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Stress-strain behavior

Posted by admin on July 23rd, 2012

Part strength

The stress-strain behavior of a material determines the material contribution to part strength (or stiffness), the relationship between load and deflection in a plastic part. Other factors that affect part strength include part geometry, loading, constraint conditions on the part, and the residual stresses and orientations that result from the molding process. There are various types of strength, such as tensile, compressive, torsional, flexural, and shear, depending on the load and restraint conditions the part is subjected to. These types also correspond to the primary load state present in the part. The stress-strain behavior of the material in the same mode as the primary load state in the part is most relevant in determining part strength.

Tensile properties

It is important to consider the relevant stress-strain behavior that corresponds to the primary (and, commonly, the multiple) load state(s) at the operation temperature and strain rate. However, because of the inherent accuracy problems regarding the current testing procedures for non-tensile tests,most of the published stress-strain data for plastics materials are limited to only short-term, load-to-failure tensile test results. Readers concerned about other types of load states than tensile properties should refer to other literature for relevant information. The figure below depicts the tensile bar test sample and the deformation under a pre-set, constant load. The stress ( ) and strain ( ) are defined as:


(a) The tensile test bar with a cross-sectional area, A, and original length L0. (b) Tensile test bar under a constant loading, F, with elongated length, L. Viscoelastic behavior and spring/dash-pot model For viscoelastic material such as plastics, the short-term tensile test data tend to reflect values that are predominantly affected by the elastic response of the plastic. However, you must also test and evaluate time-related viscoelastic behavior, as in the response to long-term loading, to determine any detrimental long-term effects. As one of the mathematical models, springs and dash-pots in various combinations have been employed to model the response of plastics materials under load. Springs represent elastic response to load The spring in Figure 2 represents the elastic portion (usually short term) of a plastic material’s

response to load. When a load is applied to the spring, it instantly deforms by an amount proportional to the load. When the load is removed, the spring instantly recovers to its original dimensions. As with all elastic responses, this response is independent of time and the deformation is dependent on the spring constant.

FIGURE 2. A spring represents the elastic response to load.  Dash-pots represent viscous response to load  The dash-pot in Figure 3 represents the viscous portion of a plastic’s response. The dash-pot consists of a cylinder holding a piston immersed in a viscous fluid. The fit between the piston and cylinder is not tight. When a load is applied, the piston moves slowly in response. The higher the loading, the faster the piston moves. If the load is continued at the same level, the piston eventually bottoms out (representing failure of the part). The viscous response is generally time- and rate-dependent.

FIGURE 3. A dash-pot represents a viscous response to load. Voight-Kelvin Mechanical model mimics typical response to load The Voight-Kelvin Mechanical model, which includes a spring and dash-pot in series with a spring and dash-pot in parallel, is the most common model (see Figure 4) to mimic the plastics’ behavior upon loading.

FIGURE 4. A Voight-Kelvin Mechanical model to mimic the typical behavior of plastics’ response to load. The components of the Voight-Kelvin Mechanical model are: The spring in series represents the elastic, recoverable response to a load. l   The dash-pot in series represents a time-dependent response that may not be recoverable when the load is removed. l   The spring and dash-pot in parallel represent a time-dependent response that is recoverable over time, by the action of the elastic spring.



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