Stress in Geology

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All what we need about Stress to determine geological deformation

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Stress Structural Geology Done by: Student:Youssef Elsherif Alexandria University Faculty of Science Geology Department

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In physics, the stress at a point in a material is the applied force per unit area. The SI unit for stress is the Pascal (symbol Pa); in US Customary units, stress is given in pounds per square inch (psi). To be exact, the stress at a point may be determined by taking the limit of the load being carried by a particular cross section, divided by that cross section, as the area of the cross section aproaches zero. In general the stress may vary from point to point, but for simple cases, such as circular cylinders with pure axial loading, the stress is constant and equal to the cross-sectional area divided by the applied load. Stress is described by a symmetric tensor. What is Stress?

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Types of Stress a. Tensional Stress Tension may be defined as “pull.” It is the stress of stretching an object or pulling at its ends. An elevator control cable is in additional tension when the pilot moves the control column. Tension is the resistance to pulling apart or stretching, produced by two forces pulling in opposite directions along the same straight line.

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Tensile stress is the ratio of the tensile load F applied to the specimen to its original cross-sectional area A S = F /A

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2. Compressional Stress If forces acting on an aircraft move toward each other to squeeze the material, the stress is called compression. Compression is the opposite of tension. Tension is a “pull,” and compression is a “push.” Compression is the resistance to crushing, produced by two forces pushing toward each other in the same straight line. While an airplane is on the ground, the landing gear struts are under a constant compression stress.

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Compressional stress is the ratio of the compression load F applied to the specimen to its original cross-sectional area A S = F /A

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c. Shear Stress Cutting a piece of paper with a pair of scissors is an example of shearing action. Shear in an aircraft structure is a stress exerted when two pieces of fastened material tend to separate. Shear stress is the outcome of sliding one part over the other in opposite directions. The rivets and bolts in an aircraft experience both shear and tension stresses.

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Shear stress is the ratio of the force F applied to the specimen to its original cross-sectional area A S = F /A

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d. Bending Stress Bending is a combination of tension and compression. Consider the bending of an object such as a piece of tubing. The upper portion stretches (tension) and the lower portion crushes together (compression). The wing spars of an aircraft in flight undergo bending stresses.

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e. Torsion Stress Torsional stresses are the result of a twisting force. When you wring out a chamois skin, you are putting it under torsion. Torsion is produced in an engine crankshaft while the engine is running. Forces that cause torsional stresses produce torque.

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Stress vs Strain If a specific sample is exposed to a range of applied stress and the resulting strain is measured, a graph similar to Figure 5.14 results. This graph shows that the relationship between stress and strain is linear over some range of stress. If the stress is kept within the linear region, the material is essentially elastic in that if the stress is removed, the deformation is also gone. But if the elastic limit is exceeded, permanent deformation results. The material may begin to "neck" at some location and finally break. Within the linear region, a specific type of material will always follow the same curves despite different physical dimensions. Thus, we can say that the linearity and slope are a constant of the type of material only. In tensile and compressional stress, this constant is called the modulus of elasticity or Young's modulus, as given by where stress = F/A in N/m2 (or Ib/in2) strain = Dl/l unitlessE = Modulus of elasticity in N/m2

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Moduli that control Stress – Strain relations: Young's modulus, E, can be calculated by dividing the tensile stress by the tensile strain: where E is the Young's modulus (modulus of elasticity) F is the force applied to the object; A0 is the original cross-sectional area through which the force is applied; ?L is the amount by which the length of the object changes; L0 is the original length of the object. In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or µ, is defined as the ratio of shear stress to the shear strain where = shear stress; F is the force which acts A is the area on which the force acts = shear strain; ?x is the transverse displacement I is the initial length

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The bulk modulus K can be formally defined by the equation: where p is pressure, V is volume, and ?p/?V denotes the partial derivative of pressure with respect to volume. The inverse of the bulk modulus gives a substance's compressibility. where ? is the resulting Poisson's ratio, is transverse strain (negative for axial tension, positive for axial compression) is axial strain (positive for axial tension, negative for axial compression). The Poisson’s Ratio can be formally defined by the equation:

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Stress upon Geologic Structures Introduction This section introduces the rationale behind structural studies in geology and hence why it is important to understand forces, stresses and strains. These concepts are outlined and differences between them explained.

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a. Stress at Microscopic Scale Linear Defects - Dislocations Dislocations are another type of defect in crystals. Dislocations are areas were the atoms are out of position in the crystal structure. Dislocations are generated and move when a stress is applied. The motion of dislocations allows slip – plastic deformation to occur. Edge Dislocations: The edge defect can be easily visualized as an extra half-plane of atoms in a lattice. The dislocation is called a line defect because the locus of defective points produced in the lattice by the dislocation lie along a line. This line runs along the top of the extra half-plane. The inter-atomic bonds are significantly distorted only in the immediate vicinity of the dislocation line.

