By Neil D Kelley
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Extra resources for Analysis Of A Wind Turbine
The consequence is that the critical value of K at which the specimen fails - its fracture toughness - will be virtually identical in every specimen tested. For absolutely identical behaviour, the pdf would be a delta function and the corresponding CDF would be a step function. In any test, however, there are experimental errors. The central limit theorem states that random experimental errors are distributed in a Gaussian manner. This implies that the pdf becomes a Gaussian and the CDF the error function (erf).
The first type of embrittlement can be observed if an alloy steel containing impurities is either cooled slowly to room temperature, or is held for a length of time at temperatures in the range 450°C-550°C, following tempering (at temperatures greater than 575°C). There is a thermodynamic driving force for segregation, most plausibly related to a reduction in overall strain-energy, if the impurities are removed from lattice sites and are accommodated in the more disordered grain-boundary. " The balance of 'driving force' vs thermal energy (approximately 3kT for a solid) determines the upper limit for significant segregation.
For absolutely identical behaviour, the pdf would be a delta function and the corresponding CDF would be a step function. In any test, however, there are experimental errors. The central limit theorem states that random experimental errors are distributed in a Gaussian manner. This implies that the pdf becomes a Gaussian and the CDF the error function (erf). A convenient visual representation is to employ 'normal probability paper' which is scaled such that the erf plots as a straight line. If then, data from fracture toughness tests have CDFs which plot as single straight lines on normal probability paper and possess a standard deviation of less than, say 5 MPa m112,it is impossible to say that they do not derive from a (near-) delta function.