Stress-strain behavior elastic deformation

Deformation contributes significantly to process-flow defects. Melts with only small deformation have proportional stress-strain behavior. As the stress on a melt is increased, the recoverable strain tends to reach a limiting value. It is in the high stress range, near the elastic limit, that processes operate. 

Fig. 10.60 Compressive stress-strain behavior of PS and LLDPE at 25°C and crosshead speed of 25.4 mm/min. At a compressive stress level of 20 MPa the deformation of the soft LLDPE is large, in the dissipative region and nearly twenty times the PS deformation, which is of the order of 0.04, in the elastic nondissipative range. [Reprinted by permission from B. Qian, D. B. Todd, and C. G. Gogos, Plastic Energy Dissipation (PED) and its Role in Heating/Melting of Single Component Polymers and Multi-component Polymer Blends, Adv. Polym. Techn., 22, 85-95 (2003).]...

A plastic material is defined as one that does not undergo a permanent deformation until a certain yield stress has been exceeded. A perfectly plastic body showing no elasticity would have the stress-strain behavior depicted in Figure 8-15. Under influence of a small stress, no deformation occurs when the stress is increased, the material will suddenly start to flow at applied stress a(t (the yield stress). The material will then continue to flow at the same stress until this is removed the material retains its total deformation. In reality, few bodies are perfectly plastic rather, they are plasto-elastic or plasto-viscoelastic. The mechanical model used to represent a plastic body, also called a St. Venant body, is a friction element. The... 

Figure 10.2. Stress-strain behavior. With elastic (reversible) deformation, stress and strain are linearly proportional in most materials (exceptions include polymers and concrete). With plastic (permanent) deformation, the stress-strain relationship is nonlinear.

Before concluding this discussion of cell walls, we note that the case of elasticity or reversible deformability is only one extreme of stress-strain behavior. At the opposite extreme is plastic (irreversible) extension. If the amount of strain is directly proportional to the time that a certain stress is applied, and if the strain persists when the stress is removed, we have viscous flow. The cell wall exhibits intermediate properties and is said to be viscoelastic. When a stress is applied to a viscoelastic material, the resulting strain is approximately proportional to the logarithm of time. Such extension is partly elastic (reversible) and partly plastic (irreversible). Underlying the viscoelastic behavior of the cell wall are the crosslinks between the various polymers. For example, if a bond from one cellulose microfibril to another is broken while the cell wall is under tension, a new bond may form in a less strained configuration, leading to an irreversible or plastic extension of the cell wall. The quantity responsible for the tension in the cell wall — which in turn leads to such viscoelastic extension — is the hydrostatic pressure within the cell. 

The consistency of a grease is a complex of related properties, easily demonstrable empirically but difficult to define precisely. We can single out yield stress as a truly definable, pertinent property and then have a quantitative parameter in terms of which we can treat consistency. Criddle and Dreher [1] observed typical solid-body stress-strain behavior in greases, with an elastic region, a region of plastic deformation and an ultimate yield or rupture point. At rest grease behaves like a solid body provided the specimen is not too big, it will not flow under the force of gravity. ... 

O. H. Varga, Stress-Strain Behavior of Elastic Materials, Inteiscience, New Yoric. 1966. 20-6-9 J. M. Thorman and S. T. Hwang, Compressible Flow in Permeable Capillaries Under Deformation, Chem. Eng. Set., 33, 15 (1978). 

Ductile properties such as crack pattern and deformations prefiguring the nearing failure are important characteristics regarding the fracture behavior of structural concrete members. The tests demonstrated that in general TRC members have a distinctive ductile behavior although the stress-strain-behavior of the fabrics is linear-elastic until a brittle tensile failure. While the deformations under service loads (SLS) are rather small, the load-bearing behavior of the specimens is characterized by a distinctive stabilized crack pattern as well as high deformations in ultimate limit state (ULS) of L/30 - L/20. 

As a melt is subjected to a fixed stress (or strain), the deformation vs. time curve will show an initial rapid deformation followed by a continuous flow (Fig. 1-6). The relative importance of elasticity (deformation) and viscosity (flow) depends on the time scale of the deformation. For a short time, elasticity dominates over a long time, the flow becomes purely viscous. This behavior influences processes when a part is annealed, it will change its shape or, with post-extrusion (Chapter 5), swelling occurs. Deformation contributes significantly to process flow defects. Melts with small deformation have proportional stress-strain behavior. As the stress on a melt is increased, the recoverable strain tends to reach a limiting value. It is in the high-stress range, near the elastic limit, that processes operate. 

Elasticity The reversible stress-strain behavior by which a body resists and recovers from deformation produced by a force. 

Since whiskers have high tensile strengths they are also capable of withstanding exceptionally large elastic strains. Metallic and even some oxide whiskers support strains of 2 to 5% before fracture or yield occurs. Towards the higher strains the stress-strain behavior is often nonlinear and substantial deviations from Hooke s law are observed. The stress-strain curves are similar to the one shown in Fig. 45 for the amorphous iron alloy fiber. At the highest strain some stress relaxation may also occur, giving rise to an irreversible residual deformation. 

It is known that the stress-strain and load-deformation relationships of the ACL are dependent on strain rate due to its viscoelastic property. Although perfectly elastic materials respond to loading and unloading instantaneously, viscoelastic materials have a time-dependent response to loading and unloading. Biological tissues usually exhibit remarkable viscoelastic behavior due to high water content. It is... 

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