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IJREAT International Journal of Research in Engineering & Advanced Technology, Volume 4, Issue 2, April - May, 2016 ISSN: 2320 – 8791 (Impact Factor: 2.317) www.ijreat.org Computation Of Stress Intensity Factor For Dynamic Load To Predict Failure Of Mechanical Components Sarvjeet Roy1, Jagabandhu Shit2 P.G. Student, Department of Mechanical Engineering, Jalpaiguri Govement Engineering College, West Bengal, India1 Associate Professor, Department of Mechanical Engineering, Jalpaiguri Government Engineering College, West Bengal, India2

Abstract: The failure of crack components is governed by the stresses in the vicinity of the crack tip and thereby the Critical Stress Intensity Factor (K1C). The stress intensity factor depends on the geometry of the component, crack size and on loading conditions. This study is to determine stress intensity factor for a crack occurred in a connecting rod subjected to cyclic loading through ANSYS 14.5. For this, the stress intensity factor of an infinite flat plate with 2-D edge crack is theoretically calculated and compared with the Finite Element Analysis using ANSYS 14.5 software. Hence the procedure has developed to analyze SIF to find in any complicated geometry.

Keywords: Critical Stress Intensity Factor (K1C), FE Analysis, ANSYS 14.5 1. Introduction Fracture mechanics is the field of mechanics concerned with the study of the propagation of cracks in materials. It uses methods of analytical solid mechanics to calculate the driving force on a crack and those of experimental solid mechanics to characterize the material's resistance to fracture. Fracture occurs when the available energy for crack growth is sufficient to overcome the resistance of the material, which may include the surface energy, plastic work, or other types of energy dissipation associated with a propagating crack [1]. Computation of SIF is another approach to predict failure. The critical stress intensity factor which is a material property is limit on SIF, if the SIF exceeds the critical stress intensity factor, the crack may grow. For various structural components, which are subjected to impact loadings ranging from aircrafts etc the Dynamic Stress Intensity Factor (DSIF) is an important parameter. The parameter helps in understanding and predicting the dynamic fracture behaviour of these components. Apart from numerical modelling, number of theoretical and experimental investigations on DSIF has been www.ijreat.org Published by: PIONEER RESEARCH & DEVELOPMENT GROUP (www.prdg.org) 77 IJREAT International Journal of Research in Engineering & Advanced Technology, Volume 4, Issue 2, April - May, 2016 ISSN: 2320 – 8791 (Impact Factor: 2.317) www.ijreat.org carried out with specimens like cracked beam or plate with various loading geometries and end- fixity conditions [2-6]. From the literature it has also been observed that impact fatigue tests [7], where DSIF plays a vital role, often used three-point bend configuration. Nikam. M. D et. Al. [8] Gopichand. A et al. [9], studied for determination of Stress Intensity Factor (SIF) for cracked component using Finite Element Analysis (FEM). The present numerical analysis aims to address SIF for 3-D crack modelling on connecting rod in a quantitative manner using finite element method. The analysis has been supported by impact experiments on a short, cracked alumina beam. Transient dynamic analysis with a finite element model was used. 1. Stress Intensity Factor (SIF) & Dynamic Stress Intensity Factor (DSIF) One of the parameter in the fracture problem is available to measure crack effectiveness or crack extension force is Stress Intensity Factor (SIF). It is applicable only for Linear Elastic Fracture Mechanics (LEFM) and the analysis account for small scale plastic deformation close to the crack tip. Stress Intensity Factor (SIF) is simpler in contrast to strain Energy Release Rate, and easier for laboratory measurements. If the components subjected to dynamic or time–dependent loading, stress intensity factor under such dynamic loading is the Dynamic stress intensity factor (DSIF). The specimen was subjected to impact loading with a swinging pendulum, the calculated stress intensity factor varied with time and reached a peak value and then decreased as the force rises to certain peak value and falls down within a short interval of time. As during the time span the crack was not propagating and hence the dynamic stress intensity factor (DSIF) can be termed as dynamic stress intensity factor for a non propagating crack

2. Failure Modes of Fracture

For a plate having a through-thickness crack, the loading on the crack is typically described as one of three types, or modes as proposed by Irwin & shown in Figure 1. In the mode I or opening mode, the body or structure is loaded by tensile forces such that the crack surfaces are pulled apart in the y direction. The deformed surfaces are symmetric with respect to the planes perpendicular to the y-axis and the z-axis.

