Strain deformation

As a melt is subjected to a fixed stress or strain, the deformation versus time curve will show an initial rapid deformation followed by a continuous flow. Elasticity and strain are compared in Fig. 8-9 that provides (a) basic deformation vs. time curve, (b) stress-strain deformation vs. time with the creep effect, (c) stress-strain deformation vs. time with the stress-relaxation effect, (d) material exhibiting elasticity, and (e) material exhibiting... 

The properties of glassy polymers such as density, thermal expansion, and small-strain deformation are mainly determined by the van der Waals interaction of adjacent molecular segments. On the other hand, crack growth depends on the length of the molecular strands in the network as is deduced from the fracture experiments. 

This method applies a constant force to the sample and monitors the strain (deformation) as a function of time This is called the creep test and gives the elastic and viscous properties of substances. 

In a similar fashion strain (deformation) y can be defined using a tensor notation ... 

The four phases are Di thrust-related tight to isoclinal (Fi) folds and associated axial planar schistosity (Si). D2 tight-to-isoclinal folds (F2), with S2, are interpreted as high strain deformation with F1/F2 fold interference structure (Fig. 6) resulting in the development of SI/S2 composite fabric elements. D3 are recumbent and best developed in the west part of the BMC, and D4 are represented as kink-folds. 

The terms are arranged into sections dealing with basic definitions of stress and strain, deformations used experimentally, stresses observed experimentally, quantities relating stress and deformation, linear viscoelastic behaviour, and oscillatory deformations and stresses used experimentally for solids. The terms which have been selected are those met in the conventional mechanical characterization of polymeric materials. 

Fluorescence EXAFS studies of a (In,Mn)As thin layer (10 nm) grown on a GaSb buffer layer and of (In,Mn)As quantum dots (QDs) on GaAs were also performed. The results show that in the thin (In,Mn)As layer, the In-site substitutional Mn and the NiAs-type MnAs coexist, whereas the majority of Mn atoms are substituted into the In-sites of InAs in (In,Mn)As QDs. It is argued that the difference of the strain deformation between the thin layer (with strain) and thick layer and QDs (strain relaxed) is responsible for the differences in the local structure of the Mn atoms (Ofuchi et al. 2001b). 

Fig. 7 a and b. Scheme of the thermomechanical behaviour of a well phase-separated thermoelasto-plastic. Stress-strain (or time) curves. Plots of heat effects versus time. First loading (ABC) and unloading (CD) cycle. Second loading (AC) and unloading (CD) cycle. The yielding point occurs at B. AD indicates the residual deformation after the first cycle. AB on the dQ/dT-time curve is the endo-effect resulting from the initial small-strain deformation AB U9)... 

A typical curve has an essentially linear portion (OA) in which the deformation is proportional to the applied load, See Fig. 1. It follows that the unit stress iload divided by original area) is proportional to the unit strain (deformation divided by original gage length) in accordance willi Hooke s Law. The numerical value of this ratio (e,g in psi) is known as Young s Modulus or Modulus of Elasticity,... 

Where no linear region is discemable from a force/deformation or a stress/strain curve, use a secant modulus. Construct a secant line from a desired stress (force) point and extend it to the zero strain (deformation) point. Use the slope of this secant line to give the secant modulus. 

Immediately following a step strain deformation, all of the segments of a fully entangled melt can be assumed to have the same degree of orientation. In other words, both the short and the long chains will be characterized by identical functions (uu)f Q+, where... 

An element of an elastic solid body under a shear stress deforms as shown in Figure 10.4. The shear strain (deformation)... 

Figure 8 Relaxation of a polymeric chain after a step-strain deformation[6] process A (8c) reequilibration of chain segments process B (8d) reequilibration across slip links process C (8e) reptation.

D.C.Venerus, C.M.Vrentas, J.S.Vrentas, Step strain deformations for viscoelastic fluids experiment, J. Rheol. 34 (1990), 657-682. 

