Fatigue Prediction for Aluminum Materials - AMAP GmbH€¦ · Fatigue Prediction for Aluminum...

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Fatigue Prediction for Aluminum Materials C. Broeckmann 1 AMAP Colloquium, Aachen, January 15, 2015 F. Klubberg, N. A. Giang Institute for Materials Applications in Mechanical Engineering , RWTH Aachen

Transcript of Fatigue Prediction for Aluminum Materials - AMAP GmbH€¦ · Fatigue Prediction for Aluminum...

Page 1: Fatigue Prediction for Aluminum Materials - AMAP GmbH€¦ · Fatigue Prediction for Aluminum Materials C. Broeckmann1 AMAP Colloquium, Aachen, January 15, 2015 F. Klubberg, N. A.

Fatigue Prediction for Aluminum

Materials

C. Broeckmann1

AMAP Colloquium, Aachen, January 15, 2015

F. Klubberg, N. A. Giang

Institute for Materials Applications in Mechanical Engineering , RWTH Aachen

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Outline

1. Introduction

2. Fatigue prediction of aluminum components based on S-N-diagrams

3. Fatigue prediction based on the simulation of crack initiation and growth

4. Summary

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S-N diagram (Wöhler curve)

N = cycles to fracture

Ngrenz = ultimate number of cycles

Ngrenz = 108 (for light metals)

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Conventional fatigue evaluation of

components

example: brake calliper

Loading of component

Stess analysis (FEA), local stress

Multiaxial fatigue model

Specimen based S-N-diagrams: sW, sSch,

tW

material

(composition, heat

treatment,

strength,

inhomogenity)

component

(geometry,

surface, machining

porosity,

corrosion,)

Service condition

(direction of loading,

collective, multiaxial

loading)

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S-N-diagram for axial loading

Axial R = -1

Axial R = 0

Specimen for axial testing

Spannungsverhältnis:

𝑅 = 𝜎𝑢

𝜎𝑜

stress ratio:

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S-N-diagram for torsional loading

R = -1 Specimen for torsion

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Testing of components

S-N diagram of component (R = 0,05)

material: AlSi7Mg

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Endurance limit under biaxial stesses

NH: maximum prinicpal

stress criterion

GEH: von Mises criterion

SH: maximum shear stress

criterion (Tresca)

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The role of the biaxiality ratio in multiaxial

fatigue

biaxiality ratio:

NH: fW,t = 1,0

SH: fW,t = 0,5

GEH: fW,t = = 0,577

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Fatigue endurance limit for biaxial reversed

stress states

s1a /sW

s2a /sW

−0,5

0,5

0,5

−0,5

−1,5

−1,5

1,5

1,5

1/√3 ≤ ≤ √3

(invariants)

fully reversed

loading case

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Prediction of fatigue strength under non

proportional multiaxial loading (I)

examples for non proportional loading situations:

rotation of principal coordinate system

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Prediction of fatigue strength under non

proportional multiaxial loading (II)

• static stress components σi,m and

• variable stress components σi,a with constant principal stress direction

1. Sines criterion:

2. Dang Van creiterion:

σhm = average of static stress

σhmax = maximum of static stress

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Prediction of fatigue strength under non

proportional multiaxial loading (III)

Failure criteria for nonproportional multiaxial fatigue under out-of-phase loading

1. Criteria using integral material effort

criterion of Simbürger

criterion of shear stress intensity (SIH)

2. Criteria using critical plane approaches

generalized criterion of Dang Vang

criterion of Nokebly

criterion of Bongbhibhat

criterion of Fatemi-Socie

3. Combination of both approaches

criterion of quadratic failure potential (QVH)

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Prediction of component endurance limit

Zusatzmass

e

Prüfvorrichtun

g

Stress tensors for amplitude and mean

component at critical areas:

5,100,0

0,01,65 ,

5,90,0

0,09,58,, mijaij ss

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Endurance ratio of Aluminum alloys

Altern

atin

g a

xia

l te

nsio

n-c

om

pre

ssio

n

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Mean stress sensitivity of fatigue strength (I)

Definition of load ratio

time

fluctuating

compression

reversed,

tension- compression

fluctuating

tension

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Mean stress sensitivity of fatigue strength (II)

Haigh diagram

En

du

ran

ce

Lim

it lo

g s

A

Cycles log N

The endurance limit decreases with increasing static mean stress !

