2014. 04. 01. Jong hyoung Kim Contents

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Evaluation of residual stress using Instrumented Indentation Technique

2014. 04. 01.

Jong hyoung Kim

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Contents

1) Introduction (Evaluation of residual stress using IIT)

2) Estimation of stress-free state using Elastic modulus & Stiffness 3) Evaluation of through-thickness residual stress

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Instrumented indentation technique (IIT)

Hardness Elastic modulus Tensile properties Fracture toughness

Residual stress Indentation load-depth curve

Load

Depth Loading

Unloading

••

•

Easier and simpler to measure quantitative mechanical properties

4

Evaluation of residual stress using IIT

h_t

ΔL L_T ΔL

L₀

Depth Load

Compressive Tensile Stress

free

L_C

L

σ

_res

 

= Indentation load in compressive stress state

= Indentation load in stress-free state

= Indentation load in tensile stress state

= Indentation depth (experimentally measured)

= Elastic deflection height

= Pile-up height

= Sink-in height

= Real contact depth in compressive stress

= Real contact depth in tensile stress

L_C

Compressive stress

ht

hp h^d

C

hc

L_T

Tensile stress

ht T

hc

s

d h

h 

















T c C c s p d t T 0 C

h h h h h h L L L

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Interaction of residual stress with indentation load

Hydrostatic stress

Deviatoric stress

Core

Indenter

Plastic zone

Indentation load Residual stress,

h_t

Load

L₀

Stress free

Elastic zone

L_T ΔL

Stressed

σres

σres

σres

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Contents

1) Introduction (Evaluation of residual stress using IIT)

2) Estimation of stress-free state using Elastic modulus & Stiffness 3) Evaluation of through-thickness residual stress

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Necessity of stress-free state estimation

Stress-free

zone Weld

 L

< Determination of stress-free zone >

- Heat treatment -

< Stress relaxation – generation of stress-free state>

- Substrate etching -

Layer removing

Free-standing film

Estimation of load-depth curve of stress-free state

from stressed load-depth curve

(without determination of stress-free zone or generation of stress-free state)

8

Stress effect to indentation curve and contact ⁸

< Stress effect to indentation curve > < Invariant real contact area >

[T.Y. Tsui et al., J. Mater. Res. (1996)]

h_t

ΔL L_T ΔL

L₀

Depth Load

Compressive Tensile Stress

free

L_C

9

Invariant elastic modulus, hardness and contact area

[T.Y. Tsui et al., J. Mater. Res.(1996)]

< Invariant hardness regardless of stress state >

[Y.H. Lee, D. Kwon, J. Mater. Res.(2002)]

[T.Y. Tsui et al., J. Mater. Res.(1996)]

Compressive stress (-290 MPa)

Tensile stress (+251 MPa)

< Invariant contact area regardless of stress state >

c 0

A H L

10

-300 -200 -100 0 100 200 300

0 2 4 6 8 10

Invariant stiffness

• Elastic modulus

[T.Y. Tsui et al., J. Mater. Res.(1996)]

Compressive Tensile

Stiffness (kgf/um)

c

eff A

S 2 E 1 



Sum of applied stress (MPa) - Material : S20 - Maximum load : 50 kgf

- Stiffness at stress-free state : 8.73 kgf/um Experimental results

Invariant stiffnessInvariant elastic modulus

10/54

11

Reason for invariant contact area

< Stress-free >

L0

0

ht

hc h^d

hp

p d 0 t

c h h h

h   





p d

h

h = Elastic deflection

= Pile-up

L₀

Depth Load

Compressive Stress Tensile free

0

ht h^T_t

C

ht C

hp

 h^T_p

[M.F. Doerner, W.D. Nix, J. Mater. Res.(1986)]

[W.C. Oliver, G.M. Pharr, J. Mater. Res. (1992)]

S h_d  L^max



 



 



 



 

total e

p W

f W E

f H h

[Y.T. Cheng, C.M. Cheng, Appl. Phys. Lett.(1998)]

