FINITE ELEMENT METHOD ANALYSIS OF STRESS INTENSITY FACTOR IN I CHANNEL SECTION

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1 JPE (2016) Vol.19 (1) Pawar, P., Ballav, R., Kumar, A. Preliminary Note FINITE ELEMENT METHOD ANALYSIS OF STRESS INTENSITY FACTOR IN I CHANNEL SECTION Received: 03 March 2016 / Accepted: 18 April 2016 Abstract: In this research, a I channel section containing an semi-elliptical crack has been modeled and investigated using finite element method. The stress intensity factor of mode I and J-Integral have been calculated and analyzed. Key words: Finite element method, Semi elliptical crack, stress intensity factor Analiza faktora intenziteta napona kod i profila metodom konačnih elemenata. U okviru ovog istraživanja je izvršena analiza i modelovanja metodom konačnih elemenata I profila sa polu-eliptičnom pukotinom. Faktor intenziteta napona I i J integrala je izračunat i analiziran. Ključne reči: Metoda konačnih elemenata, Polu eliptična pukotina, faktor intenziteta napona 1. INTRODUCTION Fracture mechanics are often utilized to characterize such failure. For linear elastic materials, it is satisfactory to use Stress Intensity Factor (SIF) to investigate the crack behavior [1]. The stress intensity factor accomplished a highest value near the corner point and then declined to zero at the point is approached [2]. The thickness as well as the initial surface cracks length have a major role on fatigue life up for failure in cyclic loading [3] The stress intensity factor is dependent on elastic-plastic properties of material and fracture toughness [4]. The stress intensity factors were amplified when the values of relative depth of crack ratio amplified [5]. In fracture mechanics, SIF and J-integral is essential in order to calculate the consistency of crack structures. Recently, mode I SIFs has agreed more priority since its effect is considerable compared with other types of SIFs for example mode II and III [6]. J-integral firstly introduced by Rice and it is defined as an arbitrary curve around the crack tip and it is estimated counterclock wise [7]. In this research, the stress intensity factor of mode 1 and J-Intergral has been analyzed using ANSYS with 31 nodes isoparametric threedimensional stainless steel NL solid elements. Crack shape semi elliptical with major radius of 4.e m and minor radius of 4.e m. Circumferential divisions are 8 and mesh contours are METHODOLOGY The Geometric modelling of I channel section was done using ANSYS workbench. Meshing was done by using a tetrahedron type of element in ANSYS mesh tool. Loading and boundary conditions were applied to I channel section to ascertain the critical region or crack zone of I channel section shown in fig.1. Further, crack was introduced in the critical region of I channel section. Semi-elliptical crack geometry in the crack zone for various crack lengths was initiated till stress intensity factor for mode I and J-Integral condition. Fig. 1. FE Model with benchmarking of problem. 103

2 3. BENCHMARKING PROBLEM The assumptions were considered to obtain stress intensity factor solution solved by using a fracture module in ANSYS. The analysis of stainless steel NL solid elements of I channel section specimen having a length of 56.08mm, width of 50mm and thickness of 30mm is conducted on ANSYS. The applied pressure magnitude of 500pa. from top side and bottom side is applied fixed support. The density of material 7750 kg. m -3, Specific heat 80J. kg -1. C -1, Young's Modulus is 1.93E11Pa, Poisson's Ratio is 0.31, and Yield Strength is 2.1E8 Pa. The total numbers of nodes are and elements are Fig. 3. Meshed model of I channel section. 5. TOTAL DEFORMATION The fig. 4. Shows that total deformation obtained with respect to its crack lengths. The maximum total deformation obtained is e -10 m. Fig. 2. Static structure of I channel section. 4. FINITE ELEMENT MODEL Finite element modelling is identified as the analyst s choice of material models, finite elements meshes, constraint equations, pre and post processing options, governing matrix equations and their solution techniques available in a chosen commercial FEA program for the intended analysis [8]. The proposed finite element model involves a fine mesh of isoparametric tetrahedron solid elements. While introducing the crack, the most important region is the region between top and bottom portion I channel section of the crack. Fig. 4. Total deformation of I Channel Section. 104

