A novel fuzzy digital image correlation algorithm for non-contact measurement of the strain during tensile tests

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0.1−1 0.5−5◦ 5000−300000µε 99% 882.2±108.3 49.3±6.2 15746±2567µε 19887±3790µε 26.0±7.1% 3.78±0.07 0.374±0.02

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3.16±0.61 0.373±0.08 1.27 15712±357µε −0.5±7.1% 3.8±0.4 0.368±0.025 1.1±0.3% −6.5±3.6% 1.1±0.3%

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0,1−1 0,5−5◦ 300000µε 99% 880±110 49±7

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15750±2570 19890±3790µε 26±8% 3,78±0,07 0,37±0,02 3,16±0,61 0,37±0,08 1,27 15712±357µε −0,5±7,1% 3,8±0,4 0,368±0,025 1,1±0,3% −6,5±3,6% 1,1±0,3%

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℄ ℄ u v u v 0.5◦ u=v=0.1 5◦ ∂v ∂y=50000µε 100000µε 450000µε 50000µε 500000µε1000000µε 2000000µε

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u v µε CF=1.287

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u v

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1.27

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℄ 1.4 ℄ ℄ ℄ ℄ 80 ℄ ℄ ℄ ℄ ℄ ℄

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℄ ℄ ℄ 1928 1933 ℄ ℄ ℄

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℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ 1983 4197 762 4197 18% ℄ ℄ ℄ 43% 100% 433 762 57% 43% 762 ℄

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17% ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄

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℄ E 20−500MPa 3GPa 1−15MPa 100MPa 150 ℄ ℄ ℄ ℄ 40% ℄

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℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ #1

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#2 #3 #1 #2 #3 #1

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20000µε #2 #3 #4

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Literature review

Development and

implementation of a novel

Fuzzy DIC algorithm

Numerical verification

Experimental validation

Investigation and

reproduction of the optimum

speckle pattern

Analysis of errorsin DIC

measurement Conclusion

Introduction

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℄ ℄ ℄ ℄ 1 100

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℄ ℄

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℄ ℄ ℄ ℄ ℄ ℄ (x0,y0) (xi,yj) (x0 ′_,y 0′) (x0,y0)

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Deformedimage Reference subset ℄ 8 ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ 2 10

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℄ 4 2.5 1 4 4 ℄ 1−20 2−5 ℄ ℄ ℄ ℄ ℄ ℄ ℄ 4% 15% ℄ δf= W i=1 H j=1 |▽f(xij)|/(W ·H),

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W H |▽f(xij)|= fx(xij)2+fy(xij)2 fx(xij)fy(xij) ij) x y 5 ℄ N i=1 N j=1 [fx(xij)]2∼=N·δf, N 0.05 ℄ SP P SP= 3 i=1 3 j=1 |aij−a| aij a P SP SF= _{W ·H}P∈FSP, P F SF

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Reference

image

POI

Subset

℄ 2−5 10 ℄

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510 20 ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ 21×21 71×71

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ε0=0.01, 45×45 53×53 27×27 35×35 ε0=0.01. ℄ 21×2131×31 41×41 ℄ PA P(x,y) A (x+ dx,y+dy) PA x y dx dy

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P A P′ _A′ P(x,y) x y (u,v) A x y uA=u+∂u_∂xdx+1₂∂ 2_u

∂x2dx2+∂u_∂ydy+1₂

∂2_u ∂y2dy2+ ∂ 2_u ∂x∂ydxdy+..., vA=v+∂v_∂xdx+1₂∂ 2_v ∂x2dx2+∂v_∂ydy+1₂ ∂2_v ∂y2dy2+ ∂ 2_v ∂x∂ydxdy+.... A ′ x′

A=x+dx+uA=xA+u+∂u_∂xdx+1₂∂

2_u ∂x2dx2+ ∂u ∂ydy+ 1 2 ∂2_u ∂y2dy2+ ∂2_u ∂x∂ydxdy+..., y′ A=y+dy+vA=yA+v+∂v_∂xdx+1₂∂ 2_v ∂x2dx2+∂v_∂ydy+1₂ ∂2_v ∂y2dy2+ ∂ 2_v ∂x∂ydxdy+.... P A 1 st ₂nd xi′=xi+u, yj′=yj+v, (xi,yj)i,j 0 (xi′,yj′) (u,v)

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1st

xi′=xi+u+∂u_∂xdx+∂u_∂ydy,

yj′=yj+v+∂v_∂xdx+∂v_∂ydy, dx dy (xi,yj) (x0,y0) x y 1st ₂nd x′

i = xi+u+∂u_∂xdx+∂u_∂ydy+1₂∂ 2_u ∂x2dx2+ 1 2∂ 2_u ∂y2dy2+ ∂2_u ∂x∂ydxdy, y′ j = yj+v+∂v_∂xdx+∂v_∂ydy+1₂∂ 2_v ∂2_xdx2+ 1 2∂ 2_v ∂2_ydy2+ ∂2_v ∂x∂ydxdy, ∂2_u ∂x2,∂ 2_u ∂y2,∂ 2_v ∂x2,∂ 2_v ∂y2,∂ 2_u ∂x∂y ∂ 2_v ∂x∂y 2nd (u,v) x y 1 st 2 nd ℄ ℄ ℄

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CC SSD CCC CCC= M i,j=−M f(xi,yj)×g(x′i,yj′). NCC [−1,1] CNCC= M i,j=−M f(xi,yj)×g(x′i,yj′) ¯ f×¯g . ZNCC ZNCC [−1,1] CZNCC= M i,j=−M [f(xi,yj)−fm)]× g(x′i,yj′)−gm ∆f×∆g . SSD [0,4] 0 CSSD= M i,j=−M f(xi,yj)−g(x′i,y′j)2. NSSD [0,4] 0 CNSSD= M i,j=−M f(xi,yj) ¯ f − g(x′ i,yj′) ¯ g 2 .

