Analysis of Stress Concentration Effect around Countersunk Hole in Composite Plate under Transvers Loading

Investigation of Stress Concentration Effect in Composite Plates with Countersunk Holes

by B. B. Farande*, V. V. Kulkarni,

- Published in Journal of Advances in Science and Technology, E-ISSN: 2230-9659

Volume 12, Issue No. 25, Dec 2016, Pages 559 - 563 (5)

Published by: Ignited Minds Journals


ABSTRACT

Stress concentration around countersunk hole is an important problem for mechanical engineering, used in various engineering applications. Abrupt change in geometry of component is known as stress concentration. The stress concentration around hole in different plate sizes and changes in hole with different loading conditions using FEA to reduce the need and expenditure of experimental testing by developing procedures that allow the use of FEA to simulate experimental stress test For comparison purposes, a structure having similar identical geometry and material properties are used. The FEA results and experimental results are compared and discussed with respect to different loads. And stress concentration is determined under tensile loading by using universal testing machine and strain indicator. The investigations are carried out by varying the tensile load and diameter of the hole. This paper includes mathematical analysis for calculating average strain from which stress is calculated for each specimen according to applied conditions. The calculated parameters such as stress concentration factor, stress, nominal stress are also graphically represented to get summary of the result.

KEYWORD

stress concentration, countersunk hole, composite plate, transvers loading, mechanical engineering, geometry, component, plate sizes, loading conditions, FEA, experimental testing, simulated stress test, comparison, geometry, material properties, FEA results, experimental results, loads, tensile loading, universal testing machine, strain indicator, tensile load, diameter, mathematical analysis, average strain, applied conditions, stress concentration factor, nominal stress, graphical representation

INTRODUCTION

The use of composites is increasing in engineering industrial application, because of their high strength to weight ratio, high stiffness, low density and long fatigue life. As the application of composite to commercial product has increased, so the need for design aspects for structural components increased. The mechanical joint is the best choice for detachable assembly of components in structures and machines to maintain integrity in fastened structure. The prime reason behind selection of mechanical joints is due to their high reliability, strong load bearing capacity, easy maintenance and inspection at low cost. The mechanical joints with countersunk holes are preferred for flush joint rather than lap joint as they offer good aesthetic with high strength. Countersunk hole when applied in composite plate generate stress concentration and need to be analyzed. So it is necessary to analyze the deflection, stresses and stress concentration factors for design of plates with countersunk joints under different loadings. The plates with discontinuities like circular or elliptic holes exist in all metal structure. Those areas represented dangerous zones because of the multiplication of the stresses values under the effect of the stress concentration phenomenon. So stress concentration zones are often areas of crack initiation. The loading conditions allow the brutal propagation of the cracks and then promote the rupture. Stress concentration arises from any abrupt changes in geometry of plate under loading. Stress distribution is not uniform throughout the cross section. Failure such as fatigue cracking and plastic deformation frequently occur at point of stress concentration. Hence for the design point of view the plate with different hole shapes plays an important role and accurate knowledge of stress. For the study detailed literature review is conducted. Parveen K. Saini, (2014) investigated the stress concentration around countersunk hole in isotropic plate under transverse loading. The investigation of the effect of countersunk depth, plate thickness, countersunk angle and plate width on the stress concentration around countersunk hole is carried out with the help of finite element analysis. Hardik Acharya, (2014) investigated the stress reduction using semi elliptical slots in axially loaded plate having circular hole. The work is related to study the effect of semi-elliptical slot on each side of the hole and the maximum stress induced in a

