YSA competition

BSSM 2015 10thEdingburgh UK

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A new method of measuring non-uniformresidual stress with reduced plasticity effect

Hokyeom Kim(HK.kim@bristol.ac.uk)

Department of Mechanical EngineeringThe University of Bristol, UK

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Introduction

I Mechanical strainrelaxation(MSR) methodsconsist of 4 steps:

1. Choose geometry andanalytical model

2. Cutting

3. relaxation measurement

4. solution of inverse problem

I Assumptions

1. Uniform stress assumption

2. Purely elastic relaxationassumption

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Timoshenko’s ”Theory of Elasticity”, 3rd ed, 1970, p. 61:

f = Ce−γx1/c(ξ cosγx2c

+γx2c

sinγx2c

)

g = Ce−φx1/c(ψ sinφx2c

+φx2c

cosφx2c

)

x1 = 0 :

∫ c−c

σ11dx2 =

∫ c−c

σ12dx2 = 0

x2 = ±c : σ22 = σ12 = 0

BC→ γ,φ, ξ,ψ

θ =

∞∑i=1

aiRefi+bi Imfi+ciRegi+di Imgi

Ω = (a1, b1, c1, d1, . . . aN , bN , cN , dN)

minΩ

||AΩ− u||2

Semi-infinite 2D stripof width 2cu - disp.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4-point bending & relaxation

-12-10.5

-9-7.5

-6-4.5

-3-1.5

0 1.5

3 4.5

6 7.5

9 10.5

12

-0.02 -0.016 -0.012 -0.008 -0.004 0 0.004 0.008 0.012 0.016 0.02

Wid

th o

f Sp

ecim

en(m

m)

Displacement(mm)

Distance from edgec(12.5mm)Ratio =

0Ratio 0.2

0.40.60.8

1

I 25 × 25 mm bar under 9 mmvertical displacement,P = 53.05KN.

I The maximum displacement, atthe edge, around 21 µm

I Decays very quickly! At 0.4caway from the edge, only 5 µm.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Optical system and DIC result

I 7.6µm/pixel spatial resolution.

I Field of view is 10.6 × 8mm

I 175 mm working distance.

I P180 sandpaper & Ring right

I 10bit CCD with a 1392 × 1040

I 25 by 25 subset size

Figure: *

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Reconstructed residual stress [1]

Figure: *I Pattern preservation.

I High mag = Many images −→stitching & Complex experiment

I Out-of-plane motion

-12

-10.5

-9

-7.5

-6

-4.5

-3

-1.5

0

1.5

3

4.5

6

7.5

9

10.5

12

-400 -200 0 200 400

Wid

th o

f S

pec

imen

(m

m)

Stress (MPa)

FE surface FE interiorExp. result

Neutron Dffraction

Figure: *

Calculated residual stress.I Surface measurement−→ plane stress condition

I Challenge of getting betteraccuracy of measured disp.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Thin friction stir welding plateI The method works better with

relatively thin components

I The use of 3D DIC resolves :

1. out-of plane motion2. discontinuity due to stitching

0

10

20

30

40

50

60

70

-80 -60 -40 -20 0 20 40 60 80 100

Wid

th o

f S

pec

imen

(m

m)

Stress(MPa)

σ11

results from X-ray diffrationσ

11 from disp upto 5 mm

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

7

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Two different cutting schedules

Figure: *

Conventional slitting method [2]

I Cutting along the x2, from toptoward bottom

I The stress along the cuttingedge is constant.

I Causing the residual stress toincrease on the bottom surface

Figure: *

Proposed slitting method

I cutting along x3, from the frontface to the rear face.

I The stress along the cuttingedge is non-uniform,self-equilibrated.

I No redistribution!. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Plastic flow on cutting

-12

-10.5

-9

-7.5

-6

-4.5

-3

-1.5

0

1.5

3

4.5

6

7.5

9

10.5

12

-0.001 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

Wid

th o

f S

pec

imen

(mm

)

Equivalent plastic strain

2D PEEQ at x1 = 0.09 plastic cutting2D PEEQ at x1 = 0.5 plastic cutting

2D PEEQ at x1 = 0.09 elastic cutting 2D PEEQ at x1 = 0.5 elastic cutting

3D PEEQ at x1 = 0.09 Plastic cutting3D PEEQ at x1 = 0.5 Plastic cutting3D PEEQ at x1 = 0.09 Plastic Front3D PEEQ at x1 = 0.5 Plastic Front3D PEEQ at x1 = 0.09 Elastic top3D PEEQ at x1 = 0.5 Elastic top

-12-10.5

-9-7.5

-6-4.5

-3-1.5

0 1.5

3 4.5

6 7.5

9 10.5

12

-400 -300 -200 -100 0 100 200 300 400

Wid

th o

f Sp

ecim

en(m

m)

Residual stress(MPa)

Residual stress

I At cut depths of between 9 and 13 mm, corresponding to x2 between-1.5 and 4.5 mm, the plastic flow is substantial. This region matchesthe region of the residual stress peak.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

9

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Effect on 2D and 3D reconstructed residual stress

-12

-10.5

-9

-7.5

-6

-4.5

-3

-1.5

0

1.5

3

4.5

6

7.5

9

10.5

12

0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008

-600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600

Wid

th o

f S

pecim

en

(mm

)

Equivalent plastic strain

Residual stress (MPa)

