What is Stress Concentration? Its Causes, Ways to Overcome, Effects on the Material (PDF)

What is Stress Concentration?

Whenever a mechanical part changes its cross-sectional shape, stresses are developed, the stress distribution doesn’t happen at all places and results in different stress concentrations. Irregularities in stress distribution due to this sudden shape change are called stress concentrations. Various types of stresses occur with fillets, notches, holes, keyways, surface roughness, and scratches.

The stress concentration factor is dependent on the geometrical changes of cross-section, such as a hole, notch, or fillet in the component. This can be designed for as it only depends on the geometry and not on load condition. Moreover, the stress concentration factor is a dimensionless factor that is used to quantify how concentrated the stress is in a material.

The stress intensity factor is a bit different; it is an inherent property of the material that is tested and defined for cracks or flaws. The stress intensity factor is dependent on geometry and load.  

This article majorly focuses on stress concentration & its effects.

Why Stress Concentration should be Avoided?

Stress concentration
Stress concentration

Whenever there is an abrupt change in body shape due to cracks, sharp corners, holes, and cross-sectional area reductions; the development of local stresses may increase near these cracks, sharp corners, holes, and cross-sectional area reductions. At these places of stress concentration, the body is prone to failure. Therefore, stress concentrations should be avoided or reduced to prevent body breakdown.

To fully understand the concept of stress concentration, consider elements of different cross-sections under tensile loading, as shown in the figure. On a little reflection, the nominal stress is the same on the right and left sides, but in the area where the cross-section changes, a force redistribution must occur inside the bar. The material near the edge is stressed well above average. The maximum stress occurs at a point of the fillet and is directed parallel to the boundary of that point.

What are the Causes of Stress Concentration?

When designing mechanical parts, it is assumed that the material is uniform throughout the part. In practice, there is variation in material properties from end to end due to:

  • Internal cracks and scratches such as blow holes.
  • Weld voids.
  • Air holes in steel parts.
  • Non-metallic and foreign inclusions.

These variations act as component discontinuities and cause stress concentrations.

Causes of Stress concentration
Causes of Stress concentration

Forces Acting on the Body

Forces are applied to mechanical parts. These forces act on a single point or small area of ​​the component. Due to the small area, the pressure at these points is too high. This leads to the concentration of stress. Examples of these load applications are:

  • Contact between meshing teeth of driving gear and driven gear
  • Contact between cam and follower
  • Contact between balls and ball bearing raceways
  • Contact between rails and wheels
  • Contact between crane hook and chain

Sudden Changes in Section

To attach gears, sprockets, pulleys, and ball bearings to the transmission shaft, the shaft is step cut and has a shoulder for assemblies. While these features are essential, they introduce variations in shaft cross-section. This concentrates the stress on these cross sections.

Discontinuity of Components

Certain features of mechanical parts, such as oil holes or grooves, keyways, and threads, cause the cross-section of the part to be discontinuous. These discontinuous regions have stress concentrations.

Machining Scratches

Machining scratches, embossed marks, and inspection marks are surface irregularities that cause stress concentration.

What are the ways to Overcome Stress Concentration?

Specify a fillet radius for sharp corners to avoid sharp corners:

By giving sharp corners a fillet radius, the cross-sectional area decreases gradually rather than abruptly. And it distributes the body’s stress more evenly.

By providing notches or undercuts in sharp corners.

A circular section bar with a shoulder subjected to a bending moment is shown in the figure.

A ball bearing, gear, or belt pulley is attached to this shoulder. A shoulder introduces a change in the cross-section of the shaft, causing a stress concentration. This provides a gradual transition from small diameter to large diameter. The fillet radius should be as large as possible to reduce stress concentrations. In practice, the rounding radius is limited by the corresponding part design. The fillet radius can be increased by undercutting the shoulder. Notches cause stress concentrations. Cutting excess notches is an effective way to reduce stress concentrations.

