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
The method of dynamic photoelasticity is used to study the dynamic failure of structural members in the form of plates with a curvilinear (circular or elliptic) hole and an isolated crack under impulsive loading. The time-dependences of the stress intensity factors and the crack tip velocity are investigated for two types of models Introduction. Considerable advances have been made in the development of the theory and methods of solving static and dynamic problems for isotropic and anisotropic structural members weakened by stress concentrators of various types and shapes (holes, cutouts, cracks) [1-3, 11, 14, etc.]. The publications [2-6] provide the most complete account of the results obtained in using analytic and numerical methods to determine stress intensity factors (SIFs) for bodies with stress concentrators (cracks) under static and dynamic loading.Also of interest is to use the recent achievements in the field of classical and computational mathematics to solve dynamic problems for bodies of various configurations with holes and cracks. Note that experimental methods applied to analyze the dynamics of crack propagation [11] allow us to model their mechanical behavior in one way or another. An analysis of studies on the subject indicates that the mathematical description of the final stage (fast crack propagation) involves severe difficulties. All the available theoretical solutions are idealized ones and have been obtained, except in [2], by using the linear approach. The theoretical solutions cannot unambiguously explain the spasmodic crack propagation, the finiteness of the crack growth rate, microdamages ahead of the crack front, their influence on crack development, etc.The difficulties faced in measuring the parameters of fast-growing cracks restrict the number of experimental investigations in this field compared with the total number of strength studies. Practically all experimental studies in this area were conducted using the methods of dynamic photoelasticity and dynamic caustics [7][8][9][10][11][12][13][14][15][16].Of chief interest are studies of the diffraction of waves by stress concentrators (holes, cracks). In many cases, waves cause high local stress concentration at the hole periphery or crack tip. This phenomenon may lead, for example, to fast crack growth and even to real failure. However, the available experimental data are not yet sufficient to understand the mechanism of interaction of stress waves and stress concentrators, since the majority of studies address compressional waves. It is well known that other types of waves such as tensile waves can equally be generated in complex structures.The present paper studies the failure of plates with stress concentrators (holes and cracks) under single pulses of tension. Use is made of the dynamic photoelasticity method and high-speed photographic recording [9, 10].1. Choice of Model. When the crack growth rate is high, inelastic strains develop only within a small area near the crack tip; therefore, the only criterion for deciding on a...
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 .
Photoelastic plates made of an orthotropic material are used to model the dynamic stress state near free and reinforced circular holes under blast loading. The diffraction of stress waves by holes in a thin-walled plate is studied. Experimental data are used to analyze the dynamic stress concentration in a plate with a hole in which quasilongitudinal and quasitransverse waves propagate Keywords: dynamic photoelasticity, orthotropic plate, blast loading, free and reinforced circular holes, dynamic stress concentration Introduction. The stress concentration near holes of different shapes induced by longitudinal waves of different durations was studied in [12,14,15] using the photoelastic method. In some experiments, the effect of a transverse wave on the hole was also taken into account, but the experiment parameters were such that the stress state around it was determined by both transverse and longitudinal waves. The diffraction of transverse waves by a circular hole was experimentally studied only in [5], which is due to the difficulty of obtaining a pure S-wave. The diffraction of elastic waves in multiply connected bodies is addressed in [2]; and some dynamic problems for structural members are solved in [3,10].Data on the distribution of dynamic stresses around a mine working in a rock mass are of importance for the strength analysis of underground structures subject to blast loads [7,11,13]. Different waves superimposed at the obstacle produce a complicated stress pattern varying in space and time, which gives rise to certain difficulties in solving linear stationary diffraction problems for waves in isotropic and reinforced multiply connected bodies [7,11,13]. To study wave stress fields in bodies of complex geometry, both a general approach and an efficient practical procedure are needed. Note that in modeling a rock mass with a mine working, natural anisotropy should be taken into account [1].The present paper analyzes the dynamic stress concentration around free and reinforced holes in thin anisotropic plates in which plane quasilongitudinal and quasitransverse waves propagate. The wave stress field near the boundary of an anisotropic plate subject to an impulsive load is studied in [6].1. Problem Formulation and Experiment Description. Consider a thin rectangular plate with a circular hole free or reinforced with a ring of certain shape. The plate is made of an orthotropic material with given mechanical characteristics and is subjected to a blast load that generates plane quasilongitudinal P-wave and plane quasitransverse S-wave (Fig. 1); p and q are the principal axes of orthotropy. Considering the available developments and results [5,[16][17][18][19][20], we will study the diffraction of these stress waves by the hole.We used the dynamic photoelastic method [8] to test model plates ( Fig. 1) with the following dimensions (in mm): à = 300, b = 120, h = 3, c 1 90 = , c 2 110 = , where a, b, and h are the length, width, and thickness of the plates; ñ i (³ = 1, 2) is the distance from the center of the h...
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