The concept of yield strength is crucial when working with stressed materials. The plastic or yield point is the location on a stress-strain curve when a material begins to deform rather than bend.
Regarding the reliability and durability of materials in the building, manufacturing, and other fields, yield strength is a must-have metric. Let’s look at How To Calculate Yield Strength From Stress-Strain Curve.
Understanding Stress-Strain Curve
A stress-strain curve can graphically represent a material’s response to stress or strain. Usually, the y-axis represents stress, and the x-axis represents strain when plotting the curve.
The strain of a material is defined as the percentage of its original length that has been altered about the total length of the material. The material’s behaviour under varying stresses typically results in a stress-strain curve with distinct sections.
When a load is applied, a curve deforms but returns to its original shape when the force is released; this initial portion of the curve is known as the elastic area.
The portion of the curve labelled “plastic” is where the material undergoes permanent deformation and does not recover its original shape when the load is removed. The area of the curve where the material fails or breaks under the applied load is called the failure region.
Calculating Yield Strength
After a material reaches a particular stress, known as its yield strength, plastic deformation begins, and the stress-strain curve shifts into the plastic area. Drawing a line parallel to the elastic zone of the stress-strain curve and then turning it by a predetermined amount yields the offset method commonly used to calculate yield strength.
Below are the steps you need to take to determine yield strength by employing the offset method:
Step 1: Select the elastic region of the stress-strain curve
Choose the linear region of the stress-strain curve where the material exhibits elastic behaviour. It’s important to restrict this area and maintain a steady gradient throughout.
Step 2: Draw a line parallel to the elastic region
Please look at the stress-strain graph and locate the elastic zone by drawing a perpendicular line. Offset values are commonly set at 0.002; therefore, when removing the line, ensure it crosses the x-axis. The term “offset” is used to describe this line.
Step 3: Determine the intersection of the offset line and the stress-strain curve
Calculate where the stress-strain curve meets the offset line. This point reflects the values of stress and strain at which the material begins to deform plastically or enters the plastic zone of the stress-strain curve.
Step 4: Calculate the yield strength
When an offset line intersects a stress-strain curve, that stress value represents the yield strength. This number can be derived from the following formula or read off of a stress-strain graph:
Yield strength = Stress at offset / (1 – Offset)
Where:
Stress at offset = stress value at the point of intersection of the offset line and the stress-strain curve.
Offset = strain value used for the offset line (usually 0.002)
Bottom Line
So, this was a simple guide to how to calculate yield strength from stress strain curve. Whether you are designing a new product, evaluating the quality of a material, or assessing the structural integrity of a building, knowing the yield strength of a material can help you make informed decisions and avoid costly errors.
