PSI - Issue 28

L.R. Botvina et al. / Procedia Structural Integrity 28 (2020) 1686–1693 L.R. Botvina et al. / Structural Integrity Procedia 00 (2019) 000–000

1688

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2. Statistical approach to analysis of microhardness testing 2.1. The experiment

One of the most common material testing methods is microhardness evaluation. It is obvious, that direct measurements can vary dramatically even in the same area, so the solution lies in statistics. The specimen of low carbon steel (C=0.2%) was divided into 10 zones (fig. 1 a) and then subjected to static tensile test. After fracture in each zone the attenuation coefficient of ultrasonic longitudinal waves α using the flaw detector in a frequency range 2.25-20 MHz and 100 of microhardness measurements using Vickers microhardness meter were done. After that it was cut along the main axis, perpendicular to microhardness measurements surface and grain aspect ratio, namely ratio of the longitudinal (a) and transverse (b) grain sizes, was measured in the same sections. In each zone 50 grains were measured (fig. 1 b). The experimental results for each section are given in Table 1.

Fig. 1. (a) Specimen geometry with sections 1-10; (b) aspect ratio (ξ=a/b) - ratio of the longitudinal (a) and transverse (b) grain sizes.

Table 1. Experimental results in sections 1-10.

№ of section

1 0

2

3

4

5

6

7

8

9

10

Ψ*, %

3.26 31.02

7.82 13.44 19

24.74 31.49 32.68

35.59 2.28

38.46 0.78

Distance from fracture surface, mm Attenuation coefficient α, dB/mm

40.22

20.45

14.08

12.31

9.27

7.28

5.88

0.75

0.658

1.138

1.48

1.18

1.9

2.05

2.435

6.52

7.93

Average HV

190.28 167.6

182.98 179.02 184.91 188.96 199.89 212.4

244.42 253.15

The microhardness measurements results are represented as cumulative distributions in the inverse axes, as proposed earlier (Botvina and Demina, 2010), using the following equation: P Ae HV   (3), where HV – microhardness value, P – cumulative probability, γ – the slope coefficient of cumulative distributions and A – constant. The main idea is that the meaningful parameter is the slope of such cumulative distributions γ (fig. 2). It follows from the graph that near the fracture surface, the slope of the cumulative microhardness curves increases, which indicates a general increase in the level of microhardness - hardening of the material. The main advantage of method of inverse coordinates is its simplicity – the slope coefficient γ reflects material hardening.