Residual stress relaxation in typical weld joints and its effect on fatigue and crack growth

Transcription

1 Acta Metall. Sin.(Engl. Lett.)Vol.22 No.3 pp June 2009 Residual stress relaxation in typical weld joints and its effect on fatigue and crack growth Liangbi LI 1,2), Zhengquan WAN 2), Zili WANG 1) and Chunyan JI 1) 1) School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang , China 2) China Ship Scientific Research Center, Wuxi , China Manuscript received 25 August 2008; in revised form 5 November 2008 Many factors influence the fatigue and crack growth behavior of welded joints. Some structures often undergo fairly large static loading before they enter service or variable amplitude cyclic loading when they are in service. The combined effect of both applied stress and high initial residual stress is expected to cause the residual stresses relaxation. Only a few papers seem to deal with appropriate procedures for fatigue analysis and crack growth by considering the combined effect of variable amplitude cyclic loading with residual stresses relaxation. In this article, some typical welded connections in ship-shaped structures are investigated with 3-D elastic-plastic finite element analysis. The effect of residual stress relaxation, initial residual stress, and the applied load after variable amplitude cyclic loading is revealed, and a formula for predicting the residual stress at hot spot quantitatively is proposed. Based on the formula, an improved fatigue procedure is introduced. Moreover, crack growth of typical weld joints considering residual stresses relaxation is studied. KEY WORDS Residual stress relaxation; Weld joint; Finite element; Fatigue crack growth 1 Introduction When the sum of the applied and residual stress reaches the yield stress of the material, a part of elastic strains related to the residual stress are converted into the plastic deformation. Consequently, the residual stresses are relieved. The relaxation means a gradual disappearance of the residual stresses in the cyclical loaded structure. Residual stresses relaxation with its effect on the fatigue strength and crack growth has been investigated by experimental methods [1 6]. Most of welded specimens and loading patterns are simple and some loading patterns are limited in these experiments. Moreover, the cost of experiment is expensive, so numerical methods [1,7 9] are developed. Dattoma et al. [9] evaluated residual stress relaxation of a simple butt-welded joint under a sinusoidal external load. Eckerlid and Ulfvarson [1] carried out one-dimensional fatigue investigations Corresponding author. Associate professor, Master; Tel.: ; Fax: address: liniangbi@hotmail.con (Liangbi LI) DOI: /S (08)

2 203 of cutouts in ship structures considering residual stress relaxation. Kim et al. [8] and Zhang et al. [7] studied the effects of static load on residual stress relaxation for welded joints on ship structures. Especially, Zhang and Moan [7] considered residual stress as mean stress to study residual stress relaxation and fatigue. However, previous research has not fully explained the combined effect of the initial residual stress and the applied load on the residual stress relaxation and the fatigue strength and crack growth after a variable amplitude cyclic loading. On this background, the aim of the present article is to carry out 3-D finite element analyses to develop a formula for the residual stress that comes from the initial residual stress and applied load during variable amplitude cyclic loading. Based on this stress level, an improved fatigue procedure compared with previous procedure [7] are proposed to evaluate the structure under arbitrary variable amplitude cyclic loading; moreover, crack growth of these structures is studied. 2 Representative Stress for Fatigue Analysis Local stresses for fatigue analysis need to be determined by shell or solid finite elements and appropriately fitting the format of the fatigue resistance. The SN approach may be based upon nominal or hot spot stress approaches and SN curves, which are consistent with the stress definition. Two alternative methods [10,11] are proposed for hot spot stress derivation; i.e. based on a linear extrapolation of the stresses to the intersection line from the read out points at 0.5 t and 1.5 t from the intersection line or the stress at the read out point 0.5 t away from the intersection line and multiplied by 1.12 (Fig.1). The hot spot stress obtained by the latter method is applied in the fatigue analysis conducted in this article. Fig.1 Nominal, hot spot, and notch stress in a plane structure. 3 FE Analysis of Residual Stresses Relaxation in Typical Welded Joints 3.1 General The finite element method was used to evaluate the initial residual stress field and its relaxation. In order to efficiently obtain the residual stress relaxation at the hot spot of these specimens, a simplified inherent strains method [12] was applied to simulate the initial residual stress distribution. In this article, the FE analysis was carried out with ABAQUS in the following steps: (1) inherent strain was input into the model; (2) self-equilibrating analysis of the strain and the stress was used to obtain the initial residual strain and stress; (3) elastic-plastic analysis was referred to simulate the residual stress relaxation in different external load cases. Since it is the longitudinal residual stresses of the specimen that mainly affect the fatigue damage, the focus is on the longitudinal stress in the article.

