 0.21998E+17 0.25119E-03 0.21996E+17 0.43652E-03 0.21991E+17 0.75858E-03 0.20832E+17 0.13183E-02 0.20820E+17 0.22909E-02 0.20800E+17 0.39811E-02 0.17702E+17 0.69183E-02 0.14500E+17 0.12023E-01 0.95509E+16 0.20893E-01 0.10764E+16 0.36308E-01 0.77238E+05 0.63096E-01 0.54508E+05 0.10965E+00 0.38172E+05 0.19055E+00 0.24080E+05 0.33113E+00 0.11826E+05 0.57544E+00 0.43195E+04

Analysis Procedures


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This data can be used to generate a calibration curve, similar to the one below:

Figure 3-14 Calibration curve for identifying flaw size

Once a flaw size calibration curve is generated for an element with representative strain range, it will then be used to find the flaw size corresponding to known fatigue results in a similar application, at a similar strain range.

Edit the material as discussed above in section 3.2.3 above to include the calibrated value of initial flawsize (fcgr:c0 (mm))

Initial flaw sizes would usually be expected to fall within the range:

1x10-6 m < c0 < 200x10-6 m

0.40x10-4 in < c0 < 8.0x10-3 in

3.4 Diagnostic Techniques including additional outputs

This section describes procedures for exporting additional diagnostic results from an analysis. These are useful when it is desired to better understand fatigue failure process details such as how the critical plane experiences the given load history, what individual cycles are identified in the rainflow count and how they rank in terms of damage contribution, and the dependence of fatigue life on plane orientation.

1.E+03

1.E+04

1.E+05

1.E+06

1.E+07

1.E-02 1.E-01 1.E+00

Com

pute

d Fa

tigue

Life

, Rep

eats

Initial Flaw Size, mm

Known fatigue life

Calib

rate

d fla

w si

ze

Solution Overview


Issue: 3 Date: 08.09.2015

To access the optional Settings for the plug-in algorithm, click on the Settings button as shown in Figure 3-7 above, and the Edit Plug-in Settings dialogue will appear as shown in Figure 3-8. Available diagnostic outputs include:

• Setting 2: Output Load History on critical plane (see section 3.4.2 below)

• Setting 3: Output rainflow count (see section 3.4.2 below)

• Setting 4: Output plane dependence (see section 3.4.2 below)

3.4.1 Identifying Failure Planes at a Point of Failure

It is sometimes of interest to predict the plane on which crack nucleation first occurs. This information can be useful as additional validation when comparing fatigue life predictions to experiments, or as a first step towards understanding the loading experienced at the failure location.

As part of its fatigue life calculation, fe-safe/RubberTM computes a fatigue life for each potential plane of failure. The failure plane with the shortest fatigue life is reported as the predicted failure plane. If multiple failure planes have identical minimum fatigue lives, fe-safe/RubberTM will report only one of the planes. However, it is possible to identify the other planes by plotting the damage sphere.

Setting 4: Output plane dependence (YES)

This produces a damage sphere log file. For example if C:/temp/example.odb is the name of the output file the log file C:/temp/exampleDAMAGESPHERE.log will be created. Inspect the text file to see that one table of failure plane data is generated for each of the elements analysed, this includes five columns:

• Increment of the Theta (Θ) ordinate of the spherical coordinate system (ITHETA)

• Increment of the Phi (Φ) ordinate of the spherical coordinate system (IPHI)

• Component 1 of the unit vector normal to the plane (R1)



• Fatigue Life on the plane (LIFE)

• Minimum Cracking Energy Density (CEDMIN)

• Maximum Cracking Energy Density (CEDMAX)

Analysis Procedures


Issue: 3 Date: 13.07.2016

For instance:

