FATIGUE ANALYSIS OF A NOTCHED CANTILEVER BEAM USING ANSYS WORKBENCH. N. Sinan Köksal, Arif Kayapunar and Mehmet Çevik

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1 Proceedings of the Fourth International Conference on Mathematical and Computational Applications June 11-13, Manisa, Turkey, pp FATIGUE ANALYSIS OF A NOTCHED CANTILEVER BEAM USING ANSYS WORKBENCH N. Sinan Köksal, Arif Kayapunar and Mehmet Çevik Department of Mechanical Engineering Celal Bayar University, Muradiye, Manisa, Turkey sinan.koksal@cbu.edu.tr Abstract- In automobiles, ships, aircraft wings and fuselages, turbines, nuclear reactors and other machine components subjected to cyclic loading, fatigue is the major threat and has come into question with the technological development. In this study, the fatigue analysis of a notched cantilever beam is carried out using Ansys Workbench. The loading is assumed to be zero based. The effects of notch size and fatigue load are analyzed. The safe design life of the material and critical notch sizes are determined in the analyses for loadings in the elastic region. Key Words- Fatigue Analysis, Finite Element Method, Notch Size 1. INTRODUCTION It is significant to estimate the material life depending on the operating conditions. Design assumptions, material properties and loading conditions are effective in determining the material life. 90% of damages occurring in structural elements are caused by fatigue. In many cases, fatigue is the main failure mechanism, consisting of initiation, propagation and final fracture. Especially in notched components, the propagation phase occupies an important part of the component s total life. The processes of casting, welding and machining might enhance the significance of propagation phase by initiating small defects that behave as local stress concentrators. These may be micro voids, non-metallic inclusions, roughness in surface, abrupt changes in cross-section, quenching cracks or grinding cracks. Consequently, factors such as high temperature, corrosion, excessive loading, residual stresses, stresses under combined loadings, stress concentrations, surface quality and metallographic structure are effective in crack formation [1-7]. In components subjected to cyclic loading, the number of cycles is more effective than the magnitude of the load. The microstructure of the material exhibits changes due to repeated loading. The damage may occur much below the static yield strength. Fatigue crack initiation has been studied in the past using notched small specimens by evaluating local stress or strain at the notch tip considering the stress or strain concentration, equivalent energy density method and low cycle fatigue curve [8]. In recent decades, the local stress strain approaches have been widely accepted and used to predict the fatigue life of a notched member [9-11]. The local stress strain approaches generally include a stress analysis and a fatigue analysis. The stress analysis is to determine the local stress and strain by an approximate method such as the finite

2 112 N. S. Köksal, A. Kayapunar and M. Çevik element method (FEM). The fatigue analysis is conducted by using a fatigue damage criterion based on the stress and strain output from the stress analysis. Fracture mechanics-based approaches can be used to explain the notch fatigue behavior based on a valid physical argument. However, there is no extensively accepted method for fatigue crack growth from a notch, especially considering both near threshold short crack and long crack. Verification of the fracture mechanics-based approach for different materials and notch geometries is limited [12]. 2. FINITE ELEMENT MODELING The material of the beam is selected as structural steel with elasticity modulus of 200 GPa, Poisson s ratio of 0.3 and yield strength of 250 MPa. The prismatic cantilever beam has a length of 1000 mm, a width of 100 mm and a height of 75 mm. The side view of the beam and the position of the notch are shown in Figure 1. Figure 1. The side view of the beam and the position of the notch In order to simulate the behavior of the beam under static and cyclic loading, Ansys Workbench 14.0 finite element software package [13] is used. Ansys Workbench has an integrated fatigue module which is able to further supplement advances that are offered. This module allows stress life decisions and strain life decisions for various loading types. Solid elements with three degrees of freedom at each node and a free mesh are used for modeling the beam. To determine the optimum mesh size for the FEM solution, a convergence analysis is carried out for various mesh sizes. Table 1 shows the convergence of the FEM results with respect to mesh size. According to the convergence analysis, a mesh size of 5mm is accepted. Table 1. Convergence analysis Mesh size (mm) No. of cycles (10 5 ) In order to prove that the stress due to the load is far below the yield point of the material, a static loading analysis is performed before the fatigue analysis. The suitable range of fatigue loads is determined to be between 8 kn and 14 kn; plastic deformation occurs above this range. Table 2 shows the maximum Von Mises stress values and the maximum deflections at the free end of the beam for θ = 90 and different notch sizes (H) under 10 kn static loading. The notch size can be used to predict failure at the notch.

