Stress-deformation curve

Consider the schematic stress-deformation curve of Figure 2.6. Here elastic strain e dominates until the stress reaches Y0 then, plastic deformation 8 dominates. Note that plastic flow begins as soon as a small stress is applied,... 

Figure 2.6 Schematic stress-deformation curve with linear deformation-hardening.

These results summarize a large amount of work carried out in our laboratory on polysiloxane based Interpenetrating Polymer Networks (IPNs). First, a polydimeth-ylsiloxane (PDMS) network has been combined with a cellulose acetate butyrate (CAB) network in order to improve its mechanical properties. Thanks to a perfect control of the respective formation rates of networks it has been possible to avoid polymer phase separation during the IPN synthesis. Indeed, PDMS/CAB IPNs are transparent and only one mechanical relaxation was detected by DMTA measurements which are characteristic of trae IPNs. In addition, a synergy effect is observed on the stress-deformation curves. Second, a PDMS network was combined with a fluorinated polymer network and the resulting IPNs can also be considered as true IPNs. In this case, a synergy of the surface properties was displayed. 

FIG. 156, Stress deformation curves of a clay plastic mass (from Norton, 1952 ). 

Figure 7. The graph on the left shows the ideal shear stress-deformation curves for small beech specimens (right) with an ideal elastic adhesive coimection or with an ideal plastic adhesive connection. The industrial partner prepared several adhesive layers which exhibited stress-deformation diagrams close to the theoretical requirements. Three of them are shown above 027-2,009-05 and 013-1.

Fig. 14.12. Schematic of (a) the intrinsic stress-deformation curve of a polymer and (b) the force per unit area of an undefbrmed specimen observed as a function of total deformation in a tensile test.

Another comparison is given in Figure 10 which shows the stress-deformation curves for polymer films containing polar or nonpolar functional monomers and prepared by solution or emulsion polymerization. In the case of N-methylol methacrylamide, the latex polymer was again much stronger than the solution polymer. In the case of the nonpolar glycidyl methacrylate (6MA) the polymerization method made little difference in the film strength. 

Figure 10. Stress-deformation curves of films obtained from latexes (2 and 4) and from solutions (1 and 3) of EA/MOMAM (3 and 4) and EA/GMA (1 and 2) content of the functional monomer in each case is 6.6 mole %, (Yeliseyeva, Ref. 28)...

Figure 1. Average stress-deformation curves from the tensile-tensile (A ) the tensile-compressive B j cyclic tests and an envelope ciirve ( C ].

The residual compressive deformations of the specimens were measured for the tensile-compressive loading. Their values were assumed to be equal to a distance from the maximum compressive stress point in a cycle to the tangent line corresponding to the ascending tensile branch of the stress-deformation curve in the direction of axis (Fig. 4). A slow... 

Then the stress-deformation curve follows the envelope curve till the next unloading. 

The elasticity of a fiber describes its abiUty to return to original dimensions upon release of a deforming stress, and is quantitatively described by the stress or tenacity at the yield point. The final fiber quaUty factor is its toughness, which describes its abiUty to absorb work. Toughness may be quantitatively designated by the work required to mpture the fiber, which may be evaluated from the area under the total stress-strain curve. The usual textile unit for this property is mass pet unit linear density. The toughness index, defined as one-half the product of the stress and strain at break also in units of mass pet unit linear density, is frequentiy used as an approximation of the work required to mpture a fiber. The stress-strain curves of some typical textile fibers ate shown in Figure 5. 

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

The ratio of stress to strain in the initial linear portion of the stress—strain curve indicates the abiUty of a material to resist deformation and return to its original form. This modulus of elasticity, or Young s modulus, is related to many of the mechanical performance characteristics of textile products. The modulus of elasticity can be affected by drawing, ie, elongating the fiber environment, ie, wet or dry, temperature or other procedures. Values for commercial acetate and triacetate fibers are generally in the 2.2—4.0 N/tex (25—45 gf/den) range. 

Little error is introduced using the idealized stress—strain diagram (Eig. 4a) to estimate the stresses and strains in partiady plastic cylinders since many steels used in the constmction of pressure vessels have a flat top to their stress—strain curve in the region where the plastic strain is relatively smad. However, this is not tme for large deformations, particularly if the material work hardens, when the pressure can usuady be increased above that corresponding to the codapse pressure before the cylinder bursts. 

For stainless steel, the stress-strain curve (see Fig. 26-37) has no sharp yield point at the upper stress limit of elastic deformation. Yield strength is generally defined as the stress at 2 percent elongation. 

When metals are rolled or forged, or drawn to wire, or when polymers are injection-moulded or pressed or drawn, energy is absorbed. The work done on a material to change its shape permanently is called the plastic work- its value, per unit volume, is the area of the cross-hatched region shown in Fig. 8.9 it may easily be found (if the stress-strain curve is known) for any amount of permanent plastic deformation, e. Plastic work is important in metal- and polymer-forming operations because it determines the forces that the rolls, or press, or moulding machine must exert on the material. 

The energy expended in deforming a material per unit volume is given by the area under the stress-strain curve. For example,... 

When a foam is compressed, the stress-strain curve shows three regions (Fig. 25.9). At small strains the foam deforms in a linear-elastic way there is then a plateau of deformation at almost constant stress and finally there is a region of densification as the cell walls crush together. 

Long-term deformation such as shown by creep curves and/or the derived isochronous stress-strain and isometric stress-time curves, and also by studies of recovery for deformation. 

The stage is now set to determine the largest load the laminate can carry. Only the outer layers resist the load N after the knee of the load-deformation curve. There, the stress in the outer layers is, from... 

Shear-stress-shear-strain curves typical of fiber-reinforced epoxy resins are quite nonlinear, but all other stress-strain curves are essentially linear. Hahn and Tsai [6-48] analyzed lamina behavior with this nonlinear deformation behavior. Hahn [6-49] extended the analysis to laminate behavior. Inelastic effects in micromechanics analyses were examined by Adams [6-50]. Jones and Morgan [6-51] developed an approach to treat nonlinearities in all stress-strain curves for a lamina of a metal-matrix or carbon-carbon composite material. Morgan and Jones extended the lamina analysis to laminate deformation analysis [6-52] and then to buckling of laminated plates [6-53]. 

When a plastic material is subjected to an external force, a part of the work done is elastically stored and the rest is irreversibly (or viscously) dissipated hence a viscoelastic material exists. The relative magnitudes of such elastic and viscous responses depend, among other things, on how fast the body is being deformed. It can be seen via tensile stress-strain curves that the faster the material is deformed, the greater will be the stress developed since less of the work done can be dissipated in the shorter time. 

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