ITEM= 2827, SUBITEM= 1 ITHETA, IPHI, R1, R2, R3, LIFE, CEDMIN, CEDMAX 1 1 1.0000000 0.0000000 0.0000000 0.97500E+18 0.00000E+00 0.00000E+00 1 2 0.9238796 0.0000000 0.3826834 0.97500E+18 0.00000E+00 0.00000E+00 1 3 0.7071068 0.0000000 0.7071068 0.97500E+18 0.00000E+00 0.21019E-43 1 4 0.3826834 0.0000000 0.9238795 0.97500E+18 0.00000E+00 0.00000E+00 1 5 0.0000001 0.0000000 1.0000000 0.97500E+18 0.00000E+00 0.00000E+00 2 1 0.9135455 0.4067366 0.0000000 0.58945E+17 0.00000E+00 0.75265E-01 2 2 0.8440060 0.3757756 0.3826834 0.72860E+17 0.58855E-43 0.66163E-01 … 5 1 -0.1045284 0.9945219 0.0000000 0.11088E+06 0.40638E-43 0.28971E+00 5 2 -0.0965716 0.9188185 0.3826834 0.14260E+06 0.00000E+00 0.26765E+00 5 3 -0.0739127 0.7032332 0.7071068 0.75930E+16 0.00000E+00 0.19675E+00 5 4 -0.0400013 0.3805870 0.9238795 0.58945E+17 0.61657E-43 0.77709E-01 5 5 0.0000000 0.0000001 1.0000000 0.97500E+18 0.00000E+00 0.00000E+00 … 15 4 0.3495986 -0.1556515 0.9238795 0.52575E+18 0.22421E-43 0.11486E-01 15 5 0.0000001 0.0000000 1.0000000 0.97500E+18 0.00000E+00 0.00000E+00 16 1 1.0000000 -0.0000003 0.0000000 0.97500E+18 0.00000E+00 0.00000E+00 16 2 0.9238796 -0.0000003 0.3826834 0.97500E+18 0.00000E+00 0.00000E+00 16 3 0.7071068 -0.0000002 0.7071068 0.97500E+18 0.00000E+00 0.10370E-42 16 4 0.3826834 -0.0000001 0.9238795 0.97500E+18 0.00000E+00 0.98091E-44 16 5 0.0000001 0.0000000 1.0000000 0.97500E+18 0.00000E+00 0.00000E+00

Above, the lowest life in the table (0.11088E+06) is underlined. It corresponds to a normal vector of (-0.1045284, 0.9945219, 0.0000000). Three other normal vectors in the plane of the surface report lives close to this lowest life. For analyses using the Plug-in algorithm Surface, the fatigue life can be plotted as a function of the orientation angle Theta in the plane of the surface (Phi=1) as shown in Figure 3-15:

Figure 3-15 Damage sphere at Phi=1 for surface algorithm

5.10541

5.04485

5.04489

5.10541

0

5

10

15

201

2

3

4

5

6

7

89

10

11

12

13

14

15

log1

0(lif

e)

Solution Overview


Issue: 3 Date: 08.09.2015

The 3D damage sphere can be visualized using a third-party graph-plotting software, as colour contours of the logarithm of fatigue life. The contours would typically be plotted on the half-sphere defined by the tips of the plane unit normal vectors:

Figure 3-16 Damage sphere plotted in 3D and coloured according to log of life

Note: The coordinate system of reported unit vectors is the same as that used to describe the strain history components, that is, the local element system.

3.4.2 Computing the loading history experienced by the failure plane(s)

Comparing the loading history experienced locally on the failure plane to the loading history applied to the overall structure can reveal which events in the overall structural history contribute to the failure process, and which do not. Local loading history in fe-safe/RubberTM is always reported on the most critical plane, in terms of the parameter Cracking Energy Density. See the fe-safe/RubberTM Theory manual for definition of the Cracking Energy Density. Strain energy density, maximum principal stresses and strains are also reported.

