Investigation of clamping effect on the welding residual stress and deformation of Monel plates by using the ultrasonic stress measurement and finite element method

Welding of nickel-based alloys is increasingly used in the industry to manufacture many important components of the marine industries, chemical processing, etc. In this study, a 3D thermo-mechanical finite element analysis is employed to evaluate residual stresses and deformations caused by the tungsten inert gas (TIG) welding of Monel 400 (Nickel-Copper alloy) plates. The finite element (FE) results related to the residual stresses and deformations have been verified by using the hole-drilling stress measurement and common dimensional measurement tools, respectively. Residual stresses analyzed by the FE simulation are then compared with those obtained from ultrasonic stress measurement. The ultrasonic stress measurement is based on acoustoelasticity law, which presents the relation between the acoustic waves and the stress of material. The ultrasonic stress measurement is carried out by using longitudinal critically refracted ( L CR ) waves which are longitudinal ultrasonic waves propagated parallel to the surface inside the tested material. Two welded plates are experimentally prepared (with and without using clamp) to investigate the clamping effect on the welding residual stress and deformations. By utilizing the FE analysis along with the L CR method, the distribution of longitudinal residual stress could be achieved. It has been concluded that the applied methodologies are enough accurate to distinguish the clamping effect on the welding residual stresses and deformations of Monel plates.

Conventional welding processes can be used to produce high-quality joints in nickel alloys.
However, some of the characteristics of nickel alloys necessitate employing somewhat different techniques than those used for commonly encountered materials such as carbon and stainless steels [1]. Welding procedures for nickel alloys are comparable to those used for austenitic stainless steel. In this study, Monel plates are joined by employing tungsten inert gas (TIG) welding process, which is widely used for nickel alloys joining.

Welding residual stress and deformations
Residual stresses are defined as remaining stresses inside the material after manufacturing process, in the absence of any external loads or thermal gradients. The engineering properties of industrial equipment particularly fatigue life, dimensional stability, corrosion resistance, and brittle fracture can be considerably influenced by residual stresses. Welding processes, as essential production processes in the industry, produces residual stresses at a significant level. In the presence of geometric constraints, the welding residual stresses and deformations are results of non-uniform thermal expansions and solidifications caused by the welding processes.
The welding residual stresses and deformations can be undesirable in various industrial cases related to the Monel joining. However, studies on the stress analysis of such weldments are scantly found in the literatures. Yegaie et al. [2] investigated the welding residual stresses of Monel 400 plates. They utilized finite element (FE) simulation of welding process to evaluate the residual stresses while the hole-drilling method was employed to validate the FE model. Korsunsky and James [3] evaluated welding residual stress of the nickel alloys by using a highenergy synchrotron X-ray diffraction. They succeeded to measure residual stresses of the nickelbased alloys, nondestructively. However, the ultrasonic stress measurement (which is used in this study) is not considered in the previous studies related to the nickel-based alloy.

Three-dimension thermo-mechanical finite element analysis of the welding process
It has been more than 40 years since Ueda and Yamakawa [4] firstly described a thermal elastic plastic finite element method (FEM) to predict the welding residual stress and deformation. Under the efforts of many researchers, numerous progresses have been made in the field of computational welding mechanics [5][6][7], which has been an important branch in the area of welding science and technology.
The majority of studies conducted before the year 2000 simulated the welding process by assuming two-dimension (2D) FE models, which have shown serious limitations in prediction of the welding residual stresses and, particularly, various types of welding deformations. Hence, the 2D model is not considered in this study to analyze the welding deformation and residual stresses.
By improving the calculation efficiency of computers, many numerical studies have been conducted to analyze the residual stresses and deformations by employing three-dimension (3D) FE models. For example, a 3D model has been used by Sattari-far and Javadi [8] to predict the welding deformations of stainless steel pipes. They investigated influence of welding sequence on welding distortions concluding that the 3D models could accurately predict the welding deformations. Since the welding deformations are also considered in this study, hence the 3D FE model is used to simulate the welding process.

