Failure function

The failure function, as defined in section 4.1, can be measured directly or indirectly. Once again, the indirect ways are much 

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This ranking implies that human errors are more likely to occur than active equipment failures (functioning equipment, such as a mnning pump) and that active equipment failures are more likely to occur than passive equipment failures (static, nonfunctioning equipment, such as a storage tank). 

The 23-valent pneumococcal polysaccharide vaccine is recommended for use in all adults 65 years of age or older and adults less than 65 years who have medical comorbidities that increase the risk for serious complications from S. pneumoniae infection, such as chronic pulmonary disorders, cardiovascular disease, diabetes mellitus, chronic liver disease, chronic renal failure, functional or anatomic asplenia, and immunosuppressive disorders. Alaskan natives and certain Native American populations are also at increased risk. Children over the age of 2 years may be vaccinated with the 23-valent pneumococcal polysaccharide vaccine if they are at increased risk for invasive S. pneumoniae infections, such as children with sickle cell anemia or those receiving cochlear implants. 

Congestive heart failure-. Functional status, cough, dyspnea on exertion, paroxysmal nocturnal dyspnea, exercise tolerance, and ventricular function... 

Common laboratory tests are used to classify the cause of acute renal failure. Functional acute renal failure, which is not included in this table, would have laboratory values similar to those seen in prerenal azotemia. However, the urine osmolality to plasma osmolality ratios may not exceed 1.5 depending on the circulating levels of antidiuretic hormone. The laboratory results listed under acute intrinsic renal failure are those seen in acute tubular necrosis, the most common cause of acute intrinsic renal failure. 

A precise definition of the flowability of a powder is only possible with several numbers and curves, derived from a family of yield loci of the powder (measured with a shear cell) - see section 4 for further detail. Jenike23 proposed a simpler classification, according to the position of one point of the failure function (at a fixed value of the unconfined yield strength, say 5 lbf (22.3 N) with the Jenike shear cell, i.e. 3112 Pa or 65 lbf/ft2) with respect to the flow factor line (straight line through the origin, at a slope l///where//is the flow factor) - see Fig. 8 for a schematic representation of this. 

If the point on the failure function at 5 lbf (22.3 N) lies on flow factor line of ... 

In addition to the above classification, Williams24 has also defined simple powders as those whose failure function is a straight line through the origin when designing hoppers for such powders,... 

In hopper design, the failure function which represents the strength of the powder on a free surface at different states of consolidation, is compared with another curve which describes the actual stresses in a hopper and the size of the opening is derived from this comparison to give flow every time the outlet is opened. 

Lower values of yield loci and failure functions measured than with the Jenike shear cell. 

The indirect methods for measuring the failure function are based on the shear cells discussed in section 4.3.1. 

The failure function can be measured directly in a number of ways. Some are rather complex and still under development, like the new plane strain biaxial tester with flexible boundaries30, but the simplest method so far is the uniaxial compression test. Only the version developed by Williams et al,24 gives results close to those obtained indirectly with the Jenike shear cell, the other versions yield relative measurements only. 

Uniaxial Compression - Williams Method This method was developed by Williams, Birks and Bhatta-charya24. A compact is first formed in a split mould by applying an axial compressive force, the mould is then removed to leave a cylindrical specimen with its axis vertical. The compressive vertical stress needed to cause failure of the specimen is then found and this is the unconfined yield stress for the consolidating stress used in the compaction of the specimen. The failure function is found by forming a number of compacts under different consolidating stresses and finding the unconfined yield stress for each specimen. 

The results obtained for the failure function of the Ti02 used in the study agreed closely with that obtained using a Jenike shear cell. 

J.C. Williams, A.H. Birks and D. Bhattacharya, The direct measurement of the failure function of a cohesive powder, Powder Technology, 4 (1970/71), 328-37. 

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