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ANSYS. Dharmendra S. Sharma (2011) investigated the stress concentration around circular /elliptical /triangular cutouts in infinite composite plate general stress functions for determining the stress concentration around circular, elliptical and triangular cutouts in laminated composite infinite plate subjected to arbitrary biaxial loading at infinity are obtained using Muskhelishvili‘s complex variable method. Mohammed Diany (2013) investigated the effects of the position and the inclination of the hole in thin plate on the stress concentration factor, The stress concentration factors are widely used to predict the maximum stress value above which the mechanical structure can be destroyed. Lotfi Toubal (2005) investigated the stress concentration in a circular hole in composite plate, A non-contact measurement method, namely electronic speckle pattern interferometer (ESPI), was used to investigate the tensile strain field of a composites plate in the presence of stress concentrations caused by a geometrical defect consisting of circular hole. C. K. Cheung (2000) investigated the composite strips with a circular stress concentration under tension. A series of tensile experiments were performed on S2 glass/toughened epoxy composite strips with a center hole or a pin joint at various temperatures within the range of −60oC and 125oC. J. Rezaeepazhand , M. Jafari (2008) investigated the stress analysis of composite plates with non-circular cutout. The high stress concentration at the edge of a non-circular shaped cutout is of practical importance in designing of the engineering structures. Moon Banerjee (2013) investigated stress concentration in isotropic & orthotropic composite plates with center circular hole subjected to transverse static load. Nitin Kumar Jain (2009) investigated analysis of stress concentration and deflection in isotropic and orthotropic rectangular plates with central circular hole under transverse static loading. The effect of D/A ratio (where D is hole diameter and A is plate width) upon stress concentration factor (SCF) and deflection in isotropic and orthotropic plates under transverse static loading was analyzed. Patel Dharmin (2012) investigated a review on stress analysis of an infinite plate with cut-outs, in this paper an effort is made to review the investigations that have been made on the stress analysis of an infinite plate with cut-outs. From the literature review it is found that majority of research is concerned with the stress concentration in circular hole with isotropic material plate but only few studies are reported in composite plate and there is scope in studying the stress concentration around the countersunk hole in composite plates.

2. PROBLEM DEFINITION

We have considered the hex dominant method for element having size 7.8 mm throughout the FFA analysis for all specimens. Figure 2.5 states that we get desirable results for optimum element size with dimension 7.8 mm. It is to be noted that by decreasing specimens the element size is preferred to be 7.8 mm.

3. EXPERIMENTAL AND FEA WORK

3.1 Dimensions of Specimen: Carbon epoxy plate was selected to conduct experiment to calculate stress concentration around countersunk hole. Plate size was selected as per the ISO 527 or NF T57-301 standard. Countersunk hole was drilled on rectangular plate. The dimensions of the specimen are represented in figure 3.1.

Figure 3.1 Work specimen.

Different dimensions of the specimen are shown in table no. 3.1 such as length, width, thickness, diameter etc. It is to be noted that diameter value is incremented from 4 mm to 6 mm and all other parameters are kept constant.

Tabl 3.1 Dimensions of Specimen

Where, l = Length of the plate (mm) w = width of plate (mm) t = thickness of plate (mm) d = Straight shank hole diameters (mm)

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Өc = Angle of countersunk hole

3.2 Model

Meshing option helps to select number of elements in which model is to be subdivided and selection of meshing type depending upon accuracy required. The solid model is imported into ANSYS Workbench for analysis. The material of the model is carbon epoxy. Formulation of elements in Finite element analysis is an important factor that can influence the simulation results considerably. All the types of plate with countersunk hole are meshed using Hex Dominant method with Quad/ tri mesh type having mesh size 7.8 mm with fine relevance as shown in Figure 3.2.

Fig. 3.2 Meshing of Solid Model

3.3 Mesh Refinement

We have considered the hex dominant method for element having size 7.8 mm throughout the FFA analysis for all specimens. Figure 3.3 states that we get desirable results for optimum element size with dimension 7.8 mm. It is to be noted that by decreasing size of the element we get proper results but it consumes much times for processing. Hence in all specimens the element size is preferred to be 7.8 mm.

Fig. 3.3 Mesh Refinement. Material properties of Carbon epoxy plate (LY-556 & HY-951) used are shown in Table 3.2. Table 3.2 Material properties of carbon epoxy plate.

4. ANALYTICAL APPROACH

Calculate stress concentration in Composite plates with countersunk holes subjected to UDL.