[S.K. Kang et al., J. Mater. Res. (2010)] Parameters

dependent on material properties

C

hp





T

hp





Change of pile-up height by residual stress

Compressive

Tensile

C t 0

t h

h 

T t 0

t h

h 

(No change by residual stress)

11/54

12

Reason for invariant contact area

L0

< Stress-free >

L0

< Compressive > < Tensile >

0

ht

hc

hd

hd

hp

0 t

c h

h 

hd

L0

T

ht

hc

T p

p h

h 

C p

p h

h 

C

ht

C t

c h

h  ^T

t

c h

h 

hc

- Increased pile-up by compressive stress - Decreased pile-up by tensile stress p

d h

h 



C

hp



 hd hp h^T_p h_d h_p

12/54

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Concept of stress-free state estimation

< In case of tension >

hd

L0

T

ht

hc

T p

p h

h 

depth

L0

T

hf

Stiffness

T

ht load

Ac

Measurement of contact area A_c

Determination of h⁰_t

L0

0

ht ^depth

load Estimating stress-free L-h curve

2 c c 24.5(h )

A  (by Vickers’ geometry)

) h h , h ( f

h⁰_t  _c ^T_t  ^T_f

Calculation of real contact depth h_c

* Assumption : - Invariant contact area - Invariant stiffness

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Calculation of real contact depth h_c

 Optical measurement of indent

• Measurement of real contact area A_c

2 c c 24.5(h )

A  (by Vickers’ geometry)

• Calculation of real contact depth h_c

) A ( f h

_c



_c

-

• A_cis measured from stressed state.

• h_cis calculated from stressed state of A_c.

14/54

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Relation between h_cand h_t⁰in stress-free state

[S.K. Kang et al., J. Mater. Res. (2010)]

0 . h 1 h 10 h 9 . h 9 h

0 f 0 t

0 3 t 0

t

c 

 

 ^

) h h , h ( f

h⁰_t  _c ⁰_t  ⁰_f



L0

0

ht load

0

hf

(for unstressed materials)

stress-free curve

< Stress-free >

L₀

0

ht

hc

h_cfrom stressed state by invariant contact area

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Estimation of h_t⁰using invariant stiffness

- Elastic deflection, h_d

C f C t T f T t 0 f 0

t h h h h h

h     



^{9.9 10 (h ) (h h )(h}T ^hTf^{) 0}

t c 0 t 2 0 t

3    

 ^

) h h , h ( f

h⁰_t  _c ^T_t  ^T_f

L0

0

ht ^depth

load

0

hf h^T_f h^T_t

f 0 t

d h h

S

h L  

- Stiffness S is invariant,

so, elastic deflection is consistent.

0 . h 1 h 10 h 9 . h 9 h

0 f 0 t

0 3 t 0

t

c 

 

 ^

0 . h 1 h 10 h 9 . h 9 h

T f T t

0 3 t 0

t

c 

 

 ^

S S

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Estimation of stress-free state

depth

L0

T

hf

Stiffness

T

ht

load • Measurement of real contact area A_c

h_cfrom stressed state

2 0 0 k(h_t ) L 

(Kick’s law) - k : fitting coefficient

• Fitting the stress-free curve

L0

0

ht ^depth

load

T

ht )

h h

h h

h h (

C f C t

T f T t

0 f 0 t











• Estimation of

) h h , h ( f

h⁰_t  _c ^T_t  ^T_f

0

ht

• Calculation of real contact depth h_c

2 c c 24.5(h )

A  (by Vickers’ geometry)

Invariant h_cInvariant S

0 . h 1 h 10 h 9 . h 9 h

0 f 0 t 0 3 t 0

t

c 

 

 ^

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Necessity of new approaches

 In case of difficult to measure contact area - Small indentation depth (ex. nanoindentation) - Nonmetal materials (ex. polymer)

Without measurement of contact area

Calculation of contact area using invariant properties

Elastic modulus, Stiffness

(invariant in stressed state) Calculation Contact area

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Calculation of contact area

 Calculation of contact area using elastic modulus and stiffness

- Sneddon’s relationship

Elastic modulus,

C

eff A

E S

2

 

