Corrosion formed on the surface of a metal has the potential to alter its mechanical properties such as flexural strength, axial strength, fatigue limit, elasticity, etc. The resulting damage can ultimately lead to an overall decrease in a material's load carrying capacity and ductility. By knowing exactly how much a specific mechanical property is affected, engineering analysis can be used to assess the current condition of the structure and predict its expected performance under operating loads. One such property that is affected by the presence of corrosion damage in metal structures is the stress concentration factor (Kt).
In this article, we will explain the stress concentration factor in detail and explore its usefulness when evaluating corrosion in metal structures.
What is the Stress Concentration Factor (Kt)?
To understand how the stress concentration factor is used to evaluate corroded structures, it is first important to grasp the concept of stress and stress concentration. Stress is defined as the amount of resistance offered by a body per its unit area.
σ = Nominal stress
F = Applied force
A = Gross cross-sectional area of the material
It is a physical quantity that expresses the internal forces that particles in a continuous body exert on each other under an applied load. Generally, objects tend to be stronger (offer greater resistance to deformation) when these internal forces are evenly distributed over its area. In other words, there is a uniform flow of stress throughout the material.
However, sudden changes in the section or shape of the material (also termed discontinuities) will result in abrupt changes in the flow of stress at that area. Corners, cavities, grooves and cracks abruptly redirect the flow of stress and cause a highly localized stress concentration (also known as a stress raiser or stress riser) at the discontinuity. The value of stress at these discontinuities can be many times greater than the nominal stresses at other uniform areas of the material.
The stress concentration factor is defined as the ratio of the maximum stress in a material (usually at the discontinuity) to the reference nominal stress of the gross-cross section area.
σmax = Maximum stress
σref = Reference stress
This reference stress will usually be taken at a uniform area of the object that is free from discontinuities. The Kt value is used as an indicator to determine how concentrated the stress in a given material is. A ratio of 1 indicates that no discontinuities are present. Discontinuities will naturally give rise to a stress value higher than the reference stress, therefore resulting in a Kt value greater than 1. The higher the Kt value, the greater the intensity of the stress concentration, and therefore the higher the maximum stress value.
How is the Stress Concentration Affected by Corrosion?
If abrupt changes to the shape of a material can cause an increase in stress concentration, then we can see how corrosion damage on a metal substrate can affect the Kt value of a given material section. (Related reading: Effect of Corrosion on a Material's Tensile Strength and Ductility.)
Pitting corrosion, for instance, is a form of highly localized corrosion that is characterized by the formation of holes or cavities in the material. Pitting can be induced by several factors including:
- Localized chemical attack that causes damage to the protective oxide film or coating
- Local damage to or poor application of the protective coating
- Non-uniform elements in the metal structure of the component
This type of corrosion is deemed to be more dangerous than uniform corrosion since it is relatively difficult to predict, detect and design against. If left untreated, pitting can not only cause a loss of material thickness but can cause the build-up of excessive stress concentrations around the damaged areas, which can exceed the capacity of the material (yield stress) and lead to failure. Several studies of fatigue, stress corrosion cracking and other failure mechanisms on real components, have found pits at the origin of the fracture surface.
Pitting corrosion is considered to be so dangerous that even one pit in a large component (such as a storage vessel or a pipe) is capable of causing catastrophic failure to the entire system.
Ways to Calculate the Load Carrying Capacity of a Structure
The Kt value is a useful parameter when predicting the degradation in the load carrying capacity of a structure. If the extent of the pitting corrosion is known, engineers can use analytical methods to analyze the structure's behavior, performance and stress concentrations around the pits under applied loading. For instance, Kt values may be found in typical engineering reference manuals to calculate the stress concentrations around discontinuities caused by pitting, which can then be used to determine the maximum stress in the structure. With the value of the maximum stress known, proper strengthening or repair methods can be recommended to prevent structural failure. (Recommended reading: 6 Tests to Measure a Material's Strength.)
Another method that may be used to determine the value of stress concentrations is finite element analysis (FEA), which involves using specialized engineering software to simulate the structure as an assembly of finite elements. Though more accurate and thorough, this method can be expensive due to the cost of software and personnel.
Cracks readily nucleate from the pits formed due to pitting corrosion. This gives rise to excessive stress concentrations around the damaged areas that result in Kt values greater than 1. This value gives a clear indication of the amount of overstress at the specified location, which is then used by engineers as inputs into calculations to:
- Determine the maximum expected stresses in the structure
- Help make informed decisions on dealing with the corrosion damage