Mechanics of Materials
Analysis of Fatigue Crack Propagation Behavior of Structures with One-Sided Welding in Fillet Welded Joint for Load-Carrying Type
2022 Volume 63 Issue 7 Pages 1037-1045
Details
2022 Volume 63 Issue 7 Pages 1037-1045
The structures of a hydraulic excavator with one-sided welded joints are investigated in this study. We investigated the fatigue lifetime evaluation method using S-version FEM. Especially we considered combination of cracks from multiple crack origins. Moreover, to achieve a more precise evaluation, we obtained the crack growth rate of the excavator weld using the unloading elastic compliance method instead of some engineering standard values. Results show that, the fatigue lifetime obtained from the analysis of all width crack; type1 - all cracks named in this study is extremely short compared with test results. Considering the combination of cracks from multiple crack origins, the S-version FEM provides an evaluation similar fatigue lifetime of a test piece imitating the excavator.
Fatigue lifetime estimation using the S-version FEM (The number of cracks comparison).
The attachments of hydraulic excavators are structures comprising numerous one-sided welded joints. Although one-sided welded joints are easily implemented and economical, the unwelded portion frequently initiates crack propagation. Therefore, manufacturer have attempted to reduce the unwelded portion by welding on both sides and by adding a groove. However, attachments with box-like structures are difficult to weld at both sides, and grooving cannot completely remove the unwelded portion because high-quality full penetration welds are difficult to achieve. Despite the necessity for an accurate evaluation method for crack propagation from the unwelded portion, the fatigue fracture mechanism, and fatigue evaluation method of practical fillet joints with one-sided welding are yet to be elucidated. Whereas the fatigue evaluation analysis method of the unwelded portion of load-carrying cruciform-welded joints has been extensively investigated,1–5) investigations pertaining to the actual structure and machine has been reported6,7) as well as one-sided welded joints investigated8) are scarce. We typically regard the unwelded portion as the initial crack and calculate the stress intensity factor and lifetime based on Paris’ law using the crack growth rate of IIW9) or WES.10) Moreover, current analysis methods calculate the stress intensity factor of the crack depth direction rather than the width direction. However, cracks in long welding lines, such as excavators, propagate in the depth and width directions. Three-dimensional observations revealed that fatigue cracks initiated from the tip of the unwelded portion and propagated in the depth and width directions of the welding materials. Moreover, cracks initiated at multiple sites. As the number of cycles increased, cracks propagated and combined reported in Refs. 11, 12). By considering crack development behaviors in fatigue evaluation analysis, the lifetime can be estimated more accurately. Therefore, in this study, we perform an analysis using the S-version FEM (three-dimensional crack propagation analysis) based on the crack growth rate of the excavator acquired via the unloading elastic compliance method. We analytically investigated the crack propagation behavior of multiple initial cracks and the effect on the fatigue lifetime of one-sided welding in fillet welded joint.
In this study, we estimated the lifetime by performing a simulation using the S-version FEM, which was proposed by Kikuchi.13–16) Using the S-version FEM, we can easily simulate crack growth by calculating the stress intensity factor around a crack leading edge. The S-version FEM requires a global mesh that represents a test piece shape; a local mesh represents the crack shape and is re-meshed automatically and periodically. In this study, the S-version FEM we performed is liner elastic simulation.