Ac

W. C. Oilver, G. M. Pharr 1992

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Correction factor (β≠1)

Axisymmetric flat punch Sharp indenter

c

eff A

E S

2

 

c

eff A

E S

2 1 



Sneddon’s solution Application of Sneddon’s solution

 1

Plastic flow Plastic flow

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Correction factor (β≠1)

 Evaluation of correction factor using real contact area and Sneddon’s relationship

- β=1.04±0.04

eff Ac

S E 2

1 

 

SK3 SKD11 STS304 STS316 500HMV 800HMV

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

 (beta)

Specimen

1.04(±0.04)

∴ β = 1.04

c

eff A

E S

2 1 

 

Good agreement with previous research (β=1.0226~1.085, W. C. Oilver, G. M. Pharr 2003)

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Estimation of stress-free state

Stress-free State (Estimation) Compressive Stress State

(Real experiment)

Lmax

S

hmax

hc

Lmax

0

hmax

Ac

Ac

hc

 Step 1 : E_effA_c

depth

Lmax

S

hmax S

hf

S ^{ Step 2 : Achc h0max} A^c 24.5(h^c)² 00 . 1 10

06 .

1 _{0 0}

max 0 2 max 0

max

 



 ^

f c

h h

h h

h

) h h h h

( ⁰_max ⁰_f  ^S_max ^S_f

 Step 3 : L=kh²L_maxk(h⁰_max)²

) L , h ( ⁰_{max max}

Input Output

0

hmax

(Kick’s law)

(f-function)

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Experimental conditions

Model NANO-AIS

Maximum load 60 mN

Method Single indentation (load control)

Machine & Indenter

Indenter Berkovich Shape Three-sided

Pyramidal Included angle 142.35º

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Experimental conditions

Jig & Specimen

Materials Elastic modulus(GPa) Yield strength(MPa)

SKD11 217.35 342.87

SUS304 189.97 321.31

SUS316 203.56 282.74

Al6061 69.92 262.46

Strain gauge Kyowa

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Experimental conditions

Contact area measurement

Model Quanta FEG 250

Magnification 15000x, 20000x

HV 5kV, 20kV

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A E_eff S

2 1 

 

Calculation of contact area

 Calculation of contact area using elastic modulus and stiffness - Calculation : using elastic modulus and stiffness

- Direct measurement : by SEM

(β=1.04)

 Average error : 7.54%

SKD11 SUS304 SUS316 Al6061

0 10 20 30 40 50 60

Ac (m2 )

Calculation (from E, S) Direct measurement (by SEM)

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0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

0 10 20 30 40 50 60 70

Stressed Stress-free Stress-free (estimated)

Load (mN)

Depth (m)

Estimation of stress-free state

0.0 0.2 0.4 0.6 0.8

0 10 20 30 40 50 60 70

Stressed Stress-free Stress-free(estimated)

Load (mN)

Depth (m)

Materials (MPa)

SKD11 138.24

y res x

res 

 

h_max⁰=0.7558μm

Materials (MPa)

SUS304 196.62

y res x

res 

 

h_max⁰=0.6530μm

• Experimental condition : Tensile stress state • Experimental condition : Tensile stress state

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0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

0 10 20 30 40 50 60 70

Stressed Stress-free Stress-free (estimated)

Load (mN)

Depth (m)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0 10 20 30 40 50 60 70

Stressed Stress-free Stress-free (estimated)

Load (mN)

Depth (m)

Estimation of stress-free state

Materials (MPa)

SUS316 164.88

y res x

res 

  Materials (MPa)

Al6061 186.41

y res x

res 

 

h_max⁰=0.6863μm h_max⁰=1.2331μm

• Experimental condition : Tensile stress state • Experimental condition : Tensile stress state

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Evaluation of residual stress

 Average error : 12.3%

y res x

res 

  _(MPa)

