Acta Metall. Sin.(Engl. Lett.)Vol.21 No.4 pp289-294 Aug. 2008
SIMULATION OF VIBRATION STRESS RELIEF AFTER WELDING BASED ON FEM X.C. Zhao1,2)∗ , Y.D. Zhang1,2), H.W. Zhang1,2) and Q. Wu1,2) 1) School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China 2) State Key Laboratory of Virtual Reality Technology, Beijing University of Aeronautics and Astronautics, Beijing 100083, China Manuscript received 12 September 2007 A finite element model is developed for the simulation of vibration stress relief (VSR) after welding. For the nonresonant vibration, the reduction in stress strongly depends on the amplitude of vibration. For the resonant vibration, the vibration frequency is the key for stress relief. The vibration frequency should be close to the structure natural frequency for the desired vibration mode. Only small vibration amplitude is required, which will be amplified during vibration. Vibration time does not have a major impact on vibration stress relief. When the amplitude of vibration stress relief is large, the treatment will be more effective. KEY WORDS Residual stress; Vibration stress relief; Simulation
1. Introduction Welding process inevitably induce residual stress into welded structures. This creates potential problems in terms of dimension stability. Traditionally, post-weld heat treatment (PWHT) was used to relieve residual stress, which is an effective process, but it suffers from numerous disadvantages: oxidization of heating surface and change in material properties. Vibratory stress relief has been proposed as an alternative to relieve weld residual stress for several years. Recently, various industries have used the vibratory stress relieving methods to reduce the residual stress in welded components. As the mechanism of vibration stress relief is not well understood, this process is not widely used in industries. If the vibration applied on a welded structure is not adequate, the weld residual stress cannot be reduced. Furthermore, as the cost of weld residual stress measurement is high and time consuming, it is difficult to know the extent of reduction of residual stress by the VSR. With the development of modeling technology, it is possible to model the process of VSR using a commercial finite element code Marc. In this article, a finite element model has been developed to investigate the mechanism of the VSR process and the effect of the parameters of VSR, vibration time, frequency and amplitude, on the reduction of weld residual stress. A three-dimensional solid modal was ∗
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· 290 · used to simulate the development of weld residual stress and vibration stress relief process after welding. 2. Weld Residual Stress Modeling
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The weld specimen, as shown in Fig.1, is produced from 7075 aluminum alloy. The toFig.1 Schematic diagram of weld specimen. tal length of the specimen was 300 mm and the cross-section 80 mm by 6 mm. Weld bead was deposited near the clamping area. The mechanical properties of the specimen are shown in Fig.2. The voltage and current used for the welding process were 24 V and 200 A, respectively. The travel speed was 20 mm/s. Welding process was simulated with MSC. Marc software.
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Fig.2 Material properties of 7075 aluminum alloy.
3. Thermal Analysis Goldak′ s ellipsoid model was applied to simulate a moving-arc weld flux. The distribution of heat flux is expressed as follows: √ −t)]2 −3z 2 6 3Qη −3x2 2 −3[y+v(τ c2 √ e a e q(x, y, z, t) = f e b2 abcπ π (1) where a, b and c are the semi-axes of the ellipsoid as shown in Fig.3, η is the heat efficiency, and Q is the power (welding current multiply by voltage).
Fig.3 Schematic diagram of Goldak′ s ellipsoid model.
4. Weld Stress Analysis The temperature histories predicted in the thermal analysis were inputted to a thermalmechanical model to perform weld stress analyses. Proper boundary conditions were added to simulate the clamp of the fixed end. Fig.4 shows the distribution of transverse and
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Fig.4 Distribution of residual stress.
longitudinal residual stress. To clearly demonstrate the vibration stress relief, the residual stress was mapped to a twodimensional cross-section. 5. Nonresonant Vibration Stress Relief Nonresonant vibration analysis was performed with Marc dynamic analysis. Displacement load was applied near the end of the plate with a sine wave as shown in Fig.1. A low frequency, 25 Hz was selected for these analyses. The effects of vibration time and vibration amplitude were studied. 5.1 Effect of vibration time on stress reduction Fig.5 shows the effect of vibration time on the reduction of residual stress. Residual Fig.5 Effect of vibration time on longitudinal stress was mostly reduced in the first cycle. residual stress reduction. Small reduction occurred in the second cycle. The distribution of residual stress after the third cycle was almost the same as after the second cycle, it is hardly to see any further reduction of stress after the third cycle. Munsi observe the similar phenomena during the experiment of vibration stress relief[1] . This means that stress reduction depends on the amplitude of vibration rather than the vibration time for the VSR. 5.2 Effect of vibration amplitude on stress reduction The frequency of vibration was kept constant and the amplitude of vibration was varied to investigate the effect of vibration amplitude on the reduction of residual stress. As shown in Fig.6, with the increase of vibration amplitude, both longitudinal and transverse residual stresses were reduced which is in good agreement with Munsi′ s results[1] . When the vibration amplitude reached 24 mm, the transverse stress near the weld toe area became compressive and Von Mises stress increased further with the increase in vibration amp-
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Fig.6 Effect of vibration amplitude on residual stress reduction.
