This section discusses and summarizes the test results obtained in tensile test and linear density measurements (Tables 1, 2, 3, 4, 5, 6). Moreover, effect of yield strength to ratios of tensile and yield strength of the two lots are presented. The results of YS, TS, EL, M/L and TS/YS vs YS are compared one another for all bar sizes in both lots and aggregate results of each lot. All the mean values of YS, TS and EL were compared with ASTM A615/A615M recommended values of 420MPa, 620MPa and 9%, respectively. It’s also recommended that tensile strength should exceed yield strength by 25%. The recommended mass per length values are different based on bar diameters.
Mechanical and linear density properties for 8mm diameter bars
It is found that the bars investigated exhibit variability in yield and tensile strengths. One (1) bar from a sample of thirty seven (37) bars (i.e. 2.70%) from Lot 1, exhibits a yield strength below the value specified by the ASTM A615/A615M standard while the remaining thirty six (36) bars have the mean yield strength greater than 420MPa. In Lot 2, all the thirty nine (39) bars fulfilled the requirement of ASTM A615/A615M standard. Based on tensile strength, one bar (i.e. 2.70%) from Lot 1 exhibited tensile strength below the value specified by ASTM A615/A615M standard. But, all the bars in Lot 2 have a tensile strength greater than 620MPa as per the requirement of ASTM A615/A615M.
The elongation percentage showed significant variability for 8mm diameter bars in both lots. The mean elongation percentage in Lot 1 and Lot 2 are 13.6 and 12.9, respectively. There is no specified ASTM requirement for 8mm diameter steel bar.
For 8mm diameter reinforcing bar, the histogram and distribution curves of yield and tensile strengths are presented in Fig.1. Lot 1 and Lot 2 showed significant variability for yield and tensile strength. The average yield strength of samples in Lot 1 and Lot 2 were 630.4MPa and 621.1MPa, respectively. The average tensile strength of samples in Lot 1 and Lot 2 were 746.8MPa and 711.9MPa, respectively. Moreover, Lot 1 had greater SD and COV values than Lot 2 in both yield and tensile strength results.
The influence of yield strength (YS) on the TS/YS ratio is found to be as expected for Lot 1 and Lot 2. The ratio decreases with increasing the yield strength which in turn is expected to reduce the ductility of the materials at higher yield strength. The mean TS/YS ratio of Lot 1 and Lot 2 is 1.20 and 1.15, respectively, which is below ASTM requirement25. 68% of the samples in Lot 1 and 82% in Lot 2 fail to meet the ASTM requirement for TS/YS ratio.
The statistical analysis including the values of maximum, minimum, average, variance, coefficient of variance, standard deviation, skewness, and kurtosis for yield strength, tensile strength, elongation and mass per length are calculated. Tables 3, 4 and 6 summarize the statistical analysis of yield strength, tensile strength, elongation and mass per length for 8, 10, 12, and 16mm diameter bars and aggregate result of the two lots. From the results of COV, it’s noted that mass per length in both lots show high hom*ogeneity (COV < 5%)4 while the rest of the data show moderate hom*ogeneity.
Mechanical and linear density properties for 10mm diameter bars
One (1) bar from a sample of forty four (44) bars (i.e. 2.27%) from Lot 1, exhibits yield strength below the value specified by the ASTM A615/A615M standard while in Lot 2, all the twenty seven (27) bars have the yield strength greater than 420MPa as per the requirement of ASTM. Based on tensile strength, four bars (i.e. 9.09%) from Lot 1 exhibited tensile strength below the value specified by ASTM A615/A615M standard. But, all the bars in Lot 2 have tensile strength greater than 620MPa as per the requirement of ASTM A615/A615M.
Five bars (i.e. 11.36%) in Lot 1 exhibits elongation percentage lower than ASTM A615/A615M requirement while all bars in Lot 2 surpasses the minimum elongation percentage requirement. The mean elongation percentages in Lot 1 and Lot 2 are 13.7 and 14.4, respectively.
In mass per length analysis, 5 bars (i.e. 11.36%) in Lot 1 fail to meet the minimum ASTM standard for their bar size and grade. But, all the bars in Lot 2 meet the minimum requirement. The mean mass per length values in Lot 1 and Lot 2 are 0.6114 and 0.6001, respectively.
For 10mm diameter reinforcing bar, the histogram and distribution curves are presented in Fig.3. Lot 1 and Lot 2 show significant variability for yield and tensile strength. The mean yield strength of samples in Lot 1 and Lot 2 are 607.9MPa and 614.7MPa, respectively. The mean tensile strength of samples in Lot 1 and Lot 2 are 696.5MPa and 695.9MPa, respectively.
Even though the ratios decreased with increasing the yield strength which in turn is expected to reduce the ductility of the materials at higher yield strength, the mean TS/YS ratio of Lot 1 and Lot 2 was 1.15 and 1.13, respectively, which was below ASTM requirement. 91% of the samples in Lot 1 and 96% in Lot 2 fail to meet the TS/YS ratio of ASTM requirement. Figure4 shows the linear regression line plot of TS/YS to YS for both lots.