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Figure 1: Crack Opening Modes

Finally, in the mode III or tearing mode, the body or structure is loaded by shear forces parallel to the crack front and the crack surfaces slide over each other in the z-direction. The deformed surfaces are skew-symmetric with respect to the plane perpendicular to the z-axis and the y-axis. K is designated by the mode of loading, such as KI, KII, and KIII The cracks, with radius of curvatures approaching zero at the crack tip, causes stress fields that approach infinity proportional to the reciprocal of the square root of the distance from the crack tip [10]. 3. Mathematical Calculation of Stress Intensity Factor (SIF)

A sample under plane stress conditions, which typically occurs in thin plates, has a highly variable

K1C value whereas, a thick sample under plane strain conditions, has a constant value for K1C. Part of Irwin’s revisions of Griffith’s equations was to rewrite the strain energy density in terms of stress because a value for stress is much easier to obtain than a value for strain energy. The

resulting equation is: K = β 𝜎f √Пa

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It has unit MPa√� �, where β is a geometry factor, σf is the stress at failure and unit is MPa, and a is the crack length. Values for β have been determined from equations empirically fitted to the results of numerous fracture tests of varying geometry conducted under constant loading conditions. The equations for different geometries can be found in fracture handbooks. The stress intensity experienced by a material is dependent on the loading conditions, crack geometry and the crack size.

4. Experimental Procedure

The load cell, which is holding in a fixed position of the impact fatigue-testing machine where the ceramics samples (Figure 4) are held for fatigue testing. One end of the load cell probe is connected to the load cell and other end to the data acquisition card. The line sketch of experimental set up is shown in Figure 2. The output from data acquisition card is taken to the computer where OROS has been installed. The spherical ball, which will strike the load cell, is attached at the end of the swing pendulum (Figure 3) of the machine. The angle of released of the pendulum from its equilibrium position is determined by the size of the cam. Changing the size of the cams and the diameter of the balls the no of variations can be obtained. As the pendulum strikes the load cell the output signal is captured with the help of the OROS software. Changing the size of the cams and the diameter of the balls the no of signals have been captured. The output signals are looking like sin wave, which are the plots of ms vs. mv. Where ms and mV are indicating time and impact force respectively. At particular time the reading in terms of mv is taken with the help of crusher. The readings in terms of mv, converted to force in Newton as per conversation chart, supplied by the OROS developer. Changing the size of the balls and size of the cams the various plots are obtained. Error: Reference source not found

Figure 2 : line sketch of experimental set up.

Figure 3: Swing pendulum. Figure 4: Ceramic sample.

Where m is the mass of the ball attached with the pendulum is being released at an angle of θ as shown in the figure varies as 150, 200and 250 etc.

Considering m= 0.372 kg and θ = 150 the force Vs time plots are shown in the Figure: 5

Considering m= 0.372 kg and θ = 150 and varying the crack dimension the DSIF Vs time plot is shown in the Figure: 7 and corresponding data are shown in the Table:1.

a) For ball of mass m= 0.372 kg.

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0 5 0 1 0 0 1 5 0 2 0 0 m s

Figure 5 : Force (mV) Vs Time (ms) curve at an angle of release 150.

Force Vs Time

16 7.14, 14.603 14 4406 12

) 10 17.85, 8.896 N

( 1.78, 8.8964

e 8 4 c r

o 6 F 4 2 0 0, 0 35.71, 0 0 10 20 30 40 Time(ms)

Figure 6 : Derived Force (N) Vs Time (ms) curve at an angle of release 150.

