·Home ·Table of Contents ·Materials Characterization and testing  Dynamic Elastic Constants of Weld HAZ of SA 508 CL.3 Steel Using Resonant Ultrasound Spectroscopy
YongMoo Cheong, JooHag Kim, JunHwa Hong, and HyunKyu Jung Nuclear Materials Technology Team, Korea Atomic Energy Research Institute Yusong P. O. Box 105, Taejon, 305600, Korea
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ABSTRACT
The dynamic elastic properties of the thermal cycle simulated weld heataffected zone (HAZ) of SA 508 Class 3 RPV (reactor pressure vessel) steel were investigated by resonant ultrasonic spectroscopy (RUS). The resonance frequencies of rectangular parallelepiped samples were calculated from the initial estimates of elastic stiffness c_{11}, c_{12} and c_{44} with an assumption of isotropic property, dimension and density. Through the comparison of calculated resonant frequencies with the measured resonant frequencies by RUS, very accurate elastic constants of SA 508 Class 3 steel less with than a 0.15% RMS error were determined by iteration and convergence processes. Clear differences of Young's modulus and the shear modulus were shown from samples with different thermal cycle and microstructure. Young's modulus and the shear modulus of the samples with finegrained bainite were higher than those with coarsegrained tempered martensite or a mixture of tempered bainite and tempered martensite. This tendency was confirmed from other reported results.
1. Introduction
The heataffected zone (HAZ) adjacent to the weld fusion line has been known to give lower toughness values than other regions since the local temperature peak from the welding process rises above 1100°
. A comprehensive study of microstructures and mechanical properties of actual and simulated HAZ of reactor pressure vessel steel (RPV), such as ASME SA 508 Cl. 3 steel (low MnMoNi steel) has been performed [13]. However, it is difficult to determine the local variations of the mechanical properties in the HAZ, especially by a nondestructive methodology.
Resonant ultrasound spectroscopy (RUS) can be used to determine the elastic constant for various sample shape, i.e. rectangular parallelepiped, cylindrical, or spherical. Measurement can be possible for a sample size below one mm. Theoretically, 21 tensor elements of elastic stiffness for triclinic symmetry can be determined with one specimen. However, RUS can practically determine 9 tensor elements for orthorhombic symmetry as well as highersymmetry, such as isotropic, cubic, hexagonal, tetragonal symmetry [4]. RUS has been applied to determine the anisotropic elastic constant of textured polycrystalline materials [5,6]. Because RUS can be applied to a small specimen, the local variations of the mechanical properties in the complex region, such as a weld HAZ region can be determined.
One of the important factors in RUS is to determine the symmetry and an initial estimate of the elastic constant in advance. The initial estimate should be close to the true value and can be obtained from the literature, experience, other measurements, etc. The specimen should be accurately machined. The calculated resonance frequencies and modes should be matched to the measured values by RUS and the elastic constant can be calculated by comparison and iteration.
The RUS has been applied to investigate the variation of the local elastic constant in the weld HAZ region of reactor pressure vessel steel. The specimens simulate a specific region of the HAZ. The initial estimate of the elastic constant is calculated with the assumption of isotropic symmetry. The calculated resonance frequencies are compared with the measured frequencies and the final elastic constants are determined. The elastic constants in the different HAZ regions are discussed with the microstructures and other physical properties.
2. Experiments
2.1. Materials
The base material is ASME SA508 Cl. 3 low alloy MnMoNi steel for reactor pressure vessel. The chemical composition of the material is listed in Table 1 [7]. The microstructure of the base material is tempered bainite after quenching and tempering.
Elements
 C
 Si
 Mn
 P
 S
 Ni
 Cr
 Mo

wt. %
 0.19
 0.08
 1.35
 0.006
 0.002
 0.82
 0.17
 0.51

Table 1: Chemical composition of SA 5083 steel 
The full thickness (220 mm) of the RPV weld was welded through a multipass narrowgap submerged arc welding process. Each characteristic region in the actual HAZ was classified in Fig. 1 after calculating the heat cycles by the welding process. Table 2 lists the thermal cycle conditions for the simulated HAZ specimens. The final microstructures with the identification codes corresponding to the regions of the actual HAZ are shown in Fig. 1. The optical microstructures of the corresponding regions are shown in Fig. 2.