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ZNSSD [0,4] 0 CZNSSD= M i,j=−M f(xi,yj)−fm ∆f − g(x′ i,yj′)−gm ∆g 2 , ¯ f = M i,j=−M [f(xi,yj)]2, ¯ g = M i,j=−M g(x′ i,yj′)2, fm = 1 (2M +1)2 M i,j=−M f(xi,yj), gm = 1 (2M +1)2 M i,j=−M g(x′ i,yj′), ∆f = M i,j=−M [f(xi,yj)−fm]2, ∆g = M i,j=−M g(x′ i,yj′)−gm 2, ℄ CZNSSD CZNCC CZNSSD=2(1− CZNCC) CNSSD=2(1−CNCC) g ′_(x′ i,yj′)=a×g′(x′i,y′j)+b CZNCC CZNSSD CSSD ℄ ℄ CZNCC CZNSSD ℄

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CC SSD ℄ ℄ 4 P(x ′_,y′₎

P1(i,j),P2(i+1,j),P3(i,j+1) P4(i+

1,j+1). g(x

′_,y′₎ _(x′_,y′₎

g(x′_,y′_)=a

00+a10·δx+a01·δy+a11·δx·δy,,

δx,δy (i,j)a00,a10,a01,a11

℄

a00= P1(i,j)

a10= P2(i+1,j)−a00

a01= P3(i,j+1)−a00

a11= P4(i+1,j+1)−a00−a10−a01

40%

℄ ℄ ℄

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PO

I

1

3

2

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4×4 P(x′_,y′₎ g(x′_,y′₎₌ 3 l,k=0 alk·δxl·δyk, δx,δy (i,j)alk(l,k= 0,...,3) 16 16 16 1st _x _y 2nd alk X X =[ a00 a10 a20 a30 a01 a11 a21 a31 a02 a12 a22 a32 a03 a13 a23 a33] B

B =[ g(i,j) g(i+1,j) g(i,j+1) g(i+1,j+1) gx(i,j) gx(i+1,j)

gx(i,j+1) gx(i+1,j+1) gy(i,j) gy(i+1,j) gy(i,j+1) gy(i+1,j+1)

gxy(i,j) gxy(i+1,j) gxy(i,j+1) gxy(i+1,j+1) ] A·X =B, A δx×δy alk ℄ ℄ 0−1 0 0.5 1

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℄ 2−40 ℄ ℄ ℄ ℄ 0.001 0.005 0.008 ℄

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17th f(x) x=x0 f(x) x=x0 f(x)=f(x0)+f′(x0)·(x−x0)+f ′′_(x 0)·(x−x0)2 2! +...+f (n)_(x 0)·(x−x0)n n! +Rn(x). 1st ₀ f(x)≈f(x0)+f′(x0)·(x−x0)=0. x f(x) f′_(x)=f′′_(x 0)·(x−x0)+f′(x0)=0. 2nd _f′′_(x 0)=0 x=x0 x=x0− f ′_(x 0) f′′_(x₀₎, x 1 st ₂nd _f(x) n f(x) xn+1=xn− f ′_(x n) f′′_(x_n₎. ℄ f(x) x

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℄

p= u;v;∂u_∂x;∂u_∂y;_∂x∂v;∂v_∂y .

C=f u,v,∂u

∂x,∂u∂y,∂v∂x,∂v∂y .

∆p

℄ ℄

℄

∆p = (∆u)2_{+ max(∆x)·∆}∂u

∂x

2

+ max(∆y)·∆∂u_∂y2

+(∆v)2_{+ max(∆x)·∆}∂v ∂x 2 + max(∆y)·∆∂v_∂y2 1 2 ≤ 0.001pixels, ≤0.001 ∆p = (∆u) 2_+(∆v)2 ℄ ℄ C1 C4 ∆p = √ ∆u2_+∆v2 C1: ∆p 10−1_pixe_ls_, C2: ∆p 10−2_pixe_ls_, C3: ∆p 10−3_pixe_ls_,

C4: |∆u| 10−4_pixe_ls_,|_{∆v| 10}−4_pixe_ls_,

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∆p 31×31 61×61 91×91 ∆p C1,C2,C3 31×31 C1,C2 C3 61×61 91×91 ℄ C1 C4 C4 C2,C3 C4 0.01 C2 ℄ ℄ ℄

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℄ ℄ ℄ ℄ ℄

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1 2 ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ 3 4 ℄ ℄ 100

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℄ ℄ 1 5 R= max( (u0−u) 2_+(v₀_−v)2_{) u}_,v u0v0 3

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The principle of the Fuzzy DIC algorithm

Newton -Raphson iteration Correlation

function and shape function

Optimization of the Hessian

matrix Gray scale

interpolation of subpixel

locations

Fullfieldsearch for

integerinitial guess fuzzyFDT process initial guess for

Newton-Raphson process for accurate displacements and strains

100 (x ′ int,yint′) x y

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(uint,vint)

uint = x′int−x0,

vint = y′int−y0,

℄ (x ′ int,yint′) NN (x ′ int,y′int) NN wm= _NNcm−cmin m=1(cm−cmin), cm m th _c min NN m th (x ′ int,yint′) (x ′ int,yint′) (x′ int,yint′)

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∆um = wm×(x′m−x′int),

∆vm = wm×(y′m−yint′),

x′ m ym′ m th mth m th m th (∆um,∆vm) NN ufuzzy = uint+ NN m=1 ∆um, vfuzzy = vint+ NN m=1 ∆um.