Setting 3: Output load history on critical plane (YES)

Setting 4: Output rainflow count (YES)

Setting 3 produces a cracking energy density log file. For example if C:/temp/example.odb is the name of the output file the log file C:/temp/exampleCEDHISTORY.log will be created. Inspect the text file to see that one line of orientation and one table of history data is generated for each of the elements analysed, this includes nine columns:

Orientation

• Unit vector in 3 components of the plane of largest damage, with respect to Elemental coordinate system (Orientation)

History Table

-1

-0.5

0

0.5

1

-1-0.8-0.6-0.4-0.200.20.40.60.81

0

0.2

0.4

0.6

0.8

1

Analysis Procedures


Issue: 3 Date: 13.07.2016

• Instant or time point in the history series (INSTANT#)

• Cracking Energy Density (CED) on the critical plane

• Strain Energy Density (SED)

• Max Principal Strain 1 (MPE1)

• Mid Principal Strain 2 (MPE2)

• Min Principal Strain 3 (MPE3)

• Max Principal Stress 1 (MPS1)

• Mid Principal Stress 2 (MPS2)

• Min Principal Stress 3 (MPS3)

The example output is shown in Table 3-17.

The histories can be plotted in a third-party spreadsheet, for instance:

Figure 3-17 Local loading history on the critical plane

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30

Crac

king

Ene

rgy

Dens

ity (m

J/m

m3 )

time

Solution Overview


Issue: 3 Date: 08.09.2015

Figure 3-18 History of principal nominal strain

ITEM= 2827, SUBITEM= 1 ORIENTATION= 0.1045285 -0.9945219 0.0000000 INSTANT#, CED, SED, MPE1, MPE2, MPE3, MPS1, MPS2, MPS3 1 0.0000000E+00 0.1497603E-26 0.0000000E+00 0.0000000E+00 0.0000000E+00 -0.2997602E-11 -0.2997602E-11 -0.2997602E-11 2 0.1306290E-01 0.1262087E-01 0.8539510E-01 -0.3130800E-01 -0.4886055E-01 0.3023008E+00 0.4175706E-01 0.1230826E-04 3 0.5054469E-01 0.4926823E-01 0.1731749E+00 -0.6068128E-01 -0.9247273E-01 0.5654348E+00 0.7506965E-01 0.6139479E-04 4 0.1102905E+00 0.1083075E+00 0.2629688E+00 -0.8817786E-01 -0.1315388E+00 0.7990421E+00 0.1016899E+00 0.9859927E-04 5 0.1905114E+00 0.1882647E+00 0.3543851E+00 -0.1138772E+00 -0.1666352E+00 0.1010004E+01 0.1228851E+00 0.3048800E-04 6 0.2897097E+00 0.2877658E+00 0.4470367E+00 -0.1378694E+00 -0.1982532E+00 0.1203556E+01 0.1400054E+00 0.1611329E-03 7 0.0000000E+00 0.1497603E-26 0.0000000E+00 0.0000000E+00 0.0000000E+00 -0.2997602E-11 -0.2997602E-11 -0.2997602E-11 8 0.1306290E-01 0.1262087E-01 0.8539510E-01 -0.3130800E-01 -0.4886055E-01 0.3023008E+00 0.4175706E-01 0.1230826E-04 9 0.5054469E-01 0.4926823E-01 0.1731749E+00 -0.6068128E-01 -0.9247273E-01 0.5654348E+00 0.7506965E-01 0.6139479E-04 10 0.1102905E+00 0.1083075E+00 0.2629688E+00 -0.8817786E-01 -0.1315388E+00 0.7990421E+00 0.1016899E+00 0.9859927E-04 11 0.0000000E+00 0.1497603E-26 0.0000000E+00 0.0000000E+00 0.0000000E+00 -0.2997602E-11 -0.2997602E-11 -0.2997602E-11 12 0.1306290E-01 0.1262087E-01 0.8539510E-01 -0.3130800E-01 -0.4886055E-01 0.3023008E+00 0.4175706E-01 0.1230826E-04 13 0.5054469E-01 0.4926823E-01 0.1731749E+00 -0.6068128E-01 -0.9247273E-01 0.5654348E+00 0.7506965E-01 0.6139479E-04 14 0.1102905E+00 0.1083075E+00 0.2629688E+00 -0.8817786E-01 -0.1315388E+00 0.7990421E+00 0.1016899E+00 0.9859927E-04 15 0.1905114E+00 0.1882647E+00 0.3543851E+00 -0.1138772E+00 -0.1666352E+00 0.1010004E+01 0.1228851E+00 0.3048800E-04 16 0.2897097E+00 0.2877658E+00 0.4470367E+00 -0.1378694E+00 -0.1982532E+00 0.1203556E+01 0.1400054E+00 0.1611329E-03 17 0.0000000E+00 0.1497603E-26 0.0000000E+00 0.0000000E+00 0.0000000E+00 -0.2997602E-11 -0.2997602E-11 -0.2997602E-11 18 0.1306290E-01 0.1262087E-01 0.8539510E-01 -0.3130800E-01 -0.4886055E-01 0.3023008E+00 0.4175706E-01 0.1230826E-04 19 0.0000000E+00 0.1497603E-26 0.0000000E+00 0.0000000E+00 0.0000000E+00 -0.2997602E-11 -0.2997602E-11 -0.2997602E-11 20 0.1306290E-01 0.1262087E-01 0.8539510E-01 -0.3130800E-01 -0.4886055E-01 0.3023008E+00 0.4175706E-01 0.1230826E-04 21 0.5054469E-01 0.4926823E-01 0.1731749E+00 -0.6068128E-01 -0.9247273E-01 0.5654348E+00 0.7506965E-01 0.6139479E-04 22 0.1102905E+00 0.1083075E+00 0.2629688E+00 -0.8817786E-01 -0.1315388E+00 0.7990421E+00 0.1016899E+00 0.9859927E-04 23 0.1905114E+00 0.1882647E+00 0.3543851E+00 -0.1138772E+00 -0.1666352E+00 0.1010004E+01 0.1228851E+00 0.3048800E-04 24 0.2897097E+00 0.2877658E+00 0.4470367E+00 -0.1378694E+00 -0.1982532E+00 0.1203556E+01 0.1400054E+00 0.1611329E-03 25 0.0000000E+00 0.1497603E-26 0.0000000E+00 0.0000000E+00 0.0000000E+00 -0.2997602E-11 -0.2997602E-11 -0.2997602E-11

