Deviations from Ideal Stress-Strain Behavior

3 Deviations FROM Ideal Stress-Strain Behavior 

Stage I The strain mainly is caused by the changes in the chain length and angle. The deformation is reversible and approximately follows the Hooke s law. 

Stage II The polymer chain segments start to move and orientation starts to occur. The characteristic of this stage is strain softening, i.e., the stress decreases with increase in strain. (The stain softening phenomenon disappears if true stress and true strain are used in the stress-strain curve. However, the 

Stage ni Polymer chain segments continne to move and cold flow occurs. The deformation is irreversible. Due to the molecular orientation and the 

Stage III The sliding and orientation still occur, but are largely limited by tie molecules or entanglements. The stress increases until the fiber breaks. The deformation in this stage is irreversible. 

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The response of rubbery materials to mechanical stress is a slight deviation from ideal elastic behavior. They show non-Hookean elastic behavior. This means that although rubbers are elastic, their elasticity is such that stress and strain are not necessarily proportional (Figure 14.3). 

The idealized laws just reviewed can, however, not describe the behavior of matter if the ratios of stress to strain or of stress to rate of strain is not constant, known as stress anomalies. Plastic deformation is a common example of such non-ideal behavior. It occurs for solids if the elastic limit is exceeded and irreversible deformation takes place. Another deviation from ideal behavior occurs if the stress depends simultaneously on both, strain and rate of strain, a property called a time anomaly. In case of time anomaly the substance shows both solid and liquid behavior at the same time. If only time anomalies are present, the behavior is called linear... 

However, no real material shows either ideal elastic behavior or pure viscous flow. Some materials, for example, steel, obey Hooke s law over a wide range of stress and strain, but no material responds without inertial effects. Similarly, the behavior of some fluids, like water, approximate Newtonian response. Typical deviations from linear elastic response are shown by rubber elasticity and viscoelasticity. 

When the shear stress of a liquid is directly proportional to the strain rate, as in Fig. 2.4a, the liquid is said to exhibit ideal viscous flow or Newtonian behavior. Most unfilled and capillary underfill adhesives are Newtonian fluids. Materials whose viscosity decreases with increasing shear rate are said to display non-Newtonian behavior or shear thinning (Fig. 2.4b). Non-Newtonian fluids are also referred to as pseudoplastic or thixotropic. For these materials, the shear rate increases faster than the shear stress. Most fllled adhesives that can be screen printed or automatically dispensed for surface-mounting components are thixotropic and non-Newtonian. A second deviation from Newtonian behavior is shear thickening in which viscosity increases with increasing shear rate. This type of non-Newtonian behavior, however, rarely occurs with polymers. ... 

According to the Hooke s law (Eq. 7.2), the application of a stress leads to an instantaneous response strain on the material and once the stress is removed the strain instantaneously reverts to zero. Nevertheless, polymeric materials may often deviate from this ideal behavior, mainly because their mechanical response presents a/an (Bower, 2002 Sperling, 2006) ... 

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