SM 2 13 Rheology RHEOLOGY timedependent behaviour of

SM 2 -13: Rheology RHEOLOGY (time-dependent behaviour of materials) M. Chrzanowski: Strength of Materials /10

SM 2 -13: Rheology Πάντα ῥεῖ καὶ οὐδὲν μένει panta rhei kai ouden menei everything flows and nothing remains still Heraclitus of Ephesus (540 -480 BC) Ἡράκλειτος ὁ Ἐφέσιος (Herakleitos ho Ephesios) M. Chrzanowski: Strength of Materials 2/10

SM 2 -13: Rheology Tempus fugit, aeternitas manet t - time Hourglass is the trademark of Rheological Society M. Chrzanowski: Strength of Materials 3/10

SM 2 -13: Rheology p –loading e – deformation Solids Fluids e=0 p 0 Stiff body Perfect fluid Euclid, ~ 300 BC p 0 B. Pascal, 1629 -1662 e 0 Elastic body R. Hooke, 1635 -1703 M. Chrzanowski: Strength of Materials e p 0 e 0 Viscous fluid e=0 I. Newton, 1643 -1727 e 0 4/10

SM 2 -13: Rheology T – temperature Dots indicate time derivatives M. Chrzanowski: Strength of Materials 5/10

SM 2 -13: Rheology Elementary rheological models SERIES coupling HOOKE NEWTON MAXWELL MODEL HOOKE NEWTON KELVIN MODEL PARALELL coupling M. Chrzanowski: Strength of Materials 6/10

SM 2 -13: Rheology SERIES coupling NEWTON MAXWELL MODEL HOOKE NEWTON PARALELL coupling HOOKE KELVIN MODEL M. Chrzanowski: Strength of Materials Time derivative notation 7/10

SM 2 -13: Rheology MAXWELL M. Loading „CREEP (of deformation) programme” Steady creep, unbounded (linear) M. Chrzanowski: Strength of Materials Loading „RELAXATION (of stress) programme” Complete relaxation (nonlinear) 8/10

SM 2 -13: Rheology KELVIN M. Loading „CREEP (of deformation) programme” Nonsteady creep, bounded (nonlinear) M. Chrzanowski: Strength of Materials Loading „RELAXATION (of stress) programme” No relaxation response! 9/10

SM 2 -13: Rheology There are two fundamental characteristics of rheological processes: • Its dependence on the history of loading • Energy dissipation - causing irreversibility Macroscopically observable effects are due to material microstructure changes (see material science and Ashby maps). These changes can lead not only to irreversible deformation and stress relaxation but to the formation and growth of microstructural defects. Following this deterioration process a structure can be fatally damaged at arbitrary level of loading or deformation – after a sufficiently long period of loading time. This is, however, a subject of another important branch of solid mechanics – mechanics of damage and failure. M. Chrzanowski: Strength of Materials 10/10

SM 2 -13: Rheology stop M. Chrzanowski: Strength of Materials 11/10