Intro to ANSYS nCode DL 14 5 L02 CAE Fatigue

Introduction to ANSYS nCode DesignLife

Customer Training Material

Lecture 2: Introduction to CAE Fatigue


L2-2 ANSYS, Inc. Proprietary

© 2013 ANSYS, Inc. All rights reserved. Release 14.5

April 20133

Customer Training Material Agenda

• Review basics of fatigue

– what is fatigue

– physics of fatigue cracks

– fatigue history

– fatigue testing

• Introduce basics of CAE durability

– fatigue approach

• stress-life and strain-life

– crack-growth

• Introduce basics of fatigue analysis

– stress cycle

– cycle counting

– damage accumulation




April 20133

Customer Training Material Introduction

• Fatigue damage is the initiation and/or growth of a crack under

fluctuating loading

– progressive damage

– component seems to lose strength and get tired after multiple load

applications, hence the name “fatigue”

– almost all structural components are subjected to cyclic service

Time

Str

es

s

σy

Fatigue failure occurs after

repeated loadings even

though the stress is low




April 20133

Customer Training Material Fatigue Life

• Fatigue failure is typically viewed as a 3-stage phenomena

– stage 1: crack initiation

– stage 2: stable crack growth

– stage 3: fast fracture

• Fatigue life = crack initiation + crack growth

– no precise transition from crack initiation to crack growth




April 20133


• Surface flaws initiate at tiny dislocations in the material’s

microstructure

– very localized stress concentration

– practically undetectable and impossible to model using FE

• These tiny surface flaws create persistent slip bands that propagate

along the maximum shear plane under alternating stress

– bands slip back and forth like a shifting deck of cards

Crack Initiation

Alternating Stress

Crystal surface

Slip bands form

along planes of

maximum shear

giving rise to

surface extrusions

and intrusions




April 20133


• Slip bands grow into micro-cracks (Stage I cracks)

– small compared to material’s microstructure

• difficult to detect, invisible to the naked eye

– grow in direction of maximum shear stress

• 450 to the direction of the applied load

Stage I Cracks




April 20133


• After traversing 2-3 grain boundaries, the micro-cracks grow into

fatigue cracks (Stage II cracks)

– large compared to material’s microstructure

– crack itself physically interrupts the flow of stress

• stress concentration causes plastic stresses at the crack tip

– local plastic stress causes the crack to change direction

• growth is now propagated by cyclic plastic stress at the crack tip

• oriented perpendicular to maximum principal stress

Stage II Cracks




April 20133

Customer Training Material Fatigue Failure

• If sufficient energy exist, Stage II cracks continue to grow until tensile

failure occurs

– most lack sufficient energy to propagate across grain barriers

• crack “arrests”

fatigue damage

producing striations

(aka “beach marks”)

fast final fracture due

to tensile failure - no

striations

initial crack

slip bands micro-cracks fatigue cracks tensile failure




April 20133

Customer Training Material History of Fatigue Analysis

• Fatigue failures has been investigated for more than 150 years

– initially applied to the study axel failures in the railroad industry

• first industrial components to be subjected to millions of cycles

– failures continue




April 20133


• 1837 - Wilhelm Albert publishes the first article on fatigue

• 1860 – August Wöhler devises a test for fatigue

• 1901 - O.H. Basquin proposes a log-log relationship for S-N curves

• 1945 - A.M. Miner introduces a linear damage hypothesis

• 1958 - Fatigue crack growth explained in terms of plastic strain

• 1968 - Tatsuo Endo introduces the rainflow cycle count algorithm

Key Events in Fatigue Analysis




April 20133

Customer Training Material Fatigue Analysis

• Initially fatigue analysis was done after an in-service failure, if at all

– build > break > redesign

Customer

Usage Life

Re-Design




April 20133

Customer Training Material Incorporating Fatigue Testing

• As customer usage became better understood, it was applied to

fatigue testing

– build > test > redesign

Customer

Usage

Test Life

Re-Design




April 20133

Customer Training Material Fatigue Testing Limitations

• Fatigue testing has many limitations

– requires many physical prototypes

– realistic tests are difficult or impossible to achieve

– slow and expensive

– fails to deal with over-design

– difficult to handle late changes and design variations

– test results may differ significantly

• requiring statistical interpretation




April 20133

Customer Training Material CAE Fatigue Analysis

• CAE can predict fatigue damage in a virtual environment

– evaluations can be performed during design phase

– can assess cumulative damage caused by multiple loads




April 20133

Customer Training Material 5 Box Trick

• CAE fatigue analysis are built around five basic actions

– so called “5 box trick”

inputs > pre-processing

solver post-processing




April 20133

Customer Training Material CAE Durability Approaches

• Two basic approaches for performing CAE durability analysis


– fracture mechanics

• also known as crack-growth or crack-life method

• Fatigue approach

– use calculated stresses/strains and material fatigue curve to predict

cycles to failure (life)