Mechanical and linear density properties for 12mm diameter bars
One bar from a sample of 40 (i.e. 2.50%) bars in Lot 1 exhibits a yield strength which is below the value specified by the ASTM A615/A615M standard whereas in Lot 2, 3 bars from a sample of 60 ( i.e. 5.00% ) bars fail to meet the minimum requirement for yield strength set by ASTM standard. Based on tensile strength, 3 bars (i.e. 7.5%) in Lot 1 and 14 (i.e. 23.33%) in Lot 2 exhibit tensile strength below the value specified by ASTM A615/A615M standard.
The average yield strength of samples in Lot 1 and Lot 2 are 562.9MPa and 556.9MPa, respectively. The average tensile strength of samples in Lot 1 and Lot 2 are 678.7MPa and 655.0MPa, respectively. For 12mm diameter reinforcing bar, the histogram and distribution curves are presented in Fig.5.
All samples in both lots exhibit elongation percentage values greater than the minimum requirement set by ASTM A615/A615M standard. The mean elongation percentages are 15.9 and 15.8 in Lot 1 and Lot 2, respectively.
In mass per length analysis, all bars in both lots meet the minimum ASTM standard. The mean mass per length values in Lot 1 and Lot 2 are 0.8768 and 0.8581, respectively.
The TS/YS ratios show decrement with increasing the yield strength. The mean TS/YS ratio of Lot 1 and Lot 2 was 1.22 and 1.18, respectively, which is below ASTM requirement25. 75% of the samples in Lot 1 and 90% in Lot 2 fail to meet the TS/YS requirement set by ASTM.
Mechanical and linear density properties for 16mm diameter bars
One (1) bar from a sample of thirty one (31) bars ( i.e. 3.23% ) in Lot 1 and three (3) bars from a sample of fifty one (51) (i.e. 5.88%) in Lot 2 exhibited a yield strength below the value specified by the ASTM A615/A615M standard. Based on tensile strength, two bars (i.e. 6.45%) in Lot 1 and six bars (i.e. 11.76%) in Lot 2 exhibited tensile strength below the value specified by ASTM A615/A615M standard. The mean yield strength of samples in Lot 1 and Lot 2 were 566.4MPa and 531.3MPa, respectively. The mean tensile strength of samples in Lot 1 and Lot 2 were 682.1MPa and 655.2MPa, respectively. For 10mm diameter reinforcing bar, the histogram and distribution curves are presented in Fig.7.
The mean elongation percentages are 16.3 and 17.7 in Lot 1 and Lot 2, respectively and all bars in both lots surpass the minimum elongation percentage requirement set by ASTM.
The mean mass per length values in Lot 1 and Lot 2 are 1.5541 and 1.5240, respectively and all bars in both lots surpass the minimum requirement.
The TS/YS ratios showed decrement with increasing the yield strength. The mean TS/YS ratio of Lot 1 and Lot 2 was 1.21 and 1.25, respectively. 71% of the samples in Lot 1 and 75% in Lot 2 failed to meet the minimum TS/YS requirement i.e. 1.25 set by ASTM.
Mechanical strength variability of aggregate results
Figure9 and Table 4 summarize the aggregate results of yield strength, tensile strength and elongation percentage of the two lots irrespective of diameter of the bars. From the aggregate result, it is noted that the parameters in both lots show moderate hom*ogeneity. The mean yield strength value shows a decrease from 593.1MPa in Lot 1 to 572.5MPa in Lot 2. Similarly, the ultimate strength decreases from 701.1MPa in Lot 1 to 673.8MPa in Lot 2. Even though the aggregate result shows a decrease in overall mechanical strength values from Lot 1 to Lot 2, the mean yield and tensile strength values are higher than the findings from others studies3,4,6,7,14,15,29,30.
Histogram of YS and TS of aggregate.
The mean elongation percentage, on the contrary, shows an increase from 14.78 in Lot 1 to 15.47 in Lot 2. This result is close to the findings from few studies4,6 but less than the findings from other studies3,13,29.
The skewness values of the strength parameters of the aggregate result exhibits a positive value in Lot 1 where as in Lot 2 yield strength and tensile strength values have a negative skewness. Similarly, Lot 1 shows relatively higher kurtosis value than Lot 2.
ANOVA generalized table1 is used to compare calculated variance ratio (F-cal) with tabulated critical variance ratio (F-table) values for statistical significance value of 95%. This ratio was used to measure the significance of the factor under the investigation with respect to the variance of all other unseen factors. A factor is significant when F-cal is greater that F-table. Table 5 indicated the ANOVA results of Lots 1 and 2 in terms of YS, TS, EL and TS/YS.
From the ANOVA of yield stress in Lot 1, the computed value for F-cal value, 362.3 is greater than the critical F-table value for f. 05 (1, 152), 95% confidence i.e., 3.84151,28. Hence, with 95% confidence, the reinforced bars appeared to be dissimilar. The apparent data spread contributes about 70% to the sample variability while the remaining 30% variation was caused by other factors. F-cal values of all parameters in both lots are greater than f. 05, 95% confidence for its respective tabular values. Percent contribution to the variability of the data in Lot 2 is less than in Lot 1 in terms of YS, TS and elongation percentages.
