NEW SOLUTION TO THE PROBLEM OF A CRACK IN AN ORTHOTROPIC PLATE UNDER TENSION

V V Vasil’Ev,V A Salov,S A Lurie

doi:10.3103/s0025654421060200

V V Vasil’Ev, V A Salov + Show 1 more

Open Access

https://doi.org/10.3103/s0025654421060200

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Abstract

—A classical plane problem of the theory of elasticity about a crack in a stretched orthotropic elastic unbounded plane is considered, which leads to a singular solution for stresses in the vicinity of the crack edge. The relations of the generalized theory of elasticity, including a small scale parameter, are given. The equations of the generalized theory are of a higher order than the equations of the classical theory and allow eliminating the singularity of the classical solution. The scale parameter is determined experimentally. The results obtained determine the effect of the crack length on the bearing capacity of the plate and are compared with the experimental results for plates made of fiberglass and carbon fiber reinforced plastic.

Highlights

Let us consider an unrestricted orthotropic plate with a crack of length 2c under conditions of uniaxial tension by stress σ0 (Fig. 1)
EQUATIONS OF THE PLANE PROBLEM OF THE GENERALIZED THEORY OF ELASTICITY The generalized theory of elasticity allows one to obtain a regular solution to problems that have a singular solution within the framework of classical elasticity [2]
We will use a particular form of the equations of the generalized theory of elasticity obtained in the previous section, taking b = dy, that is, we assume that the size of the element shown in Fig. 2 is finite in the direction of the x axis and infinitesimal in the direction of the y axis

Summary

INTRODUCTION – THE CLASSIC SOLUTION TO THE CRACK PROBLEM

Let us consider an unrestricted orthotropic plate with a crack of length 2c under conditions of uniaxial tension by stress σ0 (Fig. 1). Let us take y = 0 and consider the interval −с < x < c corresponding to the boundaries of the crack (Fig. 1) It follows from equalities (1.1) and (1.2) that σx = σy = 0 on this interval. Equality (1.1) implies that for these values of the coefficients σx tends not to zero, but to σ0 at x → ∞ To eliminate this effect, the stress state of the plate, corresponding to Fig. 1, should be subjected to compression in the direction of the x axis with a stress of σ0 [1]. From equalities (1.1)– (1.3) and (1.5) we obtain σx pqσ0 p p −

EQUATIONS OF THE PLANE PROBLEM OF THE GENERALIZED THEORY OF ELASTICITY

GENERALIZED SOLUTION TO THE CRACK PROBLEM

EXPERIMENTAL STUDY

CONCLUSIONS