strain analysis · · 2009-03-30ii strain dept. of geology strain analysis ... ii strain dept. of...

II Strain

Dept. of Geology

STRAIN ANALYSIS

UNDEFORMED DEFORMED

Strain is defined as the change in size and shape of a body resulting from the action of an applied stress field

II Strain

Dept. of Geology

KINEMATIC ANALYSISKinematic analysis is the reconstruction of movements

cf

a

cde

ba

cf

A. Rigid Body Translation

ba

f

d

e b

a

B. Rigid Body Rotation

E. Nonrigid Deformation by Distortion

C. Original Object

c

e

b

e d

f c

d ad

f

e

b

D. Nonrigid Deformation by Dilation

(Davis and Reynolds, 1996)

II Strain

Dept. of Geology

(volume change)

The nature of strain : dilation, distortion, and rotation

(volume change)dilation

distortion

total strain

rotation

KINEMATIC ANALYSIS

II Strain

Dept. of Geology

NON-RIGID DEFORMATION

HOMOGENOUS HETEROGENOUS

TYPES OF STRAIN

KINEMATIC ANALYSIS

II Strain

Dept. of Geology

B. Inhomogeneous strain

A. Homogeneous strain

H

I

H

TYPES OF STRAIN

KINEMATIC ANALYSIS

II Strain

Dept. of Geology

A.

L

l = 5 cmo

L' = 3 cm

L

l = 8 cmf

Davis dan Reynolds (1996)

L' = 4.8 cm

8 cm - 5 cm 5 cm Strech (S) = l/lo e = = 0.6

extension (e) = (l - lo)/lo dimana lo = panjang semula dan l = panjang akhir

Extension (e) = (lf – lo)/lo

Stretch (S) = lf/lo = 1 + e

Lengthening e>0 (+) shortening e<0 (-)

LENGTHENING1

Fundamental Strain Equations

(Davis and Reynolds, 1996)(Davis and Reynolds, 1996)

Quadratic elongation (λ) = S2

λ’ = 1/λ = 1/S2 = 1/(1+e)2

II Strain

Dept. of Geology

Angular shear (ψ) = 90-αtan ψ = x/y = (γ) = shear strain

VOLUME CHANGE

Angular Shear

2

3


II Strain

Dept. of Geology

Strain

B. Shear strain

Deformed State

Strain

R e = n

Deformed State

Undeformed State

A. Extension and stretch

Undeformed State

R = 1θ

θr

θ

θ

r = Sn

T

Re tans = 1/2 ψt

ψ

((TwissTwiss and Moore, 1997)and Moore, 1997)


II Strain

Dept. of Geology

STRAIN CALCULATION

LLORIGINALORIGINAL

LLFINALFINAL Strain (e) = (Lf – Lo)/Lo

II Strain

Dept. of Geology

STRAIN ELLIPSE

II Strain

Dept. of Geology


STRAIN CALCULATION

II Strain

Dept. of Geology

STRAIN ELLIPS EQUATION

II Strain

Dept. of Geology

Kasus Deformasi

Peregangan suatu garis (ε)

II Strain

Dept. of Geology

SHEAR STRAIN

tan ψ = γ

Reciprocal shear strain elongation

II Strain

Dept. of Geology

Mohr circle for Finite Strain

Equation

Center of the circle

Radius of the circle

II Strain

Dept. of Geology

Mohr Circle for Finite Strain

Otto Mohr (1882) generated Mohr diagram strain. A diagram representing systematic variation changed of quadratic elongation and shear strain.

II Strain

Dept. of Geology

DEFINING Ψmax dan γmax

II Strain

Dept. of Geology

Mohr Strain Diagram

Ad

θd = +15º

C

λ'3

Distorted Clay Cake

S1

1 Unit

A

S1

3.0

γ/λ

Minus

1.01.0

C

2 θd

λ −λ

2' '3 1

λ λ' + ' 2

1 3

2.01.0

B

λ'3.0

.56

γ/λ

.49

0

1.01.0

C

2 = +30ºθd

(λ γ λ', / )

λ' 2.43 = λ'1 = .42 2.01.0

λ −λ . 2θ2

' ' COS 3 1 d

0

A

A'λ'1

Equals

γ λ = λ −λ . 2θ

2/ ' ' SIN 3 1

d

λ'(Davis and Reynolds, 1996)

II Strain

Dept. of Geology

HOMOGENOUS DEFORMATION

II Strain

Dept. of Geology

O

N

Simple Shear(Noncoaxial Strain)

A B

M

S1

ML

Pure Shear(Coaxial Strain)

S3S3

S1

25% FlatteringS3

S1

S3 S1+ 22º

+ 31º S3S1

S1

S3

30% Flattering

+ 45º

40% Flattering

Progressive Deformation


II Strain

Dept. of Geology

D. Microscope scale

100 mμ

A. Regional scale

100 m

B. Outcrop scale

10 mm

C. Hand sample scale

D.

