We have been producing mild steel rivets and shoulder rivets for over 30 years now and over those 30 years I have seen more than my fair share of stress relieving callouts that were simply wasting the customer’s money! I truly believe that there is not enough practical teaching on the topic of metallurgy and cold forming in post secondary engineering curriculum.  I am going to take a stab at simplifying the topic.  As I sit here thinking and typing and reading and erasing it's not that simple! Let's start by trying to understand what stress is, and why it can become a problem.  The word "cold forming" is used somewhat loosely as, while there is no heat introduced intentionally, "heat" is simply a by-product of moving metal.  The more we try and move the metal, the more heat we generate.  Heat changes the molecular structure of the steel and this in turn changes the mechanical properties of the steel. The heat generally concentrates where most of the metal moving is happening.  When we make a simple rivet, we usually start with stock that is quite close to the shank diameter.  (1/4" rivet = 1/4" stock)  When we squash the 1/4" rivet to make a head (hence the word "heading") the heat is generated primarily in the head area.  If enough heat is generated we end up with a head that has different mechanical properties from the shank.  This can be a serious problem as it weakens the transition from the head to the shank.  The result is rivet heads that pop off either during assembly or under load in the assembly.  The solution is to stress relieve the rivets by taking the whole rivet to the same high temperature and slowly cooling them down to get consistant mechanical properties
from head to shank.  The trouble is that stress relieving, normalizing and annealing all similar processes are not always required and add cost to the product.  Let's take a look at the underlying factors.  The amount of stress created by the cold forming process is a function of part geometry, material grade and processing condition and the cold forming process used to make the part.

Part geometry
As mentioned above, the more we move the metal, the more heat we generate, the more stress we create.  The larger head parts typically are the problematic parts requiring stress relieving.  The question is, how do you determine where the cutoff point is?  It is actually a calculation based on the head diameter, the head height and the stock size.  We call it the upset ratio.  When the upset ratio creeps above 80% we recommend stress relieving.  The "rule of thumb" is actually 85% but we use the 80 as a bit of a safety cushion.  Because I am not an engineer, I don't know the actual formula as I cheat with a forging calculator called the "Dr. Forge".  They were developed and sold by Asahi Sunac of Japan.  I am pretty sure there is an online version available but I still like my "Dr. Forge"!

Material Grade and Processing Condition
Since stress and heat go hand in hand, we need to understand how different steel grades react when forming pressures are applied to them.  As a general rule of thumb, the higher the carbon content in the steel, the more heat is generated from the forming process.  This is called work hardening.  This becomes more of a factor when high carbon and alloy steels are involved.  The state of the raw material is another factor.   Spherodised raw material greatly reduces heading stress vs. non spherodised raw material.  Today, with the exception of only a few specific jobs most cold headed product is made from spherodized raw material while years ago when some of these stress relieving callouts were made spherodized wire was not always the norm.

Forming Process Used

Some rivets and shoulder rivets can be made successfully with more than one heading process.  Shoulder rivets made with a two die process typically produce less head stress than single die produced rivets.  This is because we start with a larger diameter raw material in the case of a two die process (using an extrusion in the first die).  This results in a lower upset ratio and thus lower heading stress.

In conclusion, if you are an engineer designing a fastener for an assembly, feel free to reach out and ask an opinion on the need for stress relieving.  If you are a buyer and looking for cost savings, ask your supplier if eliminating stress relieving is an option.