FINITE ELEMENT MODELING (FEM) FOR EVALUATION OF STRESS ...€¦ · Finite Element Modeling (Fem) For Evaluation Of Stress Intensity Factor For A Crack At An Angle And For V-Notch

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 3, Issue-8, Aug.-2015

Finite Element Modeling (Fem) For Evaluation Of Stress Intensity Factor For A Crack At An Angle And For V-Notch Specimen

164

FINITE ELEMENT MODELING (FEM) FOR EVALUATION OF STRESS INTENSITY FACTOR FOR A CRACK AT AN ANGLE AND

FOR V-NOTCH SPECIMEN

1MAHANTESH S YALAWAR, 2R. A. SAVANUR

1M.Tech student, Department of Mechanical Engineering, BLDEA’S V.P. Dr.P.G.Halakatti College of Engineering and Technology, Vijayapur

2Professor, Department of Mechanical Engineering, BLDEA’S V.P. Dr.P.G.Halakatti College of Engineering and Technology, Vijayapur

Email: [email protected], [email protected] Abstract- The finite element modeling (FEM) for evaluation of stress intensity factor for a ‘crack at an angle’ and for ‘v-notch specimen’ has been investigated in this study, FE modeling is performed through which the behavior of the material is understood at different loads and at different crack length of the specimen. Here stress intensity factor KI and the stress intensity factor KII are determined. The theoretical and ANSYS values are compared with the target solution provided in the NEFMS benchmark problems. The stress intensity factor elegantly the crack characterizer and for mode one, two, three, the stress intensity factor is expressed as KI, KII, and KIII investigation is closer to the crack tip, often implies minute details to understand how elastic materials deform and dislocation behavior. This paper work emphasizes the study of stress intensity factor of ‘crack at an angle’, of a specimen in various loading conditions for different ‘crack angles’ and similarly the study of stress intensity factor for ‘v-notch’ of a specimen in various loading condition under different ‘crack length’ using the target solution is performed. Keywords- Stress intensity factor, loading conditions, crack length, crack angle, Target values. I. INTRODUCTION In these days minute details are focused more to know big things, the crystalline materials as they deform plastically, dislocations are to be understood first, as the diameters of the dislocations are very small they can be viewed in microscope, material under exist with crack front as similar to line, which runs from one region from to the form of another. So crack tip vicinity information with interesting magnitudes of the stress is extremely high component. The wooden stick breaks at the notch by bending. High stress is created through the notch, in turn notch tip easily moved, the displacement field or stress is to be known in the vicinity of crack tip. A designer who is going to modify some of the features as like notch, keyways, cut outs, so as to minimize the stress needs this minute information. An experimentalist measure strain or the stress by characterizing crack, the analysis of stress parameter is defined for crack through stress intensity factor (SIF). There are three modes to enable a crack by applying forces in three ways, 1) Tensile stress 2) shear stress 3) shear stress acting parallel to plane of crack. The stress intensity factor K is directly proportional to the applied load (휎) on the material, that amplifies the magnitude of the applied stress which includes geometrical parameter 휎 (load type).The KI can be empirically determined, for a sharp crack to be made in a material at opening mode. KII can be applied to sliding mode of a crack. KIII is the stress intensity factor at tearing mode of the specimen. Usually mode I play a dominant role in many engineering applications and is considered to be most dangerous. However in certain applications,

components fail through the dominant roles played by mode II or mode III. The finite element modeling (FEM) for evaluation of stress intensity factor for a ‘crack at an angle’ and for ‘v-notch specimen’ has been investigated in this study, FE modeling is performed through which the behavior of the material is understood at different loads and at different crack length of the specimen. Here stress intensity factor KI and the stress intensity factor KII are determined. The theoretical and ANSYS values are compared with the target solution provided in the NEFMS benchmark problems. The stress intensity factor elegantly the crack characterizer and for mode one, two, three, the stress intensity factor is expressed as KI, KII, and KII. As investigation is closer to the crack tip, often implies minute details to understand how elastic materials deform and dislocation behavior. The project work represents the study of stress intensity factor of ‘crack at an angle’, of a specimen in various loading conditions for different ‘crack angles’ and similarly the study of stress intensity factor for ‘v-notch’ of a specimen in various loading conditions under different ‘crack length’ using the target solution is performed. II. METHODOLOGY The evaluation are carried and performed using the ANSYS software 14.5 version, the material property chosen for this evaluation, is structural, linear, elastic, isotropic material. As it a solid material structural mass, in the library of element it was defined as 8 node plane 183 as element type. the material model was defined as linear elastic isotropic material young’s modulus 207 Gpa, as Poisson’s ratio of 0.3,

