IJIRST –International Journal for Innovative Research in Science & Technology| Volume 3 | Issue 02 | July 2016 ISSN (online): 2349-6010
Estimation of Stress Concentration Factor for Different Crack Length on Plate under Compressive Loading on Circular Polariscope Tushar D. Kale PG Student Department of Mechanical Engineering KDKCOE, Nagpur (M.S.) India
S. R. Ikhar Assistant Professor Department of Mechanical Engineering KDKCOE, Nagpur (M.S.) India
A. V. Vanalkar Professor Department of Mechanical Engineering KDKCOE, Nagpur (M.S.) India
Abstract In this paper an effort is made to find the stress concentration factor (Kt) near the crack tip in a plate having different crack length to width ratio by applying the compressive load on the rectangular plate with an edge crack. Firstly the material fringe value is determined or calculated by loading the circular disc on polariscope under compression. The stress concentration in the rectangular plate with an edge crack is calculated & at the end of this paper a graph is plotted between stress concentration factor and the crack length to width ratio of the rectangular plate. Keywords: Epoxy Resin Material, Circular Polariscope _______________________________________________________________________________________________________ I.
INTRODUCTION ABOUT PHOTOELASTICITY
The photoelastic phenomenon was first described by Brewster and extended by the works of Coker and Filon of the University of London. In 1853, Maxwell related the birefringence to stress and developed the stress-optical laws. Coker and Filon applied this technique to structural engineering in 1902. Photoelasticity is an experimental method to determine the stress distribution in a material where mathematical methods become quite cumbersome. Unlike the analytical methods of stress determination, photoelasticity gives a fairly accurate picture of stress distribution even around abrupt discontinuities in a material. The method serves as an important tool for determining the critical stress points in a material and is often used for determining the stress concentration factors in irregular geometries. The method is based on the property of birefringence, which is exhibited by certain transparent materials. Birefringence is a property where a ray of light passing through a material experiences two refractive indices. The property of birefringence or double refraction is exhibited by many optical crystals. But photoelastic materials exhibit the property of birefringence only on the application of stress and the magnitude of the refractive indices at each point in the material is directly related to the state of stress at that point. When a ray of light passes through a photoelastic material, it becomes polarized and gets resolved along the two principal stress directions and each of these components experiences different refractive indices. The difference in the refractive indices leads to a relative phase difference between the two component waves, which is usually called phase retardation Photoelasticity can be applied to three and two dimensional states of stress However the application of photoelasticity to the two dimensional plane stress system is much easier to analyze especially when the thickness of the sample is much smaller as compared to dimensions in the plane. In this case, the only stresses act in the plane of the solid, as the other stress components are zero. Photoelasticity is an experimental technique for stress and strain analysis that is particularly useful for members having complicated geometry, complicated loading conditions, or both. For such cases, analytical methods (that is, strictly mathematical methods) may be cumbersome or impossible, and analysis by an experimental approach may be more appropriate. While the virtues of experimental solution of static, elastic, two-dimensional problems are now largely overshadowed by analytical methods, problems involving three-dimensional geometry, multiple-component assemblies, dynamic loading and inelastic material behavior are usually more amenable to experimental analysis. The name photoelasticity reflects the nature of this experimental method: photo implies the use of light rays and optical techniques, while elasticity depicts the study of stresses and deformations in elastic bodies. Through the photoelastic-coating technique, its domain has extended to inelastic bodies. Photoelastic analysis is widely used for problems in which stress or strain information is required for extended regions of the structure. It provides quantitative evidence of highly stressed areas and peak stresses at surface and interior points of the structure and often equally important, it discerns areas of low stress level where structural material is utilized inefficiently.
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Estimation of Stress Concentration Factor for Different Crack Length on Plate under Compressive Loading on Circular Polariscope (IJIRST/ Volume 3 / Issue 02/ 022)
The photoelastic method is based upon a unique property of some transparent materials, in particular, certain plastics. Consider a model of some structural part made from a photoelastic material. When the model is stressed and a ray of light enters along one of the directions of principal stress, a remarkable thing happens. The light is divided into two component waves, each with its plane of vibration (plane of polarization) parallel to one of the remaining two principal planes (planes on which shear stress is zero). Furthermore, the light travels along these two paths with different velocities, which depend upon the magnitudes of the remaining two principal stresses in the material. The incident light is resolved into components having planes of vibration parallel to the directions of the principal stresses Ďƒ1 and Ďƒ2. Since these waves traverse the body with different velocities, the waves emerge with a new phase relationship, or relative retardation. Specifically, the relative retardation is the difference between the number of wave cycles experienced by the two rays traveling inside the body.
