Tensile deformation critical strains

FIG. 20-70 The influence of moisture as a percentage of sample saturation S on granule deformabihty. Here, deformation strain (AL/L) is measured as a function of applied stress, with the peak stress and strain denoted by tensile strength and critical strain (AL/L) of the material. Dicalcium phosphate with a 15 wt % binding solution of PVP/PVA Kolhdon VAG4. [Holm et al., Powder Tech., 43, 213 (1.9S.5J,] With land permission from Elsevier Science SA, Lausanne, Switzerland. 

The tensile curve of a polymer fibre is characterised by the yield strain and by the strain at fracture. Both correspond with particular values of the domain shear strain, viz. the shear yield strain j =fl2 with 0.04rotation angle of -0y=fl2 and the critical shear strain 0-0b=/iwith /f=0.1. For a more fundamental understanding of the tensile deformation of polymer fibres it will be highly interesting to learn more about the molecular phenomena associated with these shear strain values. 

Crazes usually form under tensile stress when a critical strain is surpassed they do not occur under compressive stress applying hydrostatic pressure during tensile deformation can even inhibit their development. Crazes always nucleate preferentially at points of triaxial stress concentration. It is the dilatational strain which initiates crazes and cracks. 

Figure 2-23. Scale failure diagram of tensile deformation according to Eq. (2-39) for several oxides (Schiitze, 1995). The critical strain is given in absolute values. For percentage values a factor of 100 has to be applied.

If forces are applied to a semicrystalline pol3rmer in the way of a tension, a compression or a simple shear, deformations take place imder a constant volume. Hence, they are always composed of a reversible elastic shear and an irreversible shear 3delding. In this section, we discuss the properties of tensile deformations. As it is found, here deformation mechanisms change at three critical strains associated with a strain softening, a strain hardening and a loss of memory of the initial sample shape. The drawing stress is set up of contributions from the amorphous network, the skeleton of crystallites and viscous forces, and experiments enable a separation to be carried out. 

Figures 10.9 to 10.11 illustrate how stretching curves and critical strains vary with temperature, again with results for PEVA12, and with the crystallinity here polyethylenes with different crystallinities are compared. Curves demonstrate a further general property of semicr3 talline pol5oners. While the stresses vary in systematic manner, there is no effect on the critical strains for softening (en 0.1) and hardening (en 0.6) and virtually no change in the elastic-plastic composition of the strains. Hence, tensile deformation of semicrystalline polymers is strain-controlled and changes the mechanism at two critical strains that are temperature and crystallinity invariant.

As one example, in thin films of Na or K salts of PS-based ionomers cast from a nonpolar solvent, THF, shear deformation is only present when the ion content is near to or above the critical ion content of about 6 mol% and the TEM scan of Fig. 3, for a sample of 8.2 mol% demonstrates this but, for a THF-cast sample of a divalent Ca-salt of an SPS ionomer, having only an ion content of 4.1 mol%, both shear deformation zones and crazes are developed upon tensile straining in contrast to only crazing for the monovalent K-salt. This is evident from the TEM scans of Fig. 5. For the Ca-salt, one sees both an unfibrillated shear deformation zone, and, within this zone, a typical fibrillated craze. The Ca-salt also develops a much more extended rubbery plateau region than Na or K salts in storage modulus versus temperature curves and this is another indication that a stronger and more stable ionic network is present when divalent ions replace monovalent ones. Still another indication that the presence of divalent counterions can enhance mechanical properties comes from... 

The continuous chain model includes a description of the yielding phenomenon that occurs in the tensile curve of polymer fibres between a strain of 0.005 and 0.025 [ 1 ]. Up to the yield point the fibre extension is practically elastic. For larger strains, the extension is composed of an elastic, viscoelastic and plastic contribution. The yield of the tensile curve is explained by a simple yield mechanism based on Schmid s law for shear deformation of the domains. This law states that, for an anisotropic material, plastic deformation starts at a critical value of the resolved shear stress, ry =/g, along a slip plane. It has been... 

Physical characterization of polymers is a common activity that research and development technologists at the Dow Chemical Company perform. A material property evaluation that is critical for most polymer systems is a tensile test. Many instruments such as an Instron test frame can perform a tensile test and, by using specialized software, can acquire and process data. Use of an extensometer eliminates calibration errors and allows the console to display strain and deformation in engineering units. Some common results from a tensile test are modulus, percent elongation, stress at break, and strain at yield. These data are then used to better understand the capabilities of the polymer system and in what end-use applications it may be used. 

The Tensile Stress Field, The main tool used in industry to assess the structural integrity of the propellant grain is a commercially available finite-element code that solves problems of finite elastic deformations. From numerical investigation performed with the code, one of the maximum strain locations (the critical point) is identified. This point (M) is located at the surface of the combustion chamber near the middle of the symmetry axis. 

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