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℄ 1st p p C C u,v,∂u

∂x,∂u∂y,∂v∂x,∂v∂y =

M i,j=−M f(xi,yj)−fm ∆f − g(x′ i,yj′)−gm ∆g 2 (xi,yj) (x′i,yj′) f(xi,yj) g(x ′ i,yj′) (xi,yj) (x′i,y′j) fm gm ∆f ∆g C f(xi,yj) g(x ′ i,yj′) f(xi,yj) (xi,yj) (x ′ i,yj′) (x ′ i,y′j) f(xi,yj) g(x′_,y′₎₌ 3 l,k=0 alk·δxi·δyj, alk x′ lu:x′lu+1,ylu′:ylu′+1℄ δxi,δyj x ′ i,yj′

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x′ lu,ylu′ δxi = x′i−x′lu, δyj = yj′−ylu′. alk (u,v) p (ufuzzy,vfuzzy) C p p pn+1−pn (n+1) th _nth_p pn+1 p pn+1−pn=−_∇∇C(p₂_C(pn) n), ∇C(pn) ∇2C(pn) ∇C(pn)= ∂C∂u ∂C∂v _∂₍∂C∂u ∂x) ∂C ∂(∂u ∂y) ∂C ∂(∂v ∂x) ∂C ∂(∂v ∂y) ∇2_C(p n)=                ∂2_C ∂u2 ∂ 2_C ∂u∂v ∂ 2_C ∂u∂(∂u ∂x) ∂2_C ∂u∂(∂u ∂y) ∂2_C ∂u∂(∂v ∂x) ∂2_C ∂u∂(∂v ∂y) ∂2_C ∂v∂u ∂ 2_C ∂v2 ∂ 2_C ∂v∂(∂u ∂x) ∂2_C ∂v∂(∂u ∂y) ∂2_C ∂v∂(∂v ∂x) ∂2_C ∂v∂(∂v ∂y) ∂2_C ∂(∂u ∂x)∂u ∂2_C ∂(∂u ∂x)∂v ∂2_C ∂(∂u ∂x) 2 ∂ 2_C ∂(∂u ∂x)∂(∂u∂y) ∂2_C ∂(∂u ∂x)∂(∂x∂v) ∂2_C ∂(∂u ∂x)∂(∂v∂y) ∂2_C ∂(∂u ∂y)∂u ∂2_C ∂(∂u ∂y)∂v ∂2_C ∂(∂u ∂y)∂(∂u∂x) ∂2_C ∂(∂u ∂y) 2 ∂ 2_C ∂(∂u ∂y)∂(∂x∂v) ∂2_C ∂(∂u ∂y)∂(∂v∂y) ∂2_C ∂(∂v ∂x)∂u ∂2_C ∂(∂v ∂x)∂v ∂2_C ∂(∂v ∂x)∂(∂u∂x) ∂2_C ∂(∂v ∂x)∂(∂u∂y) ∂2_C ∂(∂v ∂x) 2 ∂ 2_C ∂(∂v ∂x)∂(∂v∂y) ∂2_C ∂(∂v ∂y)∂u ∂2_C ∂(∂v ∂y)∂v ∂2_C ∂(∂v ∂y)∂(∂u∂x) ∂2_C ∂(∂v

∂y)∂(∂u∂y)

∂2_C ∂(∂v ∂y)∂(∂v∂x) ∂2_C ∂(∂v ∂y) 2               

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n n=1,...,N ∇C(pw)=−2 M i,j=−M F(xi,yj) ∆f − G x′ i,yj′ ∆g ×∂p∂w G x′ i,yj′ ∆g , ∇2_C(p wpv)= 2 M i,j=−M ∂ ∂pw G x′ i,yj′ ∆g ∂p∂v G x′ i,y′j ∆g −2 M i,j=−M F(xi,yj) ∆f − G x′ i,yj′ ∆g ∂2 ∂pw∂pv G x′ i,yj′ ∆g , w,v=1,...,6 p F(xi,yj) = f(xi,yj)−fm, G(x′ i,y′j) = g(x′i,yj′)−gm. ℄ pn C F(xi,yj)/∆f−G x′i,yj′/∆g≈0, ∇2_C(p wpv)≈2 M i,j=−M ∂ ∂pw G x′ i,yj′ ∆g × ∂∂pv G x′ i,y′j ∆g .

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℄ ∂ ∂pw G(x′ i,yj′) △g = ∂p∂w g(x ′ i,yj′)−gm × M l,k=−M [g(x′ l,y′k)−gm]2 − g(x′ i,yj′)−gm × M l,k=−M [g(x′ l,yk′)−gm] × ∂ ∂pw[g(x ′ l,yk′)−gm] × M l,k=−M [g(x′ l,yk′)−gm]2 −3 2 , ∂ ∂pw[g(x ′ l,y′k)−gm]. gm ∂ ∂pw gx ′ i,yj′ −gm = ∂_∂p wgx ′ i,yj′ − 1 (2M +1)2 M l,k=−M ∂ ∂pwg(x ′ l,yk′), ∂ ∂ugx′i,yj′ =_∂(δx∂ i)gx ′ i,yj′ ×∂(δx_∂ui)=_∂(δx∂ i)gx ′ i,yj′ ×1, ∂ ∂vgx′i,yj′ = ∂_∂(δy j)gx ′ i,y′j ×∂(δy_∂vj)= ∂_∂(δy j)gx ′ i,yj′ ×1. ∂ ∂ ∂u ∂x gx′ i,yj′ = ∂_∂(δx i)gx ′ i,yj′ ×∆x, ∂ ∂(∂u ∂y) gx′ i,y′j = ∂_∂(δx i)gx ′ i,y′j ×∆y, ∂ ∂ ∂v ∂x gx′ i,yj′ = ∂_∂(δy j)gx ′ i,yj′ ×∆x, ∂ ∂(∂v ∂y) gx′ i,yj′ = ∂_∂(δy j)gx ′ i,yj′ ×∆y.