A.

perpendicu larto layer



E.

C.

F.

B.

^^

S1

S2S3

S1^

^

^ ^ ^

^

S1^

S1^

S2^

S2^

S2S3^

S3^

S3

S2 < 1 S2 = 1 S2 >1

STRAIN HISTORY

Structural development in competent layerStructural development in competent layerbased on orientation of Sbased on orientation of S11, S, S22 and Sand S33

Scale Factor

II Strain

Dept. of Geology

Strain Measurement

• Geological Map • Geologic Cross-section• Seismic Section• Outcrop• Thin Section

Knowing the initial objects• Shape• Size

• Orientation

II Strain

Dept. of Geology

S2

S2S3

S3

S3

S1

S1

S1

Strain Ellipsoid

S1 = Maximum Finite StretchS3 = Minimum Finite Stretch


II Strain

Dept. of Geology

FINITE AND INFINITESIMAL STRAIN

II Strain

Dept. of Geology

II Strain

Dept. of Geology

Field of Compensation

Field of Expansion

1.0

Field ofNo Strain

Strating Sizeand Shape

Fieldof

LinearShortening

Field of Contraction

S1

1.0

S3

Field of Linier Strecthing

Strain Field Diagram

II Strain

Dept. of Geology

X

Z

Y

Z

X

Y

A

Z

Y

X

B

^1

b = S

S2

3^

^a =

SS

1

2^

K = 1

K = 0

ConstrictionalStrain

FlatteringStrain

Plane S

train

Sim

ple

Ext

ensi

on

Simple Flattering1

k = χ

Special Types of Homogenous Strain

A. Axial symmetric extension (X>Y=Z) or Prolate uniaxialB. Axial symmetric shortening (X=Y>Z) or Oblate uniaxial

C. Plane strain (X>Y=1>Z) or Triaxial ellipsoid

Flinn Diagram

STRAIN DIAGRAM

II Strain

Dept. of Geology

S2

S2S3

S3

S3

S1

S1

S1

Flinn Diagram

II Strain

Dept. of Geology

Strain Measurement from Outcrop

II Strain

Dept. of Geology

Δ = gap

Δ

Δ

II Strain

Dept. of Geology

STRESS vs. STRAIN

II Strain

Dept. of Geology

Relationship Between Stress and Strain

• Evaluate Using Experiment of Rock Deformation

• Rheology of The Rocks• Using Triaxial Deformation Apparatus• Measuring Shortening• Measuring Strain Rate • Strength and Ductility

II Strain

Dept. of Geology

2 3 4 61

C

Strain (in %)

Diffe

rent

ial S

tress

(in

MP

a)

ReptureStrength

400

5

100

200

300Yield

Strength

UltimateStrength

Yield StrengthAfter StrainHardening D

A

EB

Stress – Strain Diagram

A. Onset plastic deformationB. Removal axial loadC. Permanently strained D. Plastic deformationE. Rupture

II Strain

Dept. of Geology

0 2 4 6 8 10 12 14 16

Diff

eren

tial S

tress

, MPa

Strain, percent

300

200

100

70

20

Crown Point Limestone

40

140130

60

80

5 10 15

2000

1500

1000

0 Strain (in %)

800ºC

700ºC

500ºC

300ºC

500Diff

eren

tial S

tress

(in

MP

a)

25ºC

Effects of Temperature and Differential Stress

II Strain

Dept. of Geology

(Modified from Park, 1989)

Deformation and Material

A. Elastic strainB. Viscous strainC. Viscoelastic strainD. ElastoviscousE. Plastic strain

Hooke’s Law: e = σ/E, E = Modulus Young or elasticityNewtonian : σ = ηε, η = viscosity, ε = strain-rate

II Strain

Dept. of Geology

(Modified from Park, 1989)

Effect increasing stress to strain-rate

II Strain

Dept. of GeologyStress Strain

II Strain

Dept. of Geology

Limitation of The Concept of Stress in Structural Geology

• No quantitative relationship between stress and permanent strain• Paleostress determination contain errors• No implication equation relating stress to strain rate that causes the deformation

strain analysis · · 2009-03-30ii strain dept. of geology strain analysis ... ii strain dept. of...

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