Threshold loading

Although in practice the formation of inner cracks requires a certain threshold loading, for most brittle ceramic materials this threshold is negligibly small (usually less than 1 newton, seen clearly in hardness tests). It is thought that cracks make well defined spheres entirely beneath the contact zone, and that they grow downwards as the load is applied. Such a system presents a complicated elastic-plastic problem. 

Hence, above a certain threshold loading of about 1 atom nm-2, chromium evaporates from the catalyst during calcination. If this occurs in a porous catalyst, the airborne species may deposit somewhere else and anchor subsequently to the support. Hence, gas-phase transport may be expected to play an important role in the redispersion of chromium species through the calcination of a high-surface area polymerization catalyst. 

Sprensen et al. [63] also examined the effect of incommensurability. The tip was made incommensurate by rotating it about the axis perpendicular to the substrate by an angle 0. The amount of friction and wear depended sensitively on the size of the contact, the load, and 0. The friction between large slabs exhibited the behavior expected for incommensurate surfaces There was no wear, and the kinetic friction was zero within computational accuracy. The friction on small tips was also zero until a threshold load was exceeded. Then elastic instabilities were observed leading to a finite friction. Even larger loads lead to wear like that found for commensurate surfaces. 

Optical microscopy photographs of typical indentations on treated samples are reported in Figure 10. If the indentation load is 40 N no cracks are generated conversely, at 50 N well-developed cracks are generated therefore, a threshold load for crack formation can be pointed out for the strengthened samples, which is much higher than that for as-received glass, estimated equal to about 4 N. The effect of the compressive residual stress is absolutely clear. 

An expression for the minimum threshold load for lateral cracking, P/, has been derived as [14,45] ... 

This relationship would apply only above a threshold load of F. The critical load F that will initiate crack can be determined by... 

Foster, G. E., J. Nakano, A. W. Shed, J. A. Simpson, J. D. Road, and W. D. Reid (2012). Serum skeletal troponin I following inspiratory threshold loading in healthy young and middle-aged men. EurJ Appl Physiol 112 3547-3558. 

To make anisotropic networks, the linear chains have to be ordered prior to the crosslink reaction. This orientation can be achieved in the melt state under strain by simple extension. The crosslinking reaction is performed in a two-step process. In the first step, a well-defined weak network is synthesized, which is deformed with a constant load to induce the network anisotropy. The load has to exceed the threshold load which is necessary to obtain a uniform director orientation. In the second step, a second crosslinking reaction occurs and locks in the network anisotropy. This procedure is shown schematically in Figure 9.12. 

In Fig. 1.60b, the radial crack is visible and its occurrence occurs at a threshold load. It has been observed experimentally that, for most ceramic materials indented by Vickers tester, the threshold load is at an indentation of 250 N. 

The load is apphed as a rising step load or step-modified slow strain rate testing protocol under displacement control that measures the threshold load for the onset of hydrogen assisted stress cracking by a drop in load that can be used as a quantitative, accelerated (S24 h) test method. Equivalence between the displacement control test method is assumed to occur when the threshold load in the accelerated test is >75 % of the notched ftBcture strength of the square bar in bending. 

There will be a threshold load that will produce a cracked indent such that we can imagine the situation where this is reached and the crack is just equal in size to the diagonal of the impression 2a. Thus we can rewrite equation (5.88) using a, as the threshold indent diagonal size... 

In equation (5.26), represents a threshold for the analysis, not to be confused with a threshold load necessary to initiate cracks. 

As equation (5.91) shows, the threshold load can be estimated from a knowledge of Hy, K, and all of which are found by the indentation hardness technique. In the case just considered, with Kc = 0.75 MN Hy = 6 GN m, ( c = 130 MN m , and A = 0.076, an estimate for P is 0.43 N. This small load over the area represented by a, is of course a large local stress, but the estimate does emphasize that small particles can generate critical flaws beneath the surface. The effect of the surface compression layer can be seen by removing the -1.6critical load decreases to 0.068 N for this glass. 

Because alveolar recruitment is less of an issue in obstructive lung injury than in parenchymal lung injury, the need for PEEP is less. Table 2 summarizes an approach to ventilation for patients with obstructive airway disease. A role for PEEP occurs when intrinsic PEEP serves as an inspiratory threshold load for the patient attempting to trigger a breath. Under these conditions, judicious application of PEEP, up to 75-85% of measured intrinsic PEEP, can balance expiratory pressure throughout the ventilator circuitry to facilitate the triggering process (71,72). 

Figure 5 Respiratory muscle resistive training with threshold loading in a patient weaning from mechanical ventilation.

When contacted, a glass may deform (over some threshold load) irreversibly, that is, plastically and/or with fracture. It is of utmost importance to understand, control and tailor glass response. In this perspective, brittleness index introduced by Lawn and Marschall (1979) as the ratio of hardness and toughness is of great importance ... 

Lawn and Evans (1977) showed that brittleness is closely related to the critical load to initiate a median-radial crack (see also Ishikawa and Shinkai, 1982). The threshold load is... 

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