Dynamic Mechanical (Low Strain Deformation). When a cyclic strain of small ampUtude is applied to a strip of material, a cyclic stress will be generated in response by the sample. If the material is ideal (Hookian) and stores all the input energy, the cyclic stress is in phase with the applied cyclic strain. Viscous components cause a finite phase lag or phase angle, 8, between the stress and strain. represents the elastic, real, or storage modulus while E" is the viscous, imaginary, or loss modulus. Tan 8 is equal to the ratio E /E" and is related to the molecular relaxations that occur in the sample. Transition temperatures and associated activation energy can be determined (72) by varying the frequency of oscillation at a fixed temperature or the temperature at a fixed frequency. 

The brittle-ductile transition temperature depends on the characteristics of the sample such as thickness, surface defects, and the presence of flaws or notches. Increasing the thickness of the sample favors brittle fracture a typical example is polycarbonate at room temperature. The presence of surface defects (scratches) or the introduction of flaws and notches in the sample increases Tg. A polymer that displays ductile behavior at a particular temperature can break in the brittle mode if a notch is made in it examples are PVC and nylon. This type of behavior is explained by analyzing the distribution of stresses in the zone of the notch. When a sample is subjected to a uniaxial tension, a complex state of stresses is created at the tip of the notch and the yield stress brittle behavior known as notch brittleness. Brittle behavior is favored by sharp notches and thick samples where plane strain deformation prevails over plane stress deformation. 

Forces applied to a water-saturated porous medium will cause stresses which result in strain (deformation). The stress, strain and groundwater pressure in a water-saturated porous medium are coupled, as first recognized by Biot (1941). Under the assumed stress conditions, the vertical normal component of total stress (o ) that acts downwards on a horizontal plane at any depth is caused by the weight of the overlying water-saturated rock. This stress is born by the solid matrix of the porous medium (o ) and by the pressure of the groundwater in the pores (p ) (e.g. Hubbert andRubey, 1959)... 

In order to use these general momentum conservation equations to calculate the velocity field, it is necessary to express viscous stress terms in terms of the velocity field. The equations which relate the stress tensor to the motion of the continuous fluid are called constitutive equations or rheological equations of state. Although the governing momentum conservation equations are valid for all fluids, the constitutive equations, in general, vary from one fluid material to another and possibly also from one type of flow to another. Fluids, which follow Newton s law of viscosity (although it is referred to as a law, it is just an empirical proposition) are called Newtonian fluids. For such fluids, the viscous stress at a point is linearly dependent on the rates of strain (deformation) of the fluid. With this assumption, a general deformation law which relates stress tensor and velocity components can be written ... 

The ratio of strain (deformation per unit length) caused by a stress (force per unit cross-sectional area) applied to a polymeric material is called Young s modulus. A sufficiently high Young s modulus is desired for a polymer when it is spun to hollow fibers. 

When a solid is subjected to a shearing force, the solid (simultaneously with the application of force) deforms, and internal stresses develop until a condition of static equilibrium is reached. Within the elastic limit of a substance, these internal stresses are proportional to the induced shearing strains (deformation). The ability of a material to reach static equilibrium, rather than deform continuously, is due to a property called shear strength. 

Another important characteristic of viscous liquids close to Tg is nonexponential relaxation. Consider the response of a system to a perturbation, such as the polarization in response to an applied electric field, the strain (deformation) resulting from an applied stress, the stress in response to an imposed deformation, the volume response to applied pressure, or the temperature response to a heat flux. It is found experimentally that the temporal behavior of the response function 0(t), following an initial instantaneous response, can often be described by the stretched exponential, or Kohlrausch-Williams-Watts (KWW) function (Kohlrausch, 1854 Williams and Watts, 1970),... 

On the basis of the SANS results, a molecular mechanism has been recently proposed for the toughness enhancement of DN gels [34]. This mechanism rationalizes the changes in molecular structure of the DN gel constituents observed via in-situ neutron scattering measurements, the composition dependence of the solution viscosity, and the thermodynamic interaction parameters of PAMPS and PAAm molecules obtained previously from neutron scattering studies. More specifically, this proposed mechanism provides an explanation for the observed periodic compositional fluctuations in the micrometer range induced by large strain deformation. 

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