3 Modeling Four types of specimens (Fig.2) were considered. They represent typical welded connections in ship-shaped structures and were selected from the perspective of both geometry and fatigue loading. In this article, the specimens of nonload carrying box fillet welded joint, the welded joint of gussets on the plate edge, welded joint with the padding plate, and welded joint of the hopper corner structure are denoted by Model 1, Model 2, Model 3, and Model 4, respectively. The material used in the specimens is ship structural steel with nominal thickness of 10 mm for Model 1 Model 4. The yielding stress of Models 1 3 is about 315 MPa, and for Model 4, it is about 350 MPa. Fig.2 Shape and size of models. The FE models are shown in Fig.3. For Model, only one-eighth of the specimens 1, 2, and 3 are modeled due to the symmetry features. Half of the Model 4 are considered by imposing symmetrical boundary conditions for the Y direction. Moreover, the fillet weld geometry is considered. FE analyses have been performed to simulate the distribution of the residual stress in these specimens.

4 205 The attachments in models are connected to the main plate by means of only weld bead, and flank angle of the weld bead is assumed to be 45 with the leg length of 5.0 mm. A finer mesh has been used close to the weld seam. The seam of Models 1 3 is along these Models length and that of Model 4 is along its width. Twenty-node solid elements (C3D20) are used. A mesh sensitivity analysis was first carried out. A minimum element size of 1.6 mm 2 mm 2.5 mm around the weld toe is found as the best compromise between the model accuracy and the computational time. 3.3 Residual stress relaxation under different cyclic loading Load cases Fig.3 FE models. Note: 1 As-welded condition; 2 Preload corresponding to a tensile nominal stress of 0.5σ y; 3 Preload corresponding to a tensile nominal stress of 0.85σ y. Different types of static preloaded conditions (Table 1) were applied to these welded joints (Fig.2) for tests. Results from the residual stresses analysis are compared with the test data (FPSO JIP-Fatigue Capacity [13], 2000). Residual stress at the centerline surface of the main plate apart mm from the weld toe between the FEM analysis and experiments in Model 1 are given in Table 2.

5 206 Table 2 Longitudinal residual stress apart mm from the weld toe (MPa) (Model 1) Case FEM analysis Experimental σ x,res σ res σ x,res,average σ res Condition Condition Condition From Table 2, we can see that (i) Initial welding residual stresses decrease when the applied preload increase; (ii) The analysis result of condition 1 with FEM agrees reasonably well with the experimental results; (iii) The analysis result of condition 2 with FEM is larger and condition 3 is more less than that of experiment. The reason is that now it is difficult to measure residual stress accurately, and on the other hand, the analysis with FEM is difficult to reasonably simulate some physical process such as microstructure change influence on the residual stress. But as a whole, these results and the experimental data are accordant in entire trend. Hence, it is appropriate to obtain residual stress relaxation with FEM Different preload and subsequent variable amplitude loading Sea loads are variable amplitude cyclic loadings in load history, so different preload and variable amplitude loading (Table 3) is selected to estimate the fatigue strength and the fatigue life of the weld components quantitatively. Table 3 Loading cases including different static preload and variable amplitudes cyclic loadings Load cases Preload/MPa s (the maximum nominal stress range)/mpa σ y 3 0.5σ y 80, 100,120,140,160, σ y σ y σ y Fig.4 shows the relative magnitude of residual stress as a function of initial residual stress and applied stress as obtained by FE analysis. The residual stress is referred to a point 0.5 t away from weld toe (Fig.1). It is observed from the figure that there is no relaxation for a load condition of [(σ res ) ini + σ app ]/σ y <1. A full relaxation of the residual stress is achieved when the [(σ res ) ini + σ app ]/σ y reaches a value of 1.9 at the weld toe for these four models. Above this value, a tensile residual stress would change to a compressive residual stress. Through investigations Fig.4 Change in (σ res ) after max /(σ res ) ini due to [(σ res) ini + σ app]/σ y (four models).

