STRESS–STRAIN BEHAVIOUR OF POLYMERS IN GEOMEMBRANES

The stress–strain behaviour of polymers used to manufacture geomembranes is largely determined by the properties discussed above, namely the molecular weight, molecularweight distribution and crystallinity or density. Figure shows a typical stress–strain curve for HDPE which identifies the following:

? The linear elastic region (where it obeys Hooke’s Law);

? The plastic region where the polymer draws and extends;

?the yield stress;

?the ultimate strength (or tensile strength at break);

?the modulus of elasticity (i.e. the gradient of the initial linear slope).

First figure is a similar stress–strain curve which also identifies the elongation at yield (also know as the yield strain) and the elongation at break (also known as the breaking strain). Second figure shows the stress–strain curves for various polymer types. If the load riseslinearly to fracture with no plastic deformation then the material is said to be brittle as is the case for PVC liners where the plasticizers have been extracted or, for HDPE geomem-branes after extensive oxidation. More commonly though the behaviour of geomembranes is ductile but may exhibit brittle behaviour depending on the temperature. The brittle transition occurs at sub-zero temperatures for common geomembranes (see section on low temperature properties) (Scheirs, 2000). For geomembranes applications either hard and tough (e.g. HDPE) or soft and tough (e.g. CSPE, fPP, EIA) polymers are the most suitable.

YIELD BEHAVIOUR

'Yield’ is defined as the onset of plastic deformation in a polymer under an applied load.This is an important parameter because it represents the practical limit of use more than does ultimate break or rupture. The yield properties depend on the polymer crystallinity and the polymer morphology. The yield behaviour also depends on the test conditions used. The yield properties vary with both the test temperature and the speed of the test. For this reason it is very important that tensile testing of polymer geomembranes be conducted at 23?C where possible. This may therefore cast doubt on field tensiometer measurements where higher or lower temperatures might be encountered. Since the speed of the tensile test is also critical, the tensile test speed (also known as the cross head speed and determined by the strain rate) must be standardized and defined (Scheirs, 2000).

PLASTIC DEFORMATION

‘Plastic deformation’ is the deformation that remains after a load is removed from a polymer sample. It is also called permanent deformation or non-recoverable deformation. Under small enough loads less than the yield stress the deformation is elastic and is recovered after the load is removed (i.e. the specimen returns to its original length). Yielding thus represents the transition from elastic to plastic behaviour. Con-sider a HDPE geomembrane sample under an applied tensile load. The length of the specimen will increase (as measured by the elongation). As the elongation increases,the load at first increases linearly but then increases more slowly and eventually passes through a maximum where the elongation increases without any increase in load. This peak in the stress–strain curve (i.e. the load–elongation curve) is the point at which plastic flow (permanent deformation) becomes dominant and is defined as the yield point. Not all polymers exhibit a defined yield point such as that exhib-ited by HDPE. PVC, for example, shows no obvious yield point in the stress–strain curve.

STRESS

The shape and magnitude of the load–elongation curve depends on the particular polymeric geomembrane being tested. Rather than load, the properly normalized variable is stress which is defined as the load per unit cross-sectional area of the test specimen. Stress therefore has units of pressure (1 MPa=1MN/m2=145 psi).

STRAIN

Rather than quoting elongation, the proper normalized variable is strain which is the extension divided by the initial length. Strain is therefore dimensionless whereas elongation isexpressed as a percentage.

TYPES OF LOADING

The most common type of loading used for testing polymeric geomembranes is uniaxialtension but other types of loading are arguably more important such as compression, hydrostatic compression and uniaxial (i.e. multiaxial tensile) loading. The simplest varia-tion of the tensile test is the uniaxial compression test which should not be confused with hydrostatic compression in which the load is applied from all sides. It has been found that compressive stresses are higher than tensile stresses for a given strain value.

TEMPERATURE EFFECTS

The shape and magnitude of the stress–strain curve is very dependent on temperature. Asthe temperature increases, the yield stress, elastic modulus (i.e. stiffness) and yield energyall decrease while the yield strain (elongation at yield) increases.

STRAIN RATE EFFECTS

Strain rate determines to the speed of the application of force on the material being tested.High strain rates (i.e. high testing speed) have the effect of making the polymer behave in a more brittle fashion – in the same way that reducing the temperature makes the polymer stiffer and more brittle

MELTING POINTS

Polymer geomembrane resins have very different melting points as shown in Table.The polymer melting point (or more correctly the melting range) is of importance during thermal welding; particularly when welding different geomembrane materials to eachother.