Table of Contents
Stress Concentration – Definition
Whenever the machine component changes the shape of its cross-section the stress distribution pattern no longer holds good and the neighborhood of the discontinuity is different. The stresses induced in the neighborhood are much higher than the stress induced in the other part of the component. This abrupt change in cross-section or the discontinuity form is called stress concentration.
It occurs for all kind of stresses in the presence of fillets, notches, holes, key-ways, splines, surface roughness are scratches etc
It is for all kinds of stresses caused due to keyways, grooves, notches, roughness, or scratches.
Consider a member with different cross-sections under a tensile load as shown in the figure. It shows that nominal stress in the right and left-hand sides will be uniform but in the region where the cross-section is changing, a redistribution of the force lines within the member must take place. The material near the edges is stressed considerably higher than the average value. The maximum stress occurs at the same point on the fillet and is directed parallel to the boundary at that point.
Causes of Stress Concentration
1. Variation in Properties of Materials:
- In the design of machine components, it is assumed that the material is homogeneous throughout the component
- In practice, there is a variation in material properties from one end to another due to the following factors:
(a) Internal cracks and flaws like blow holes;
(b) Cavities in welds;
(c) Air holes in steel components; and
(d) Nonmetallic or foreign inclusions.
- These variations act as discontinuities in the component and cause stress concentration.
2. Load Application:
- Machine components are subjected to forces.
- These forces act either at a point or over a small area of the component.
- Since the area is small, the pressure at these points is excessive. This results in stress concentration.
The examples of these load applications are as follows:
(a) Contact between the meshing teeth of the driving and the driven gear
(b) Contact between the cam and the follower
(c) Contact between the balls and the races of ball bearing
(d) Contact between the rail and the wheel
(e) Contact between the crane hook and the chain
- In all these cases, the concentrated load is applied over a very small area which results in stress concentration.
3. Abrupt Changes in Section:
- In order to mount gears, sprockets, pulleys, and ball bearings on a transmission shaft, steps are cut on the shaft and shoulders are provided from assembly considerations.
- Although these features are essential, they create change of the cross-section of the shaft.
- This results in stress concentration at these cross-sections.
4. Discontinuities in the Component:
- Certain features of machine components such as oil holes or oil grooves, keyways and splines, and screw threads result in discontinuities in the crosssection of the component.
- There is stress concentration in the area of these discontinuities.
5. Machining Scratches:
- Machining scratches, stamp marks or inspection marks are surface irregularities, which cause stress concentration.
Methods to Reduce Stress Concentration
1. Additional Notches and Holes in Tension Member
- A flat plate with a V-notch subjected to tensile force is shown in Fig. (a).
- It is observed that a single notch results in a high degree of stress concentration.
- The severity of stress concentration is reduced by three methods: (a) Use of multiple notches, (b) Drilling additional holes; and (c) Removal of undesired material.
- These methods are illustrated in Fig. (b), (c) and (d) respectively.
- In these three methods, the sharp bending of a force flow line is reduced and it follows a smooth curve.
2. Fillet Radius, Undercutting and Notch for Member in Bending:
- A bar of circular cross-section with a shoulder and subjected to bending moment is shown in Fig. (a).
- Ball bearings, gears or pulleys are seated against this shoulder.
- The shoulder creates a change in the cross-section of the shaft, which results in stress concentration.
- There are three methods to reduce stress concentration at the base of this shoulder.
- Fig. (b) shows the shoulder with a fillet radius r. This results in a gradual transition from a small diameter to a large diameter.
- The fillet radius should be as large as possible in order to reduce stress concentration.
- In practice, the fillet radius is limited by the design of mating components.
- The fillet radius can be increased by undercutting the shoulder as illustrated in Fig. (c).
- A notch results in stress concentration.
- Cutting an additional notch is an effective way to reduce stress concentration. This is illustrated Fig. (d).
3. Drilling Additional Holes for Shaft:
- A transmission shaft with a keyway is shown in Fig. (a).
- The keyway is a discontinuity and results in stress concentration at the corners of the keyway and reduces torsional shear strength.
- In addition to giving fillet radius at the inner corners of the keyway (as shown in Fig. (c)), there is another method of drilling two symmetrical holes on the sides of the keyway.
- These holes press the force flow lines and minimize their bending in the vicinity of the keyway. This method is illustrated in Fig. (b).
4. Reduction of Stress Concentration in Threaded Members:
- A threaded component is shown in Fig. (a).
- It is observed that the force flow line is bent as it passes from the shank portion to the threaded portion of the component. This results in stress concentration in the transition plane.
- In Fig. (b), a small undercut is taken between the shank and the threaded portion of the component and a fillet radius is provided for this undercut.
- This reduces the bending of the force flow line and consequently reduces stress concentration.
- An ideal method to reduce stress concentration is illustrated in Fig. (c), where the shank diameter is reduced and made equal to the core diameter of the thread.
- In this case, the force flow line is almost straight and there is no stress concentration
5. The methods of reducing stress concentration in cylindrical members with shoulders hole, subjected to tensile load.
Theoretical Stress Concentration factor
- In order to consider the effect of stress concentration and find out localized stresses, a factor called theoretical stress concentration factor is used.
- It is denoted by Kt and defined as,
Kt= Highest value of actual stress near discontinuity / Nominal stress obtained by elementary equation.
Effect of stress concentration on the material in case of static loading and cyclic loading.
- In static loading, stress concentration in ductile materials is not so serious as in brittle materials, because in ductile materials local deformation or yielding takes place which reduces the concentration. In brittle materials, cracks may appear at these local concentrations of stress which will increase the stress over the rest of the section.
It is, therefore, necessary that in designing parts of brittle materials such as castings, care should be taken. In order to avoid failure due to stress concentration, fillets at the changes of section must be provided.
- In cyclic loading, stress concentration in ductile materials is always serious because the ductility of the material is not effective in relieving the concentration of stress caused by cracks, flaws, surface roughness, or any sharp discontinuity in the geometrical form of the member.If the stress at any point in a member is above the endurance limit of the material, a crack may develop under the action of repeated load and the crack will lead to failure of the member.
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