Fig. 1: Fringes observe while loading the plate on polariscope
II. MATERIAL USE IN THIS PROJECT Epoxy resin material is used in this project for determining stress concentration .this plate is generally use because it has an orthotropic properties i e it shows the orthotropic properties (principal stress in two mutually perpendicular dimention).it has a property to castable in large sizes. Epoxy resin is also known as araldite 230 with 10% hardner having youngs modulus 2570 & poisons ratio 0.38. III. OBJECTIVE The primary objectives of this project are to introduce the concept of stress concentration factors in edge structural configurations. The notion of stress concentration is experimentally explored qualitatively, using photoelasticity, and quantitatively, using experimental, analytical, and numerical methods. Firstly examine photoelastic stress analysis techniques to illustrate features of locally concentrated stress and strain distributions around crack and other geometric discontinuities then present analytical solutions for the stress distribution around crack in an infinite plate, subjected to remote compressive loading, and quantitatively introduce the concept of a stress concentration factor. Estimates of the stress concentration factor for various notch geometries will be obtained from approximate engineering solutions. We will then measure the strain distributions around a crack. The experiment performed was aimed to investigate the stress concentration factor for specimens having different edge crack to study the stress concentration factor for specimens with different crack length to width ratio. Plane Polariscope Plane polariscope consists of a polariser, stressed model & analyser. The polariser and analyser are place in a crossed position due to which the plane or linearly polarise light pass between polariser and analyser as the stressed model is doubly refracting or orthotropic which distribute the principal stress in two perpendicular direction.
Fig. 2: Fringes observe while loading the plate on polariscope
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Estimation of Stress Concentration Factor for Different Crack Length on Plate under Compressive Loading on Circular Polariscope (IJIRST/ Volume 3 / Issue 02/ 022)
Circular Polariscope In circular polariscope arrangement the light source is provided through which a ray of light enters the polariser and polarise light comes out from polariser then it enters the second filter ie. the first quarter wave plate these quarter wave plate is having doubly refracting material having two orthogonal axis fast and slow axis in the arrangement of circular polariscope these two axis makes an angle of 450 with respect to polariser or π/4 with axis of polariser .The quarter wave plate is design so that the relative retardation between components of light vector coming out from these two axis is equal to first quarter of wavelength ie ƛ/4 of the light use or π/2 in terms of angular retardation these arrangement gives the circular polarise light the light from first quarter wave plate enters the second quarter wave plate these plate is arrange so that its fast axis is parallel to slow axis of first quarter wave plate and fast axis is parallel to slow axis of first quarter wave plate these two plates are set to be cross the second quarter wave plate converts the circular polarise light again into plane polarise.
Fig. 3: Fringes observe while loading the plate on polariscope
Sr no 1 2 3 4 5
Load p Newton 6 6 6 5 5
a mm 4 11 20 10 18
Table - 1 Below table shows stress concentration for a plate with an edge crack w t Fringevalue Crack Length To Width Ratio (a/w) σmax = Nfσ/h mm mm Nmean 40 5 5/30=0.1 1.4 0.392 40 5 6/30=0.2 1.6 0.448 40 5 9/30=0.5 2 0.56 30 5 0.33 1.5 0.42 30 5 0.6 1.8 0.50
σnom=P/A A=w*t 0.03 0.03 0.03 0.03 0.03
Kt 13 14.9 18.6 12.6 15
IV. CONCLUSION From above table it is found that as the crack length increases the stress concentration also increases. REFERENCES [1]
Ali O. Ayhan Three-dimensional mixed-mode stress intensity factors for cracks in functionally graded materials using enriched finite elements: International Journal of Solids and Structures 46 (2009) 796–810 [2] Liang Wu, Lixing Zhang, Yakun Guo Extended finite element method for computation of mixed mode stress intensity factors in three dimensions: Procedia Engineering 31 (2012) 373–380 [3] Garrett J. Pataky, Michael D. Sangid, Huseyin Sehitoglu, Reginald F. Hamilton, Hans J. Maier, Petros Sofronis Full field measurements of anisotropic stress intensity factor ranges in fatigue: Engineering Fracture Mechanics 94 (2012) 13–28 [4] M. Beghinia, M. Benedetti, V. Fontanari, B.D. Monelli Stress intensity factors of inclined kinked edge cracks: A simplified approach: Engineering Fracture Mechanics 81 (2012)120–129 [5] Chaitanya K. Desai, Sumit Basu, Venkitanarayanan Parameswaran Determination of complex stress intensity factor for a crack in a biomaterial interface using digital image correlation: Optics and Lasers in Engineering 50 (2012) 1423–1430 [6] Rui Zhang, Lingfeng He Measurement of mixed-mode stress intensity factors using digital image correlation method: Optics and Lasers in Engineering 50 (2012) 1001–1007 [7] Dr.Abdul Mubeen Experimental stress analysis 2nd edition Dhanpat Rai & Co.(2011-12) [8] Calvin Rans, Riccardo Rodi, René Alderliesten Analytical prediction of Mode I stress intensity factors for cracked panels containing bonded stiffeners: Engineering Fracture Mechanics 97 (2013) 12–29 [9] Paulo J. Tavares, Frederico Silva Gomes, P.M.G.P. Moreira A Hybrid Experimental-Numerical SIF Determination Technique: Procedia Materials Science 3(2014)190–197 [10] R. Evans, A. Clarke, R. Gravina, M. Heller, R. Stewart Improved stress intensity factors for selected configurations in cracked plates: Engineering Fracture Mechanics 127 (2014) 296–312
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