3 6. STRESS INTENSITY FACTOR The fracture tool is used to calculate the stress intensity factor mode I and J-Integral the following steps are followed 1) Define a local crack front with X-axis parallel to crack face and Y-axis perpendicular to crack face 2) Define crack front divisions and mesh contours 3) Obtain stress intensity factor of mode 1 and J- Integral 7. RESULTS OF STRESS INTENSITY FACTOR MODE 1 The The table 1 shows that values obtained by using ANSYS software. The tabulated values show that stress intensity factor for mode I with their each contour of semi elliptical crack with respect to their length of each cracks. Sr. No Length Stress Intensity Factor mode I er 1 er 2 er 3 er 4 er e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e Table 1. Stress intensity factor mode 1 Various iterations were carried out for different crack lengths and depths and it was found that stress intensity factor for mode 1 is minimum of Pa m 0.5 and maximum at Pa m 0.5 Fig. 5. Profile of the critical crack of SIF mode 1 SIF for J-Integral was evaluated for different crack lengths. The plot below shows the stress intensity factor for J-Integral with their 5 numbers of contour verses length of cracks. Fig.6. SIF for various contours for mode 1 verses crack length 8. RESULTS OF STRESS INTENSITY FACTOR J-INTEGRAL The table 2 shows that values obtained by using ANSYS software. The tabulated values show that stress intensity factor for J-Integral with their each contour of semi-elliptical crack with respect to their length of each cracks. 105

4 Sr. No. Length er 1 Stress Intensity Factor J-Integral er 2 er 3 er e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e Table 2. Stress intensity factor J-Integral Cou nter Various iterations were carried out for different crack lengths and depths and it was found that stress intensity factor for J-Integral is minimum at e -8 J/m² and maximum at e -8 J/m². Various iterations were carried out for different crack Fig. 7. Profile of the critical crack of SIF J-Integral SIF for J-Integral was evaluated for different crack lengths. The plot below shows the stress intensity factor for J-Integral with their 5 numbers of contour verses length of cracks Fig. 8. SIF for various contours for J-Integrals verses crack length 106

5 9. CONCLUSION 1) Static stress analysis for the operating conditions on was performed. Crack zone in the I channel section was identified middle of section of the channel, maximum stress of 500MPa occurred in this region. 2) The stress intensity factor (SIF) is found to have the maximum value of the middle part of the channel. 3) Stress intensity factor for mode 1 is minimum of Pa m 0.5 and maximum of Pa m 0.5 4) It is found that the stress intensity factor for J- Integral minimum of e -8 J/m² and maximum of e -8 J/m². 10. REFERENCES Authors: Mr. Pravin Pawar, Ph.D. Research Scholar, Manufacturing Engineering Department, National Institute of Technology, Jamshedpur, Jharkhand, India, Phone.: Dr. Raj Ballav, Associate Professor, Manufacturing Engineering Department, National Institute of Technology, Jamshedpur, Jharkhand, India, Phone.: Dr. Amaresh Kumar, Head of Department and Associate Professor, Manufacturing Engineering Department, National Institute of Technology, Jamshedpur, Jharkhand, India, Phone.: rsprod004@nitjsr.ac.in rballav.prod@nitjsr.ac.in akumar.prod@nitjsr.ac.in [1] Ismail, A.E., Ariffin, A.K., Abdullah, S. and Ghazali, M.J.: J-Integral Evaluation of Surface Cracks in Round Bar under Mode III Loadings, Research Journal of Applied Sciences, Engineering and Technology, 7(10), pp , [2] Hayashi, K., Abe, H.: Stress intensity factors for a semi-ellip surface of a semi-infinite solid, International journal of fracture. Vol.16, No.-3, 1980, pp [3] Boljanovic, S.: Fatigue Strength Analysis of a Semi-Elliptical Surface Crack, Scientific Technical Review, Vol.62,No.1, pp.10-16, 2012 [4] Sharma, R.K., Shrivastava, S.K., Dixit, P.M., Basu, S.: On the problem of an axial semielliptical crack in a hollow ductile cylinder, International journal of fracture, 140, pp , [5] Nami, M.R., and Eskandari, H.: Stress Intensity Factors in a Rotating Impeller Containing Semi- Elliptical Surface Crack, Mechanics Based Design of Structures and Machines: An International Journal, 40: 1 18, 2012 [6] Raju, I.S., and Newman, J.C.: Stress-intensity factor for internal and external surface cracks in cylindrical vessels, Int. J. Pressure Vessels Technol., 104, pp , [7] Rice, J.R.: A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35, pp , [8] Sharma, R.S., Ranganath, B., Vikyath Monnappa, B.M., Vinay Sagar, N.B.: Evaluation of Stress Intensity Factor and fatigue life for Mixed-Mode crack propagation in Drive Shaft of an All-Terrain Vehicle, International Journal of Engineering Research & Technology, Vol. 2, Issue 11, ACKNOWLEDGEMENT The author would like to acknowledge the financial support from the TEQIP II and Department of Manufacturing Engineering, National Institute of Technology, Jamshedpur, India. Author would also like to acknowledge the continous motivational support from Dr. Raj Ballav and Dr. Amaresh Kumar. 107