– two basic fatigue analysis approaches

• stress-life (SN)

– uses elastic stresses

• strain-life (EN)

– uses elastic-plastic strains




April 20133

Customer Training Material CAE Fatigue Methods

• Stress-life (SN) uses elastically calculated stress and stress vs. cycle

fatigue failure curves (S-N curves)

– assumes stress drives fatigue

– only applicable high cycle fatigue

• greater than 100,000 cycles for ductile metals

• Strain-life (EN) uses elastic-plastic strains and Strain Life

Relationship Equation

– assumes local plastic strains drives fatigue

– applicable to low and high cycle fatigue




April 20133

Customer Training Material Stress-Life Approach

• Stress-life (SN) fatigue method assumes that fatigue damage is

produced by fluctuating stresses

– only applicable to elastic stress, so limited to limited to low stress/high

cycle applications

• usually more than 100,000 cycles to failure for ductile metals

– fatigue life is based on alternating stress range and Wöhler fatigue curve

(S-N curves)

– original numerical fatigue approach

– vast amount of industry experience

– simple technique

• often can be checked with hand calculations




April 20133

Customer Training Material S-N Curves

• S-N curves are plots of elastic stress versus total cycles to failure

– usually log-log plots

– S (y-axis): either full stress amplitude or alternating stress range

– N (x-axis): total cycles to failure (initiation and propagation)




April 20133

Customer Training Material Strain-Life Fatigue

• Strain-life fatigue (EN) assess fatigue damage using cyclic strain

ranges and the Strain Life Relationship equation

– applicable to both low cycle and high cycle applications

• stresses less than or greater than yield

– uses local elastic-plastic strains

• either directly calculated or adjusted from elastic results

– predicts crack initiation

• Relatively new fatigue analysis technique

– usage began approximately 30 years ago

– difficult to implement with hand calculations

• limited to CAE




April 20133

Customer Training Material Strain-Life Fatigue

• EN method is based on assumption that material behavior at notch

root is analogous to small test specimen under strain controlled

conditions

F

Δ

F

overall body remains elastic

local deformation is strain controlled

behavior of notched component with localized plasticity

can be simulated using smooth test specimen Δ




April 20133

Customer Training Material Strain Life Relationship

bef

f

NE

22

cpff N2

2

cbfff

f

NNE

22 2

Basquin’s equation

Coffin-Manson’s equation




April 20133

Customer Training Material Cyclic Loading Terms

• Fatigue damage is caused a changing stress/strain state

– sine curve is a simple representation of cyclic loading

– stress ratio (R) = Smin/Smax

– amplitude ratio (A) = Sa/Sm

Sa

Sa

S

Smax

Smin

Sm

Smax = maximum stress

Smin = minimum stress

Sm = mean stress

Sa = alternating stress

ΔS = stress range

Common loadings:

fully reversed: R = -1, A = infinity

zero to maximum: R = 0, A = 1




April 20133

Customer Training Material CAE Cycle Counting

• If multiple cyclic loadings occur, magnitude and number of each

stress/strain reversal must be determined

– minimum stress, maximum stress, mean stress, and number of cycles

associated with each stress reversal must be determined

• Rainflow is the most common cycle counting algorithm

– applicable to stress-life (SN) and strain-life (EN) methods

– automated in DesignLife

• Rainflow counts number of closed strain loops




April 20133

Customer Training Material Rainflow Cycle Counting

• Rotate strain history 90 degrees and plot vs time

• Cyclic behavior can be visualized as rain flowing off of a pagoda roof

fatigue cycles are:

