Stress Concentration in an Orthotropic Plate with a Circular Hole under Dynamic Loading

A method is developed for determining the three displacement components by the method of holographic interferometry from two interferograms used to measure residual stresses by hole drilling. The displacements are determined at the intersection points of the principal axes and the hole boundary. The method is experimentally validated by measuring the stress state of a plate under uniaxial tension Keywords: displacement determination method, holographic interferometry, hole-drilling technique, residual stress, plate under uniaxial tensionIntroduction. Experimental stress-strain analysis of structural members occupies an important place in solid mechanics. Associated methods are strain-gauging, X-ray diffraction, ultrasonic and optical methods, etc. [1][2][3][4][5][6][7][8][12][13][14]. Note that ultrasonic stress analysis is based on the dependence of the wave velocity on elastic constants of high order. Guz [3] has derived analytic relations between unknown residual stresses and the velocity of elastic waves within the framework of linearized solid mechanics.The importance and expediency of solving problems of linearized solid mechanics for various design models were pointed out in [9]. Exact solutions to mixed plane problems of solid mechanics in the cases of statics, dynamics, stability, and fracture were analyzed in [10].Residual stresses in modern metal structures are induced by various processes such as welding, soldering, casting, and forming. Quantitative assessment of residual stresses is important for predicting the load-bearing capacity and life of structures. In this connection, the development of efficient experimental techniques for determination of residual stresses is of practical interest.Of the well-known residual-stress measurement techniques, hole-drilling strain gauge method [4] has become the most popular. The idea of the method is to remove a small amount of metal by drilling a hole in a specimen with residual stresses. The relieved surface strains can then be measured with a special strain gauge rosette.Holographic interferometry has opened up new opportunities for further perfection the hole-drilling method. The advantages of holographic interferometry are that it is a noncontact procedure and that it allows determining the three components of the displacement vector from fringe patterns over the entire laser-illuminated surface of the specimen. The experimental determination of displacements by holographic interferometry to calculate residual stresses is the subject of the papers [1,[5][6][7][8]12].To determine residual stresses, we need to establish the displacement-stress relationship. One of the ways to do this is to use the Kirsch solution [11] for an infinite plate with a circular hole. The paper [5] was the first to combine the hole-drilling method and holographic interferometry. For blind holes, the authors of [12] proposed to determine the coefficients of the relationship between the displacement components and the surface stresses from a finite-element model of the three-dimensio...

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Displacement Determination by Holographic Interferometry for Residual Stress Analysis in Elastic Bodies

Andrushchenko

Krotenko

2005

“…The photoelastic method has successfully been used in stress-strain analysis of structurally anisotropic bodies under both static [14] and dynamic [7,18] loading. This method made it possible to solve specific problems in the fracture mechanics of isotropic plates with stress concentrators such as holes and cracks [11,20]. It should be pointed out that the involved mathematical description of dynamic processes in anisotropic materials is a reason why there are few publications on the subject and, hence, little data on the kinetics of crack growth in anisotropic media.…”

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Photoelastic determination of dynamic crack-tip stresses in an anisotropic plate

Malezhik

Chernyshenko

2006

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The paper outlines a technique of determining the dynamic stress-intensity factors (SIFs) in structurally anisotropic composites from photoelastic measurement data. A composite is considered a linear elastic, homogeneous, orthotropic body. An equation is derived that relates the fringe order with the SIFs and the far-field stresses at the tip of a crack, which is parallel to the orthotropy axis Keywords: dynamic photoelasticity, anisotropic plates, cracks, stress intensity factors Introduction. Model studies of the deformation and fracture of composite materials and structural members are necessary to predict their behavior under service conditions and to justify methods of creating materials with prescribed properties. The photoelastic method has successfully been used in stress-strain analysis of structurally anisotropic bodies under both static [14] and dynamic [7,18] loading. This method made it possible to solve specific problems in the fracture mechanics of isotropic plates with stress concentrators such as holes and cracks [11,20]. It should be pointed out that the involved mathematical description of dynamic processes in anisotropic materials is a reason why there are few publications on the subject and, hence, little data on the kinetics of crack growth in anisotropic media. The papers [1, 2, 4] study the growth and limiting state of a crack in a plate and analyze failure criteria for cracked anisotropic plates. In particular, the crack-tip stress field in plane samples of a viscoelastic homogeneous orthotropic material was studied in [4] in the case where the crack propagates along one of the orthotropy axes. The relations derived allow us to assess the life of composite plates with cracks.Given the current state of the art in the development of the photoelastic method for anisotropic bodies [8,10,19], it is quite efficient to apply it to the experimental determination of dynamic crack-tip stress-intensity factor (SIFs) in optically sensitive plates made of anisotropic composite materials.The present paper outlines a technique of determining the dynamic SIFs in structurally anisotropic composites and presents specific results of photoelastic measurements.1. Problem Formulation and Governing Equations. Consider a structurally anisotropic plate [9] with a central crack parallel to the reinforcement direction q. A pulse of uniform tension P(t) is applied to two opposite sides of the plate. We choose a coordinate system (x, ó) with the origin at the middle of the crack and the Ox-axis directed along the crack; r and θ are polar coordinates (Fig. 1).For an orthotropic plate under plane strain, the stresses and strains are related by

“…This reduces considerably the strength and life of separate load-bearing members and the whole structure as well. Specific results on the dynamic behavior of elastic plates with holes are presented in [6][7][8][10][11][12]. Elastic or elastoplastic stress analyses of plates with a crack under long-term static loading were performed in [2, 4-9].…”

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Stress wave fields in plates weakened by curvilinear holes with edge cracks

Malezhik

Zirka

et al. 2006

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The dynamic fracture of plates weakened by holes with edge cracks and subjected to impulsive loading is studied using the dynamic photoelastic method. The time dependences of the stress intensity factors and the crack growth rate are examined for three models of plates with circular holes and edge cracks Introduction. Members of engineering structures such as plates and shells of various shapes with stress concentrators are widely used in aircraft construction, mechanical and chemical engineering, industrial and civil engineering, and other sectors of the national economy. Manufacturing or operating factors are responsible for cracks of various forms occurring at the edges of holes in structural members under dynamic loading. This reduces considerably the strength and life of separate load-bearing members and the whole structure as well. Specific results on the dynamic behavior of elastic plates with holes are presented in [6][7][8][10][11][12]. Elastic or elastoplastic stress analyses of plates with a crack under long-term static loading were performed in [2, 4-9].Stress wave fields in plates with a hole and an isolated through crack located near its edge were studied in [7]. The same paper outlines an experimental technique and presents specific numerical results obtained using the dynamic photoelastic method. Expanding upon the study [7], we will discuss experimental results on dynamic fracture of a plate with one or two circular holes and symmetric radial cracks at their edges. The numerical data have been obtained using the technique developed in [7].1. Models and Results. Three basic models of plates are considered. Each was tested against three and more samples. Model 1 is a rectangular plate with two symmetric edge cracks reaching the boundary of a central circular hole (Fig. 1). The plate is made of ÉD-20 epoxy resin cured with maleic anhydride and has the following dimensions: a = 90 mm, b = 120 mm, d = 15 mm, and l = 5.5 mm. The elastic and optical constants are the following: elastic modulus E = 2.4 MPa; Poisson's ratio ν = 0.35, and photoelastic constant C = 1.5⋅10 -4 MPa -1 .