Intralaboratory comparison for the anisotropy test of sheet metals

The plastic strain ratio is an important parameter for the evaluation of the anisotropy of sheet metals in deep-drawing processes. This paper presents the results of an intralaboratory comparison for the anisotropy test, using normalized error as statistic method of analysis. The study was carried out through the comparison of the results obtained from different operators for the same sheet metal. The results of the study are considered satisfactory.


Introduction
According to ASTM E517:2010 [1], the plastic strain ratio (r) is a parameter that indicates the ability of a sheet metal to resist thinning or thickening when subjected to either tensile or compressive forces in the plane of the sheet. It is a measure of plastic anisotropy and is related to the preferred crystallographic orientations within a polycrystalline metal. The r value, therefore, is considered a measure of sheet metal drawability.
The value of r can be calculated according to equation (1), where w o and l o represent the initial width and length of test specimens, and w f and l f represent the final width and length, respectively. quality assurance of test results: the standard demands the laboratory to apply periodically procedures to monitor the quality of the measurements, using statistical techniques to analyze the results [2]. The Normalized Error (E n ) method tests the compatibility of measured values (X 1 and its uncertainty, u 1 ) to a reference value (X 2 , with its uncertainty, u 2 ). E n is calculated according to equation (3), and the result is considered compatible when E n ≤ 1. This method is widely used in quality assurance programs (intralaboratory and interlaboratory comparisons) according to the literature [3][4][5][6][7].
Several cases of intralaboratory comparison are found in literature. For example, Cools et al. [8] have studied forest soil analysis, evaluating interlaboratory and intralaboratory variation. Lee and Hill [9] have evaluated intralaboratory repeatability of residual stress determined by the slitting method and, finally, Smagunova et al. [10] have discussed on-line control of the intralaboratory precision in chemical analysis.
Thus, the main purpose of this paper is to present the results of an intralaboratory comparison for the anisotropy (plastic strain ratio) test for sheet metals, using normalized error.

Material and methods
Test specimens have been taken from a sheet metal with dimensions 500 x 300 mm (figure 1) in three directions: 0° (parallel), 45° (diagonal), and 90° (transverse) to the rolling direction, in order to calculate r m . Two operators ('A' and 'B') have received three test specimens, one from each direction (0°, 45° and 90°). They were individually instructed to carry out the test using a caliper rule for dimensional measurement, and a universal testing machine for the elongation of test specimens.
The values of l o and w o were measured before executing the test. Then, test specimens were inserted in the testing machine. The specified elongation was 10%, i. e., test specimens should be deformed until the relation (l f -l o )/l o was approximately equal to 0.1. After the deformation, the values of l f and w f were measured and used in the calculation of r 0 , r 45 , r 90 and r m .
Finally, measurement uncertainty of the results was estimated according to ISO/GUM [11].

Results and discussion
Tests were carried out using a universal tensile testing machine as illustrated in figure 3. Longitudinal strains were measured using a strain gauge extensometer while the strain in the width was measured with a digital caliper.  The value of the normalized error associated to r m was calculated according to equation (4).
Since E n = 0.039 ≤ 1, the result of the intralaboratory program is considered satisfactory. The differences between test executors (operators 'A' and 'B') were smaller than the measurement uncertainty.
The use of normalized error in intralaboratory comparisons and test validation is consistent with literature. For example, Alves et al. [12] have used this method in atomic absorption spectroscopy, obtaining E n ≤ 1 and, consequently, validating the results. Similar studies have been carried out by other authors [3][4][5][6][7], in the fields of hardness, dimensional and hygrometry measurement, using the same acceptance criteria.
However, the uncertainty values in this work have been large, approximately equal to 20% of the calculated values of r m . Measurement uncertainty of r m was estimated considering the following uncertainty sources for each dimensional variable: data from equipment calibration, equipment resolution and standard deviation of repeatability. The deviation of repeatability was responsible by approximately 75% of combined uncertainty, while data from calibration certificate was responsible by 16% of contribution and resolution by 9%.
The large deviation of repeatability is probably caused by the type of measurement equipment used (digital caliper). Perhaps different equipment could improve uncertainty values. Thus, future works could focus on further evaluation and improvement of the uncertainty of this test.

Conclusions
This paper has presented the implementation of a procedure to evaluate quality assurance of the anisotropy test of sheet metals. An intralaboratory comparison through the normalized error has been carried out, and the results were satisfactory.
Nevertheless, the uncertainty of the test was large, about 20% of the measured values of rm. Future work is necessary to analyze and reduce measurement uncertainty caused by deviation of repeatability in dimensional measurement for this test.