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Time Dependent Deformations

Explore the concepts of creep, relaxation, viscosity, and shrinkage in materials under different loading conditions and temperatures. Learn the behavior changes with stress and time, and predict creep using various methods.

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Time Dependent Deformations

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  1. Time Dependent Deformations • Properties depend on rate and duration of loading • Creep • Relaxation • Viscosity • Shrinkage Tikalsky – Penn State University

  2. Stress Strain Review: Elastic Behavior • Elastic material responds to load instantly • Material returns to original shape/dimensions when load is removed • Modulus of Elasticity = ds/de • Energy and strain are fully recoverable Tikalsky – Penn State University

  3. Stress – Strain Curve Modulus of Toughness: Total absorbed energy before rupture Modulus of Elasticity Modulus of Resilience: Recoverable elastic Energy before yield Ductility: Ratio of ultimate strain to yield strain Tikalsky – Penn State University

  4. Creep Time dependent deformation under sustained loading Tikalsky – Penn State University

  5. Creep Behavior • Stress changes the energy state on atomic planes of a material. • The atoms will move over a period of time to reach the lowest possible energy state, therefore causing time dependent strain. In solids this is called “creep”. • In liquids, the shearing stresses react in a similar manner to reach a lower energy state. In liquids this is called “viscosity”. Tikalsky – Penn State University

  6. Idealized Maxwell Creep Model  • Maxwell proposed a model to describe this behavior, using two strain components: • Elastic strain, 1= /E • Creep strain, e 1=/E e  = constant e2   e1 time Tikalsky – Penn State University

  7. Creep Prediction • Creep can be predicted by using several methods • Creep Coefficient creep/elastic • Specific Creep creep/elastic Tikalsky – Penn State University

  8. Creep Behavior changes with Temperature Strain Tertiary Secondary Primary High Temperature Ambient Temperature Time Tikalsky – Penn State University

  9. Strain High Temperature Tertiary Secondary Primary High Stress Low Stress Time Creep Behavior changes with Stress Tikalsky – Penn State University

  10. Relaxation Behavior Strain t Stress t to Relaxation Time dependent loss of stress due to sustained deformation Tikalsky – Penn State University

  11. Idealized Relaxation Model • Maxwell’s model can be used to mathematically describe relaxation by creating a boundary condition of , Tikalsky – Penn State University

  12.  0 time Plot of Relaxation e= constant Tikalsky – Penn State University

  13. Viscosity • Viscosity is a measure of the rate of shear strain with respect to time for a given shearing stress. It is a separating property between solids and liquids. • Material flows from shear distortion instantly when load is applied and continues to deform • Higher viscosity indicates a greater resistance to flow • Solids have trace viscous effects • As temperatures rise, solids approach melting point and take on viscous properties. Tikalsky – Penn State University

  14. Shear Stress t, sec Shear Strain dg/dt t, sec t0 Viscous Behavior • Energy and strain are largely non-recoverable • Viscosity, h h = t / dg/dt shear strain rate = dg/dt h is coefficient of proportionality between stress and strain rate Tikalsky – Penn State University

  15. Shrinkage • Shrinkage deformations occur in hydrous materials • Loss of free water, capillary water, and chemically bound water can lead to a deduction of dimensions of a material • Organic materials like wood shrink and/or expand over time, depending on the ambient environmental conditions. • Hydrous materials like lime mortar shrink over time. The rate of shrinkage is largely related to relative humidity. Tikalsky – Penn State University

  16. Shrinkage Mechanism e0 e0-esh • The loss of capillary water is accomplished by a variety of mechanisms • Heat • Relative Humidity • Ambient Pressure • Stress (mathematically included in creep) • Shrinkage can also be related to the dehydration of hydrated compounds CaSO4*2H2O (gypsum) to CaSO4*½H2O or Ca(OH)2 to CaO. This type of dehydration is also accompanied with change in mechanical strength properties. Tikalsky – Penn State University

  17. Summary of time dependent effects • Creep • Relaxation • Viscosity • Shrinkage • Temperature increases deformation • Microstructure of material • Atomic structure • Crystalline • Amorphous • Bonding Tikalsky – Penn State University

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