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Nondimensional form of Haigh diagram

ductile material

brittle material

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Haigh diagram of aluminium materials

ductile behaviour

PEAK

PEAK

[F. Klubberg, I. Klopfer, C. Broeckmann, R. Berchtold, P. Beiss: Fatigue testing of materials and components under mean load conditions.

XXVIII. GEF Encuentro del Grupo Español de Fractura, Gijón, 6. – 8. April 2011]

[

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Haigh diagram of aluminium materials

brittle behaviour

[F. Klubberg, I. Klopfer, C. Broeckmann, R. Berchtold, P. Beiss: Fatigue testing of materials and components under mean load conditions.

XXVIII. GEF Encuentro del Grupo Español de Fractura, Gijón, 6. – 8. April 2011]

[

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Mean stress sensitivity according to FKM-

guideline compared to results obained in

fatigue tests

Al-casting 2,0+MPa

R001,0=M

m

Al-wrought 04,0+MPa

R001,0=M

m

Mea

n s

tress s

en

sitiv

ity M

Tensile strength (UTS) suts , Rm

Mean stress sensitivity M(exp)

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Correlation between pulsating and fully

reverse fatigue strength

Reversed fatigue strength sa(R=-1)

Pu

lsa

tin

g fa

tig

ue

str

en

gth

am

plit

ud

e s

a(R

=0

)

Pu

lsa

tin

g to

rsio

n a

mp

litu

de

ta

(R=

0)

Reversed torsion strength ta(R=-1)

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Outline

1. Introduction

2. Fatigue prediction of aluminum components based on S-N-diagrams

3. Fatigue prediction based on the simulation of crack initiation and growth

4. Summary

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Different stages of fatigue life

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Stages of Fatigue

time spent in stages of crack growth

(molybdenum alloy)

[S. P. Wilson and D. Taylor, “Reliability assessment from fatigue micro-crack data,” IEEE Transactions on reliability, vol.

46, pp. 165–172, 1997.

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Lifetime prediction based on crack growth

𝑁𝑇 = 𝑁𝑖𝑛𝑐 + 𝑁𝑚𝑠𝑐/𝑝𝑠𝑐 + 𝑁𝑙𝑐

prediction of the total lifetime:

𝑁𝑇 total lifetime

𝑁𝑖𝑛𝑐 incubation time

𝑁𝑚𝑠𝑐/𝑝𝑠𝑐 short crack growth

𝑁𝑙𝑐 long crack growth

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High speed steel AISI M3:2 (HS6-5-3)

AISI C Si Cr W Mo V Mn

Cast M3:2 1.19 0.72 4.4 6.9 4.6 2.9 0.29

Forged M3:2 1.21 0.44 4.0 6.1 4.8 2.8 0.25

PM M3:2 1.31 0.60 3.9 5.9 4.9 2.9 0.47

Chemical composition

as cast as cast (details) as forged

Microstructure

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Mechanical properties for mesoscopic FEA-

modelling

Phase E[GPa] [-]

sy0[MPa]

sult[MPa]

c[GPa]

r[MPa]

s[MPa]

[-]

carbide 400 0.25 - 1604 - - - -

matrix 210 0.3 1500 - 112.1 200 417 137

J. L. Mishnaevsky, N. Lippmann, and S. Schmauder, “Experimental-numerical analysis mechanisms of damage initiation in

tool steel,” in Proceeding 10th international Conference Fracture, (Milan, Italy), pp. 1–10, 2001..

R. Prasannavenkatesan, Microstructure-sensitive fatigue modeling of heat treated and shot peened martensitic gear steels.