a-d, b-c, e-f, and g-h




April 20133


• Rainflow cycle counting can also be visualized as water draining

from valleys

– determine peaks and valleys of stress/strain during cycling

– invert stress/stain history and imagine it is filled with water

– drain water - start at deepest valley and repeat until all valleys are drained

• total depth drained = stress range

• mean depth = mean stress

time

100

300

200

400

500

45

0

22

5

time

100

300

200

400

500

time

100

300

200

400

500

drain water starting

at lowest valley

imagine filled with

water

time

100

300

200

400

500

invert and reorder to

start with absolute max




April 20133


• Rainflow approach divides any arbitrary load history into groups

(“bins” or “blocks”) of similar loading

– rainflow matrix can be visualized using a histogram

• Each group represents a number of loading cycles for a particular

stress range and mean stress




April 20133

Customer Training Material Damage Accumulation

• Multiple cyclic loading conditions have a cumulative fatigue effect

• Rainflow groups the loading history into blocks loading blocks

– each block causes a fraction of the total damage (“partial damage” or

“damage fraction")

i

ii

N

nD fraction damage

Di = damage fraction caused by loading block (i)

ni = number of applied cycles of loading block (i)

Ni = available fatigue life for loading block (i)




April 20133

Customer Training Material Damage Accumulation

• Damage fraction is the amount of life that has been “used” by a block

of loading

• If ni = 1e5 and Ni = 1e6, the damage fraction is 0.10

– 10% of the total fatigue life has been used up by loading block i

allowable

actual

N

n

i

i fraction damage




April 20133

Customer Training Material Miner’s Rule

• Miner’s Rule assumes that the total damage is simply the linear

summation of the partial damages

– first proposed by Palmgren in 1924 and further refined by Miner in 1945

– also referred to as “Linear Damage Rule”

– applicable to both SN and EN

– widely used

• simple to implement and as accurate as more complicated methods

– load sequence is not considered

– failure occurs when sum of damage fractions equals the fatigue life

• D is equal to or greater than 1.0

– automated in DesignLife

n

i i

i

n

n

N

n

N

n

N

n

N

n

N

nD

13

3

2

2

1

1 damage total




April 20133

Customer Training Material Accuracy

• Fatigue calculations are much less precise than strength calculations

– statistical, not deterministic, phenomenon

– empirical rules

– order of magnitude errors in life estimates are common

– large factor of safety (FS) typically assumed to ensure safe design

• FSs of 10 are common

• CAE fatigue can enable smaller FSs




April 20133

Customer Training Material Crack-Life Approach

• Crack-life method uses fracture mechanics parameters (e.g., J-

integral, stress intensity, etc.) to predict flaw propagation under

cyclic service

– typically uses Paris’s Law (da/dN) to relate fracture mechanics

parameters to crack growth rate

– often used to establish inspection intervals

• for an inspection technique the smallest detectable flaw size is known

• number of cycles required to grow a crack from smallest detectable size to

critical size is determined

• inspection intervals are based on crack growth rate

• ANSYS Mechanical APDL and DesignLife both have some fracture

mechanics capabilities




April 20133

Customer Training Material Flowchart of CAE Durability Analysis

CAE Durability

Fatigue Approach Crack Life Approach

Strain-Life (EN) Stress-Life (SN)

Paris Law

crack growth

rate

rainflow cycle counting

Miner’s rule damage accumulation

number of cycles

to failure (life)




April 20133

Customer Training Material Summary

• Fatigue cracks start at surface dislocations and are driven by

reversing local plastic flow

• Fatigue failure occurs at stress levels insufficient to cause failure in a

single application

– damage is cumulative and unrecoverable

– difficult to detect progressive deterioration during fatigue process

• catastrophic failures can occur without warning

• Fatigue failure is typically viewed as a 3-stage phenomena

– stage 1: crack initiation

– stage 2: stable crack growth

– stage 3: fast fracture

• Fatigue life = crack initiation + crack growth




April 20133

Customer Training Material Summary

• Fatigue testing is slow and expensive

• CAE durability analysis predict fatigue in a virtual environment

– characterize capability of a component to survive cyclic service

– known as “fatigue analysis”

– fatigue life calculations are less precise than strength calculations

• Two basic CAE durability analysis approaches


• stress-life (SN) or strain-life (EN)

– fracture mechanics

• crack life

– Rainflow method commonly used to count cycles for both SN and EN

– Miner’s Rule commonly used to accumulate damage for SN and EN




April 20133

Customer Training Material Workshop 1

• Workshop 1: WB - DesignLife interface

– restore archive of existing WB project

– review WB project page

– review Engineering Data

– open Mechanical and solve

– review DesignLife results from project schematic

– modify design points in Parameter Manager

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Intro to ANSYS nCode DL 14 5 L02 CAE Fatigue

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