tailieunhanh - Statistics of Fracture

Một khía cạnh rắc rối đặc biệt của gãy xương, đặc biệt là trong các vật liệu có độ bền cao và dễ vỡ, là sự biến đổi của nó. Các nhà thiết kế phải có khả năng để đối phó với điều này, và giới hạn nhấn mạnh đến những làm giảm xác suất của sự thất bại đến một mức độ chấp nhận được thấp. | Statistics of Fracture David Roylance Department of Materials Science and Engineering Massachusetts Institute of Technology Cambridge MA 02139 March 30 2001 Introduction One particularly troublesome aspect of fracture especially in high-strength and brittle materials is its variability. The designer must be able to cope with this and limit stresses to those which reduce the probability of failure to an acceptably low level. Selection of an acceptable level of risk is a difficult design decision itself obviously being as close to zero as possible in cases where human safety is involved but higher in doorknobs and other inexpensive items where failure is not too much more than a nuisance. The following sections will not replace a thorough study of statistics but will introduce at least some of the basic aspects of statistical theory needed in design against fracture. The text by Collins1 includes an extended treatment of statistical analysis of fracture and fatigue data and is recommended for further reading. Basic statistical measures The value of tensile strength ơf cited in materials property handbooks is usually the arithmetic mean simply the sum of a number of individual strength measurements divided by the number of specimens tested 1 A ơ N X 1 i i where the overline denotes the mean and ơf i is the measured strength of the ith out of N individual specimen. Of course not all specimens have strengths exactly equal to the mean some are weaker some are stronger. There are several measures of how widely scattered is the distribution of strengths one important one being the sample standard deviation a sort of root mean square average of the individual deviations from the mean 1 s N - 1 N E - ơx i 2 i 1 2 The significance of s to the designer is usually in relation to how large it is compared to the mean so the coefficient of variation or . is commonly used 1 Collins . Failure of Materials in Mechanical Design Wiley 1993. 1 . zS ơf This is often expressed as