Time Dependent Deformations

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