Table 3-17 Example CEDHISTORY log file

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

0 5 10 15 20 25 30

Max

imum

Prin

cipa

l Str

ain

time

MPE1

MPE2

MPE3

Analysis Procedures


Issue: 3 Date: 13.07.2016

Setting 4 produces a rainflow-counted cycle log file. For example if C:/temp/example.odb is the name of the output file the log file C:/temp/exampleRAINFLOW.log will be created. Inspect the text file to see that one table of cycles counted is generated for each of the elements analysed, this includes six columns:

• Event Pair Number (EVENTPAIR#)

• Peak Cracking Energy Density (PEAK)

• Load Ratio (R)

• Rate of growth of initial crack precursor due to the event pair (r)

• Instant of Minimum CED in the Pair (IMIN)

• Instant of Maximum CED in the Pair (IMAX)

For instance:

ITEM= 2827, SUBITEM= 1 EVENTPAIR#, PEAK, R, r, IMIN, IMAX 1 0.289710E+00 0.000000E+00 0.100000E-09 19 24 2 0.289710E+00 0.000000E+00 0.100000E-09 25 6 3 0.110291E+00 0.000000E+00 0.316200E-10 7 10 4 0.289710E+00 0.000000E+00 0.100000E-09 11 16 5 0.130629E-01 0.000000E+00 0.100000E-17 17 18

The most damaging event-pair can be identified by sorting the data in terms of the rate of initial crack growth (e.g. damage). The given instants of Minimum and Maximum CED can be referenced back into the original load history through columns IMIN and IMAX. The magnitude and damage contributions of all event-pairs can be compared by plotting them in a third-party spreadsheet, for instance:

