Simulation and Analysis on the Blind Hole Method
Using the Finite Element Method
Chun-Ho Yin
1,a, Chao-Ming Hsu
2,b, Ping-Shen Su
1,c, and Jao-Hwa Kuang
1,d 1Department of Mechanical & Electro-Mechanical Engineering, National Sun Yat-sen University, Kaohsiung, Taiwan, 80424, R.O.C.
2
Department of Mechanical Engineering,
National Kaohsiung University of Applied Sciences, Kaohsiung, Taiwan, 80778, R.O.C. a
d963020002@student.nsysu.edu.tw, bjammy@cc.kuas.edu.tw, c
m983020030@student.nsysu.edu.tw, dkuang@faculty.nsysu.edu.tw
Keywords: Residual stress, Blind-hole method, Hole-drilling method, Finite element method
Abstract. This study investigates the effectiveness of the hole-drilling strain gage method on residual
stress estimation. The thermal-elastic-plastic model of the commercial Marc finite element method package is used to simulate and build up the hole-drilling process and residual stress distribution. Two Inconel 690 alloy plate welded with GTAW filler I-52 solder are first simulated using the Marc software. The traditional hole-drilling process is then simulated. The simulated residual strain variation data is incorporated into the hole-drilling strain-gage method to derive the possible residual stress components. The effects of drilling depth and drill size on the accuracy of residual stress estimates are also discussed. A comparison of stress components estimated from the traditional hole-drilling strain gage method and simulated from the Marc software is presented. The modified dimensionless parameters are provided by applying the optimum technique. The numerical results indicate that the proposed dimensionless parameters can significantly improve the accuracy of estimated residual stress components.
Introduction
When a structural member in not under influence of external stress or a temperature gradient, its interior should be under residual stress[1], caused by the uneven distribution of the material or the local plastic deformation of the structural member. Residual stress is generated in many processes, such as welding, plasticity, sputtering and impact. It can deeply affect the life and safety of a structure. Thus, measuring residual stress is extremely important in engineering.
Strain-gage hole-drilling is the most commonly used method. The American Society for Testing and Materials (ASTM) has stipulated standard for hole-drilling methods for measuring residual stress [2]. The hole drilling method was first proposed in 1934 by Mathar[3] but, at the time, only the stress of a single axial direction was measured. Mathar measured the displacement of a hole’s symmetrical points before and after drilling to determine the extent and direction of residual stress. However, hole diameters up to 12mm resulted in poor accuracy. In 1940, Soete and Vancrombrugge[4] adopted resistance strain-gage. The strain-gage was 8mm and the hole diameter was reduced to 6mm, thus improving the irregular variation of strain values caused by vibration and significantly enhancing strain value accuracy.
In 1966, Rendler and Vigness[5] used experimental data of through hole drilling theory and blind hole drilling method as proved that through hole drilling theory was applicable in the blind hole drilling method. When hole depth was approximately equal to hole diameter, the stress released after drilling tended to be stable, thus drilling through test samples was no longer required, significantly reducing the degree of damage incurred. In 2007, Lee[6] used arc welding and laser welding to connect two nickel alloy 690 and observed the resulting residual stress. The present study also uses this welding process as a basis for simulation.
Applied Mechanics and Materials Vol. 328 (2013) pp 990-994 © (2013) Trans Tech Publications, Switzerland
doi:10.4028/www.scientific.net/AMM.328.990
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standard, the applicable r is 0.9~1.5mm. When 0 r is 1.5mm, 0 a and b can be found in the standard;
when the drill hole radius(r ) is 0.5, 2.0 or 2.5mm, the ratio of blind hole radius(0 r ) to measurement 0
radius( r ) exceeds the range of 0.3 to 0.5, thus a and b cannot be found in the standard. Therefore, the dimensionless coefficients a and ∗ b can be determined using the proposed coefficient ∗ modification method, with resulting values shown in Table 2.
Using the residual principal stresses in Figs. 5(a) and (b), the changes in hole radiuses at locations near the center line can be observed, and a significant variance is found in the residual stress measurement results. When the hole radius increases, the calculated principal stress gradually decreases. A comparison between the stress results and the residual principal stress after welding indicates that changes in hole diameters have a significant impact on measurement accuracy, and the error rate rises significantly when hole diameter is close to measured location point.
Conclusions
Based on modifying the simulation processing, theoretical calculation, numerical analysis and boundary condition, we present the following conclusions:
1. Observation of the von Mises Stress of the post-welding plate indicates that increased distance from the weld line corresponds to decreased stress in the interior of the metal and reduced variation in the range of stress, with the greatest value occurring within 25mm from the center line.
2. Using the dimensionless coefficients a and b provided in the blind hole drilling method standard for determining strains of nodes, shows that blind hole drilling method is applicable for finite element simulations. The results of a comparison of the principal stresses determined before and after the drilling indicate an error to a certain extent.
3. Applying the penalty function method allows for the planning of new dimensionless coefficients a and ∗ b , which are then applied to the theory of blind hole method, showing that the ∗ determined stress has a lower error rate than that calculated using a and b.
4. At different depths and hole diameters, the residual stress calculated by the blind hole method has a more significant influence on accuracy than that calculated after welding.
References
[1] Leonard Mordfin, Mechanical Relaxation of Residual Stresses, American Society for Testing and Materials, Philadelphia, Pa, 1988.
[2] Annual Book of ASTM Standards, “Standard Test Method for Determining Residual Stresses by the Hole Drilling Strain-Gage Method”. ASTM E837-01, 2001.
[3] Mathar, J., “Determination of Initial Stress by Measuring the Deformation Around Drilled Holes”, Transcations of the American Society of Mechanical Engineers, 56(4), pp/ 249-254, 1934.
[4] Soete, W. and Vancrombrugge R., “An Industrial Method for the Determination of Residual Stress”, Proc. SESA, VIII, pp. 17-261, 1950.
[5] Rendler, N. J. and Vigness, I., “Hole-drilling Strain-gage Method of Measuring Residual Stresses”, Proc. SESA, XXIII, pp. 577-586, 1966.
[6] Meng-Hsuan Lee, “Study of Residual Stress on Inconel 690 Alloy Butt-Welded by GTAW and LBW Processes”, Master’s Thesis, Department of Mechanical Engineering, National Cheng Kung University, 2007.