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∂

∂(δxi)gx

′

i,yj′ = a10+a11·δyj+a₁₂·δyj2+a₁₃·δyj3+2·a₂₀·δxi

+2·a21·δxi·δyj+2·a₂₂·δxi·δyj2+2·a₂₃·δxi·δy3j

+3·a30·δx2i+3·a31·δx2i·δyj+3·a₃₂·δx2i·δyj2

+3·a33·δx2i·δy3j,

∂

∂(δyj)gx

′

i,yj′ = a01+2·a02·δyj+3·a₀₃·δyj2+a₁₁·δxi

+2·a12·δxi·δyj+3·a₁₃·δxi·δyj2+a₂₁·δx2i

+2·a22·δx2i·δyj+3·a₂₃·δx2i·δyj2+a₃₁·δx3i

+2·a32·δx3i·δyj+3·a₃₃·δx3i·δyj2.

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Numerical studies In terms of accuracy and

limitation

Study on the accuracy of Fuzzy DIC algorithm

Withimagessimulating rigid body translation, rotation and uniaxial tensile

Study on the measurement limit ofFuzzy DIC algorithm Withimages simulatingdifferent

levels of tensile deformation Image generation

Generateimages with computer algorithm

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℄ ℄ k th Ns xk,yk R x k Ryk I0 k I(x,y) I(x,y)=Ns k=1 I0 k·exp − x−x_Rxk k 2 ·exp − y−y_Ryk k 2 . (x,y) ℄ u v ∂u

∂x∂u∂y∂v∂x∂v∂y

256×256 4 15000 0.1−1 u v ν0.33 θ

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u,v ◦ _θ µε ∂v ∂y 0.5◦ ₅◦ p P (xi,yj) O(x0,y0) PO x y dx dy P θ P x′ i = x0+u+cosθ·dx+sinθ·dy, y′ j = y0+v−sinθ·dx+cosθ·dy, xi=x0+dx yj=y0+dy x′ i = xi+u+(cosθ−1)·dx+sinθ·dy, y′ j = yj+v−sinθ·dx+(cosθ−1)·dy, uv O P (xi,yj) (x0,y0)

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x y u v ∂u ∂x = cosθ−1; ∂u ∂y = sinθ; ∂v ∂x = −sinθ; ∂v ∂y = cosθ−1. 5 441 61×61 pn+1−pn ≤0.001 ℄ θ θ 10◦ θ= 1 2 ∂v ∂x−∂u∂y ,

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100×100 0.5◦ (u,v) u v 91.2 −100 −1 3.3 40.6 32.0 −60.2 0.48 15.7 0.33 −0.34 −0.05 0.13 6.9 7.5 8% #1 u=v=0.1

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u v

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X Y 60 80 100 120 140 160 60 80 100 120 140 160 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 X Y 60 80 100 120 140 160 60 80 100 120 140 160 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4 u v 0.5 ◦ θ=5◦ ∂v ∂y=50000µε 45· u=v θ ∂v ∂y ∂u∂x 45◦ u 0.0007−0.0012 0.0026−0.0034◦ _40._62−87._38µε 0.05±0.1% −0.05±0.05% 0.08±0.18% 1%

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50 100 150 200 50 100 150 200 100 150 200 50 100 150 200 50 100 150 200 40 60 80 100 120 140 160 180 200 X Y u=v=0.1 5◦ ∂v ∂y=50000µε

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Assignedvalue(pixel) Di sp la ce me nt co mp on en t( pi xe l) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1

DIC-computed 45degreeline

Assignedvalue(degree)

Ro ta ti on an gl e( de gr ee ) 0 1 2 3 4 5 0 1 2 3 4 5

DIC-computed 45degreeline

Assigned value (microstrain)

St ra in s ( mi cr os tr ai n) -20000 -10000 0 10000 20000 30000 40000 50000 -20000 -10000 10000 20000 30000 40000 50000 DIC-computed 45 degreeline

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0.1 1 0.5 1 −0.01 0.01 −0.1 0.4 ℄ −0.006 ◦ ₅◦ −0.13 99.6 5000µε 50000µε −20µε 20µε −0.2% 0.8% 500000µε 1000000µε 2000000µε

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-0.20% -0.10% 0.00% 0.10% 0.20% 0.30% 0.40% 0.50% -0.001 -0.0008 -0.0006 -0.0004 -0.0002 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0 0.2 0.4 0.6 0.8 1 1.2

Re

la

ti

ve

e

rr

or

(

%)

Ab

so

lu

te

e

rr

or

(

pi

xe

l)

D

isp

lacement

(p

ixe

l)

Absolute errorin u Absolute errorin v Relative errorin u Relative errorin v -0.14% -0.12% -0.10% -0.08% -0.06% -0.04% -0.02% 0.00% 0.02% 0.04% 0.06% -0.007 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0 0.001 0 1 2 3 4 5 6

Re

la

ti

ve

e

rr

or

(

%)

Ab

so

lu

te

e

rr

or

(

°)

Rotated

ang

le

(°)

Absolute error Relative error

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500000µε 50000µε 300000µε 100µε 100000µε 1% 1% 5000µε 300000µε ℄ ℄

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100000µε 450000µε 50000µε

500000µε 1000000µε

(83)

-0.40 -0. -120 -100 -80 -60 -40 -20 0 20 40 -50000 0 50000100000150000200000250000300000350000

Re

la

ti

ve

e

rr

or

(

%)

Ab

so

lu

te

e

rr

or

(µ

Ɛ)

Ass

igned

stra

in

(µƐ)

Absolute error Relative error

(84)

(85)

(86)

Mechanical experiments

Uniaxialtensile test

Speckle pattern application

To optimize the correlation

Strain gaugeinstallation

Provide a group of strain as

reference

Specimen preparation

PMMA bone cement material

Image acquisition

Reference and deformedimages

during the test

DIC computation

To getfull-field strain results

Strains correction

Correct the strains using Error

Factor(EF=1.27)

Gauge data acquisition

Measure another group of strain

result using gauge rosettes.

