Photoelastic modeling of the fracture of viscoelastic orthotropic plates with a crack

Abstract

The well-known equations of photoelasticity of linear viscoelastic bodies are used to describe the photoelastic behavior of a viscoelastic orthotropic plate with a crack. Expressions for the stress intensity factors (SIFs) at the crack tip are obtained using photoelastic measurements. The time dependence of the SIFs is analyzed and shown to be determined by the angles between directions of the crack and tension Keywords: photoelasticity, viscoelastic orthotropic plate with a crack, tension, stress intensity, fracture Introduction. Intensive loading causes early damage of the material of structural members due to the growth of existing and the initiation of new submicro-and microdefects. In many fibrous composites, such processes mainly occur at the fiber-matrix interface. Even at normal temperature, they show viscoelastic behavior [15]. Experimental data [3,4,10,12] suggest that the fracture of such materials largely depends on their rheological properties and may occur at low stresses as a slowly growing crack. Efficient experimental nondestructive methods for the quantitative assessment of the damage of anisotropic materials under loading, especially in the plastic range, are yet to be developed.Among the direct nondestructive methods that could be used to study the kinetics of damage growth, the acoustic-emission method is the most promising [1]. A review of literature on the use of this method for the evaluation of accumulated damage shows that some well-known data are empirical, which significantly limits their use [14].The photoelastic method makes it possible to determine stresses and strains and also their distribution in anisotropic optically sensitive materials with accuracy sufficient for engineering [9,13].Solutions to nonstationary problems of fracture mechanics for anisotropic bodies with stress concentrators obtained by the dynamic photoelastic method can be found in [17-22, etc.].We will outline a technique for the determination of the stress intensity factors (SIFs) near cracks in linear viscoelastic materials based on photoelastic measurements. We will discuss results on the variation in the SIFs during precritical crack growth.1. Problem Formulation and Method of Analysis. Consider a plate made of a linear viscoelastic fibrous composite and having a central crack. The crack is parallel to the direction of preferential reinforcement of the orthotropic composite (Å Å

Stress state around cracks on the boundary of a hole in a photoelastic orthotropic plate under creep

“…The singular equations in [1] are valid in the neighborhood of r << l. By increasing the neighborhood around the crack tip, we can more accurately determine the fringe order and SIF ( ) K . The simultaneous solution of the equations of orthotropic photoelasticity and fracture mechanics of materials with cracks yields the relationship between the fringe orders m and K, as was shown in [16].…”

“…The technology of such materials and a procedure for the analysis of their mechanical and optical properties are outlined in [5]. Restricted to the mechanical and optical properties of the material, Tables 1 and 2 give values of mechanical creep functions y ij t ( ), complex parameters s t j ( ), and optical creep functions P t ij ( ) [16]. For numerical purposes, we tested plates with circular holes of radius R and symmetric cracks of length 2l (Fig.…”

“…Use will be made of a procedure that produces more accurate results than in [16]. The mathematical model discussed below allows us to increase the neighborhood around the crack tip to improve the accuracy of determining the fringe orders and, hence, the SIFs.…”

Relationship between the mechanical and optical characteristics of photoviscoelastic polymeric materials under dynamic loading

“…To minimize the error of an experimental method, use is usually made of photoelastic materials with low viscoelastic characteristics, which is quite justified [3,4]. Photoelastic data on the dynamic stresses and fracture of orthotropic plates with cracks can be found in [1,9].The present paper proposes a method to calculate the difference of principal stresses and principal strains in compressible linear viscoelastic optically sensitive materials from a time-dependent fringe pattern. We will establish the relationship between the mechanical and optical characteristics of viscoelastic bodies under dynamic loading.…”

“…To minimize the error of an experimental method, use is usually made of photoelastic materials with low viscoelastic characteristics, which is quite justified [3,4]. Photoelastic data on the dynamic stresses and fracture of orthotropic plates with cracks can be found in [1,9].…”