litude. This is in a good agreement with the model predicted results. This study shows that the nonresonant vibration stress relief strongly depends on the amplitude of vibration. 6. Resonant Vibration Stress Relief
Fig.7 Mode shape of first natural frequency.
6.1 Natural frequency analysis By applying the fixed boundary at the end of the plate, free natural vibration analysis was performed. Fig.7 shows the desired mode shape with first natural frequency 78.975 Hz. This is the mode used for the following study of resonant vibration stress relief. 6.2 Frequency effect on displacement amplitude A force, 10 N, was applied at the free end of the plate with three frequencies: 25 Hz, 70 Hz, 78.975 Hz. Fig.8 shows the displacement induced by this load. The displacement amplitudes are 0.71 mm for frequency 25 Hz, 0.78 mm for frequency 70 Hz and 1.46 mm for frequency 78.975 Hz in the first load cycle. For the case with frequency 25 Hz, the displacement keeps constant in the following load cycle, but for the cases with frequency 70 Hz and 78.975 Hz, the displacement amplitudes are amplified in the following cycles. The maximum displacement amplitude is 5.77 mm for the case with the frequency 70 Hz and 9.87 mm for the case with the frequency 78.975 Hz. This means that when load frequency is closer to the structure natural frequency, the amplified displacement amplitude will be higher. With resonant, displacement induced by the small load is amplified to the required level so that the weld residual stress can be relieved.
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Fig.8 Effect of frequency on displacement: (a) f =25 Hz; (b) f =70 Hz; (c) f =78.975 Hz.
Another interesting phenomenon can be observed in Fig.8. For the cases with frequency 70 Hz and 78.975 Hz, the displacement amplitude was amplified and then periodically reduced. The cycle time was different between these two cases. These phenomena could be induced by structure damping. 6.3 Effect of load magnitude on displacement amplitude The study on the effect of load frequency on displacement amplitude shows that the maximum displacement is 9.87 mm, which is not adequate to reduce residual stress based on the previous study. To reduce the weld residual stress, the load is increased by 2 and 10 times, respectively. Fig.9 shows the effect of load magnitude on displacement amplitude.
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Fig.9 Effect of load magnitude on displacement: (a) F =20 N; (b) F =100 N.
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· 294 · The displacement is amplified to 19.99 mm for the case with 20 N force and 41.26 mm for the case with 100 N force. It is relevant that the amplified displacement amplitude is no longer decreased for the case with 100 N force. This could be attributed to the fact that magnitude overcomes the effect of the structure damping. The amplified ration for the case with 20 N is approximately equal to two, but for the case with 100 N, it is smaller than 10. 7. Conclusion A VSR finite element model has been developed, which can be used to better understand the mechanism of VSR and optimize the parameter of VSR process. The major conclusions from the studies of nonresonant VSR and resonant VSR are as follows: (1) Load amplitude is the key parameter that reduces weld residual stress. For nonresonant VSR, load amplitude should be proper, otherwise residual stress cannot be reduced or new residual stress will be produced further. For resonant VSR, a small load is required, which will be amplified large enough to reduce residual stress. (2) Vibration time does not have a major impact on VSR. Most stress relief happened in early load cycles. If vibration time is increased, fatigue life can be decreased. (3) To reduce weld residual stress, a proper vibration mode shape should be selected. Acknowledgements—This work was supported by the National Defence Basic Research and Development Programme of China (No. 59975008). REFERENCES [1] [2] [3] [4] [5] [6]
A.S.M.Y. Munsi, A.J. Waddell and C.A. Walker, Sci. Technol. Weld. Join. 6(3) (2001) 133. A.S.M.Y. Munsi, A.J. Waddell and C.A. Walker, Mater. Sci. Technol. 17 (2001) 601. A.S.M.Y. Munsi, A.J. Waddell and C.A. Walker, J. Strain Anal. 36(5) (2001) 453. W.F. Hahn, PhD Dissertation (Alfred University, Alfred, 2002). Meta-Lax, http://www.meta-lax.com/Home/Literature/literature.html J. Goldak, A. Chakravarti and M. Bibby, Metall. Trans. 15B(2) (1984) 299.