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Screw Dislocations: The motion of a screw dislocation is also a result of shear stress, but the defect line movement is perpendicular to direction of the stress and the atom displacement, rather than parallel. To visualize a screw dislocation.

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Examples for Microstructures inside the mineral

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Sandstone deformed by pressure solution, Kodiak Is, Alaska. Width of view about 3 mm.

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Left and Above: Scaly fabrics representing distributed microfaulting in decollement thrust of Barbados accretionary prism.

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Transmission electron micrograph of dislocations in calcite. Field of view about 1.7 micron.

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Dislocations in olivine from Hawaiian mantle nodule. Optical view, scale about175 microns

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Sometimes during the growth of a crystal, or if the crystal is subjected to stress or temperature/pressure conditions different from those under which it originally formed, two or more intergrown crystals are formed in a symmetrical fashion.  These symmetrical intergrowths of crystals are called twinned crystals.

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Twinned Orthoclase Pyrite Arsenopyrite Cyclic twin Phillipsite

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b. Stress at Macroscopic Scale There are three main forces that drive deformation within the Earth. These forces create stress, and they act to change the shape and/or volume of a material. The following diagrams show the three main types of stress: compressional, tensional, and shear. Stress causes the build up of strain, which causes the deformation of rocks and the Earth's crust. Compressional stresses cause a rock to shorten. Tensional stresses cause a rock to elongate, or pull apart. Shear stresses causes rocks to slip past each other.

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a. Normal attitde of Rocks The normal position of rocks and the main properties of undeformed rocks

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i. Principles of Stratigraphy There are some principles of stratigraphy (primary characteristics) that indicate that the rock is not deformed just like:

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1. Principle of Original Horizontality

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2. Principle of Superposition

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3. Principle of Lateral Continuity

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b. Deformed Rocks When rocks bend, twist or fracture we say that they deform (change shape or size). The forces that cause deformation of rock are referred to as stresses (Force/unit area).

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i. Stress Effect Many structures can be possessed by stress just like: Folds Faults Joints Foliation & many more

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Folds Compression stress

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Compression stress

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Compression stress

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Faults Shear stress

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Shear stress

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Joints

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Tension stress

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Ice pressure from inside

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Foliation Foliation plane Stress direction

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c. Stress at Tectonic Scale Earth’s crust is formed of Tectonic Plates Those tectonic plates are affected by regional stress actions Theses actions cause tectonic drift and movement These Tectonic Drift is the main reason of how earth became as we see right now

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divergent convergent transform

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a. Divergence Divergence occurs when plates move away from each other with Tensional stress on boundary and Pressure from inner Mantle that causes the Rift Valley & Sea Floor Spreading forms.

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b. Convergence Convergence occurs when plates move toward each other with Compressional stress on boundary that causes Subduction Zones , Collision Zones & Mountain Arcs

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c. Transformation Transformation occurs when plates horizontally parallel to each other with Shear stress on boundary that causes Continental drift and Shear zones formation.

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References 1.http://www.knowledgerush.com/kr/encyclopedia/Stress_(physics)/ 2.http://scign.jpl.nasa.gov/learn/plate5.htm 3.http://www.tpub.com/content/aviation/14018/css/14018_32.htm 4.http://en.wikipedia.org/wiki/Elastic_modulus 5.http://www.ndt-ed.org/EducationResources/CommunityCollege/Materials/Structure/linear_defects.htm 6.www.mineralatlas.com 7.http://www.mhhe.com/earthsci/geology/mcconnell/pte/tpb.htm 8.http://www.indiana.edu/ 9.http://ic.ucsc.edu/~casey/eart150/Lectures/DefMech/14deformationmechanisms.htm 10.http://www.tpub.com/content/aviation/14018/css/14018_32.htm 11.http://www.tulane.edu/~sanelson/eens211/twinning.htm

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Index 1.What is Stress? 2.Types of Stress: a. Tensional. b. Compressional. c. Shear. d. Bending. e. Torsion. 3.Stress vs Strain.

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4.Stress upon Geologic Structures: a. Stress at microscopic scale b. Stress at macroscopic scale: a. Normal attitude of rocks: i. Principles of Stratigraphy. b. Deformed rocks: i. Stress effect. c. Stress at Tectonic scale. a. Divergence b. Convergence c. Transformation 5.Reference Index

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OVER