Modern industries are under constant pressure to deliver goods and services at greater efficiency while minimizing operating costs. As a result, an increasing emphasis is being placed on the optimal design of machinery parts. Mechanical components are now required to perform multiple functions while delivering performance that meets increasing industrial demand. This has led to the design of increasingly complex and sophisticated machinery parts and components. (The importance of design when trying to prevent corrosion is discussed in the article Corrosion Control Considerations in the Equipment Design Process.)
One of the consequences of complex component design is the increased likelihood of stress concentrations. The unique geometric shapes of some parts, while efficient, has resulted in tortuous load path transfers and increased concentrations of stresses. Therefore, in addition to considering functionality, designers and engineers must also assess how component geometry responds to the imposed stresses of everyday operation.
What is Stress Concentration?
Stress concentration is defined as the accumulation of stresses at a particular location of an object due to an abrupt transition in its geometry. This phenomenon is characterized by significantly higher values of localized stress near the region of the geometrical change. Stress concentrations in machine parts typically occur near irregularities such as sharp corners, cracks, corners, notches, holes, etc.
To better understand concentrations, it is worthwhile first to grasp the concept of uniform stress and stress flow.
Stress is defined as the internal force present in a body per unit of its area. This relationship is shown by the formula:
σ = F / A
σ = Nominal stress
F = Applied force
A = Gross cross-sectional area of the material
In other words, stress indicates how much force the particles of a continuous body exert on each other when subjected to an applied load. Generally, parts and components tend to be stronger (offer greater resistance to deformation) when these internal forces are distributed uniformly throughout its cross-sectional area. This even distribution of forces is usually achieved when the part or component in question has a regular shape that provides a straightforward stress flow throughout the material.
However, when the shape of the object changes suddenly, the stress has to find ways to "flow around" the area. As the stress maneuvers around the irregularity (also called a stress riser), the stress gathers near the area to produce localized concentrations where the stress values are higher than those found in other regions of the object. This also occurs where defects or cracks exist in the object.
Corrosion damage, such as pitting, act as stress risers, which can magnify local stresses beyond the component’s capacity and compromise its integrity. (For more on this topic, see Why Understanding the Stress Concentration Factor (Kt) is Important When Evaluating Corrosion in Metal Structures.)
Methods of Stress Concentration Reduction
The key to reducing stress concentrations is to ensure the smooth transition of internal stress flow from one area of the object to another. The first step to lowering stress concentrations in machine parts is intentionally designing the object's shape such that it does not contain sudden changes in its geometry.
However, in the real world this solution is rarely possible because functional requirements often necessitate complex shapes. In instances where stress risers are unavoidable, it is preferable to place them in regions where nominal stress is considered to be minimal, if possible.
Regardless of the location of the riser, all efforts should be made to ensure that the stress flow around the discontinuity does not result in local stresses, which may exceed the capacity of the material. This usually entails smoothing contours and rounding notch roots in the direction of the stress flow.
Some of the most common practical methods to reduce stress concentrations in machine parts are:
1. Provide gradual transitions between changes in cross-sections – This can be achieved by providing specific design measures, such as a fillet radii or tapers. Similar to how sharp bends in a river can cause turbulent flow, so too can abrupt shape transitions cause increases in stress. By smoothing critical areas of the component, we can influence the flow of stress in the object and prevent undue stress concentrations.
2. Provide relief notches – Another method to reduce stress concentrations in machine parts is to remove material near notches. This forms an additional groove, which is known as a relief notch. While providing an extra notch may seem counterintuitive, these non-functional grooves allow designers to guide or control the lines of stress in the component.
3. Use several smaller relief notches instead of a single long one – In instances where holes or notches are unavoidable, several small notches can be provided to facilitate smoother stress flow. In contrast to the previous method, where a single groove reshapes the irregularity, this technique involves surrounding a "design notch" with several smaller ones. Additional material is removed to create mini notches while retaining the original notch.
4. Modify welded joints - Another type of stress concentration common in machine components is due to the interface between parts that are joined by welding. The regions where the mating surfaces touch do not have weld filling and, therefore, can act as cracks that encourage stress concentrations. By boring out corners, stress flow can be improved. For example, a typical fillet welded joint is vulnerable to stress concentrations. The stress performance of the joint can be improved by boring out the corners.
The key to reducing stress concentrations in machine parts and components is understanding the flow of stress through the object. Once the stress flow is understood, appropriate measures can be employed to ensure that the stress path from one part of the object to another is as smooth as possible. Other considerations, such as strength and functionality, should also be considered to ensure that the chosen stress reduction methods align with the original design intent.