6 207 of these results, we tentatively put forward the following formula to predict the amount of relaxed residual stress at the hot spot: [(σ res ) ini + σ app ]/σ y < 1, (σ res ) 2cycles /(σ res ) ini = 1; [(σ res ) ini + σ app ]/σ y 1, (σ res ) after max /(σ res ) ini = 1{[(σ res ) ini + σ app ]/σ y } (1) Since the parameters of the proposed formula are formed with the values normalized by the yield stress of the material used, it can be reasonably applied to determine the relaxed residual stress of welded components manufactured from various steel grades. Furthermore, the formula could be applied to other similar welded joints. 4 Residual Stress Relaxation Effect on Fatigue Assessment and Crack Growth 4.1 A modified fatigue analysis procedure Modified procedure Bin and Moan [7] suggested an analysis procedure for fatigue analysis. An equivalent hot spot stress range σ eq is then obtained in the form as, σ eq = f mean σ where (1 R) B, ( 5 R < 0.5) f mean = ( R + 0.6R 2 ) B, (0.5 R < 1) 6 B, (R > 1 or R < 5) B=calibration to be fitted by fatigue test data, or (2) = { 0.4, for 5 R < , for 0 R < 1 The stress ratio including the effect of external load and residual stress is given by R = σ min = σ mean + σ res σ/2 σ max σ mean + σ res + σ/2 (3) where σ mean is the mean stress. All stresses are based on the concept of the hot-spot stress. Hot-spot stress is calculated, including the effect of geometric stress concentration and does not include the effect of the weld. The FAT90 hot-spot SN-curve can be used for the fatigue design. The residual stresses relaxation can be considered when maximum stress exceeds the yield stress. The new residual stress can be obtained with Eq.(4) and the new stress ratio after residual stress relaxation is Eq.(5). ( σ y σ mean + σ σres 2 = σ res ; ( otherwise σ y σ mean + σ 2 ) ; σ y σ max ) ; σ min σ y (4)

7 208 In the above fatigue procedure, the residual stress with its relaxation is considered according to the relevant load history. This procedure, however, failed to explain the relationship of the fatigue strength, such as the sum of the residual stress relaxation, the initial residual stress, and the applied load with variable amplitude cyclic loading. In the following, this procedure is modified. The above procedure was modified by experiment, the residual stresses by Eq.(1), whereas the other equations remain the same Analysis results obtained with modified procedure Fatigue strength under a load condition 1, 2, 3 (Table 1) is calculated with the modified improved procedure. The results for Model 1 are shown in Fig.5. In Phase I of the FPSO Fatigue Capacity JIP [13] (2000), fatigue tests were performed on some different types of welded specimens (Fig.2) by Hyundai Heavy Industries Co., Ltd. (HHI) in Korea. The test specimens were all fabricated by fillet welding in flat position except the detail A of Model 4 (Fig.2). The test specimens were subjected to different load conditions as shown in Table 1. It is observed from the original measurement data and Fig.5. Fatigue strength is clearly affected by preload; at lower cyclic stress range, fatigue strength increases with more preload applied; whereas at high cyclic stress range, fatigue strength is slightly affected by preload. Equivalent stress range / MPa B D F H J L N f / cycle Fig.5 S vs. N f curves under different load conditions of Model 1 B Condition 1 Analysis (As welded); D Condition 2 Analysis (Pre-load=0.5 yield stress); F Condition 3 Analysis (Pre-load=0.85 yield stress); H Condition 1 Measurement (As welded); J Condition 2 Measurement (Pre-load=0.5 yield stress); L Condition 3 Measurement (Pre-load=0.85 yield stress). When the equivalent stress increases, the effect of preload on the fatigue strength decreases. The fatigue strength predicted by the modified procedure agrees reasonably well with the experiment results. 4.2 Residual stress relaxation effect on crack growth Based on Paris Eq.(6), the crack growth of these weld joints (Fig.2) is analyzed using MSC Fatigue software. da dn = C ( K)m K = σy πa σ = σ max σ min (6) First, these weld joints are calculated under preload condition 2, 4 and 5 (Table 4). Then, these models with initial cracks are applied with cyclic loadings. Curves of crack growth of Model 1 with initial crack length 0.7 mm (a) at hot spot under cyclic loading of nominal stress range 240 MPa are selected to show in Fig.6. It is seen from Fig.6 and Table 5 that the life cycles are longer with the preloads increase. It means that the crack