Fig 2: . Microstructures in various HAZ regions observed through an optical microscope show Coarse Grained (CG) HAZs ((a), (b) and (c)), Fine Grained(FG) HAZs ((d) and (e)), Intercritically Reheated(IR) HAZ (f) and Subcritically Reheated (SR) HAZ (g). All of the HAZs were subjected to PostWeld Heat Treatment (PWHT).
e Fig 1: Macrostructure of the actual weld HAZ and typical HAZ regions indicating simulation conditions. 
Specimen Identification
 Thermal cycle simulation conditions
(1^{st} & 2^{nd} temperatures)
 Microstructures

S1
 1350°C & 1350 °C
 CGTM

S2
 1350°C & 950 °C
 (TM)+TB

S3
 1350°C & 750 °C
 (TM) + TB + F

S4
 900°C & 900 °C
 FGTB

S5
 900°C & 700 °C
 FGTB + (TB + F)

S6
 700°C & 700 °C
 TB + (F) + CC

S7
 650°C & 680 °C
 TB+CC

S8
 Base Material
 TB

Table 2: Thermal cycle simulation conditions and corresponding microstructures 
CGTM: Coarse Grained Tempered Martensite TM: Tempered Martensite TB: Tempered Bainite
F: Ferrite FGTB: Fine Grained Tempered Bainite
CC: Coarse Carbides
Rectangular parallelepiped specimens with dimensions of 3.0 mm x 3.5 mm x 4.0 mm were fabricated very accurately for the measurement of the resonant frequencies by RUS.
2.2. Determination of elastic constants by resonant ultrasound spectroscopy
Free vibration, or resonance, is sensitive to the microscopic and macroscopic properties of the materials. Because RUS can determine accurate elastic constants and ultrasonic attenuation, it can be applied to materials characterization, nondestructive testing, etc. [8]. An exact analytical solution on the free vibration problem to determine the resonance frequencies is not known or available a priori. Only approximated solutions are available by numerical analysis, such as the finite element method or the minimization of energy. Historically the resonance scattering theory was developed for the free vibration of a sphere, which is based on geophysics. The fundamental theory of RUS was developed by Maynard [9]. Theoretical calculations and experiments for the resonance of an elastically isotropic rectangular parallelepiped specimen have been done by Holland [10] and Demarest [11]. Those results have been generalized by Ohno [12] and comprehensive applications to the solidstate physic have been accomplished by Visscher et al. [13].
The resonance frequencies or eigenfrequencies are calculated based on the density, dimensions, and initial estimate of the elastic constants [4]. The calculated resonance frequencies are compared to the measured frequencies and accurate elastic constants can be calculated by iteration and convergence. The LevenbergMarquardt method is used for the numerical analysis and the elastic constants are determined to minimize the figure of merit in the multidimensional elastic constant space.
An initial estimate of the elastic constants of RPV steel are calculated by the following:
Assuming isotropic elastic constants and poison's ratio of n= 0.30, and a relationship, E = 207.200  57.09 T (MPa, C) [14] for SA508 Cl. 3 material, Young's modulus E, shear modulus G, Lame constant l, elastic stiffness c_{11} , c_{12} , and c_{44} at 25°C are calculated as:
3. Results and Discussions
Based on the initial estimates of the elastic constants, the lowest 30 resonance frequencies were calculated and compared with the measured frequencies. The resonance modes (k), the error between the calculated frequencies and measured frequencies, the dependency of the resonance modes, the accurate elastic stiffness tensor, the adjusted dimensions and the density of the specimen can be obtained by a computer algorithm for RUS. The measurements were repeated at least four times for four different specimens in each group. The RMS error minimum was 0.07% and maximum 0.14%, and an RMS error less than 0.2% is generally believed to be reliable.
Figs. 3 and 4 show the variation of Young's modulus and the shear modulus for each specimen group, S1 ~ S7. Young's modulus by RUS (209 ~ 212 GPa) is little higher than the initial estimate (205 GPa). It is generally accepted that the dynamic elastic constants are higher than the static measurements.
Fig 3: Young's modulus of SA508 Cl. 3 alloy by RUS. [S1: 1350°C1350°C, S2: 1350°C900°C, S3: 1350°C750°C, S4: 900°C900°C, S5: 900°C750°C, S6: 750°C 750°C, S7: 680°C680°C, S8: Base Metal.]