Ultrasonic stress measurement
Ultrasonic stress measurement is a nondestructive method based on the linear relation between ultrasonic wave velocity and the mechanical stress inside the material. This relation is called as acoustoelastic effect, which expresses that flight time of the ultrasonic wave changes with the stress. Crecraft [9] showed that the acoustoelastic law could be used to measure stress of the engineering materials. He employed transverse ultrasonic wave for ultrasonic stress measurement but in modern applications of the technique, longitudinal critically refracted (L CR ) waves are used because of their higher sensitivity to the stress. The L CR wave is a longitudinal ultrasonic wave propagated parallel to the surface. Egle and Bray [10] showed that the L CR wave sensitivity to the stress is highest among the other types of ultrasonic waves. The L CR waves were employed to measure bending stress in the steel plates by Bray and Tang [11]. They used two different testing frequencies (2.25 MHz and 5 MHz) of the ultrasonic probes to show that the ultrasonic waves, by changing testing frequency, are able to penetrate at different depths measuring sub-surface stresses. Similarly, Javadi et al. [12] employed the ultrasonic method in the stainless steel plates for sub-surface stress measurement by using four different testing frequencies. They also compared the results of ultrasonic stress measurement with those obtained from the FE welding simulation.

Goals and objectives of this study
The main goal of this study is evaluation of the welding residual stress and deformation in the Monel plates to investigate clamping effect on the residual stresses and deformations. The FE simulation of the welding process is employed to numerically analyze the welding residual stresses and deformations while the hole-drilling measurement is used to validate the FE model. Good agreement is achieved by comparing the FE simulation results with those obtained from the ultrasonic stress measurements. It means that the L CR method could be successfully used in residual stress measurement of the Monel plates. It is also concluded that using clamp leads to increasing the welding residual stresses. However, by experimental measurement and also FE simulation, the considerable decreasing trend of welding deformations of clamped Monel plates is confirmed.

L CR method
Different experimental setups could be employed for residual stresses measurements by the L CR waves. As a common configuration, three ultrasonic transducers operating at the same frequency are utilized. The transducers are normal probes could be selected from the contact or immersion ultrasonic probes. Javadi and Najafabadi [13] compared the residual stresses measured by using the contact transducers with those results obtained from the immersion probes. They showed that there is no considerable difference in the ultrasonic stress measured by using contact or immersion probes hence, the contact probes are employed in this study to produce the L CR wave measuring the residual stresses. To produce the L CR wave, the longitudinal wave is produced at the first critical angle by a transmitter (sender) transducer, and then propagates inside and parallel to the surface of tested material. Two receiver transducers assembled in different distances from the sender finally detects the wave. The reason of employing two receiver transducers is decreasing the environmental effects, like ambient temperature, on the wave velocity. More experimental details of the L CR waves could be found in several previous studies like Javadi et al. [12][13][14] where they presented different configurations needed to measure longitudinal residual stresses of the plates, hoop and axial residual stresses of the pipes. They also showed an accurate design for the wedge, which is a united plastic piece holding the transducers, which is also used in this study. The relation between travel-time measured by the L CR wave and the corresponding uniaxial stress is developed by Egle and Bray [10] to be: In Eq. (1), Δσ is stress change, E is the elastic modulus and L is the acoustoelastic coefficient (known as acoustoelastic constant) for longitudinal waves propagated in the direction of the applied stress field. The acoustoelastic constant is measured by the uniaxial tensile test carried out over the specimens extracted from the investigated material. Since the material properties for the weld zone is different from the heat-affected zone (HAZ) and also parent material (PM), hence the acoustoelastic constant is required to be measured in all the zones independently. Also, t is travel-time of the L CR wave, which is experimentally measured on the tested material while t 0 is travel-time related to the stress-free sample. Measuring the acoustoelastic constant along with the weld induced change in travel-time leads to determination of the stress changes caused by the welding process.

Finite element welding simulation
Numerical analysis of the welding residual stresses and deformations needs to take account of the mechanical properties of welds. The process is also influenced by the coupling among heat transfer, microstructure evolution and thermal stresses. However, since the finite element method is inherently a continuum-level calculation, hence simulation of the microstructural evolution is considered through simulating the material properties changes at expected transformation times and temperature. From the thermo-mechanical point of view, the heat input can be assumed as a volumetric or surface energy distribution. The fluid flow effect, which leads to homogenizing the temperature in the molten area, can be taken into account by increasing the thermal conductivity over the melting temperature. Heat transfers in solids are described by the heat equation as following: In Eq.    According to the results shown in Fig. 3-a and Fig. 3

Sample Description
In this study, the plates from Monel® 400 (UNS N04400/W.Nr. 2.4360 and 2.4361) are welded to investigate the welding residual stresses and deformations. Two 220×150×6 mm plates are welded in V-groove (90° included angle) by employing tungsten inert gas (TIG) welding process. Multi-pass butt-weld joint geometry is used while the welding procedure specifications (WPS) are listed in Table 3. The plates are tacked weld in two points while clamping is used during the welding process of Plate 2 (no clamp is used for Plate 1). It is not practical to test nonflat surfaces in the ultrasonic stress measurement hence; the weld reinforcement is removed by employing a 30000-rpm hand grinder machine. A water-cooling system is employed to control the grinding temperature and prevent producing new thermal stresses.

