EVAPRED A CODE FOR FATIGUE ANALYSIS OPTIMIZATION

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1 EVAPRED A CODE FOR FATIGUE ANALYSIS OPTIMIZATION Dorin LOZICI-BRÎNZEI, INCAS, lozicid@incas.ro Simion TǍTARU, INCAS, sitataru@incas.ro DOI: / Abstract The fatigue can be, in fact, defined as: failure under a repeated or otherwise varying load, which never reaches a level sufficient to cause failure in a single application. Physical testing is clearly unrealistic for every design component. In most applications, fatigue-safe life design requires the prediction of the component fatigue life that accounts for predicted service loads and materials. The primary tool for both understanding and being able to predict and avoid fatigue has proven to be the finite element analysis (FEA). Computer-aided engineering (CAE) programs use three major methods to determine the total fatigue life: Stress life (SN), Strain life (EN) and Fracture Mechanics (FM). FEA can predict stress concentration areas and can help design engineers to predict how long their designs are likely to last before experiencing the onset of fatigue. Introduction The elementary steps in the Fatigue Analysis and Damage Tolerance Evaluation are: Define the aircraft usage (Aircraft Missions) Develop global load spectra Select critical locations for each Principal Structural Elements (PSE) Develop load spectra for each PSE Calculate nominal stress levels for PSE s and local stress levels at critical locations Calculate fatigue life and Margin of Safety A most relevant question which arises now is, how well are we equipped with knowledge and tools to deal with all steps above? Predictions on fatigue properties are part of design studies. If S-N data are available the Miner rule may be adopted to calculate the fatigue life under spectrum loading. It may then be concluded that fatigue tests are necessary. Aircraft missions Figure 1 shows mission profile and stress distribution for military aircraft IAR

2 Figure 1. Mission profile and stress distribution Figure 2 shows mission profile and stress distribution for civil aircrafts. Figure 2. EXCEL spreadsheet determining Mission profile Figure 3 shows associated load spectrum examples. Figure 3. EXCEL spreadsheet determining load spectrum [1] 30

3 Material properties tool From basic mechanics, the following equations are valid in the elastic range. The strain Ramberg-Osgood equations are as follows, [2]: (1) The stress-modulus equations [2] are shown below. These reduced moduli correspond to slopes that are graphically illustrated in Figure 4, for axial loading. (2) Figure 4. EXCEL spreadsheet determining material properties 31

4 FEM analysis Finite element models can be constructed to perform two distinct types of analysis - Structural analysis and stress analysis. Structural analysis is performed to ascertain the distribution of forces occurring within a structure, and usually involves relatively coarse models of entire airframe structures. Stress analysis is performed to determine the distribution of stress within a component, and usually involves relatively detailed models of airframe sub components. Figure 5. IAR-99 - CAD (coarse model) Figure 6. IAR-99 - CAE (coarse model) 32

5 Users of the finite element technique should be aware that a finite element analysis represents a numerical approximation to the solution of problems not generally amenable to a closed form solution. Figure 7. Geometry FEM (detailed model) The principal normal stresses and, maximum shear stress and the angle of the principal axis can be determined from the applied stresses (fx, fy and fs ) using the following equations, [3], [4]: (3) The effective stress for von Mises is expressed as: (4) Figure 8. FEM Results (example) 33

6 Fatigue life calculation, for designers, using SN method Constant and variable amplitude loading may be considered in calculating fatigue life. The following offers a brief description of the differing results. By using an SN curve, designers can calculate the number of such cycles leading quickly to component failure. However, in cases where the component is subjected to more than one load cases, the Miner s Rule provides a way to calculate the damage of each load case and combine all of them to obtain a total damage value. The result, or Damage (D), is expressed as a fraction of the failure. Component failure occurs when D = 1.0, so, if D = 0.85 then 85% of the component s life has been consumed. This theory also assumes that the damage caused by a stress cycle is independent of where it occurs in the load history, and that the rate of damage accumulation is independent of the stress level. Figure 9. SN curve for material 7075-T6 [2] (5) 34

7 Figure 10. Materials and fatigue coefficients database Figure 11. EXCEL spreadsheet determining SN curve 35

8 The Palmgren-Miner linear cumulative damage rule It assumes that the total life of a part (PSE) may be estimated by simply adding up the percentage of life consumed by each stress cycle. Thus, if a specimen, stressed at ΔS1, has a life of N1 cycles, the damage after n1 cycles at ΔS1 will be n1/n1 of the total damage, D, at failure. Figure 12. EXCEL spreadsheet determining damage D Conclusions The tools and approaches discussed in this review can help designers to improve component safety while reducing over-engineered, heavy, and costly designs. FEA provides excellent tools for studying fatigue with the SN approach, because the input consists of a linear elastic stress field, and FEA enables consideration of the possible interactions of multiple load cases. Because of its ease of implementation and the large amounts of available material data, the most commonly used method is SN. By making use of today s technology to avoid fatigue, catastrophes can often be prevented. REFERENCES [1.] ***, CS-23 Certification Specifications for Normal, Utility, Aerobatic, and Commuter Category Aero planes, 14 Nov [2.] ***, MIL HDBK 5J, Metallic Materials and Elements for Aerospace Vehicle Structures [3.] BRUHN., E. F., Analysis and Design of Flight Vehicle Structures, June [4.] NIU, M. CHUN YOUNG, Airframe Stress Analysis and Sizing, Conmilet Press Ltd, [5.] R.J.ROARK, W.C.YOUNG, Formulas for Stress & Strains, MCGRAW-HILL International, 1989 [6.] PETRE A, Calculul structurilor de aviatie, Editura Tehnica Bucuresti, 1984 [7.] VASILIEV G., GIURGIUTIU V., Stabilitatea structurilor aeronautice, Editura Tehnica Bucuresti, 1990 [8.] PETERSON, R.E., Stress Concentration Factors, John Wiley & Sons, 1974 [9.] TATARU S, STERE M., LOZICI D., EVAPRED., INCAS,