Initial deformation

The requirement for stress crack resistance of the HDPE material used for geomembranes formulated in this way has been included in the BAM certification guideline for geomembranes in landfill liners (Muller 1992, 1999b) since it is based on genuine long-term tests. This evaluation procedure is very conservative since it assumes that the long-term available residual stress at an imposed deformation initiates a stress crack, in the same way as an imposed durable external stress does (see Sect. 5.4.1). 

Fig. 5. 23 shows an idealized stress-strain curve for a ductile polymer sample. In this case the nominal stress (r is plotted against the strain e. The change in the cross-section of a parallel-sided specimen is also sketched schematically at different stages of the deformation. Initially the stress is proportional to the strain and Hooke s law is obeyed. The tensile modulus can be obtained from the slope. As the strain is increased the curve decreases in slope until it reaches a maximum. This is conventionally known as the yield point and the yield stress and yield strain, Oy and Cy, are indicated on the curve. The yield point for a polymer is rather difficult to define. It should correspond to the point at which permanent plastic deformation takes place, but for polymers a permanent set can be found in specimens loaded to a stress, below the maximum, where the curve becomes non-linear. The situation is further complicated by the observation that even for specimens loaded well beyond the yield strain the plastic deformation can sometimes be completely recovered by annealing the specimen at elevated temperature. In practice, the exact position of the yield point is not of any great importance and the maximum point on the curve suffices as a definition of yield. The value of the yield strain for polymers is typically of the order of 5-10% which is very much higher than that of metals and ceramics. Yield in metals normally occurs at strains below 0.1%. 

It is rare to be able to observe elastic deformations (which occur for instance during earthquakes) since by definition an elastic deformation does not leave any record. However, many subsurface or surface features are related to the other two modes of deformation. The composition of the material, confining pressure, rate of deformation and temperature determine which type of deformation will be initiated. 

From standpoint of aims of the technical diagnostics (TD) it is necessary to select two probable states of the NDT objects (NDTO). The first, when defect in the material already has been formed might characterize as defective state of material (DSM). And second - when defect is not yet formed, but exist so changes in the spatial (volume) distribution (SD) of the physical-mechanical features (PMF) of the material, of its tense-deformed state (TDS), which under certain conditions will initiate defect origination. This is predefective state of material (PDSM). 

In effect of loads acting in the scope of elastic deformations (proportional) in polycristalline bodies, changes in distances between atomic surfaces of the net are observed, which change the initial magnetic permeability. 

The divergence factor (DF) introduced by the asymptotic expansion, accounts for the deformation of the refracted wavefront (initially spherical in the coupling medium). It ensures, under the GO approximation, the energy conservation of a ray-pencil propagating... 

As two surfaces are brought together, the pressure is extremely large at the initial few points of contact, and deformation immediately occurs to allow more and more to develop. This plastic flow continues until there is a total area of contact such that the local pressure has fallen to a characteristic yield pressure of the softer material. 

C - INITIALIZE TEMPERATURE SECOND IWARIANT OF RATE OF DEFORMATION TENSOR... 

Returning to the Maxwell element, suppose we rapidly deform the system to some state of strain and secure it in such a way that it retains the initial deformation. Because the material possesses the capability to flow, some internal relaxation will occur such that less force will be required with the passage of time to sustain the deformation. Our goal with the Maxwell model is to calculate how the stress varies with time, or, expressing the stress relative to the constant strain, to describe the time-dependent modulus. Such an experiment can readily be performed on a polymer sample, the results yielding a time-dependent stress relaxation modulus. In principle, the experiment could be conducted in either a tensile or shear mode measuring E(t) or G(t), respectively. We shall discuss the Maxwell model in terms of shear. 

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. 

Design Criteria. Traditionally the yield pressure has been regarded as an important design criterion because it is the largest pressure to which an initially stress-free cylinder may be subjected without the cylinder suffering any permanent deformation when the pressure is removed. Customarily,... 

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