Stress Concentration

(in elasticity theory), the concentration of large stresses on small areas adjacent to points of abrupt changes in the shape of the surface or cross section of a deformed body. The factors leading to stress concentration (”stress concentrators”) may be openings, cavities, cracks, grooves, incisions, corners, protrusions, sharp edges, or engraving, as well as various surface irregularities, such as notches, scratches, markings, and irregularities of welded seams.

The distribution of stresses σ (see Figure 1) is characterized by a sharp change in the stressed state, accompanied by rapid attenuation of stresses with increasing distance from the stressed zone. The higher the maximum stress at the site of concentration relative to the nominal stress (the average normal tensile stress at the narrowest cross section of the specimen), the more pronounced the attenuation of stress with increasing distance from the most highly stressed zone.

Figure 1. Stress concentration under tension of force P on a band of width b with a circular opening of diameter d

A measure of stress concentration is the stress concentration factor, α_σ = σ_max/σ_n and ατ= τ_max/τ_n, where σ_n and τ_n are the nominal normal and tangential stresses, respectively. The values of α_σ and α_T are not related to the properties of the material but rather depend on the type of stress concentrator, on its sharpness, absolute size, and size relative to the specimen, and on the type of deformation and stressed state. In addition to the geometric stress concentration factors (those given above), there is also a technical stress concentration factor, which takes into account the structure and plastic properties of the material.

The nature of stress distribution and the values of stress at concentration sites are determined by using the theory of elasticity and plasticity only for a few types of concentrators, because of the great difficulty of solving such problems. In most cases, stress concentration is studied using the methods of photoelas-ticity or lacquer coatings or by tensometry. Stress-relief notches, reinforcement of the edges of openings and recesses, and stiffen-ers in plates are used to reduce or eliminate stress concentration. Strengthening of the material in the stress concentration zone is achieved by various types of treatment.