The Flow Stress Characteristics Of Engineering Materials

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To devise successful manufacturing processes such as metal forming processes, an engineer must understand the behavior of the material that will be used in that process. These behaviors depend on very basic facts and vary basic principles. One of these principles is the flow stress phenomenon related to the materials. 

What Is The Flow Stress? 

True stress-shear rate graph(Image Source: Mikell P. Groover; Fundamentals Of Modern Manufacturing, 4th edition, pg 387).

To understand the flow stress phenomenon, you need to understand the stress-strain curves of materials under the different loading conditions. In these stress-strain curves, the section below the yield strength is the linear region of material in which elastic deformation occurs only. 

But in some engineering applications such as manufacturing processes that depend on the plastic deformation of the materials. The section above the yield stress on the stress-strain curve is the non-linear section of the material. At the stresses after the yield stress, plastic deformation takes place. So, the stresses above the yield stress of a specific material are called flow stress.

How The Flow Stress Is Calculated?

After the yield point, the line is non-linear. This non-linearity can be obtained with a specific exponent called the strain-hardening exponent. With this exponent, the required equation to find flow stress can be obtained like this; 

In this equation, ‘σ’ is the flow stress value(MPa or lb/in^2). ‘K’ is the strength coefficient and ‘n’ is the strain-hardening exponent. ‘ε’ is the strain(m or in). The K and n are the required coefficients for specific material. Flow stress is also called true stress, and ‘ε’ is also called true strain.

Why Flow Stress Is Important?

As we stated above, plastic deformation starts after the yield point. And plastic deformation can be required stuff in some engineering applications such as metal forming processes. In metal forming processes, some forces are applied to starting forms of metals to obtain required shapes via plastic deformation. 

The level of plastic deformation is measured with the required strain value on the material. For this specific level of strain, the required flow stress is calculated with the formula above. With this required flow stress, the required mechanical force to deform the material can be calculated. 

With the increasing strain rates, the required stress to deform material increases because of the term ‘strain hardening’. Strain hardening exponent is important because of this. 

The maximum force required to deform material can be calculated via the calculation of the maximum deformation. At the maximum deformation zone, the force required to deform material will be maximum. 

Average Flow Stress Term

In the calculatioın of the required forces or stresses in engineering applications, average flow stress is also calculated. Average flow stress in an application can be calculated with the equation below. This equation is obtained by integrating the flow stress formula above. 


These facts related to engineering materials are extensively used in most engineering applications where plastic deformation is a fact.

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