The crack growth rate is given as:
| \begin{equation*} \frac{\text{d}a}{\text{d}N} = \text{C}(\Delta K_{\text{eq}})^{\text{n}} \end{equation*} |
| \begin{equation*} \Delta K_{\text{eq}} = \frac{\Delta K_{\textit{I}}}{2} + \frac{1}{2} \sqrt{\Delta K_{\textit{I}}^{2} + 4(1.155\Delta K_{\textit{II}})^{2} + 4(\Delta K_{\textit{III}})^{2}} \end{equation*} |
Figure 1 shows the global and local meshes. The element type is 20-node hexahedral element. The global mesh was modeled with the same dimensions as the fatigue test piece shown by panel (a) in Fig. 1. The root face and root opening measured 3 and, 0.1 mm, respectively, as shown by panel (d) in Fig. 1. Dimensions were the same as the real excavator. Figure 2 shows initial crack locations on the root tip. In this study, one to four initial cracks were applied to the global mesh as a local mesh. We labeled the cracks as “Type N”, where N represents the number of initial cracks. Two initial crack sizes were applied to the local mesh, as shown in Table 1. These sizes were decided by three-dimensional observations investigated.11,12) Cracks which were 0.01–0.3 mm appeared across the width of the sample (50 mm) at 5% of the estimated fracture lifetime Nf. Then we regarded the crack leading edge as the semi-elliptical crack and measured the minor and major axis of the semi-ellipse. We chose the crack size as small as possible. In fact, the crack size at 5% Nf may not be strictly equal to the actual initial crack size. However, cracks initiate at the very early stage of Nf. Moreover, the lifetime of crack propagation chiefly determines the fatigue lifetime. Therefore, we think even if we use crack size at 5% of Nf as the initial state for analysis, the lifetime can be evaluated. In this study, fracture was defined as the crack deepest length becoming 5 mm in the welded joint because fatigue fractures spread to 5 mm from the tip of the unwelded portion in the fatigue test. The coalescence of multiple cracks is defined by the time of distance between close edge of crack “L” = 0 mm as proposed in WES.10) Then when “L” reaches 0 mm, we make manually the local mesh that corresponds to the depth and width of cracks next to each other at the moment of coalescence. For the S-version FEM, following parameters were used: the Young’s modulus E = 206 GPa, and Poisson’s ratio ν = 0.3. The crack growth rate of the welding materials was determined using the unloading elastic compliance method, as explained below.
S-version FEM mesh and shapes and dimensions of specimens: unit (mm).
Location of local mesh: unit (mm).
In a previous study, a fatigue test was performed using a hydraulic servo-controlled fatigue strength-testing equipment, where the same load condition as the hydraulic excavator was used. The boundary conditions used in the analysis are shown in Fig. 3. Displacement of x, y and z freedom is zero at all nodes on the upper surface of the model. The z direction load is applied to all nodes on the lower surface of the model. Displacement of y freedom is zero at all outer nodes across the width which is 35 mm from the upper surface of the model. Displacement of y freedom is zero at all outer nodes across the thickness of two consecutive lines where lower most line is 10 mm from the lower surface of the model.
Boundary condition.
In this study, the base material was high-strength steel SS400 (JIS), which was used in the attachment part of the hydraulic excavator. In a previous study, cracks propagated only in the welding material; therefore, the crack propagation property of the welding material must be acquired. The shape of the CT test piece shown in Fig. 4 was designed based on to the ASTM E647 standard, which was used to obtain the crack growth rate. Hatching indicates welded part. We welded SS400 steel grooves via multi-layer welding. The welded part was cut into a CT test piece by wire cutting, excluding the welding start and end points. The welding rods were used as a material equivalent to JIS Z3313 (wire diameter φ = 1.2 mm). The arc welding condition, chemical composition of the welding rods, and mechanical properties were the same as the excavator. Furthermore, the chemical composition and mechanical properties of SS400 were the same as the excavator.
CT specimen dimensions.
In this study, we used the unloading elastic compliance method to observe the growth rate reported by M. Jono et al.17) The fatigue test was performed using a hydraulic servo-controlled fatigue strength testing equipment. The unloading elastic compliance method can be used to measure the crack opening with high accuracy using a relatively simple device, as well as to continuously measure the average crack length including the inside of the test piece. A constant-amplitude test based on the calibration test was performed under the following three conditions: (I) The stress ratio R = 0.5, frequency f = 1–20 Hz, and gradual increase rate C = 1.0 (= (1/K)(dK/da))[m−1]; (II) the stress ratio R = 0.05, frequency f = 1–20 Hz, and gradual increase rate C = 1.0 (= (1/K)(dK/da))[m−1]; (III) the stress ratio R = 0.05, frequency f = 1–20 Hz, and gradual decrease rate C = −0.25 (= (1/K)(dK/da))[m−1]. The pre-crack was set to 1.0 mm to decrease the machining notch effect, and crack measurement was performed every 0.3 mm in three abovementioned conditions. In this study, the stress intensity factor range ΔK was calculated using a formula based on the ASTM E647 standard.
