What Is a Stress Concentration?
A type of problem in elastic mechanics refers to the phenomenon of local increase in stress in an object, which generally occurs in places where the shape of the object changes sharply, such as notches, holes, grooves, and places with rigid constraints. Stress concentration can cause fatigue cracks in objects, and can also cause static load fracture of parts made of brittle materials. At the stress concentration point, the maximum stress (peak stress) is related to factors such as the geometry of the object and the loading method. The locally increased stress rapidly decays with increasing distance from the peak stress point. Because the peak stress often exceeds the yield limit (see the mechanical properties of the material) and causes the redistribution of stress, the actual peak stress is often lower than the theoretical peak stress calculated by elastic mechanics.
- Chinese name
- Stress concentration
- Foreign name
- Stress concentration
- A type of problem in elastic mechanics refers to the phenomenon of local increase in stress in an object, which generally occurs in places where the shape of the object changes sharply, such as notches, holes, grooves, and places with rigid constraints. Stress concentration can cause fatigue cracks in objects, and can also cause static load fracture of parts made of brittle materials. At the stress concentration point, the maximum stress (peak stress) is related to factors such as the geometry of the object and the loading method. The locally increased stress rapidly decays with increasing distance from the peak stress point. Because the peak stress often exceeds the yield limit (see the mechanical properties of the material) and causes the redistribution of stress, the actual peak stress is often lower than the theoretical peak stress calculated by elastic mechanics.
Introduction to Stress Concentration
- Stress concentration refers to the phenomenon that the maximum stress value of a local area of a structure or component is higher than the average stress value.
Effect of stress concentration on component strength
- For components made of brittle materials, the stress concentration phenomenon will remain until the maximum local stress reaches the strength limit. Therefore, the effect of stress concentration should be considered when designing brittle material components.
- For members made of plastic materials, stress concentration has almost no effect on the strength under static load. Therefore, when studying the static strength of plastic materials, the effect of stress concentration is usually not considered. However, the stress concentration has a great impact on the fatigue life of the component. Therefore, whether it is the fatigue problem of brittle materials or plastic materials, the effect of stress concentration must be considered.
Stress concentration in detail
- Stress concentration is a phenomenon in which the stress is significantly increased in the local area of the solid. Mostly appear in sharp corners, holes, notches, grooves and places with rigid constraints and their neighborhoods. Stress concentration can cause brittle materials to fracture; brittle and plastic materials cause fatigue cracks. In the area of stress concentration, the maximum stress (peak stress) is related to factors such as the geometry of the object and the loading method. The locally increased stress value decays rapidly with increasing distance from the peak stress point. Because the peak stress often exceeds the yield limit (see material mechanical properties) and causes the redistribution of stress, the actual peak stress is often lower than the theoretical peak stress calculated by elastic mechanics.
- The parameter that reflects the degree of local stress increase is the theoretical stress concentration coefficient , which is the ratio of the peak stress to the stress when the stress concentration is not considered (that is, the nominal stress). It is always greater than 1 and has nothing to do with the size of the load. For circular holes in an infinitely large flat plate subjected to unidirectional stretching, = 3. The ratio of the fatigue limit obtained from a smooth specimen to the fatigue limit of a notched specimen made of the same material is called the effective stress concentration factor, which is always less than the theoretical stress concentration factor. Generally, the latter can be obtained from its empirical formula. approximation.
- In 1898, G. Kirsch of Germany first obtained the result of stress concentration near the circular hole. In 1909, the Russian GV Kolosov worked out the formula of stress concentration near the elliptical hole. In the late 1920s, the Soviet Union's NI Musherishvili and others introduced complex variable functions into elastic mechanics, and used conformal transformation to transform an irregular piecewise smooth curve onto a unit circle, and derived Stress expression and its boundary conditions, and then obtain a batch of accurate solutions of stress concentration. The development of various experimental methods is also fast, such as electrical measurement method, photoelastic method, speckle interference method, moire method and other experimental methods (see experimental stress analysis) can measure the stress concentration of the object. With the development of science and technology, the rapid development of computers, finite element methods and boundary element methods has opened up new ways to find numerical solutions for stress concentration.
- In order to avoid the damage caused by stress concentration of materials or components, the following measures are mainly adopted in the project: surface strengthening: blasting, rolling, nitriding and other treatments on the surface of the material can improve the fatigue strength of the surface of the material; avoid Sharp corners: change the corners to excessive rounded corners, and appropriately increase the radius of the transition arc, and the effect is better; improve the shape of the part; the shape of the curvature radius gradually changes is conducive to reducing the stress concentration factor, the more ideal method is to use Streamlined or double-curvature, the latter is more convenient for engineering application; local reinforcement at the edge of the hole: the use of a reinforcing ring or thickening at the edge of the hole can reduce the stress concentration factor, and the degree of decline is related to the shape of the hole and The size, the shape and size of the reinforcing ring and the load form are related; Properly choose the location and direction of the openings: The location of the openings should avoid high stress areas as much as possible, and the increase of the stress concentration factor due to the mutual influence between the holes should be avoided For elliptical holes, the long axis should be parallel to the direction of the external force, which can reduce the peak stress; increase the stress in the low stress area and reduce the part The thickness of the low stress area, or the opening of gaps or round holes in the low stress area, makes the transition of stress from the low stress area to the high stress area smooth; Use of residual stress: after the peak stress exceeds the yield limit, it will be unloaded, and Residual stress is generated, and rational use of residual stress can also reduce the stress concentration factor.
Calculation method of stress concentration
- In the case of unidirectional stretching of an infinitely large flat plate, k = 3 in the edge of the circular hole; in the case of bending, for different ratios of the radius of the circular hole to the thickness of the plate, k = 1.8 to 3.0; in the case of torsion, k = 1.6 to 4.0.
As shown in the figure below, the slat with round holes is subjected to axial tension. From the test results, we can see that in a local area near the circular hole, the stress increases sharply, and a little far away from this area, the stress decreases rapidly and becomes uniform. This phenomenon of locally increased stress caused by a sudden change in section size is called stress concentration. Maximum stress at the edge of the hole on I-I
- It is called the theoretical stress concentration factor. It reflects the degree of stress concentration and is a factor greater than 1. Moreover, the test results also show that the more drastic the change in the cross-sectional dimension, the larger the stress concentration factor. Therefore, parts with sharp corners or holes should be avoided as much as possible, and arc transitions should be used at abrupt changes in the section of the stepped rod.
- Stress concentration is not only related to the shape and structure of the object, but also to the selection of materials. It also has a non-negligible relationship with the external application environment (such as temperature factors). In addition, it may also cause changes in stress during processing, such as tempering Improperly causing secondary quenching cracks, micro-cracks in wire cutting EDM, and mechanical design will inevitably lead to stress concentration in a certain part.