8 209 Fig.6 Crack growth of Model 1 under different conditions. growth becomes slow as the preload increases. The reason is that the preload could make the residual stress relaxed. Hence, in the stress cycles, the tensile residual stress that drives the crack is reduced. The more the preload is added, the more the residual stress is relaxed. Results of other load conditions and other models have these similar rules. Note: 2 Preload corresponding to a tensile nominal stress of 0.5σ y ; 4 Preload corresponding to a tensile nominal stress of 0.6σ y ; 5 Preload corresponding to a tensile nominal stress of 0.7σ y. 5 Conclusions and Recommendations About Future Work The results presented in this article can be summarized as follows: (1) A formula for predicting the total effect of residual stress relaxation, the initial residual stress, and the applied load after variable amplitude loading at hot spot is established. Furthermore, the relation can be applied to reasonably determine the relaxed residual stress of welded components manufactured from various steel grades. (2) The fatigue strength is clearly affected by the preload; at a low stress range, the fatigue strength increases with increasing preload, whereas at a high stress range level, the fatigue strength is only slightly affected by the preload. When the equivalent stress increases, the effect of preload on the fatigue strength decreases. (3) A modified fatigue procedure is proposed, completely considering the residual stress relaxation under different preloads. Moreover, the procedure accounts for the effect of the residual stress relaxation, the initial residual stress, and the applied load with variable amplitude cyclic loading on the fatigue strength. (4) Crack growth becomes slow as the preload increases. In the future, the following issues should be addressed: (i) These procedures outlined in this article should be used to investigate other test specimens. (ii) Fatigue crack growth procedure with residual stresses relaxation should be validated with experiments data. (iii) Residual stress simulation should be in better correlation with experimental data.

9 210 Acknowledgements This study was supported by the National Natural Science Foundation of China (No ) and Natural Science Foundation of College of Jiangsu Province (No.07KJD580056). This work is financially supported by China Scholarship Council and Research Council of Norway through scholarships to the first author. The author would appreciate Prof. Torgeir Moan of Norwegian University of Science and Technology, Dr. Bin Zhang of Vetco Aibel and Prof. Xiaoping Huang of Shanghai Jiaotong University for their invaluable guidance and constructive advice. We thank Dr. Inge Lotsberg of Det Norske Veritas for his kind provision of fatigue test data. REFERENCES [1] J. Eckerlid and A. Ulfvarson, Marine Struct 8 (1995) 385. [2] K. Iida, S. Yamamoto and M. Takanashi, Weld World 39 (1997) 39. [3] M. Takanashi, K. Kamata and K. Lida, Weld World 44 (2000) 2. [4] T.K. Lee, Y.Y. Nam, S.H. Han and B.C. Shin, Twelfth ISOPE (Japan, 2002). [5] S. Han, T. Lee and B. Shin, Steel Res 73 (2002) 414. [6] J.W. Han, S.H. Han, B.C. Shin and J.H. Kim, Fourteenth ISOPE (France, 2004). [7] B. Zhang and T. Moan, OMAE Conf (Halkidiki, Greece, 2005). [8] W.S. Kim, Y. Tomita, K. Hashimoto and N. Osawa, Seventh ISOPE (Houston, USA, 1997). [9] V. Dattoma, M.D. Giorgi and R. Nobile, J Strain Anal Eng Design 39 (2004) 663. [10] W. Fricke, Proc 11th ISOPE (Stavanger, Norway, 2002). [11] S.W. Kim and I. Lotsberg, J Offshore Mech Arctic Eng 127 (2005) 663. [12] M.G. Yuan and Y. Ueda, J Eng Mater Technol 118 (2006) 229. [13] FPSO JIP-Fatigue Capacity, Fatigue Test of Typical Weld Joints, Hyundai Heavy Industries. Co., Ltd. Nomenclature σ app Applied stress σ mean, σ m Mean stress σ x,res Longitudinal residual stress σ res Difference between residual stress and residual stress after relaxation σ x,res,average Average residual stress of the measurement σ y Yield stress (σ res ) ini Initial residual stress (σ res) 2cycles Residual stress after 2 cycles (σ res ) after max Residual stress after the maximum nominal stress R Stress ratio=σ min/σ max t Plate thickness K Effective range of stress intensity factor σ max Maximum stress σ min Minimum stress C, m Material constant Y Geometry factor a Crack size