Figure 3-19 Rainflow counted event pairs by Peak CED

1.E-13

1.E-11

1.E-09

1.E-07

1.E-05

1.E-03

1.E-01

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0 1 2 3 4 5 6

Initi

al c

rack

gro

wth

rate

, mm

/cyc

Peak

CED

, mJ/

mm

3

EventPair#

Peak CED

Initial crackgrowth rate

Solution Overview


Issue: 3 Date: 08.09.2015

3.5 Running fe-safe/RubberTM

As discussed in the fe-safe User Guide, the user must click on Analyse! once the project is configured. A summary window will display showing the configurations of the fe-safe User Interface (plug-in settings are not shown). Click Continue to start the analysis process. The Message Log window will display a percentage completion table, which will also be written to the Results Log file.

Depending on the number of potential failure locations to be evaluated and on the length of the time history, fe-safe/RubberTM analyses may be expected to run for times ranging from a few seconds to many hours.

3.5.1 fe-safe/RubberTM analysis process

The fe-safe/RubberTM analysis follows the process illustrated in Figure 3-20, for each individual item (material point) in the model. The individual item type (Centroid, Element, Node, Integration Point, Node) was determined when the FE model was first loaded into fe-safe (see Section 3.2.1).

a) The nominal strain (NE) and stress (S) are read from the FE model database into fe-safe. b) The loading history is configured according to the sequence of stress and strain datasets and the length in

seconds specified in Loading Settings (see section 3.2.6). c) Depending on the selected plug-in algorithm, adjustments are made as follows to the given history of nominal

strain: i. In the case that the Bulk with Pressure plug-in algorithm is selected, the 6 components of the given

nominal strain tensor are adjusted slightly so that the volume strain is exactly consistent with the given hydrostatic stress from the FE solution. This correction is needed because slight inaccuracies of the volume strain are common, and dependant on how strains are recovered from the model. Without correction, these variations can cause large inaccuracy of the hydrostatic pressure.

ii. In the case that the Surface plug-in algorithm is selected, the 6 components of the nominal strain tensor are calculated from the 3 in-plane nominal strain components, and from the plane stress condition (e.g. the out of plane stress is exactly 0).

iii. In the case that the Bulk plug-in algorithm is selected the nominal strain history is used “as-is”, without correction of any kind.

d) A series of material planes is generated based on the plug-in setting for damage sphere variables phi and theta (see section 3.2.8). Subsequent calculations will be repeated on each material plane, in order to identify the critical plane.

e) The local loading history is computed for each plane, giving the Cracking Energy Density as a function of time. f) A rainflow counting algorithm is then used to identify each individual cycle (e.g. peak and valley) contained

within the entire local loading history. g) A numerical integration of the crack growth rate law is made to determine the number of repeats (the life)

required to grow the initial flaw to its specified size at nucleation (see the fe-safe/RubberTM Theory manual). As a part of the computation, the crack growth rate contributions of individual cycles are summed to obtain a total rate of crack growth per repeat of the entire loading history. The initial and final flaw sizes, and all crack growth properties were specified as a part of the material definition (see section 3.2.4).

Analysis Procedures


Issue: 3 Date: 13.07.2016

h) Once the life has been computed for every material plane, then the minimum life is selected from among the results and reported as the life of the individual item.

i) Any requested auxiliary outputs are written to their respective log files.

Figure 3-20 fe-safe/RubberTM analysis process

3.5.2 After fe-safe/RubberTM has run

At the end of a successful analysis, fe-safe/RubberTM creates the Output File. This file contains the requested contour plots. A Results Log file is written in the same directory as the Output File with an extension *.log. For instance if C:/temp/example.odb is the name of the output file the Results Log file C:/temp/example.log will be created. Log outputs and History outputs requested using the fe-safe user interface will be generated as described in the fe-safe User Guide including diagnostic techniques and additional outputs.

Post processing requires viewing the Output File in the appropriate third-party post-processing software. Please see the Appendices of the fe-safe User Manual for details on post-processing.

For every material point

For every plane

Loading History on plane

Identification of Events via

Rainflow count

Integration of damage law

Identification of material point and plane with

minimum life

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