# time dependent deformations

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Time Dependent Deformations. Properties depend on rate and duration of loading Creep Relaxation Viscosity Shrinkage. Stress. Strain. Review: Elastic Behavior. Elastic material responds to load instantly Material returns to original shape/dimensions when load is removed - PowerPoint PPT Presentation

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• Time Dependent DeformationsProperties depend on rate and duration of loadingCreepRelaxation Viscosity Shrinkage

• Review: Elastic BehaviorElastic 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

• Modulus of Toughness: Total absorbed energy before ruptureDuctility: Ratio of ultimate strain to yield strainModulus of Resilience: Recoverable elastic Energy before yieldModulus of ElasticityStress Strain Curve

• Creep BehaviorStress 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.

• Idealized Maxwell Creep ModelMaxwell proposed a model to describe this behavior, using two strain components:Elastic strain, 1= /E

Creep strain, etimee1e2 = constante 1=/E

• Creep PredictionCreep can be predicted by using several methods

Creep Coefficientcreep/elastic

Specific Creepcreep/elastic

• Creep Behavior changes with TemperatureTimeStrain SecondaryPrimaryTertiaryAmbient TemperatureHigh Temperature

• Creep Behavior changes with Stress

• RelaxationTime dependent loss of stress due to sustained deformation

• Idealized Relaxation ModelMaxwells model can be used to mathematically describe relaxation by creating a boundary condition of ,

• Plot of Relaxatione = constant

• ViscosityViscosity 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 flowSolids have trace viscous effects As temperatures rise, solids approach melting point and take on viscous properties.

• Viscous BehaviorEnergy 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

• ShrinkageShrinkage 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.

• Shrinkage MechanismThe loss of capillary water is accomplished by a variety of mechanismsHeatRelative HumidityAmbient PressureStress (mathematically included in creep)Shrinkage can also be related to the dehydration of hydrated compounds CaSO4*2H2O (gypsum) to CaSO4*H2O or Ca(OH)2 to CaO. This type of dehydration is also accompanied with change in mechanical strength properties.e0e0-esh

• Summary of time dependent effectsCreepRelaxationViscosityShrinkage

Temperature increases deformationMicrostructure of material Atomic structureCrystallineAmorphousBonding

The higher energy state of stress makes materials more susceptible to elevated temperature effects, which also agitate the atomic energy. Stress and temperature are interactive. Maxwell model is a viscoelastic and can be thought of as a spring and dashpot in series. The spring constant in E and the dashpot constant is 1/n.Creep behavior can stabilize or be neglected at low temperatures for metals. However, at high temperature, metals can become viscous and fail through the onset of necking and rupture. Ni, Co, Cr alloying elements can improve the creep resistant at high temperatures. In hydrous materials, creep is primarily a function of water and capillary water stress, water loss and relative humidity. Low stress levels at high temperatures may prevent viscous flow in metals. In hydrous materials, creep is related to stress level at all temps.Maxwell model can be thought of as a spring and dashpot in series. The spring constant in E and the dashpot constant is 1/n.Exponential loss of stress.Shear strains and the rate of shear strain dominate the deformations of viscous flow. Portland cement, lime, gypsum, wood, organic fabrics are all susceptible to shrinkage. Prediction is usually exponential equation with a limit when water is no longer present.

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