Ways-to-Overcome-Stress-concentration
Ways to Overcome Stress concentration

By introducing small bore diameter holes near a large bore diameter hole

If there is an object, it has a hole inside. And the stress intensity is greater near this hole. To avoid this, create some small holes near this hole. This distributes the tension more evenly than before

By reducing the nominal diameter of the threaded object and matching it to the minor diameter

Suppose we have a thread object. And the stress strength of the screw part increases. Objects are more likely to fail on threads. This can be avoided by reducing the nominal shank diameter and matching the core diameter. This distributes tension more evenly on threaded objects.

Figure (a) shows screw parts. Observe that the force flow lines bend as you go from the shank portion of the part to the threaded portion. This concentrates the stress on the transition surface.

in figure (b) A small undercut is created between the shank and the threaded portion of the part and a fillet radius is provided for this undercut. This reduces the bending of the power flow lines and relieves stress concentrations.

An ideal way to reduce stress concentration is shown in Figure (c). This method reduces the shank diameter to match the minor diameter of the screw. In this case, the flow of lines of force is almost straight and there is no stress concentration.

Reducing-nominal-diameter-of-threaded-objects
Reducing the nominal diameter of threaded objects

What is the Theoretical or Form Stress Concentration Factor?

The theoretical stress concentration factor or Form stress concentration factor is defined as the ratio of the maximum stress over nominal stress.

The theoretical Stress concentration factor is denoted by Kt and the value of Kt depends upon the geometry & material of the part.

Kt = Maximum Stress / Nominal Stress

The Kt factor depends primarily on the notch geometry rather than the material unless the material is significantly deformed by the load. Kt values ​​are usually obtained from the expression as shown and, strictly speaking, apply to ideally elastic stiff members only. Kt values ​​can also be determined by some experimental techniques. Kt values ​​are not readily available for sharp notches and cracks, but such discontinuities can always be expected to produce maximum stress concentrations. This is why brittle, high-strength materials are so sensitive to even minor scratches. For example, in the case of fatigue, invisible tool marks can lead to premature and unexpected failure in strong steel.

There are many other factors that may be similar to Kt, but they should be carefully distinguished. The first is the true stress concentration factor, Kσ, defined as

Kσ = σmax / σave

This means that Kσ = Kt for ideally elastic materials. Kσ is the most useful in the case of ductile materials that yield at the notch tip and lower the stress level from that indicated by Kt. Similarly, a true strain concentration factor, Kϵ, is defined as

Kϵ = ϵmax / ϵave

Where ϵave = σave / E

E = Young’s modulus of Elasticity

In fracture mechanics, many stress intensity factors(K, Kc, KI) that are often confused with Kt and Kσ are used, but their definitions and usages are different.

What are the effects of Stress Concentration on the Material

In Case of Static Loading

Under static loading, stress concentrations in ductile materials are less severe than in brittle materials. This is because ductile materials experience localized deformation or yielding, which relaxes the concentration. In brittle materials, these localized stress concentrations can lead to cracking and increased stress in the rest of the section.

Therefore, care should be taken when designing parts from brittle materials such as castings. In order to avoid damage due to stress concentration, cross-section changes must be rounded.

In Case of Cyclic Loading

Stress concentrations in ductile materials are always severe because, under cyclic loading, the material’s ductility does not effectively relieve stress concentrations caused by cracks, scratches, surface roughness, or sharp discontinuities in the element geometry. is. Cracks can occur under cyclic loading., leading to component failure.

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Atul Singla

Hi ! I 'm Atul. I am PMP certified Mechanical (Piping) Engineer with more than 17 Years of experience. Worked in the field of Plant design for various industries such as refinery, petrochemical & chemical, Fertilizer, gas Processing industries. Developed passion about Piping while working with national & international engineering consultants on diverse projects involving international clients. Developed courses on Piping Engineering to share the knowledge gained after working with many industry experts, through out these years.

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