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 3, Issue-8, Aug.-2015

Finite Element Modeling (Fem) For Evaluation Of Stress Intensity Factor For A Crack At An Angle And For V-Notch Specimen

165

as the angle of the crack 22.5⁰, 67.5⁰, 90⁰ was chosen, the loading for uniform stress was chosen as 100 N/mm², the boundary condition as Uy=0 at line AD and Ux=0 at point D. Using ANSYS the key points are created in active coordinated system, as the coordinates are created as shown in the fig, the key points are joined through the straight lines , these straight lines are further chosen through the no of areas are selected through the commands, as the loading is done through analysis command by activating new analysis command for which an static loading analysis is chosen, further loads are defined as structural, displacement, on lines, on nodes are selected. as pressure of yy=100 N/mm² is chosen, further solution of analysis is carried through, new analysis static. And solution control as automatic time stepping ON is chosen as no of sub steps= 10 and max no of = 100 is chosen. The solution is carried in the current LS, solution is done, as KI and KII are obtained, the stress intensity factors are compared with the target solutions. ANALYSIS SET-UP DETAILS: Crack at angle of a linear elastic isotropic material The material having an element type solid 8 node plane 183 at plane strain condition, as the specimen with 125x100(mm) in size with a Poisson’s ratio 0.3, and young’s modulus 207Gpa, this specimen is analyzed to find the stress intensity factor through finite element modeling. We have chosen the crack angle 훽=22.5⁰, 67.5⁰, 90⁰ are the parameters for which the stress intensity factor is found.

Fig 2.1

Fig.2.1 shows the geometry of the problem and other parameters such as a/b=0.5 h/b=1.25 b=50mm

Table1. MATERIAL DETAILS FOR ‘CRACK AT AN ANGLE

TARGET SOLUTION Finite element method and standards for which the test is recommended by the national agency (U.K) from NAFEMS publications for linear elastic fracture mechanics for 2D test cases

Table2. THE TARGET VALUE OF NORMALIZED SIF

KI = Stress intensity factor at mode 1 KII = Stress intensity factor at mode 2 K₀= Stress intensity factor at crack length ‘a’ Methodology v-notch specimen To find the stress intensity factor or evaluation using the finite element modeling, as the evaluation is carried using the ANSYS 14.5 version, the following material properties has young’s modulus of 207 Gpa and Poisson’s ratio of 0.3, preference of structural and element type is solid 8 node183 and element behavior is plane strain, as in the material properties is chosen as linear elastic isotropic. Further the modeling is carried by choosing key points in active cs mode, the key points are created by updating the locations to be created in X plane and Y plane, as these key points are connected by straight line by choosing line command. After the areas are selected by choosing arbitrary plane by selecting line command, thus the areas are plotted further the crack is generated using the commands, next the meshing procedure in which areas are set by element edge then by selecting all areas further the loads are defined by applying structural, with 100 N/mm² displacement, symmetric boundary conditions on line is carried, likewise the pressure on line is selected, the solution is made with new analysis with static, solution is made thus in plot results, the results are plotted for deformed shape, nodal solution, von misses theory, where compared with theoretical calculations to find the stress intensity factor Test section (v-notch specimen) The v-notch specimen which is made to carry the load on structural displacement on lines as shown in fig below which is carried by selecting the displacement

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 3, Issue-8, Aug.-2015

Finite Element Modeling (Fem) For Evaluation Of Stress Intensity Factor For A Crack At An Angle And For V-Notch Specimen

166

nodes as shown in below, the structural pressure on the lines are selected can see in figure, The specimen with v-notch whose test geometry is modeled for one quarter of the model as shown.