Fig 4: Shear modulus of SA508 Cl. 3 alloy by RUS. 
The specimen groups S1~S3 experienced grain coarsening in the first heat cycle (1350°C) and remained (S1), retransformed (S2) or partially retransformed (S3) in the second heat cycle. The specimen groups S4 and S5 experienced grain refinement in the first heat cycle (900°C) and remained (S4), or partially retransformed (S5). The specimen groups S6 and S7 experienced partial transformation and remained (S6) or were heat affected without transformation, such as tempering (S7).
Young's modulus and the shear modulus of specimen groups S1~S3 (tempered martensite) were higher than the specimen groups S4~S8 (tempered bainite) in correlation with the microstructures. The elastic constants were highest in S4 and decreased gradually through to S7. There is a small variation of Young's moduli in the tempered martensite (S1~S3). In general, the elastic moduli decrease in the order pearlitebainitemartensite and increase in tempered martensite, but in no case did a modulus of tempered martensite exceed the corresponding modulus of pearlite [15]. The results by RUS are agreed quite well with the reference 14.
c_{11} and c_{12} of each specimen group are represented in Figs. 5 and 6. It can be noted that the data of c_{11} and c_{12 }of specimen group S1 are widely scattered compared to the others. The reason for this scattering is not clear at present. Because Young's modulus is defined as an inverse of the elastic compliance, E_{ii} = 1/S_{ii} and the elastic compliance as an inverse of the elastic stiffness, S_{ii} = 1/C_{ij}, the presence of offdiagonal terms in the c_{ij }matrix causes a difference between Young's modulus, E_{11}, and elastic stiffness, c_{11.} c_{44} is identical to the shear modulus, G.
Fig 5: Elastic stiffness (c_{11}) of SA508 Cl. 3. alloy by RUS[S1: 1350°C1350°C, S2: 1350°C900°C, S3: 1350°C750°C, S4: 900°C900°C, S5: 900°C750°C, S6: 750°C 750°C, S7: 680°C680°C, S8: Base Metal.]

Fig 6: Elastic stiffness (c_{12}) of SA508 Cl. 3 alloy by RUS. 
In addition to the elastic constants, the ultrasonic velocities can be determined by RUS experiments. The longitudinal wave velocity and the transverse wave velocity of the specimen groups are shown in Figs. 7 and 8. The values of the ultrasonic velocity of specimen group S1 are scattered, which is similar to the case of c_{11} or c_{12}. Because most of the resonance frequencies considered in the RUS experiment are mainly dependent on the shear modes, the longitudinal wave velocity does not change much with the specimen groups, while the transverse wave velocity increases from specimen group S1 through S7.
Fig 7: Longitudinal wave velocity of SA508. Cl. 3 alloy by RUS.

Fig 8: Shear wave velocity of SA508 Cl. 3 alloy By RUS. 
The ultrasonic velocity is related to the microstructure, and the lattice distortion, i.e. the size, shape and orientation of the grains. Palanichamy et al. [16, 17] reported that the transverse wave velocity increased an austenitic stainless steel is heattreated to the recovery and recrystallization stage after cold working, which is attributed to the reduction in the distortion of the lattice caused by the annihilation of point defects and dislocations. When the steel is tempered above 600°
C the following changes in the matrix take place:
a) The tetragonality of martensite decreases and disappears,
b) Dislocations anneal out, and
c) Carbide particles assume a spherical shape [18].
Therefore the transverse wave velocity increases as the grain size decreases and the transverse wave velocity of martensite is lower than that of bainite. Because the grain size of specimen group S8 is larger than that of S7, it can be concluded that the transverse wave velocity of S8 is lower than that of S7. Ahn et al. [19] reported that the microstructural analysis of low carbon steel specimens is not simple and may not show any specific relationships between their austenite grain size and the yield strength, since the grain sizes of bainitemartensite, martensite and retained austenite specimens correspond to the austenite grain size and there are many micrograins inside the austenite grains. The ultrasonic velocities measured by RUS agree with a similar experiment that the ultrasonic velocity increases in the order of martensite, martensite + bainite, ferrite + pearlite + bainite, ferrite + pearlite [20].
It has been demonstrated that RUS can determine localized elastic constants as well as ultrasonic velocities with accuracy and ease. The RUS method can be applied to the nondestructive characterization of materials, such as neutron embrittlement, high temperature elastic constants or phase transformation, anisotropic elastic constants, ultrasonic velocity, etc.
4. Conclusions
The dynamic elastic constants of each characteristic region in the weld HAZ of SA 508 Cl. 3 RPV steels were determined by RUS. The dynamic Young's modulus was in the range of 209 ~ 212 GPa, which was a little higher than the static modulus used as an initial estimate of 205 GPa. The measurements were very sensitive to the microstructure. The elastic constants of the tempered bainite structure were higher than those of tempered martensite. Within similar microstructures, the specimens with a smaller grain size showed higher elastic constants. The transverse wave velocity increased as the grain size decreased as well as in the specimens with a bainite structure compared to a martensite structure.
RUS can determine localized elastic constants or ultrasonic velocities. RUS also can be a new tool for the nondestructive characterization of materials.
Acknowledgement
The present work was carried out as a part of Basic Nuclear Research Project by Korea Atomic Energy Research Institute.
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