УДК 620.179.16
NON-DESTRUCTIVE EVALUATION OF THE YIELD STRESS FOR LOW CARBON STEEL BY ULTRASOUND MEASUREMENTS
Al. Popov, V. Kavardzhikov, D. Pashkouleva Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., Block 4, Sofia1113, Bulgaria e-mail: alpopov@abv.bg
Abstract. The non-destructive evaluation method for yield stress assessment in low carbon steels based on ultrasonic measurements of the longitudinal and transversal velocities and the longitudinal attenuation coefficient is proposed. First, the mean grain size D is calculated from the measured acoustic parameters and then the yield strength is estimated from these three parameters using the Hall-Petch relationship. Comparative non-destructive and destructive tests for yield stress evaluation are elaborated. The results obtained allow to be concluded that the accuracy of non-destructive evaluation of a is reliable enough.
Key words: low carbon steel, acoustical characteristics, yield stress.
НЕРАЗРУШАЮЩИЙ МЕТОД КОНТРОЛЯ ПРЕДЕЛА ТЕКУЧЕСТИ НИЗКОУГЛЕРОДИСТЫХ СТАЛЕЙ ПОСРЕДСТВОМ УЛЬТРАЗВУКОВЫХ ИЗМЕРЕНИЙ
Ал. Попов, В. Каварджиков, Д. Пашкулева Институт механики Болгарской академии наук, ул. Академика Г. Бончева, Блок 4, София 1113, Болгария
Неразрушающий метод контроля предела текучести низкоуглеродистых сталей основан на у. з. измерениях скоростей продольных и поперечных волн и определении коэффициента затухания продольных волн. С помощью найденных акустических параметров может быть рассчитан средний размер зерна и предел текучести, который определяется из соотношений Холла - Питча. Приведено сравнение предела прочности, полученного из акустических измерений, и найденного при разрушающих испытаниях. Полученные результаты позволяют заключить, что способ определения предела прочности неразрушающим методом обладает достаточной точностью.
Ключевые слова: низкоуглеродистая сталь, акустическая характеристика, предел текучести.
1. INTRODUCTION
In accordance to the classical method for obtaining of the fundamental mechanical characteristics of constructive materials the specimens made by these materials are undergone to tensile tests. "Stress-strain diagram" is derived by a test, which contains information about the values of elastic modulus — E, yield stress — cy, breaking strength — oB and etc. In many cases, destructive tests are unsuitable, for example in the industry, where monitoring of components is needed during the manufacturing process. The Young's modulus (E) evaluation through measurement of ultrasound wave propagation velocity is a routine approach at present [1—4]. This measurement is fast and reliable. In [5, 6] elastic module is measured specifically for metals by ultrasound testing. But there is not in the literature accessible of authors' information about some way for estimation of yield stress ay by ultrasound measurements. Such an approach would be very useful in modern engineering practice. Due to that we developed in this work an idea for non-destructive evaluation of yield stress for low carbon steels (AISI 1006, 1010, 1015, 1020).
2. NON-DESTRUCTIVE EVALUATION OF YIELD STRESS
The plasticity condition in the mechanics of plastic media [7] is presented in general as:
F K, xla) ) = 0, (1)
where a are the stress tensor components (i, j = 1,2,3), xÎ)are internal parameters of the material state. The mean grains size D, elastic modulus E, yield stress a and etc., can be considered as internal material parameters.
As it is well know in case of non-destructive testing by ultrasound method, the deformation of the material s and the respective stress a are rather small (actually
a ^ 0, s ^ 0 and deformation velocity s ^ 0 ).
At these conditions the Hall-Petch relationship, experimentally proved for many conventional polycrystalline metals and alloys [3, 4, 8, 9] is more appropriate:
y = CT0
-KyD
-1/2
(2)
where c0 and Ky are material constants; c0 is friction stress resisting the motion of gliding dislocation, and Ky is the Hall - Petch slope, which is associated with a measure of the grain boundary resistance to slip transfer.
It is seen from Eq. (2) that if the grain diameter D could be presented as a function of the longitudinal (VL) and transversal (VT) velocity of ultrasonic wave propagation in the material, an opportunity is emerged for evaluation the yield stress ay through measurements of material's acoustic characteristics — VL, VT and aL (aL — the coefficient of ultrasound longitudinal waves attenuation in the process of their propagation).
There is known in acoustics, that the average grain diameter D can be considered as one of the factors, determining ultrasound longitudinal wave attenuation aL. This fact is reflected in the Lifshitz-Parhomov-Merkulov relation [10]. The longitudinal attenuation coefficient aL for cubic crystals can be presented as:
8 л3 1 375 p2
M 2
4л
( D v
v2y
( 1 V
f4
V'
V L
V5 V
V L
(3)
T у
where p is the material density; f is the ultrasound wave frequency; M = C11 - C12-- 2C44; C = C.. (VL, VT), [1, 10], C are elastic coefficients.
44 .. y L T y
We transform and simplify the Eq. (3) as follow:
D =
1
a.
