# Stress & Strain

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19-Oct-2015Category

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Deformation:STRESS & STRAIN

DeformationDilation: a change in volumeTranslation: a change in placeRotation: a change in orientationDistortion: a change in form

Term for Stress & Strain*) Important distinction between two quantities

SCALARStemperaturespeedvolumetimelengthVECTORSforce and stress (on a surface)temperature gradientaccelerationEarths gravity fieldEarths magnetic fieldvelocityMantle convection flowocean currentsScalars vs. Vectors

VECTOR & COORDINATE SYSTEM

FORCES & VECTORS Force is any action which alters, or tends to alter

Newton II law of motion :F = M a Unit force : kgm/s2 = newton (N) or dyne = gram cm/s2; N = 105 dynesBASIC CONCEPTS(a). Force: vector quantity with magnitude and direction(b). Resolving by the parallelogram of forcesModified Price and Cosgrove (1990)Two Types of Force Body Forces (i.e. gravitational force) Contact Forces (i.e. loading)

STRESSStress defined as force per unit area: = F/A A = area, Stress units = Psi, Newton (N), Pascal (Pa) or bar (105 Pa)(Davis and Reynolds, 1996)(Twiss and Moores, 1992)

STRESS Stress at a point in 2D Types of stressStress (s)Normal Stress (sn)Shear Stress (ss)Normal stress (sN)(+) Compressive(-) TensileShear stress (sS)(+)(-)

STRESS ON A PLANE AND AT A POINT

Stress EllipsoidPrincipal Stress:s1 > s2 > s3 All stress axes are mutually perpendicular Shear stress are zero in the direction of principal stress s12 = s21, s13 = s31, s23 = s32

Stress Ellipsoida) Triaxial stressb) Principal planes of the ellipsoid (Modified from Means, 1976)

21311111222233332ELIPSOID TEGASAN1 > 2 = 3 1 = 2 > 3 1 > 2 > 3

The State of 3-Dimensional Stress at Point(Twiss and Moores, 1992)Principal Stress:s1 > s2 > s3

B. Mohr DiagramA. Physical DiagramPlanes of maximum shear stress(Twiss and Moores, 1992)

sc = so + tan q (sn)The Coulomb Law of Failuresc = critical shear stressso = cohesive strengthtan q = coefficient of internal frictionsn = normal stress (Modified from Davis and Reynolds, 1996)Compressive Fractures

Body force works from distance and depends on the amount of materials affected (i.e. gravitational force). Surface force are classes as compressive or tensile according to the distortion they produce. Stress is defined as force per unit area. Stress at the point can be divided as normal and shear component depending they direction relative to the plane. Structural geology assumed that force at point are isotropic and homogenous Stress vector around a point in 3-D as stress ellipsoid which have three orthogonal principal directions of stress and three principal planes. Principal stress s1>s2>s3 The inequant shape of the ellipsoid has to do with forces in rock and has nothing directly to do with distortions. Mohr diagram is a graphical representative of state of stress of rockSTRESS

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

TYPES OF STRAIN

- Fundamental Strain Equations Extension (e) = (lf lo)/lo Stretch (S) = lf/lo = 1 + eLengthening e>0 and shortening e
SHEAR STRAIN

S1 = Maximum Finite StretchS3 = Minimum Finite Stretch(Davis and Reynolds, 1996)

132ELIPSOID TERAKAN1321321321321321 > 2 = 3 1 = 2 > 3 1 > 2 > 3

Progressive Deformation(Davis and Reynolds, 1996)

Strain Measurement Geological Map Geologic Cross-section Seismic Section Outcrop Thin SectionKnowing the initial objects Shape Size Orientation

Strain Measurement from Outcrop

STRESS vs. STRAIN

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

(Modified from Park, 1989)Deformation and MaterialElastic strainViscous strainViscoelastic strainElastoviscousPlastic strainHookes Law: e = s/E, E = Modulus Young or elasticityNewtonian : s = he, h = viscosity, e = strain-rate

Stress EllipsoidStrain Ellipsoid

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

STRESS STRAIN RELATIONS

DEFORMATION MECHANISMS

THANK YOU

GEOLOGY CARTESIAN COORDINATE SYSTEM