Updated: Jun 15
A Monograph Authored by Dr. Conor McCaughey, Metallurgist
Residual stresses are a little counter-intuitive to the idea that a stress is defined as a load acting over an area. Residual stresses are stresses that remain after a force has been removed. They are contained within the component without any external force acting on it. Residual stresses form in two main ways: deformation of a material due to external forces, or a volumetric change in the material (usually due to a metallurgical phase transformation). The key component with both of these is that they occur more in one region compared to another. It is the variation between two regions in close proximity that causes a residual stress. Residual stresses can be considered beneficial or detrimental to the operation of a component as stresses are additive. This means that if there is a tensile residual stress and the component is operating in a way that causes tensile stresses, the stresses need to be added to give the overall stress in that region. These are considered detrimental residual stresses as they act to increase the overall stress on the component. On the other hand if the residual stress is compressive, and the component is still experiencing tensile stresses the overall stress is reduced. This is because the stresses are acting in different directions. Compressive stress is usually designated as a negative stress and tensile positive; the addition of these gives a smaller stress than the tensile applied. One of the most widely used processing techniques in the spring industry to form beneficial residual stresses is shot peening. Shot peening is the process of accelerating countless small, rounded particles (shot) at the surface of a component. Shot can be a variety of sizes and materials depending on: the material the target component is manufactured from, the size of the target component and the residual stresses required. Within the spring industry shot is typically ferrous (cast or conditioned steel) or non-ferrous (glass and ceramic) and the shot size is usually between 5 and 25% of the wire diameter. Shot peening is performed on springs, and other components, as it is known to increase the fatigue life. One of the reasons for this increased life is due to compressive residual stresses imparted on the surface of the component where the operational stresses are at a maximum. This report will attempt to describe how these residual stresses are formed and why they are beneficial.
Terms and Definitions
Before getting into the technical details of residual stresses formed due to shot peening, it is worth looking at a number of terms used in this report and defining them. Residual Stress: The stress that remains within a material when the external force (or stress) has been removed. They can be defined in terms of their direction (usually compressive or tensile) and can be detrimental or beneficial to the operation of the component. Elastic deformation: The non-permanent deformation of a material or component when exposed to a load (stress). This means when the load is removed the material will return to its original shape. An example of this is a spring operating between two safe stress limits. Plastic Deformation: The permanent deformation of a material or component when exposed to a load (stress). When the load is removed the material will not return to its original shape. E.g. a wire being coiled into a spring. Yield Strength : The stress at which the deformation of a material changes from purely elastic to elastic/plastic. When the yield strength of a material is exceeded it will not return to its original shape.
Formation of stresses
Residual stresses are formed during shot peening due to the mechanical deformation of material causing both plastic and elastic deformation at, or close to, the surface. When shot is accelerated at the surface of a component, under the correct parameters, it will force material out from the impact point, creating a small indent in the surface, Figure 1(a) and (b). As this indent remains after the shot rebounds off, plastic deformation has occurred. The plastic deformation of the surface is shown as red in Figure 1. In most materials, and especially metals, plastic deformation does not exist in isolation, elastic deformation also occurs. Elastic deformation occurs in regions where the force was not large enough to exceed the local yield strength. The region of elastic deformation is shown as green in Figure 1. To understand the formation and interactions between the regions of deformation we need to look at the impact of a shot on the surface in stages.
As the shot impacts the surface of the component it applies a force, or an impulse, to the material, causing deformation. If the force is high enough then the local yield strength is exceeded and some of this material will plastically deform. As the distance from impact into the surface of the material increases, the effect of the impulse imparted by the shot diminishes. This leads to a transition, at some critical depth, from regions of plastic deformation to a region of purely elastic deformation. This interaction between plastically and elastically deformed regions give rise to the residual stresses.
Showing the formation of residual stresses due to shot peening (a) The shot is accelerated towards the work piece, (b) the shot creates regions of plastic (red) and elastic (green) deformation, (c) once the force is removed the elastic material tries to spring back to its original shape and (d) the plastically deformed material restricts the spring back crating a compressive residual stress at the surface.
The example shown in Figure 1 only focuses on a single shot hitting the surface of a component but as more and more shot impacts the surface of the material a (near) continuous layer of plastic deformation will be present on the surface of the component.
The compressive stresses at the surface are beneficial as they oppose the stresses acting on the surface of the component during operation. As the stresses acting on a component are compounded to give the overall stress, the negative compressive stress needs to be overcome before the material starts to exhibit a positive stress which could lead to failure. For example if the compressive residual stress is 50 MPa and a spring is operating between corrected stresses of 100 MPa and 500 MPa the actual stresses seen by the spring are 50 MPa and 450 MPa. This gives an improved fatigue life, as though a lower stress was applied to the un-peened spring.
This isn’t the end of the story, however. As there is now a residual compressive stress at the surface of the peened component, there is also a subsurface tensile component to balance it out. Figure 2 shows a diagram representing the distribution of residual stresses on a shot peened work piece. Close to the surface of the material the stresses are compressive but as the depth increases the compressive stress reduce and eventually become tensile. The modulus of the maximum tensile stress is less than the modulus of the maximum compressive stress, but the tensile stress is present to a greater depth. The areas between the line and the y-axis are the same.
Showing the distribution of residual stress with respect to depth below the surface.
As residual stresses are additive, this can be overlaid with the stress acting on a spring during operation to give the overall stress in the system. Figure 3 shows the stress distribution of a shot peened spring under load. The stress created by the load (red line) on the spring reduces with distance from the surface but as the residual stress (blue line) becomes tensile, the overall stress (green line) in the system at this depth becomes higher than the stress applied. This means that the highest stress seen on a spring could be subsurface if the residual tensile are particularly high.