Ph.D. thesis, Georgia Institute of Technology, USA, 2009...

Carbide: MC and M6C

Matrix: tempered martensite

sy0 yield strength

sult ultimate tensile stress

C kinematic modulus

r dynamic modulus of rate of back stress tensor

s and coefficient and exponent of flow stress

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Estimation of the incubation lifetime Ninc

∆Γ =∆𝛾𝑚𝑎𝑥

𝑝∗

21 + 𝐾∗

𝜎𝑛𝑚𝑎𝑥

𝜎𝑦𝑠

relationship between Fatemi-Socie parameter and Manson-Coffin law:

∆Γ = 𝐶𝑖𝑛𝑐 2𝑁𝑖𝑛𝑐𝛼

Fatemi-Socie parameter :

∆𝛾𝑚𝑎𝑥𝑝∗

2: maximum plastic shear strain range on the critical plane

interaction between torsion an tension fatigue ductility 𝐾∗:

𝜎𝑛𝑚𝑎𝑥: normal stress on the critical plane

Cinc and α parameters to be determined in unit cell studies

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Flow chart for the prediction of the

incubation lifetime

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RVE models for forged and cast tool steel

as forged as cast

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Lifetime up to crack initiation

as forged as cast

∆Γ = 0.00175

Ninc = 715,000

∆Γ = 0.00160

Ninc = 890,000

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The cyclic stress intensity factor

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Increase of ΔK with the growing crack

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Crack growth rate for short and long cracks

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Short crack growth and long crack growth

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Short crack growth based on Chan‘s model

with 𝜉 =𝐸𝑠𝑠𝑝

4𝜎𝑦𝜀𝑓, 𝑑𝑜

𝑑𝑎

𝑑𝑁 𝑠𝑐

= 𝜉1𝑏 2𝑠𝑠𝑝

1−1𝑏

Δ𝐾 − Δ𝐾𝑡ℎ,𝑠𝑐

𝐸

2𝑏

Δ𝐾𝑡ℎ,𝑠𝑐 = Δ𝐾𝑡ℎ,𝑙𝑐

𝑎

𝑎 + 𝑎𝐷= 1 − 𝑅 𝜎𝑝,𝑀

′ 2𝑆𝑝

𝑎

𝑎 + 𝑎𝐷

𝑠𝑠𝑝: striation spacing

𝑑𝑜: dislocation barrier spacing

𝑎𝐷: critical defect

𝑆𝑝: carbide spacing

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Short crack growth in forged M3:2 steel

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Paris law of stable crack growth

Materials group m C

Steel 2,25 5,79∙10-11

Al-alloys 3,00 9,82∙10-12

Ti-alloys 4,00 3,56∙10-15

da/dN in mm and ΔK in N/mm3/2

acc. to Clark

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Predicted S-N-diagram in comparison to

experimental data

[138] P. Brondsted and P. Skov-Hansen, “Fatigue properties of high-strength materials used in cold-forging tools,”

International Journal of Fatigue, vol. 20, pp. 373–381, 1998.

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Effect of carbide shape on ΔΓ and Ninc

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Effect of aspect ratio on ΔΓ

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Effect of particle volume fraction on Ninc

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Local plastic defomations

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Summary

Fatigue strength of aluminum components can be estimated

based on material fatigue strength data and appropriate multiaxial

failure criteria.

Experimental investigation of a huge number of aluminum alloys

show a dependence of fatigue strength on static strength, stress

state, mean stress and production technology.

The simple rule, given by FKM-guideline does not reflect all these

influences.

A multistage, multiscale model has been developed to predict

fatigue life based on crack initiation and crack propagation.

This model has been used to investigate microstructural features

on fatigue strength.

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Thank you for your attention!

Prof. Dr.-Ing. Christoph Broeckmann

IWM – Institute for Materials Applications in Mechanical Engineering

RWTH Aachen University

Augustinerbach 4

52062 Aachen

www.iwm.rwth-aachen.de