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1.7: Summary

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  • Let's review what we've learned about rheology so far. Rheology describes and defines how a material deforms. To deform a material, stress must be applied, which causes strain. When the stress (\(\sigma\)) placed on a rock is greater than \(\sigma_{s-fric}\) or \(\sigma_{s-frac}\), the rock will reach its failure point and deform. There are two types of failure a rock can experience, failure by frictional sliding or failure by fracture.

    A rock can also deform if it experiences a high degree of stress. The two primary types of deformation are elastic and viscous. Elastic deformation is shallow and has a low magnitude of strain. If the elastic strain is big enough, failure occurs. Viscous deformation occurs deeper and at much higher pressures and temperatures than elastic deformation. Elastic deformation is \(\sigma=Ee\), and has a constitutive relation, meaning that it defines rheology. E is Young's modulus which illustrates the relationship between stress and strain in a material. Viscous deformation is \(\sigma=2\mu\dot{\epsilon}\) and is a time derivative (\(\frac{d}{dt}\)). Two common types of viscous flow are Couette Flow and flow down an inclined plane, as we seen in the asthenosphere. Different materials experience viscous deformation at different rates. There is often a large range in viscosity values for the same material, so it is common to only think about viscous flow in terms of order of magnitude.

    When all stress is removed from a material, and there is no net deformation ⇒ this is recoverable deformation.

    When stress is removed and the flow stops ⇒ this is non recoverable deformation, but it is still reversible.

    Key Terms

    Section 1.0 Introduction to Rheology

    • rheology
    • tectonic forces
    • stress
    • strain
    • strain-rate

    Section 1.1 Stress

    • normal stress
    • shear stress
    • principal stresses
    • pressure
    • lithostatic stress
    • overburden
    • lithostatic pressure

    Section 1.2 Strain and Strain Rate

    • strain
    • normal or linear strain
    • elongation
    • shortening
    • stretching
    • percent strain
    • shear strain
    • shear angle

    Section 1.3 Elastic Deformation

    • recoverable
    • irrecoverable
    • Young's modulus
    • Poisson's ratio
    • uniaxial
    • lateral strain
    • longitudinal strain
    • Andersonian Theory of Faulting