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Stress Strain Behavior of Polymers
Introduction:
The Stress/Strain behavior of solid polymers can be categorized into several classes of behavior:
1) Brittle Fracture- characterized by no yield point, a region of Hookean behavior at low strains and failure characterized by chonchoidal lines such as seen in inorganic glasses.
2) Yield Behavior- characterized by a maximum in the stress/strain curve followed by yielding deformation which is usually associated with crazing or shear banding and usually ductile failure. Ductile failure exhibits a high extent of deformation on the failure surface. Yield behavior can result in necking which exhibits a close to constant load regime and a terminal increase in the stress.
3) Rubber-Like Behavior- characterized by the absence of a yield point maximum but exhibiting a plateau in an engineering stress/strain curve. Often rubber-like behavior exhibits a terminal increase in the stress followed by failure which results in a tear with little permanent deformation exhibited in the failure surface, e.g. Jell-O.
The following figure from Ward shows that all three of these failure types can be seen in a single polymer by variation of either time (rate of deformation) or temperature. A good example of this is silly putty. Generally, a single polymer sample displays one of the characteristic failure mechanisms under normal conditions, i.e. polystyrene exhibits brittle failure, polyethylene displays necking, crosslinked polydimethylsiloxane displays rubbery behavior, high impact polystyrene displays yielding behavior. The type of behavior can also change with the type of deformation, i.e. polystyrene displays crazing or brittle failure in tension but displays shear banding and yield behavior in compression.
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
Deformation of Semi-Crystalline Polymers:
Semi-crystalline polymers such as polyethylene typically display necking behavior and a yield point in tensile stress/strain curves. Yield points are always associated with a deformation mechanism which absorbs energy. For semi-crystalline polymers this mechanism involves orientation and destruction of micron to colloidal scale semi-crystalline morphologies.
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
Shear Banding Deformation:
Many polymers display shear banding which is characterized by planes of slip at 45° to the direction of stress. Shear bands do not involve changes in the volume of the sample (dilatation) seen in crazing. Under an optical microscope using crossed polars samples which have under gone shear banding will display X's reflecting the two planes of maximum shear stress in a tensile sample. Shear banding involves localized orientation of the polymer. Because of this it is highly temperature and rate dependent.
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
Crazing Deformation:
Many polymers display another type of localized yielding behavior which results in whitening of the polymer in the region of maximum deformation. Under a microscope, these localized regions of yielding display an increase in volume (dilatation) through formation of micro-cracks which are bridged by polymer fibrils. Crazing and stress whitening are the typical deformation mechanism for polystyrene. High impact polystyrene contains small elastomer domains which serve to increase the number of crazes thereby preventing catastrophic failure by absorbing the energy of deformation. Because crazing is a dilatational mechanism it is expected to occur in regions of high dilatational stress such as in the interior of thick samples or at the lateral edges of a hole cut in a sample (see figure below).
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
Terminal Zone of Stress/Strain:
The terminal failure of a polymer stress strain curve is typically difficult to reproduce since it depends strongly on the presence of flaws. Terminal failure is usually characterized as either brittle or ductile referring to the appearance of the failure surface which is either smooth and sharp or rough and highly deformed. Elastomers typically fail which a high extent of deformation but yield smooth failure surfaces since most of the terminal deformation is reversible. The type of terminal failure is highly dependent on the temperature and rate of deformation and many polymers can display a brittle to ductile transition in temperature or rate of deformation as shown below.
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
Due to the experimental dependencies of failure in polymers, researchers have long sought controlled conditions to characterize failure. These control conditions include a fixed, high rate deformation in an impact tester (Charpy or Izod geometry), generation of controlled flaws through notched samples, and control over the experimental temperature. The design of impact testers is an area of active research and has resulted in a number of specialized instruments aimed at specific materials and specific modes of deformation including Charpy Impact Tester, Izod Impact Tester, Falling Dart Tester, and Trouser Tear instruments for elastomers.
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983
From: I. M. Ward, "Mechanical Properties of Solid Polymers, 2'nd Ed." Wiley, NY, 1983