Results evaluation

Compare the resultsin strains

measuredfrom strain gauge and F

(87)

20 15.4g 8.316g ℄ C2A−06−062WW −350 ℄ ℄ ℄

(88)

℄ ℄ 858 1394 1600×1200

(89)

638 ℄ 1.5 1.5

(90)

0.5mm/min 1261 ε=₁ Voutput 4Gain·GF·Vexc. Voutput Gain GF Vexc

(91)

0.8 1.4 −41.6 −40 −7399µε 20348µε

(92)

X Y 80 100 120 140 130 140 150 160 170 180 190 ₀_.9 1 1.1 1.2 1.3 1.4 X Y 80 100 120 140 130 140 150 160 170 180 190 −41.6 −41.4 −41.2 −41 −40.8 −40.6 −40.4 −40.2 50 100 150 100 150 200 −10000 −8000 −6000 X mean =−7399.4486 SD =1299.0371 Y Tr an sv er sa l str ai n ( mi cr os tr ai n) −9500 −9000 −8500 −8000 −7500 −7000 −6500 −6000 −5500 50 100 150 100 150 200 1.6 1.8 2 2.2 x 104 X mean =20348.528 SD =1550.4647 Y Ax ia l str ai n ( mi cr os tr ai n) 1.7 1.8 1.9 2 2.1 2.2 x 104 u v µε 90 −370±1400µε 2680±5780µε

(93)

19887±3790µε 15746±2567µε 3.16±0.61GPa 0.373±0.077 3.78±0.07GPa 0.374±0.018 882.2±108.3N 49.3±6.2MPa 20000µε ℄ 30% 30% CF CF 0.5mm/min

(94)

R 2_>0.₉₉₉ yG=KG·x, yG x KG 105.97 −40.235 R 2_>0.₉₆ R2_{> 0.}₉₉₆ yDIC=KDIC·x, yDIC KDIC 136.39 −48.015 KDIC KG CF=K_KDIC G . 136.39 105.97=1.287 1.287

(95)

1.27 1.27 1−2 3−4 1−2 3−4 CF=1.27

(96)

CF=1.27 15712±3157µε 3.8±0.4GPa 0.368±0.025 −0.5±7.1%−0.2±6.8% −2.0±9.6% 26.0±7.1% −16.8±16.8% 4.9±23.5% 50 98% y− x− ℄ ℄ 1%

(97)

ns

Time

(second)

Pri

nc

ip

al

str

ai

ns

0 50 100 150 -10000 -5000 0 5000 10000 15000 20000 DIC group Gauge group

(100)

Ax

ia

l

pr

inc

ipa

l

s

tra

in

Ax

ia

l s

tr

es

s (

MP

a)

0 5000 10000 15000 20000 25000 0 10 20 30 40 50 60 DIC group Gauge group

Ax

ia

l

pr

inc

ipa

l

s

tra

in

Ax

ia

l s

tr

es

s (

MP

a)

(101)

Ax

ia

l

pr

ic

ipa

l

s

tra

in

Ax

ia

l s

tr

es

s (

MP

a)

Ax

ia

l

pr

inc

ipa

l

s

tra

in

Ax

ia

l s

tr

es

s (

MP

a)

0 5000 10000 15000 20000 0 10 20 30 40 DIC group Gauge group

(102)

Ultimate strain Young ′_s modulus Poisson ′_s

ratio Ultimatestrain Young

′_s

modulus Poisson

′_s

ratio MaximumForce Ultimatestrength

∂v ∂y,µε E ν ∂v∂y,µε E ν F σu ± ± ± ± ± ± ± ± ± ± ± ± ± ± % ± % ± %

(103)

105.97x R² = 0.9997 y = -40.235x R² = 0.9996 -10000 -5000 0 5000 10000 15000 20000 0 50 100 150 200

Pri

nc

ip

al

str

ai

ns

T

ime

(s)

Gauge original

Linear-fitted (Gauge original)

CF ± ± ±

(104)

--10000 -5000 0 5000 10000 15000 20000 25000 0 50 100 150 200

Pri

nc

ip

al

str

ai

ns

T

ime

(s)

DIC original

in

Linear-fitted (DIC original) Linear-fitted D

(109)

0 10 40 60 0 10000

ia

l s

tr

es

s

l

pr

inc

ipa

l

s

tra

in

Linear-fitted (DIC original) Linear-fitted D 0 10 40 0 10000

l s

tr

es

s (

MP

a)

l

pr

inc

ipa

l

s

tra

in

Linear-fitted (DIC original) Linear-fitted D

(110)

(111)

℄ ℄ ℄ ℄ ℄ ℄ ℄

(112)

Pattern collection Using the atomization system

Pattern characterization Using histogram,

MIG and MSF

Mechanical experiments

Using the positioning stage

Rigid body translation test

Rigid body rotation test

DIC computation For displacement and

rotation angle Evaluation Interms of DIC accuracy

and efficiency

Reproducibility test Elementary tests

Image quality and contrast

(113)

m n probe Megneticstirrer

peristaltic pump Optical heads ple T sof

Computer Detectors

Paint solution

Laser beam gon gas

(114)