Fig 2.2

Fig.2.2 shows the geometry of the problem and other parameters involved in v-notch specimen is as given below h = length of the specimen, w = width of the specimen a = crack propagation length, 훽 = crack angle A & B = the structural displacement along the line A & B D & C = the structural pressure along the D & C V-notch specimen’s geometry, h = length of the specimen w = width of the specimen, 훽/2 = half the crack angle d = length of the crack a = length of the specimen from crack tip to point were load applied on the line H/w = 1.0 and D/w = 0.1 as per the standard given in the bench mark problem y = uniform stress distribution along the Y direction The mesh for which the one-half the quarter of the test geometry is modeled Table 3. THE TARGET VALUE OF NORMALIZED SIF Finite element method and standards for which the test is recommended by the national agency (U.K) from NAFEMS publications for linear elastic fracture mechanics for 2D test cases

KI= Stress intensity factor for mode 1 K₀= stress intensity factor at crack length ‘a’ III. RESULTS AND DISCUSSION The result for crack at angle and for v-notch specimen with a constant load of 100 N/mm2 with specified crack angle and crack length is discussed.

Fig 3.1

The Fig 3.1 shows deformed results at angle 22.5⁰.The red contour shown in figure shows maximum stress for constant load of 100 N/mm².

Fig 3.2

The Fig 3.2 shows deformed result at angle 67.5⁰.The red contour shown in figure shows maximum stress for constant load of 100 N/mm².

Fig 3.3

The Fig 3.3 shows deformed results at angle 90⁰, the red contour shown in figure shows maximum stress for constant load of 100 N/mm². The SIF for the different loads at different angles are calculated and the same are listed below as a result.

Fig 3.4

The Fig 3.4 shows the deformation results at crack length (a=5mm) and the red contour shown in figure shows maximum stress for constant load of 100 N/mm².

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 3, Issue-8, Aug.-2015

Finite Element Modeling (Fem) For Evaluation Of Stress Intensity Factor For A Crack At An Angle And For V-Notch Specimen

167

Table 4. At load of 100 N/mm² for different crack angle

The above table 5. Gives KI, KII, & K₀ and Normalized SIF for mode1 & mode2 i.e. KI/K₀, KII/K₀ for different angle at the load of 100 N/mm².

Table 5. COMPARISON WITH THE TARGET VALUER AND ERROR

The above table 6.1.8 gives results for both 22.5⁰ & 67.5⁰ angles using ANSYS 14.5 and Theoretical calculations, and also the percentage of error between the two values.

Fig 3.5

The Fig 3.5 shows SIF KI versus crack angle, at the loads of 50, 100, 150 and 200 (N/mm²). The variation of stress intensity factor KI is observed. All the curves are linear in nature up to angle 67.5⁰ and after that the curve tends to be non linear.

Fig 3.6

The Fig 3.6 shows SIF KII versus crack angle, at the loads of 50, 100, 150 and 200 (N/mm²). The variation of stress intensity factor KII is also studied and it is observed that variation is linear for all load condition with negative slope.

Table 6. THE LOAD OF 100N/MM² AT V-NOTCH

The above table7.gives KI, K₀ and Normalized SIF mode1 i.e. KI/K₀ for different crack length at the load of 100N/mm² Table 7. RESULT COMPARISON AND ERROR

The above table 8.Gives theoretical result and ANSYS results for v-notch specimen at crack length a=5mm, and percentage of error.

Fig 3.7

The Fig 3.7 shows SIF KI versus load. The variation of stress intensity factor KI is plotted for different load conditions for different crack length i.e. for 5mm, 10mm, 15mm, & 20mm respectively, and the load is varied for 50, 100, 150 & 200 (Mpa). The graph clearly shows the variation is linear and the stress intensity factor (SIF) increases with an increase in load. CONCLUSION The finite element modeling (FEM) for evaluation of stress intensity factor for a ‘crack at an angle’ and for ‘v-notch specimen’ is successfully performed.The variation of stress intensity factor KI for different load

International Journal of Mechanical And Production Engineering, ISSN: 2320-2092, Volume- 3, Issue-8, Aug.-2015

Finite Element Modeling (Fem) For Evaluation Of Stress Intensity Factor For A Crack At An Angle And For V-Notch Specimen

168

is studied, it is observed that all the curves are linear in nature up to angle 67.5⁰ and after that the curve tends to be non linear. The variation of stress intensity factor KII is also studied and it is observed that variation is linear for all load condition with negative slope. For V-notch the variation of stress intensity factor KI is plotted for different load conditions for different crack length i.e. for 5mm, 10mm, 15mm, & 20mm respectively, and the load is varied for 50, 100, 150 & 200 (Mpa). The graph clearly shows the variation is linear and the stress intensity factor (SIF) increases with an increase in load. REFRENCES

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