Figure 5 shows the relationship between the crack growth rate da/dN and stress intensity factor ΔK obtained from the gradual increase and decrease test. A straight line, which is based on the International Institute of Welding Standard and Japan Welding Engineering Standard, is additionally shown in Fig. 5. For a crack growth rate of 1.0 × 10−11 to 1.0 × 10−7 [m/cycle], a linear relationship of Paris’ law for three abovementioned conditions can be obtained. The constants for the crack growth rate from this relationship are shown in the table in Fig. 5. The crack growth rate from experimental results is lower than that of the International Institute of Welding Standard and the Japan Welding Engineering Standard. Moreover, obtained crack growth rates differ from each other. We think differences between some standard values and our experimental results are due to the specific welding material of the excavator. In addition, as for differences under three conditions, we think the stress ratio and gradual increase and decrease rate cause differences of experimental crack growth rate characteristic. This implies that the lifetime can be estimated more accurately using test values in the fatigue evaluation analysis. In this study, our aim is to evaluate the shortest test lifetime. So, we used the test value of (I) to estimate the fatigue lifetime more conservatively.
Relationship between ΔK and da/dN.
In a previous study, we measured the local strain near the weld. This strain is generated by tension, compression, and in-plane bending. Figure 6 shows locations of strain gauges attached to the fatigue test piece. Strain gauges were attached 10 mm from the toe of the fillet weld, and gauges were attached at the front and back. The stress σ was calculated from the obtained strain ε by the following equation σ = Eε. The Young’s modulus E = 206 GPa. The stress in the z direction and deformation contour diagrams obtained using the S-version FEM are presented in Fig. 6. We compared the gauge stress of the fatigue test location between the S-version FEM and fatigue test and confirmed whether the boundary conditions of the fatigue test can be reproduced by the S-version FEM. It means that we did not focus on only local consistency of analysis results. The table in Fig. 6 shows that stress values obtained via two approaches were similar. Therefore, we conclude that boundary conditions used in the S-version FEM were representative of the fatigue test.
The S-version FEM stress and deformation contour diagrams.
Figure 7 schematically shows definitions of crack propagation directions in this study. As the semi-elliptical crack propagates into the welding material, the direction in which the minor axis of the semi-ellipse expands is known as the welding depth direction, whereas the major axis of the semi-ellipse expands to the left and right along the tip of the unwelded portion is known as the width direction. As for the stress intensity factor, we calculated an approximate curve based on analysis results. Figure 8 shows the observation area for the stress intensity factor, and values at test force amplitude Fa = 9 kN are shown in Table 2. The stress intensity factor varied based on the initial crack size, number of cracks, and crack interval. In the initial state, the stress intensity factor at θ = 0° and 180° was larger than that at θ = 90° in Type1 width 3 mm, depth 0.15 mm. Therefore, the crack propagated in the width direction preferentially compared with welding depth direction as shown the stress intensity factor panel (a) in Fig. 9.
Definition of crack propagation direction.
Observation area of the stress intensity factor.
Stress intensity factor change from start to failure at Fa = 9 kN.
Results of the fatigue crack propagation behavior calculated using the S-version FEM are shown in Fig. 10. The curve in the figure shows the leading edge of the crack. The number of cycles for each leading edge is stated above each curve. We investigated the effect of the number of initial cracks located evenly on the tip of the unwelded portion. Results are shown in Fig. 10 (type1, type2-16.6, type3, type4, and type1-all cracks). As shown by type1 in panel (a) of Fig. 10, the fatigue crack propagated preferentially in the width direction instead of in the welding depth direction. As shown in panel (a) of Fig. 9, the stress intensity factors at θ = 0° and 180° were larger than the stress intensity factors at θ = 90°; consequently, crack propagation occurred in the welding width direction. By contrast, as shown by type 1 in panel (e) of Fig. 10, the crack propagated in welding width and depth directions owing to high stress intensity factor at θ = 90° and the similar stress intensity factor at θ = 0° and 180° as shown in panel (b) of Fig. 9. Based on the propagation behavior of multiple cracks shown in Fig. 10(b)–(d), it is clear that multiple cracks propagated at multiple origins and coalesced with each other, and cracks propagated in the width direction. In type2, cracks were generated from two locations combined in the center part of the test (model) piece, which exhibited a width of 50 mm. In type3, cracks located in the center propagated more compared with cracks located in the left and right, and three cracks combined with one other simultaneously. In type4, two inner cracks first combined in the center part of the test (model) piece; subsequently, they combined with the outer cracks on both sides. We found that crack propagation behaviors observed in three-dimensional observation and beach mark results; cracks propagated and combined, can be reproduced in the analysis.