(115)

0 5000 10000 15000 0 50 100 150 200 250 0 2000 4000 6000 8000 0 50 100 150 200 250 0 2000 4000 6000 8000 0 50 100 150 200 250 0 2000 4000 6000 8000 10000 0 50 100 150 200 250 0 1000 2000 3000 4000 0 50 100 150 200 250

(116)

0 500 1000 1500 2000 2500 0 50 100 150 200 250 0 2000 4000 6000 8000 0 50 100 150 200 250 0 1000 2000 3000 4000 5000 6000 0 50 100 150 200 250 0 500 1000 1500 2000 0 50 100 150 200 250

(117)

#1 #2 0 1000 2000 3000 4000 0 50 100 150 200 250 0 1000 2000 3000 4000 0 50 100 150 200 250 0.5◦ ◦ ◦ ± ± ± ± ± ± 1.1% 0.5

(118)

◦ 4.9% 0 1000 2000 3000 4000 0 50 100 150 200 250 0 2000 4000 6000 8000 0 50 100 150 200 250 0 5000 10000 15000 0 50 100 150 200 250 ◦

(119)

◦ ◦ ± ± ± ± ± ± ± ± ± #2,#1 0.96% 1.1% 0.00033 0.00036 #3 1.7% 0.0013 #2,#1 #3 0−255

(120)

(mm) (mm) (%) −2 −2.02±0.0051 1.13 0.0136±0.0105 5.4±1.9 ♯1 −1 −1.01±0.0018 0.81 0.0136±0.0112 4.3±1.2 1 1.01±0.0018 1.35 0.0138±0.0107 4.2±1.3 2 2.02±0.0036 1.50 0.0143±0.0111 5.4±3.9 −2 −2.02±0.0040 1.37 0.0138±0.0055 4.1±0.7 ♯2 −1 −1.02±0.0036 1.82 0.0143±0.0056 3.4±0.6 1 1.01±0.0007 1.35 0.0136±0.0055 3.3±0.6 2 2.02±0.0022 1.37 0.0136±0.0055 4.1±0.7 −2 −2.02±0.0029 1.45 0.0299±0.0053 4.1±0.7 ♯3 −1 −1.01±0.0014 1.27 0.0299±0.0055 3.4±0.6 1 1.01±0.0011 0.91 0.0301±0.0057 3.6±0.6 2 2.01±0.0025 0.99 0.0299±0.0058 4.1±0.7 −2 −1.92±0.0025 −3.95 0.0065±0.0029 3.9±0.7 ♯4 −1 −0.96±0.0014 −4.16 0.0066±0.0030 3.6±0.6 1 0.95±0.0014 −4.43 0.0064±0.0029 3.5±0.6 2 1.87±0.0029 −6.47 0.0068±0.0031 4.2±0.7 −2 −1.90±0.0036 −4.94 0.0236±0.0051 4.0±0.6 ♯5 −1 −0.88±0.0022 −11.48 0.0217±0.0046 3.4±0.6 1 0.93±0.0014 −6.57 0.0208±0.0039 3.2±0.5 2 1.93±0.0033 −3.09 0.0242±0.0045 3.9±0.5 −2 −2.04±0.0014 2.31 0.0185±0.0036 4.0±0.6 ♯6 −1 −1.02±0.0011 1.78 0.0170±0.0030 3.2±0.5 1 1.01±0.0011 1.47 0.0148±0.0026 2.9±0.4 2 2.02±0.0022 1.48 0.0132±0.0023 3.2±0.6 −2 −2.02±0.0022 1.23 0.0032±0.0012 3.4±0.6 ♯7 −1 −1.01±0.0011 1.18 0.0035±0.0013 2.9±0.5 1 0.99±0.0011 −0.34 0.0038±0.0013 3.2±0.5 2 2.01±0.0025 0.57 0.0039±0.0013 3.6±0.6 −2 −2.02±0.0029 1.47 0.0091±0.0031 3.6±0.6 ♯8 −1 −1.01±0.0011 0.99 0.0101±0.0034 3.4±0.6 1 1.01±0.0018 0.87 0.0100±0.0034 3.3±0.6 2 2.02±0.0033 1.06 0.0095±0.0032 3.8±0.6 −2 −2.02±0.0022 1.09 0.0128±0.0020 3.5±0.5

(121)

♯9 −1 −1.01±0.0011 1.23 0.0123±0.0019 3.0±0.5 1 1.01±0.0011 1.73 0.0140±0.0023 3.3±0.5 2 2.02±0.0025 1.29 0.0153±0.0025 4.0±0.6 −11.48% 2.31% 1.50% #4 #5 −6.47% −11.48% #8 0.0032 0.0301 #7 #3 ±1mm #1 3.5 #1 4.3 ±1mm 5.5 ±2mm

(122)

-1 0 1

er

r

ra

No 0 -1 0 1

r

ie

nt

ra

ment

(mm)

No

(123)

4 -1 0 1

It

er

ati

on

n

u

er

rans

lated

d

isp

lacement

(mm)

No No ◦ ◦ ◦ ◦ (◦₎ ₍◦₎ _(%)

(124)

