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Stress and Strain Stress and Strain • Stress is an applied force acting on a rock (over a particular cross-sectional area) METAMORPHIC STRESS • Deviatoric stress affects the textures and structures, but not the equilibrium mineral assemblage Reading: Winter Chapter 21, p. 412-417 • Strain is the response of the rock to an applied stress (= yielding or deformation) • Strain energy may overcome kinetic barriers and facilitate reactions Strain Strain Measurements • Strain is the response to stress • Units of strain are given as a · e is the symbol for strain fraction of the initial dimension · e = lim Dl/lo as Dl approaches zero • Length strain · D l is the change in length in a – el = Dl/lo line element • Volume strain · l is the original length of the 0 – ev = DV/V o same line element Hydrostatic and Lithostatic Stress Pressure • Stress is F/A (force/area) • Lithostatic (and hydrostatic) pressure is • Units are Newtons/m2, MPa, bars, etc. uniform stress is all directions § s is the symbol for stress • For hydrostatic pressure, compared with § s = lim D F/D A as D A becomes deviatoric conditions, all three components of stress are equal infinitely small 1 Deviatoric Stress Directed Stress • Deviatoric stress = unequal pressure in different directions • Tectonism produces non-uniform stress • This causes: • Deviatoric stress can be resolved into three mutually perpendicular stress (s) – Rock deformation components: – Preferred orientation of mineral grains s is the maximum principal stress – Development of large -scale structures 1 s2 is an intermediate principal stress s3 is the minimum principal stress In tension: s3 is negative, and the resulting Types of Deviatoric strain is extension, or pulling apart Stresses: original shape strain ellipsoid • Tension s1 • Compression • Shear s3 Three types of deviatoric stress with an example of possible resulting structures. a. Tension, in which one stress in negative. “Tension fractures” may open normal to the extension direction and become filled with mineral precipitates. Winter (2001) In compression s1 is dominant: folding Foliation Allows Estimation of the produces more homogenous flattening Orientation of s1 s3 s1 s1 · s1 > s2 = s3 ® foliation and no lineation · s1 = s2 > s3 ® lineation and no foliation · s1 > s2 > s3 ® both foliation and lineation Flattening of a ductile homogeneous sphere (a) with randomly oriented flat The three main types of deviatoric stress with an example of resulting disks or flakes. In (b), matrix flows with progressive flattening, and the flakes structures. b. Compression, causing flattening or folding. Winter (2001) are rotated toward parallelism normal to the predominant stress. Winter (2001) 2 Metamorphic Agents and Metamorphic Fluids Changes Shear motion occurs along planes at an angle to s Evidence for the existence of a metamorphic 1 fluid: s 1 – Fluid inclusions – Fluids are required for hydrous or carbonate phases – Volatile-involving reactions occur at temperatures and pressures that require finite fluid pressures The three main types of deviatoric stress with an example of possible resulting structures. b. Shear, causing slip along parallel planes and rotation. Winter (2001) Fluid Pressure Spatial Variations • Pfluid indicates the total fluid pressure, which is the sum of the partial pressures of each component (P fluid = pH2O + pCO2 + …) • Gradients in T, P, Xfluid across an • May also consider the mole fractions of the area components, which must sum to 1.0 (X + H2O • Zonation in the mineral XCO2 + … = 1.0) assemblages 3.
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