3 Fatigue Analysis of A Notched Cantilever Beam 113 Table 2. Variation of the maximum stress and maximum deflection with respect to notch size Analytic FEM solution Notch size (H) Max. stress (MPa) Max. deflection (mm) solution No notch 2 mm 5 mm 10 mm 20 mm 25 mm RESULTS AND DISCUSSION The fatigue analysis is performed using Ansys Workbench fatigue module. Stress life type analysis is used which is based on Stress-Cycle (S-N) curves [14]. Stress life is related with component s total life and does not distinguish between initiation and propagation. Since it is observed in the static analysis that notch sizes (H) of 20 mm and below result in very slightly varying values while a notch of 25 mm has a predominant effect, we used a notch size of H=25 mm in repeated load analyses. To decide on stress life in fatigue analysis, various factors are considered: loading type, mean stress effects, multiaxial stress correction and fatigue modification factor. In our study zero-based constant amplitude, proportional loading with a load ratio of 0 is assumed. Using our software the fatigue life is computed and the result is shown in Figure 2. Fatigue life shows the available life for the given fatigue analysis which represents the number of cycles until the part will fail due to fatigue. It is observed that the minimum fatigue life of our beam is cycles for 10 kn and this value is reached at the location where maximum stress occurs, as expected. Figure 2. Fatigue life

4 114 N. S. Köksal, A. Kayapunar and M. Çevik Figure 3 shows fatigue damage of the beam which is defined as the design life divided by the available life, for 1*10 6 cycles of fatigue life, under 10kN of load. Values greater than 1 indicate failure before the design life is reached. The maximum damage occurs at the tip of the notch with a value of 11,025. Figure 3. Fatigue damage Figure 4 shows the fatigue factor of safety at 1*10 6 cycle design life. In this case, values less than one indicate failure before the design life has been reached. The minimum value again occurs at the tip of the notch as 0,60824, which is the critical region. Figure 4. Fatigue factor of safety at 1*10 6 cycle design life

5 Fatigue Analysis of A Notched Cantilever Beam 115 In Figure 5, fatigue sensitivity chart is given which shows how the fatigue results change as a function of the loading at the critical location on the model. We wanted to see the sensitivity of the model s life if the load changed from 50% of the current load up to 150% of the current load. It is observed from the figure that when the load is increased up to 150%, the life decreases to cycles. Figure 5. Fatigue sensitivity chart In a stress life fatigue analysis, the term equivalent alternating stress is used to express the stress used to query the fatigue S-N curve after accounting for fatigue loading type, mean stress effects, multiaxial effects, and any other factors in the fatigue analysis. Thus in a fatigue analysis, the equivalent alternating stress can be thought of as the last calculated quantity before determining the fatigue life [14]. The usefulness of this result is that in general it contains all of the fatigue related calculations independent of any material properties. Therefore, we calculated the equivalent alternating stress which is illustrated in Figure 6. As can be seen in the figure, the maximum value is 141,72 MPa which occurs at the tip of the notch.

6 116 N. S. Köksal, A. Kayapunar and M. Çevik Figure 6. Equivalent alternating stress Notch sizes of 2mm, 5mm, 10mm, 20mm, and 25mm are considered along with case of no notch, assuming a notch angle of 90. Figure 7 illustrates the variation of fatigue life depending on notch size. It is observed from the graph that the fatigue life decreases slightly up to a certain notch size (20mm) and decreases considerably after that value. Figure 7. Dependence of fatigue life on notch depth for θ = 90 Finally, we analyzed the effects of notch depth and angle (θ) together. The result is illustrated in Figure 8. It can be seen that fatigue life increases with decreasing notch angle, considering 45 and 90.

7 Fatigue Analysis of A Notched Cantilever Beam 117 Figure 8. Load-cycle graph for notch angles of 90 and CONCLUSION Fatigue life estimation of a notched structural steel beam is studied. The fatigue analysis is performed using Ansys Workbench fatigue module. Stress life type analysis is used which is based on Stress-Cycle curves. To decide on stress life, various factors are considered: loading type, fatigue damage and sensitivity, fatigue factor of safety and equivalent alternating stress. The maximum damage and the equivalent alternating stress, and minimum factor of safety occurred at the tip of the notch. Two notch angles (45 and 90 ) and various notch depths are considered. Notch sensitivity increased with increasing notch angle. On the other hand, the fatigue life decreased slightly up to a certain notch size (20mm) and considerably after that value. 5. REFERENCES 1. X. B. Lin and R. A. Smith, Finite element modeling of fatigue crack growth of surface cracked plates, Part I: The numerical technique, Engineering Fracture Mechanics 63, , N. S. Köksal and M. Alkan, Stress analysis in AL based composites depending on joining quality, Proc. 1 st Int. Symposium on Computing in Science and Engineering, , Aydın, Turkey, R. Baptista, V. Infante, C. M. Branco, Study of the fatigue behaviour in welded joints of stainless steels treated by weld toe grinding and subjected to salt water corrosion, Int. J Fatigue 30, , A. Cadario, B. Alfredsson, Fretting fatigue crack growth for a spherical indenter with constant and cyclic bulk load, Engineering Fracture Mechanics 72, , A. Carpinteri, R. Brighenti, Part-through cracks in round bars under cyclic combined axial and bending loading, Int. J. Fatigue 18, 33-39, 1996.

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