−4 −3.95±0.0158 1.25 0.0137±0.0130 7.0±0.4 ♯1 −2 −2.02±0.0200 −1.00 0.0138±0.0131 4.9±0.1 2 1.98±0.0366 −1.00 0.0136±0.0133 5.0±0.1 4 3.96±0.0188 −1.00 0.0138±0.0131 7.0±0.4 −4 −4.05±0.0218 1.25 0.0193±0.0073 6.7±1.0 ♯2 −2 −2.03±0.0213 1.50 0.0186±0.0070 4.7±0.6 2 1.95±0.0213 −2.50 0.0189±0.0072 4.6±0.6 4 3.98±0.0207 −0.50 0.0189±0.0070 6.6±1.0 −4 −3.95±0.0203 −1.25 0.0406±0.0075 7.3±0.1 ♯3 −2 −1.98±0.0203 −1.00 0.0402±0.0076 5.1±0.6 2 1.95±0.0206 −2.50 0.0401±0.0075 5.1±0.6 4 4.01±0.0205 0.25 0.0413±0.0077 7.4±0.0 −4 −4.0±0.0249 0.00 0.0090±0.0040 6.1±0.9 ♯4 −2 −2.03±0.0257 1.50 0.0091±0.0042 4.4±0.6 2 2.03±0.0248 1.50 0.0090±0.0040 4.5±0.6 4 3.92±0.0262 −2.00 0.0091±0.0040 6.1±1.0 −4 −4.02±0.0168 0.50 0.0315±0.0052 7.1±0.9 ♯5 −2 −2.02±0.0167 1.00 0.0314±0.0052 4.9±0.5 2 2.05±0.0171 2.50 0.0324±0.0054 5.0±0.5 4 4.02±0.0165 0.50 0.0322±0.0055 7.0±0.9 −4 −4.00±0.0152 0.00 0.0153±0.0035 5.9±0.8 ♯6 −2 −2.06±0.0160 3.00 0.0154±0.0034 4.4±0.5 2 2.05±0.0150 2.50 0.0151±0.0034 4.6±0.5 4 3.95±0.0156 −1.25 0.0153±0.0034 6.1±0.8 −4 −3.97±0.0205 −0.75 0.0051±0.0015 5.9±0.8 ♯7 −2 −2.04±0.0200 2.00 0.0051±0.0015 4.3±0.5 2 2.01±0.0217 0.50 0.0050±0.0015 4.2±0.5 4 4.00±0.0210 0.00 0.0052±0.0015 5.9±0.8 −4 −4.04±0.0205 1.00 0.0123±0.0049 6.5±0.9 ♯8 −2 −2.01±0.0200 0.50 0.0121±0.0049 4.6±0.6 2 1.99±0.0198 −0.50 0.0114±0.0046 4.5±0.6 4 3.97±0.0188 −0.75 0.0121±0.0048 6.4±0.8 −4 −3.97±0.0158 −0.75 0.0256±0.0046 6.9±0.8 ♯9 −2 −1.97±0.0171 −1.50 0.0256±0.0045 4.9±0.5 2 2.05±0.0178 2.50 0.0254±0.0046 4.9±0.5

(125)

4 4.03±0.0177 0.75 0.0255±0.0046 6.9±0.8 −2.50 3.00 0.0090 0.0413 4.2 7.4 #8 0.75% #7 #8 2 ◦ ₄◦ #8 99%

(126)

An

gl

e

er

ro

r

n

ang

le

(deg)

No

re

la

ti

on

ie

nt

n

ang

le

(deg)

(127)

00 00 00

It

er

ati

on

n

u

er

ang

le

()

No No No #8 #8 −0.99% 4.15% 1.1% 0.0073 3.2

(128)

3.8

(129)

(mm) (mm) (%) −2 −2.03±0.0017 1.50 0.0068±0.0023 3.9±0.6 ♯1 −1 −1.02±0.0007 2.00 0.0070±0.0023 3.0±0.5 1 1.02±0.0012 2.00 0.0067±0.0023 3.0±0.5 2 2.04±0.0018 2.00 0.0069±0.0024 3.8±0.7 −2 −1.98±0.0029 −1.00 0.0063±0.0028 4.0±0.6 ♯2 −1 −0.99±0.0017 −1.00 0.0063±0.0028 3.3±0.56 1 1.0±0.0018 −0.24 0.0063±0.0028 3.3±0.5 2 1.99±0.0045 −0.50 0.0066±0.0029 3.9±0.7 −2 −2.08±0.0042 4.00 0.0076±0.0025 3.9±0.7 ♯3 −1 −1.04±0.0017 4.00 0.0072±0.0025 3.4±0.5 1 1.02±0.0010 2.00 0.0074±0.0025 3.3±0.5 2 2.05±0.0019 2.50 0.0076±0.0026 3.9±0.7 −2 −2.0±0.0029 0.00 0.0072±0.0020 3.5±0.6 ♯4 −1 −1.0±0.0009 0.12 0.0064±0.0018 3.5±0.5 1 0.99±0.0009 −1.00 0.0067±0.0019 3.2±0.5 2 1.98±0.0022 −1.00 0.0071±0.0019 3.7±0.6 −2 −2.03±0.0010 1.50 0.0088±0.0024 3.8±0.6 ♯5 −1 −1.01±0.0007 1.00 0.0091±0.0024 3.1±0.5 1 1.02±0.0009 2.00 0.0092±0.0024 2.9±0.4 2 2.02±0.0018 1.00 0.0085±0.0023 3.7±0.6 −2 −2.02±0.0378 1.00 0.0073±0.0009 3.8±0.2 −1 −1.01±0.0192 1.00 0.0072±0.0011 3.3±0.2 1 1.01±0.0141 1.00 0.0073±0.0007 3.1±0.2 2 2.02±0.0305 1.00 0.0073±0.0007 3.8±0.1

(130)