50 100 150 200 250

50 100 150 200 250

Algorithm

Experimental

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Experimental details (Macro scale)

Testing equipment: AIS3000

Specimens(total 23 materials)

* 14 power-law hardening materials (+ API steels)

* 6 linear hardening materials

* 3 nonferrous materials (Al alloys)

A S E_r 2

1 

 

depth load

Stiffness (from indentation)

Contact area

(from optical measurement)

Elastic modulus (from tensile test) Analysis

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Results (Macro Scale)

0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20

Al2024 Al6061

Al7075

API X120 API X100

API X70 SKH51

S20C

S45CSCM21 SCM4

SK3

SKD11SKD61SKS3SUJ2SUS440 SUS303

SUS304

SUS304LSUS316SUS316L SUS321



Specimens

Power-law hardening Linear hardening

Al alloys

β= 0.95 (±5% error range) For most ferrous materials

Previous researches (1.0226 ~ 1.085) Theoretical analysis (1, flat punch) Experimental results

±5% error range

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Contents

1) Introduction (Evaluation of residual stress using IIT)

2) Estimation of stress-free state using Elastic modulus & Stiffness 3) Evaluation of through-thickness residual stress

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▶ Through-thickness Residual stress

[S. Massal, 2007]

[M. Wohlschlögel, 2011]

Through-thickness direction

2

Introduction

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Through-thickness residual stress

Step 1. Step 2.

Measure Measure

Procedure

Issue

Step 3.

(1) Sensing depth (measurement of residual stress using IIT) (2) Residual stress separation : , →

,

Step 4.

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Issue 1. Sensing depth (1)

3d 10d

d : Indentation depth Elastic zone

Plastic zone

Indentation deformation

: Elastic deformation + Plastic deformation

Residual stress

Ineffective stress Effective stress

Hydrostatic stress Deviatoric stress

, = σ _, z-direction Distribution area?

Indentation depth ^{matchingmatching} z-direction Plastic zone size

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Issue 1. Sensing depth (2)

Relation between elastic deformation and residual stress

FEM simulation : elastic property Tensile residual stress : 300 MPa

[T.Y. Tsui et al, JMR, 1996]

4

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Issue 1. Sensing depth (3)

Issue : Effect of residual stress on plastic zone size Approach : sensing depth = plastic zone size

→ 1

3 σ γ

Compressive : < : c ↓ Tensile : > : c ↑

Compressive (300 MPa) Stress-free Tensile (300 MPa)

0.9 1 1.2

(relative size of plastic zone, using ABAQUS)

1

3 σ γ

- Modifying Gao’s equation

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Issue 2. Residual stress separation (1)

1 ,

res

2 ,

res

ⓐⓑ

object residual stress

1 res,

 res,2

measured residual stress

Evaluation of Through-thickness residual stress

Representative section 1 Representative section 2

Indent twice (ⓐ, ⓑ)

a res,

 res,b

σ _, = f(σ _, )

σ _, = f(σ _, , σ _, )

measured object

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Issue 2. Residual stress separation (2)

depth

load Stress free curve

Δ

Δ

σ σ

Δ σ = Δ σ +Δ σ

∆ ∗ = ∆ ∗ ∆ ∗

2 2

1



1

measured object

stress-free state

1 res,



2 res,

 ^{res ,measured}

stressed state

work of Indentation

state Diagram

Δ : change of the indentation work by residual stress

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Conclusion

 Load-depth curve of stress-free state could be estimated by the parameters which were measured from the stressed curve including real contact area under stressed state with the concept of invariant contact area and stiffness.

 But we could not measure the real contact area when the contact depth is very small in nanoindentation or for some nonmetal materials.

 By Sneddon’s relationship, contact area was estimated using elastic modulus and stiffness.

 Algorithm for estimation of stress-free state has good agreement with the experimental results.

 When we evaluate the residual stress, the sensing area of the residual stress is the plastic deformation area and can be predicted by Gao’s equation.

A E_eff S

2 1 

  (Correction factor β=1.04)

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Thank you for your attention