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

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 Stress Strain Tikalsky – Penn State University

Tikalsky – Penn State University 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

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

Tikalsky – Penn State University 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”. 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. Tikalsky – Penn State University

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  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.  e1 time Tikalsky – Penn State University

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

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

Creep Behavior changes with Stress Time Strain Secondary Primary Tertiary High Temperature Low Stress High Stress Low stress levels at high temperatures may prevent viscous flow in metals. In hydrous materials, creep is related to stress level at all temps. Tikalsky – Penn State University

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

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

Tikalsky – Penn State University Plot of Relaxation  time  0 Exponential loss of stress. e = constant Tikalsky – Penn State University

Tikalsky – Penn State University 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. Shear strains and the rate of shear strain dominate the deformations of viscous flow. Tikalsky – Penn State University

Tikalsky – Penn State University 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 Shear Stress Shear Strain t, sec t0 dg/dt Tikalsky – Penn State University

Tikalsky – Penn State University 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

Tikalsky – Penn State University 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. 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. Tikalsky – Penn State University

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