少数資料による引張強さの統計的研究

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The scattering of tensile strength results from various causes. For example, it arises from the non-uniformity of metallurgical structures caused by imperfect mixing of constituent materials, non-metallic inclusions and the change in cooling rate. Furthermore, the scattering due to the difference in shape and size of test specimens depends upon the degree of improvement of plants and machines and the human efforts (carefulness, etc.). Therefore, it may be possible to determine the scattering range from a comparatively small number of data if the impovement is proper. So we considered theoretically a method of estimating the mean value, the maximum or the upper value and the minimum or the lower value. The result of our theoretical consideration shows that the mean value σ_M of tensile strength for specimens having the same shape and size can be estimated from (TS)_<max> and (TS)_<min> by the following equation. σ_M =√<(TS)_<max>・(TS)_<min>> (1) where (TS)_<max> and (TS)_<min> are the maximum and minimum values of tensile strength for the sample. Then, the upper value (σ_∞)_r, the lower value (σ_l)_r, the maximum value (σ_<max>)_r and the minimum value (σ_<min>)_r can be obtained by the following equations: [numerical formula] where (δ_∞)_r and (δ_<max>)_r are coefficients which depend on the appraisement quantity q for the tensile strength of specimens, the degree of human improvement r and the quality of samples, In order to verify the above theoretical consideration, the estimated values were calculated from the experimental data on a few specimens (12 pieces) by means of eqs. (1) and (3), and compared with the estimated values by usual statistical techniques. The results of such comparative investigation on many specimens of different lengths (l=5.2, 13, 26, 39, 52, 78 and 104 mm) are summarized as follows: (1) As shown in Table II, the mean value σ_M for all sample except the ones with l=52 mm lies within the 95% confidence interval for the arithmetic mean value σ^^-. Consequently, σ_M and σ^^- are regarded equal in practical applications. (2) The values of (σ_<max>)_r and (σ_<min>)_r obtained from eq. (3) are quite comparable to those of σ^^- +3s and σ^^- -3s, where s is the standard deviation. (3) The scattering range of the tensile strength tends to decrease as l becomes longer or shorter than 52 mm.
社団法人日本材料学会の論文
1976-12-15

少数資料による引張強さの統計的研究

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