CW(Vl ,Vt ) f4
C =
4л4 1125
; W (Vl ,VT ) =
( V4 ^
V
v l у
V5 V
V L
T У
(4)
The Eq. (2) can be written after that in the form:
y = CT0
K
1
1
a
CW(Vl , Vt ) f4
where a0 =72 MPa; K =23.9; MPa^mm1'2 for low carbon steel [11].
40
An. nonoB, B. KaBapgrnEOB, fl. namKyjieBa
3. EQUIPMENT AND MEASURING METHOD OF ACOUSTIC CHARACTERISTICS
The following technical tools, produced by SONATEST, England and PANAMETRICS, are used for measurements velocities of ultrasonic wave propagation through investigated material (Fig. 1):
Fig. 1. Equipment for non-destructive evaluation of yield stress.
transducers with X-cut of piezo-electric element (for longitudinal waves) and Y-cut of piezo-electric element (for transversal waves) and frequency 5 MHz;
calibration block - CBV (VL = 5.93 mm/^s);
digital ultrasonic flaw detector SITESCAN 150S. The measurements are carried out by option "measurement of time propagation of ultrasonic wave" with accuracy 0.01 p,s.
A digital micrometer for thickness measure (Micromaster 0—30 mm / 0.001 mm (f. TESA — Switzerland) is used also.
A description of the method, according to which the measurement procedure is elaborated, is presented in ASTM E 494.
The "unknown" value of the longitudinal wave velocity VL is calculated by:
f„ V
V = V
y L y EL
V lE J
h
gnx
(6)
where VEL is velocity in known material (etalon) in [mm/^s]; nE, nX are numbers
of round trips for known and unknown material respectively; lE, lX are thickness of known and unknown material (mechanical measurement) in [mm], and g is range of calibration (g = R/100).
The "unknown" velocity value of transversal wave VT is calculate by
2K
V =
T
-1 v
where TX is propagation time of transversal ultrasound wave in [^s].
The value of attenuation coefficient aL is derived by the equations:
Nm - Nm
2nlv
(8)
where N h N , are the amplitudes of reflected waves, having m and (m+n)
m m+n r •> o v f
multiplicity in [dB], lX is the thickness of the studied specimen in [mm].
4. EQUIPMENT FOR DESTRUCTIVE DETERMINATION OF MECHANICAL
CHARACTERISTICS
Destructive tensile tests are carried out according to EN ISO 6892-1:2009 [12] through a universal testing machine Instron type. Seven specimens prepared according to the recommendation of the cited standard are tested. Digital recorded values of force and elongation are used to draw the stress-strain curves and to define the yield stress. An average value of = 284 MPa is obtained. It is useful to be noted that in reference [13], the yield stress value of low carbon steel with carbon content 0,15 % is given to lie in interval (200—310) MPa.
5. EXPERIMENTAL RESULTS
Seven specimens, with standard shape and dimension, are tested in the beginning and the acoustic characteristics are evaluated. Each of these specimens is undergone to destructive tensile test after that to avoid any risk for changes in the materials microstructure as a result of the destructive deformation process.
Three measurements of the acoustic characteristics VL, VT and aL are elaborated to each separate specimen, keeping the same conditions. A statistical analysis of the obtained experimental results including Average values V , Standard
deviation StDev V, Median estimation of average values Med. V and standard deviation Med. St. Dev V, as well as Confidential UCONF(a; n) and Tolerant UTOL(a; n) intervals is carried out [14, 15]. Table 1 present the results derived concerning V VT .
Experimental data of acoustic characteristics
Table 1
Characteristics VL, mm/^s VT , mm/^s
V St. Dev V Med V Med St. Dev V V + UCONF(ß; n) St.Dev V; Pr = 90% 5.932 0.003 5.941 0.004 5.922 — 5.942 3.257 0.014 3.258 0.015 3.247 — 3.267
V + UTOL(ß; n) St.Dev V; Pr = 90% 5.906 — 5.957 3.247 — 3.267
[^c(OL(Med.V FCOiUMed.V )] 5.905 — 5.948 3.252 — 3.268
where: 11 n m V =--yVV is the arithmetic mean for all samples nm*p11=1 1 (Row 1, Table 1);
42
An. nonoB, B. KaBapgrnEOB, fl. namKyneBa
i = 1, ..., m (m = 3 — number of measurements on one sample); j = 1, n (n = 7 — number of samples);
St.Dev V =
—t (v, - V)2
n-1tT ' '
is the standard deviation of the measurement (Row 2, Table 1).
The mean of the sample is estimated with the sample median Med. V [15]. If a sample contains an odd number of measurements the median is defined as the mean of an arranged row. If a sample contains an even number of measurements the median is defined as the mean of the two middle values of arranged data. The definition of the sample median Med. V of the arranged variation row
V < V < < V
K(1) -K(2) -•• n)
is:
Med. V =
n+1 2
f
V ] + V
v( n
-+1 2 )J
if n is odd
if n is even (Row 3, Table 1).
The standard deviation and mid-range are used as a measure of variability. The mid-range is the mean of the smallest and the largest values of the parameter. As a measure of
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