5. Dynamic Stress Intensity Vs Time Plots

A) FOR BALL OF MASS M = 0.372KG

D.S.I.F vs Time

1 0.9 0.8 )

r a(.123mm)

e 0.7 t

e a(.128mm)

t a(.135mm) o

o 0.5 r

a(.356mm) a

P 0.4 a(.485mm) M (

F 0.3 I a(.662mm) S

D 0.2 0.1 0 0 10 20 30 40 Time (ms)

Figure 7 : Dynamic stress intensity Vs Time curve at angle of release 150 for different crack length (a: crack length in mm)

Table1:

FOR BALL OF MASS M = .372KG . Angle DSIF at DSIFat of TIME a= DSIFat DSIFat DSIFat DSIFat FORCE (N) a=.662m release (ms) a=.128mm a=.135mm a=.356mm a=.485mm m 15deg 0.123mm 0 0 0 0 0 0 0 0 0.573571 1.78 8.8964 0.10657 0.111345 0.11612 0.3084465 0.42021504 9 0.939178 15deg 7.14 14.6034406 0.1745 0.18235 0.1902 0.50505691 0.68806911 9 17.85 8.8964 0.1055 0.11026 0.11502 0.30534959 0.41599593 0.567813 0.004429 35.71 0 0.000823 0.0008625 0.000902 0.00238202 0.00324516 5

6. Various Stress Pattern

a) For ball of mass m =0. 372kg

Figure 8: Stress pattern in ‘Y’ direction at peak load of 14.603 N at corresponding time of 7.14 ms. and crack length of the specimen 0.123mm

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Figure 10 : Stress pattern in ‘Y’ direction at peak load of 14.603 N at corresponding time of 7.14 ms. and crack length of the specimen 0.128mm

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7. Discussion: Figure 6: show that with the increase of time the impact force is increasing and reaches to maximum value, after that with the increase of time the impact force is decreasing and reaches to zero value. It can also be shown that the magnitude of the impact force will increase with the increase of angle of release of the bob. From the above stress patterns shown in Figure 8, 9, 10, 11 it is observed that for a particular load, with the increase of crack length the magnitude of compressive stress at the point of application of load is decreasing where as the magnitude of the tensile stress is decreasing with the increase of crack length. Experiment to capture p-t curve: in this experiment we have captured p-t curve (due to impact loading) with the help of “OROS” software. From the figure of the p-t curve it is found that with the increase of time the impact force is increasing and reaches to maximum value, after that with the increase of time the impact force is decreasing and reaches to zero value. The load is obtained from p-t curve at different times are put in ANSYS program to find the DSIFs of the stationary cracked sample Assuming plain strain condition, ramped loading condition and analysis type (i.e. transient dynamic analysis), the ANSYS program, which will simulate our actual model, is written and putting the experimentally obtained p-t curve in the program, the DSIF of the samples is determined. From the Figure 7 & Table 1 of the DSIF it has been found that for a particular crack dimension dynamic stress intensity factor (DSIF) is increasing with the increase of load. Figures also indicate that the magnitude of DSIF is increasing with the increase of crack dimension. From the stress patterns it is observed that for a particular load, with the increase of crack length the magnitude of compressive stress at the point of application of load is decreasing where as the magnitude of the tensile stress is decreasing with the increase of crack length.

Variation of stress intensity factor can be shown in Table 2 below. Here both values of Stress intensity factor (i.e.,Analytical and Computational) are compared.

“Table 2. Comparison of Theoretical and APDL SIF result (at 0.372Kg,14.603N) in edge crack

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Theoretical stress intensity factor for edge crack in a ceramic aluminium plate is compared & analysed with Ansys APDL values. It has been observed from the Table 2 that numerical values closely follow the theoretical values. It has also been observed that with the increase of crack length the values of SIF also increase. This stress intensity factor is compared with critical stress intensity factor (K1C) to determine whether crack will propagate or not.

As finding out the stress intensity factor for 3-D component is difficult as because of complicated geometry so we can approach for numerical analysis as discussed earlier. As sample case study we have taken Connecting rod which is a part of the engine subjected to millions of repetitive cyclic loadings, for estimation stress intensity factor of cracked 3-D component and same procedure has been followed.