Mathematical Calculations,

Formulae‘s for stress concentration around countersunk hole,

Modulus of elasticity = The nominal stress in the plate is,

Where, P = Tensile load (N). w = Width of the plate (mm). d = Diameter of the hole (mm). t = Thickness of the plate (mm) Stress concentration factor Kt is, Sample calculation for first specimen, w = 25 mm , l = 230 mm, t = 15 mm, d = 4 mm, Cs =5 mm, Өc =45°, E = 270000 MPa etc. Kt = ? Here,

Modulus of elasticity =

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Max. Stress = 270000 x 0.00006218 Max. Stress (ζmax) = 16.39 N/mm2 Then, = = 15.87 N/mm2 So, Kt =

= = 1.032

Stress concentration factor for first specimen = 1.032.

5. COMPARISON EXPERIMENTAL RESULTS WITH FEA RESULTS

The value of Kt in FEA and Experiment for specimen 1, 2 and 3 with load 5000N, 7500N and 10000N is shown in table no. 5.1, 5.2 and 5.3 respectively. The graph consist variation in Kt factor according to diameter of the specimen is shown in figure 5.1, 5.2 and 5.3.

Table 5.1 FEA and Experimental Results For 5000 N Load.

Fig. 5.1 Diameter Vs Kt For 5000N

increases, for load 5000N for both FEA results and Experimental results.

Table 5.2 FEA and Experimental Results For 7500 N Load. Fig.5.2 Diameter Vs Kt For 7500N

From the graph of diameter Vs Kt for 7500N, it is concluded that as diameter increases value of Kt also increases, for load 7500N for both FEA results and Experimental results.

Table 5.3 FEA and Experimental Results For 10000 N Load. Fig 5.3 Diameter Vs Kt for 10000N

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concluded that as diameter increases value of Kt also increases, for load 10000N for both FEA results and Experimental results.

CONCLUSION

It is concluded that as the stress concentration increases as the diameter increase. The stress concentration factor varies in the same fashion for the three loads. The FEA results and experimental results are compared and discussed with respect to different loads ranging from 5000N to 10000N.

REFERENCES

Lotfi Toubal, Moussa Karama, Bernard Lorrain, Stress concentration in a circular hole in composite plate, Composite Structures, Vol.68, 2005 , 31–36. C. K. Cheung, B. M. Liaw and F. Delale,B. B. Raju, Composite strips with a circular stress concentration under tension, International conference, U.S. Army research center, Michigan. 2000. J. Rezaeepazhand, M. Jafari, Stress Analysis of Composite Plates with Non-circular Cutout, Key Engineering Materials Vol. 2, 2008, 365-368. Nitin Kumar Jain, Analysis of Stress Concentration and Deflection in Isotropic and Orthotropic Rectangular Plates with Central Circular Hole under Transverse Static Loading, World Academy of Science, Engineering and Technology, Vol.3 2009, 12-22. Patel Dharmin, Panchal Khushbu, Jadav Chetan, A Review on Stress Analysis of an Infinite Plate with Cut-outs, International Journal of Scientific and Research Publications, Vol. 2, November 2012. Parveen K. Saini, Tarun Agarwal , Stress Concentration around Countersunk Hole in Isotropic Plate under Transverse Loading, World Academy of Science, Engineering and Technology, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, Vol.8, 2014, 1967- 1973. Hardik Acharya, Stress reduction using semi elliptical slots in axially loaded plate having circular hole, International Journal of Mechanical Engineering and Technology, Vol. 5, September 2014, 374-378. Circular/Elliptical/ Triangular Cutouts in Infinite Composite Plate, Proceedings of the World Congress on Engineering, London , U.K, Vol. 3, 2011. Mohammed Diany, Effects of the Position and the Inclination of the Hole in Thin Plate on the Stress Concentration Factor, International Journal of Engineering Research & Technology ,Vol. 2 , December 2013. 8-12. Moon Banerjee, ―stress concentration in isotropic & orthotropic composite plates with centre circular hole subjected to transverse static load‖, International Journal of Mechanical Engineering and Technology (IJMET), Vol. 3/1, (2013), 374-378.

Corresponding Author B. B. Farande*

P G Student, M. E. Design Engineering, Sanjay Ghodawat Group of Institutions, Kolhapur, Kolhapur, India

E-Mail – bahubalifarande1405@gmail.com