Abstract
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, nonmetallic 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 σM of tensile strength for specimens having the same shape and size can be estimated from (TS)max and (TS)min by the following equation.
σM=√(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 (σl)r, the maximum value (σmax)r and the minimum value (σmin)r can be obtained by the following equations
(σ∞)r=σM(δ∞)r (σl)r=σM/(δ∞)r} (2)
(σmax)r=σM(δmax)r (σmin)r=σM/(δmax)r} (3)
where (δ∞)r and (δmax)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 104mm) are summarized as follows:
(1) As shown in Table II, the mean value σM for all samples except the ones with l=52mm lies within the 95% confidence interval for the arithmetic mean value σ. Consequently, σM and σ are regarded equal in practical applications.
(2) The values of (σmax)r and (σmin)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 52mm.