Crack propagation simulation by S-version FEM (Type1, Type2 16.6, Type3, Type4 and Type1-all crack: Fa = 9 kN).
We observed fatigue cracks using a specific three-dimensional observation method and the beach mark method used in a previous study.11,12) In this section, we present a comparison of crack lengths in the welding depth direction from the S-version FEM and test results. Figure 11 shows the effect of the number of initial cracks located evenly on the tip of the unwelded portion. Test results shown in the figure are plotted using the maximum crack length in the welding depth direction. In addition, the triangle in the figure indicates the number of cycles when multiple cracks are combined. As described above, type4 indicated two stages of combined behavior: two inner cracks first combined in the center part of the test (model) piece; subsequently, they combined with the outer cracks on both sides. Therefore, the two-point triangle mark indicates the lifetime when the combined behavior is exhibited. Regions A and B in the figure show the range of fracture lifetime obtained from the fatigue test at Fa = 6 and 9 kN, respectively. As shown in Fig. 11, regardless of the test force level and number of crack origins, the crack growth rate of multiple cracks was the same as the single crack until the crack was combined. As the number of cycles increased and cracks combined, the crack growth rate increased significantly. Furthermore, we discovered that the number of cycles to the crack combination constituted almost 40% to 50% of the fracture lifetime. Furthermore, as the number of initial crack origins increased, the fracture lifetime decreased. It appeared that the number of crack combination cycles decreased because of the narrowing of the crack interval; consequently, the number of fracture lifetimes decreased. By comparing experimental and analysis results of the fatigue crack propagation behavior, we confirmed that different behaviors were presented at the force level. At Fa = 6 kN (low load amplitude), the experimental results were similar to the analysis results of a single initial crack. By contract, at Fa = 9 kN (high load amplitude), the experimental results were similar to the analysis results of multiple initial cracks; in particular, the number of fatigue lives to failure was similar to the analysis results of type2-16.6.
Crack growth rate at the longest crack tip (Type1, Type2 16.6, Type3, Type4 and Type1-all crack).
Figure 12 shows fatigue lifetime of fatigue test and analysis results, separately. At Fa = 6 and 7 kN (i.e., low load amplitudes), the dispersion of the S-N curve is more significant as compared with that at Fa = 8 and 9 kN (i.e., high load amplitudes). Comparing earlier test results of broken cases for each load amplitude level with the analysis result for the single initial crack (type1 with all cracks), the lifetime of type1 - all cracks was almost two to three times shorter than that indicated by fatigue test results. This implies that considering the entire width of the unwelded portion as the initial crack results in an exaggerated fatigue lifetime evaluation. However, comparing the analysis result of the single initial crack for type1, it was discovered that the lifetime of type1 was almost 1.5 to 2 times longer than fatigue test results. This implies that the estimation result would be inaccurate when the lifetime is evaluated based on a single crack analysis under the condition assumed in this study. However, at low load amplitude levels of 7, 6, and 5 kN, some fatigue test lifetimes were longer than obtained lifetime from the S-version FEM for type1. We think crack propagation behavior is probably different in low load amplitude. However, our aim in this study is to evaluate the shortest test lifetime. Based on analysis results of multiple crack propagations, analysis results of Type2-16.6 and Type3 were more similar to the fatigue test result than the single crack analysis result. Hence, we confirm that multiple cracks must be considered in the fatigue lifetime evaluation of the test piece in long welding lines of the excavator.
Fatigue lifetime estimation using the S-version FEM (The number of cracks comparison).
The fatigue crack propagation behavior of fillet joints with one-sided welding using the S-version FEM was investigated and compared with test results. The aim was to reproduce crack propagation behavior in the analysis and evaluate and estimate the fatigue lifetime. The conclusions are summarized as follows:
The crack growth rate obtained from the gradual increase and decrease tests differed from IIW-1823-07 and the Japan Welding Engineering Standard. Moreover, crack growth rates obtained from experimental results were lower than the standard values. By comparing the numerical analysis results, it was clarified that the combined behavior of multiple cracks significantly affected the fatigue life. In particular, analysis results of Type2-16.6 and Type3 were more similar to the fatigue test result than the single crack analysis result. The fatigue lifetime evaluation was exaggerated when the entire width of the unwelded portion was considered. We confirmed that multiple cracks should be considered in the fatigue lifetime evaluation of a one-sided welded joint test piece imitating the excavator.
