Dynamic photoelastic study of wave fields in elastic plates with stress concentrators

Abstract

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...

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

“…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].…”

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

“…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].…”

“…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.…”

“…This is indicative of the opening fracture mode at the crack tip, which, in turn, means the possibility of using the technique from [7] to determine the stress intensity factor (SIF) K(t).…”

Photoelastic simulation of the stress wave field around a tunnel in an anisotropic rock mass subject to shock load

“…Note that the currently available solutions can only be applied to a circular hole in an isotropic medium. If the hole is not circular and the medium is anisotropic, finding such solutions involves severe difficulties [8][9][10][11].1. Problem Formulation.…”