2D, at x1 = 0.09 plastic cutat x1 = 0.09 elastic cut

FEplastic cut(RMS 28) elastic cut(RMS 7.5)

2D cutting one go (RMS 7.5)

I Elasto-plastic side cut - no plastic flowI Plastic strain occurs at a peak closer

to starting plane of the cut

-12

-10.5

-9

-7.5

-6

-4.5

-3

-1.5

0

1.5

3

4.5

6

7.5

9

10.5

12

-600 -450 -300 -150 0 150 300 450 600

Wid

th o

f S

pecim

en

(mm

)

Stress(MPa)

FETop (RMS 95)

Front (RMS 72) One go (RMS 75)

Remove BC (RMS 75)

I Side cut still disagrees with FEprediction

I Top cut - significant discrepancy inthe peak. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

10

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2D vs 3D surface displacement fields

−19.

1524

−16.379

−13.6056

−10.8321

−10.8321

−10.8321

−8.05871

−8.05871

−5.28529

−5.28529

−5.28529

−2.51186

−2.51186

−2.51186

−2.51186

−2.51186

0.26156 0.26156

0.261560.261560.26156

3.03498

3.03498

3.03498

3.03498

0.26156 0.26156 0.26156

5.80841

5.80841

5.80841

8.58183

8.58183

3.03498

3.03498

11.3553

11.3553

5.80841

14.1287

8.58183

16.9021

11.3553

1 2 3 4 5 6 7 8 9 10 11 12

−10

−5

0

5

10

−20

−15

−10

−5

0

5

10

15

20

−19.

1524

−16.379

−13.6056

−10.8321

−10.8321

−10.8321

−8.05871

−8.05871

−5.28529

−5.28529

−5.28529

−2.51186

−2.51186

−2.51186

−2.51186

−2.51186

0.26156 0.26156

0.261560.261560.26156

3.03498

3.03498

3.03498

3.03498

0.26156 0.26156 0.26156

5.80841

5.80841

5.80841

8.58183

8.58183

3.03498

3.03498

11.3553

11.3553

5.80841

14.1287

8.58183

16.9021

11.3553

1 2 3 4 5 6 7 8 9 10 11 12

−10

−5

0

5

10

−20

−15

−10

−5

0

5

10

15

20

−19.0857

−15.9079

−12.7302

−12.7302

−9.55244

−9.55244

−6.37469

−6.37469

−6.37469

−6.37469

−3.19694

−3.19694

−3.19694

−3.19694

−3.19694

−0.0191916 −0.0191916

−0.0191916−0.0191916−0.0191916

3.15856

3.15856

3.15856

3.15856

−0.0191916 −0.0191916

6.33631

6.33631

6.33631

9.51406

9.51406

3.15856

3.15856

12.6918

12.691815.8696

6.336319.51406

19.0473

12.6918

Length (mm)

Wid

th (

mm

)

um

1 2 3 4 5 6 7 8 9 10 11 12

−10

−5

0

5

10

−20

−15

−10

−5

0

5

10

15

20

−19.0857

−15.9079

−12.7302

−12.7302

−9.55244

−9.55244

−6.37469

−6.37469

−6.37469

−6.37469

−3.19694

−3.19694

−3.19694

−3.19694

−3.19694

−0.0191916 −0.0191916

−0.0191916−0.0191916−0.0191916

3.15856

3.15856

3.15856

3.15856

−0.0191916 −0.0191916

6.33631

6.33631

6.33631

9.51406

9.51406

3.15856

3.15856

12.6918

12.691815.8696

6.336319.51406

19.0473

12.6918

Length (mm)

Wid

th (

mm

)

um

1 2 3 4 5 6 7 8 9 10 11 12

−10

−5

0

5

10

−20

−15

−10

−5

0

5

10

15

20

I Plastic flow distorts disp. field

I 3D peak higher than 2D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

FSW plate example

0

10

20

30

40

50

60

70

-100 -80 -60 -40 -20 0 20 40 60 80 100 120 140 160 180 200 220

Wid

th o

f S

pec

imen

(m

m)

Stress(MPa)

σ11

results from X-ray diffrationσ

11 from front cut

σ11

from top cut

I Smaller magnitude of disp. field nearthe cut is observed from the top cutdue to plasticity caused by globalredistribution, leading to significantdiscrepancy in reconstructed residualstress field.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

12

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Conclusions & Future works

I The proposed method works

1. By carefully choosing the orientation and the direction of thepropagation of the cut, plastic flow on relaxation can be minimised.

2. Stress non-uniformity is still a problem. Using 2D model for a 3Dexperiment leads to errors. Need a fully 3D model.

I To do:

1. Improve accuracy of measurement

2. Stability of the analytical model is required

3. An assessment of the sensitivity of other MSR methods to thedirection and the manner of propagation of the cut

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

13

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Thank you for listening

ANY QUESTIONS?

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14

YSA competitionHK.Kim

2 Sep 2015. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

References

[1] H K Kim, H E Coules, M J Pavier, and A Shterenlikht. Measurement of HighlyNon-Uniform Residual Stress Fields with Reduced Plastic Error. ExperimentalMechanics, 55(7):1211–1224, 2015.

[2] M. B. Prime. Plasticity effects in incremental slitting measurement of residualstresses. Engineering Fracture Mechanics, 77:1552–1566, 2010.

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