Ultrasonic stress measurement
The  heat-treatment is already required to relax the residual stresses of the tensile test specimen. By assembling the TOF measurement devices on the stress-free specimen, the t 0 is firstly achieved.
By employing a tensile test standard machine, the tensile test (σ) is increased step by step; meanwhile the flight-time (t) is measured in each step. The elastic modulus (E) could also be measured by using the tensile test results or obtaining from the material properties tables. As a result, the acoustoelastic constant (L) would be calculated based on Eq. (1).
In this study, the tensile test specimens are extracted from the weld zone and parent material (PM) to measure the E and L in each of these zones. The tensile test specimens are manufactured according to the Sheet type (0.5 in. wide) sample presented in the ASTM: E8 standard.
Finally, the acoustoelastic constant is measured equal to 1.7 and 1.96 in the PM and weld zone respectively.

Residual stress measurement by hole-drilling method
The residual stresses measured by the ultrasonic method will be compared with those obtained from the FE welding simulation. However, the FE results also need to be verified by another experimental measurement results which is the hole-drilling method. The hole-drilling method is carried out in six different points according to the characterizations described in ASTM: E837.
This semi-destructive technique measures the strains relaxed by incremental drilling of a small hole which its diameter is equal to 1.5 mm. The strains are evaluated using a strain gauge rosette after each depth increment and the residual stresses are then calculated employing equations established by ASTM: E837.

Measurement of the welding deformations
The deformations are measured to compare the Plate 1 and Plate 2 in other to find the effect of using clamp on deformations produced by the welding process. The angular shrinkage (Fig. 5) is the most important deformation type which is considered in this study. It is obvious that a considerable amount of angular shrinkage is produced in Plate 1 which was welded without using of the clamp. The angular shrinkage is accurately measured by employing a coordinatemeasuring machine (CMM). Javadi et al. [12]. It should be noticed that the L CR ultrasonic method measures average of stresses in the 2 mm depth hence, the average of stresses in 0-2 mm from the surface are also considered in obtaining the FE simulation results. Furthermore, the depth of hole produced during the hole-drilling measurement is equal to 2 mm hence; the average of stresses in this hole is also reported by the hole-drilling method. The FE simulation results have good agreement with residual stresses measured by the holedrilling method hence, the FE model has enough accuracy to be used as the verification of the ultrasonic measurements. From Fig. 6b, for the majority of the points, the difference between the residual stresses measured by the ultrasonic method with those obtained from the FE simulation does not exceed 25 MPa, which is about 10% of the yield strength of the Monel plate. It means that the ultrasonic and FE simulation results have reasonable agreement, which is the confirmation of the L CR potential in stress evaluation of Monel plates.

Deformation measurement results
The angular shrinkage of Plate 1 is measured by employing a CMM. The measurement is carried out on the surface of plate in Z=110 mm that is the middle of weld line. The results are shown in Fig. 7 which shows that the maximum of vertical displacement is produced in left corner of the plate and is equal to 7.32 mm.

Influence of using the clamp
The effect of clamping is investigated by comparing the residual stress and deformation measured on Plate 1 (no clamp) and Plate 2 (with clamp). The comparison results are shown in Fig. 8 and Fig. 9  to about 10 percent increase in the residual stress however, the angular shrinkage is less than a quarter of no clamp sample. It can also be concluded that the ultrasonic stress measurement using the L CR waves (which is used for comparing Plate 1&2) has enough resolution to distinguish less than 25 MPa differences in the longitudinal residual stresses caused by using the clamp.

5-CONCLUSIONS
The main goal of this study is evaluation of the welding residual stress and deformation in the Monel plates to investigate the clamping effect on the residual stresses and deformations. The finite element welding simulation, the L CR ultrasonic stress measurement, the hole-drilling method and the angular shrinkage measurement are employed to reach this goal. According to the achieved results, it can be concluded that: 1) The reasonable agreement achieved in comparing the FE simulation with the ultrasonic stress measurement shows that the L CR ultrasonic method has good potential to be employed in residual stress measurement of Monel plates.
2) The ultrasonic stress measurement by using the L CR waves shows enough accuracy to distinguish the clamping effect on the longitudinal residual stresses. Table 1. Chemical composition of Monel 400 used in this study Table 2. Details of six FE models compared to optimize mesh size Table 3. WPS for Monel welding process