Critical deformation strain

B/ Fragmentation rate g/s Ib/s (AL/Ll Critical agglomerate deformation strain ... 

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. 

Fig. 14.11. Typical data for recrystallised grain size as a function of prior plastic deformation. Note that, below a critical deformation, there is not enough strain energy to nucleate the new strain-free grains. This is just like the critical undercooling needed to nucleate a solid from its liquid (see Fig. 7.4).

The three inelastic processes (flow, twinning, and phase changes) all require the shearing of atomic neighbors, so they all tend to occur at the same critical elastic strain (at low temperatures i.e., temperatures below the Debye temperature of the specimen material). As they occur, they interfere with one another, thereby increasing the stress needed for further deformation. 

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. 

Concerning the above-mentioned critical quantities the authors have in fact established (i) that irrespective of stress level damage is apparently initiated at a critical creep strain ec of 3 to 3.5% (ii) that a notable deviation of creep data from the potential law starts just at this strain level and (iii) that although the strain rate dev/df is a function of stress, the minimum in the Sherby-Dorn plot also occurs (for the tubular specimens) at ec. The postulated changes in sample morphology at about the time when the strain values started to deviate from Findley s equation, were in fact seen by these and other authors [42,52], who detected in U PVC deformed micro-cavities later... 

Crack growth models in monolithic solids have been well document-ed. 1-3,36-45 These have been derived from the crack tip fields by the application of suitable fracture criteria within a creep process zone in advance of the crack tip. Generally, it is assumed that secondary failure in the crack tip process zone is initiated by a creep plastic deformation mechanism and that advance of the primary crack is controlled by such secondary fracture initiation inside the creep plastic zone. An example of such a fracture mechanism is the well-known creep-induced grain boundary void initiation, growth and coalescence inside the creep zone observed both in metals1-3 and ceramics.4-10 Such creep plastic-zone-induced failure can be described by a criterion involving both a critical plastic strain as well as a critical microstructure-dependent distance. The criterion states that advance of the primary creep crack can occur when a critical strain, ec, is exceeded over a critical distance, lc in front of the crack tip. In other words... 

When considering a ductile substrate coated with a brittle film and subjected to a uniaxial strain during loading and before debond of the film (perfect adhesion), the displacement is assumed to be continuous at the interface. Then, the substrate deformation is entirely transmitted to the film through the interface. When exceeding the critical cracking strain of the film, a network of transverse cracks develops. At the interface, each crack tip will be surrounded by a... 

Chapter 3. In-plant measurement of flow behavior of fluid Foods. Using a vane-in-a-cup as a concentric cylinder system. The vane yield stress test can be used to obtain data at small- and large-deformations. Critical stress/strain from the non-linear range of a dynamic test. Relationships among rheological parameters. First normal stress difference and its prediction. 

For URPs, the emphasis is somewhat different. Due to their relatively low stiffness, component deformations under load may be much higher than for metals and the design criteria in step (b) are often defined in terms of maximum acceptable deflections. Thus, for example, a metal panel subjected to a transverse load may be limited by the stresses leading to yield and to a permanent dent. Whereas a URPs panel may be limited by a maximum acceptable transverse deflection even though the panel may recover without permanent damage upon removal of the loads. Even when the design is limited by material failure it is usual to specify the materials criterion in terms of a critical failure strain rather than a failure stress. Thus, it is evident that strain and deformation play a much more important role for URP than they do for metals. As a consequence, step (a) is usually required to provide a full stress/strain/ deformation analysis and, because of the viscoelastic nature of plastics, this can pose a more difficult problem than for metals. 

Axial compression of high modulus polymeric filaments results in the formation of so-called kinkbands. These are regions of sub-micron thickness where the compressive defonnation is concentrated. This mode of failure is characteristic for anisotropic materials. The processes involved in kinkband formation are not yet well understood. In this work the kinkband formation in single aramid filaments is measured as a function of the applied compressive strain. Above a critical compressive strain the kinkband density initially increases yery rapidly until eventually a maximum density is obtained. The experimental results are compared with an elastic stability model. The kinkbands form before elastic instability occurs and are therefore attributed to a plastic deformation process. A model is developed to describe the kinkband density as a function of the applied strain. 

Fig. 5.21. Schematic illustration of craze formation in the creep test on transparent amorphous thermoplastics. Visible crazes occur at a certain time and strain dming the creep test. These times are indicated in the creep curves measured at different stresses. The connecting line of these points provides a curve which describes the strain limit at which craze formation occnrs as a function of time or deformation rate respectively. An extrapolation of the cnrve towards great times yields the critical limiting strain for craze formation...

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