(◦₎ ₍◦₎ _(%) −4 −4.03±0.022 0.75 0.0057±0.0023 6.4±0.8 ♯1 −2 −2.10±0.020 5.00 0.0055±0.0022 4.6±0.5 2 1.98±0.019 −1.00 0.0054±0.0022 4.4±0.5 4 4.02±0.020 0.50 0.0057±0.0023 6.4±0.8 −4 −4.03±0.024 0.75 0.0053±0.0020 6.4±0.8 ♯2 −2 −2.04±0.024 2.00 0.0050±0.0019 4.5±0.5 2 1.95±0.021 −2.50 0.0050±0.0018 4.3±0.5 4 3.41±0.024 −14.75 0.0056±0.0020 5.6±0.7 −4 −3.98±0.020 −0.50 0.0065±0.0023 6.2±0.8 ♯3 −2 −1.97±0.019 −1.50 0.0062±0.0023 4.3±0.5 2 2.03±0.018 1.50 0.0061±0.0022 4.5±0.5 4 4.02±0.020 0.50 0.0064±0.0023 6.3±0.8 −4 −4.08±0.018 2.00 0.0068±0.0020 6.3±0.7 ♯4 −2 −2.07±0.017 3.50 0.0067±0.0020 4.6±0.5 2 2.00±0.017 0.00 0.0068±0.0020 4.5±0.5 4 3.94±0.020 −1.50 0.0067±0.0020 6.1±0.7 −4 −4.03±0.018 0.75 0.0074±0.0021 6.3±0.8 ♯5 −2 −2.07±0.016 3.50 0.0072±0.0021 4.7±0.5 2 2.07±0.017 3.50 0.0072±0.0021 4.7±0.5 4 3.97±0.017 −0.75 0.0075±0.0022 6.4±0.7 −4 −4.03±0.032 0.75 0.0063±0.0007 6.3±0.1 −2 −2.05±0.044 2.50 0.0061±0.0008 4.5±0.1 2 2.01±0.041 0.30 0.0061±0.0008 4.5±0.1 4 3.87±0.033 −3.20 0.0064±0.0007 6.2±0.3

(131)

−14.75% 5.00% 0.08% 0.0050 0.0074 0.0062 4.5 2 ◦ _6.₃ 4◦ 0.015mm 0.12◦ 0.15 0.2◦ #8 #2 #3 #3

(132)

(133)

℄ ei u=eu+eiran, eu e i ran ith ℄ ℄ ℄ eu=_N1 N i=1 (ui

comp−uimp),

ui comp ith uimp N e%=_ueu imp, e i ran ith e i u eu

(134)

80 800 ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ eu eu −0.1% 0.4% 0.05% −0.13% 5◦ −0.2% 0.8% 5000µε 300000µε ℄ ℄ ℄ ℄ ℄ ℄ ℄ ℄ 2.12%

(135)

Algorithmic category

Algorithmic components

Shape function, correlation criteria andinterpolation function.

Processing parameters

Grid step, POI number, subset size, convergence criteria.

Inhomogeneous structure of specimens

Air bubbles, non-uniformity of dimensions, weight, etc.

Speckle pattern

Speckle size, histogram, gray scale distribution, etc.

Physical

environment

St

an

da

rd

or

of

me

an

(

µ

Ɛ)

ment

(mm)

0 400 600 1000 1400 1600 0 1

St

an

d

or

of

t

me

an

(µ Ɛ)

ment

(mm)

1

(138)

240µε 30µε 144 8281 87.5% 8281 1538µε 122µε 31×31 61×61 61×61 1000 61×61 C4 ℄ ℄ ℄ ℄ ℄ 15% 0.013 0−1 ℄ ℄ 50%

(139)

98% 1 4 ℄ 2−5 ℄ ℄ ℄ ℄ ℄ 1.1% 0.07% ℄ ℄ ℄ ℄ 12 ◦_C ℄ 200µε ℄ ℄ ℄ ℄ 1394 4

(140)

u v

(141)

℄ θ = 1₂ ∂v_∂x−∂u_∂y , γ = 1 2 ∂v ∂x+∂u∂y , 4 12 400µε −100µε ℄ ℄ ℄ 1500µε 680µε

(142)

300µε 26% ℄ ℄ ℄ 100µε −20µε 215µε ℄ 50µε 150µε 300µε 5000µε 10000µε 15000µε 26%

(143)

µε ± ± 668±23µε 635±28µε ℄ 4 12 8

(144)

1500µε 1394 #3 #4 −20µε

(145)

0 4 6 10 14 0 1 4

Dis

pl

ac

e

me

nt

co

mp

on

en

ts

(P

ix

el)

T

ime

(Hours)

Displacement u Displacement e (deg) -100 0 100 400 0 1 4

St

ra

in

s

(µ

ε)

T

ime

(Hours)

Transversalstrain hear strain

(146)

-74.368 --100 -50 0 50 100 150 200 250 300 350 0 5000 10000 15000 20000

St

ra

in

e

rr

or

(

µε

)

ε)

0 degree

(147)

85% 99% 300000µε

(148)

5000µε 1.27 99%

(149)

(150)

(151)

85% 99%

(152)

300000µε 5000µε 1,27 99%

(153)

(154)

(155)

main.py ImageParameters.txt

run.pbs ImageParameters.txt run.pbs ImageParameters.txt u,v ∂u

∂x,∂u∂y,∂v∂x,∂v∂y

∂v ∂x,∂u∂y run.pbs

Putty.exe qsubrun.pbs

(156)

(157)

CorrCoeffCalculationmulti.sce

mpiinfo.py nr.py nrexecute.py runparallel.pbs

CorrCoeffCalculationmulti.sce

Scilab.exe CorrCoeffCalculationmulti.sce

execute

nrexecute.pyrunparallel.pbs

nrexecute.py runparallel.pbs

(158)

(159)

Stationmanager JuanValiThreeSystems

6directionsgauges.vi run

270 1.5

(160)

start .dat .lvm .bmp file exportfullsequencetobmpimages export

(161)

(162)

(163)

(164)

(165)

(166)

(167)

(168)

(169)

(170)