Connecting rod is made by steel is designed using CATIA V5. Semi elliptical crack is formed in the connecting rod. Meshing is done using ANSYS 14.5 and Stress intensity factor of Cracked Connecting rod is determined using ANSYS software.

Figure 12 and Figure 13 shows the Connecting rod mesh view and Crack meshing of connecting rod (close view) respectively. Figure 14 shows the stress pattern at force of 10N and corresponding stress intensity factor is also calculated as shown in the Figure 15. Figure 16 shows the close view of elliptical crack. This stress intensity factor is compared with the critical SIF to determine whether crack will propagate or not.

Figure 12: Connecting rod mesh view

Figure13: Crack meshing of connecting rod (close view)

Figure14: Equivalent stress pattern at load 10N

Figure15: Stress Intensity Factor calculation

Figure16: Close view of elliptical crack

8. Conclusion:

Numerical value of stress intensity factor has been checked with the analytical value of stress intensity factor for very simple crack geometry and found that result closely matches with each other. This idea can be applied for any complicated cracked geometry where theoretical values could not be obtained to predict failure/fracture of the mechanical components.

www.ijreat.org Published by: PIONEER RESEARCH & DEVELOPMENT GROUP (www.prdg.org) 90 IJREAT International Journal of Research in Engineering & Advanced Technology, Volume 4, Issue 2, April - May, 2016 ISSN: 2320 – 8791 (Impact Factor: 2.317) www.ijreat.org 9. References:

[1] E. Dieter George, A text book of Mechanical Metallurgy.

[2] Enderlein, M., Ricoeur, A.,Kuna, M.: Comparison of finite element technique for 2D and 3D crack analysis under impact loading. International Journal of Solids and Structures. 40(13-14), 3425 3437(2004).

[3] Isida M.: Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions. International Journal of fracture. 7, 301 316 (1971).

[4] John R.: Stress intensity factor and compliance solutions for eccentrically loaded single crack geometry. Engineering Fracture Mechanics. 58, 87 96, (1997).

[5] John R. and Rigling B.: Effect of height to width ratio on K and CMOD solutions for a single edge cracked geometry with clamped ends. Engineering Fracture Mechanics. 60, 147 156 (1998).

[6] Kishimoto K., Aoki S. Sakata M.: Dynamic stress intensity factors using J-integral and finite element method. Engineering Fracture Mechanics. 13(2), 387 394 (1980).

[7] Maity S. Sarkar B.K: Impact fatigue of porcelain ceramic. International Journal of Fatigue. 17(2), 107 109 (1995).

[8] Nikam M. D., Patil G. V., Thokal G. N., Khatawate V. H. : Estimation of Stress Intensity Factor (SIF) on crack component by using Finite Element Analysis. International Journal of Mechanical Engineering and Technology (IJMET). Volume 5, Issue 1, January (2014), pp. 98-107

[9] Gopichand A., Srinivas Y., . Sharma A. V. N. L, Computation of Stress Intensity Factor of Brass plate with edge crack using J-Integral technique. International Journal of Research in Engineering and Technology. Volume: 01 Issue: 03,| Nov-(2012) pp. 261-266.

[10] E. Byskov, “The Calculation of Stress Intensity Factors Using the Finite Element Method with Cracked Elements,” International Journal of Fracture Mechanics,vol. 26.4, pp. 329-337, 1984.

Note: I would like to request for colour printing in my final paper.

Biographical notes

1. Sri Sarvjeet Roy is a Post Graduate student of Mechanical Engineering of Jalpaiguri Government Engineering College, West Bengal. He has completed his B.E in Mechanical Engineering from EWIT, Bangalore in 2013. He is very much sincere and entirely devotes himself for this work.

2. Dr. Jagabandhu Shit is an Associate Professor of Mechanical Engineering at Jalpaiguri Govt. Engg. College, West Bengal. He is engaged in teaching and research activities since the last 10 years. His field of specialization is Fatigue, Fracture and Damage Analysis of structure. He has published several papers in various national, international journals, conferences and. He has completed his PG from Mechanical Engineering Department Jadavpur University.

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