What Is Stress-Strain Curve？

Where Li is the instantaneous length.

What Are the Stages of the Stress-Strain Curve?

A stress-strain diagram has three stages. In the first stage, the material experiences only elastic deformation. When the applied stress is released, the material returns to its original dimensions. 

Uniform plastic deformation takes place in the second stage. This stage begins at the yield point and continues for as long as the material can continue to strengthen through strain hardening (the same process that occurs in cold forming) with every new increment of the applied load. Eventually, the material's capacity for stable plastic deformation is exhausted. The amount of plastic strain that can be tolerated during this phase tells us a lot about the material's relative brittleness or ductility.

The final stage of a tensile test is referred to as “necking.” This stage occurs after the material’s ultimate tensile stress is reached, and no further strain hardening is possible. Instead of continued, stable deformation, a region of localized deformation forms somewhere in the cross-section of the test specimen. The excessive tensile stresses reduce the material’s dimensions that are perpendicular to the applied force which causes a significant reduction in area. This makes the material have the shape of a “neck”. Once necking begins, the engineering stress of the material decreases while the true stress continues to increase.  The material fractures soon after necking begins.

How To Read the Stress-Strain Graph?

The general steps for how to read a stress-strain graph are described below:

1. Pick a stress value on the Y-axis.
2. Trace a horizontal line from the Y-axis until it intersects the stress-strain curve’s line. 
3. Mark the point where the horizontal line and stress-strain curve line intersect.
4. Trace a vertical line down from the intersection point to X-axis. The two traced lines should form a sharp, 90° corner.
5. The stress value chosen from step 1 shows the stress that corresponds to the strain, or deformation, experienced by the test specimen at that point.

The steps above can be used to determine the strain experienced by the test specimen at the moments the yield stress, ultimate tensile strength, and fracture point are reached.

What Are the Different Regions of the Stress-Strain Curve Graph?

Five significant points can easily be picked off a stress-strain curve. The interpretation of each point offers unique insight into the mechanical behavior of a material. The five points are described in detail below:

1. Proportional Limit

The proportional limit refers to the point at the end of the linear portion of the stress-strain curve.All of the deformation up to the proportional limit occurs with one proportionality constant, called Young's modulus. It is calculated as the slope of the line (stress divided by strain) up to the proportional limit. In this region, Young’s modulus can be obtained by calculating the slope of the line. 

2. Elastic Limit

The elastic limit is the observed point on the stress-strain curve where elastic deformation ends and plastic deformation begins. When the applied load is released at any point up to the elastic limit, the material will regain its starting dimensions. In metals, the elastic limit is often difficult to distinguish from the proportional limit and the yield point since the points on the curve are so close to each other. Therefore, the elastic limit is more often used for educational purposes rather than actual characterization of a material’s properties.

3. Yield Point

The yield point is similar to the elastic limit of the stress-strain curve in that it also describes the point where elastic deformation ends and plastic deformation begins. The primary difference between the two is that the yield point is a calculated value that precisely describes the elastic limit, or yield strength of the material. The yield point is determined by offsetting the linear portion of the stress-strain curve by +0.2% along the horizontal (strain) axis. The intersection point of the offset line with the original stress-strain curve is considered the yield strength of the material.

4. Ultimate Stress Point

The ultimate stress point, or ultimate tensile strength, is the highest stress observed on the stress-strain curve. After the ultimate tensile strength is reached, the test specimen begins to “neck.” It’s important to note that while the ultimate stress point is the highest point observed on the stress-strain curve, the actual highest stress is actually the true stress at fracture.

5. Fracture or Breaking Point 

The fracture or breaking point is the point on the stress-strain curve where the test specimen has deformed so much that its microstructure gives and the part fractures.

How To Make a Stress-Strain Curve?

A stress-strain curve is made by conducting a tensile test using a universal testing machine. The testing machine will automatically capture the data to produce a stress-strain curve as the load increases and the specimen deforms. 

What Is the Use of the Stress-Strain Graph?

The stress-strain graph is used to determine various mechanical properties of a material, including elastic modulus, Poisson’s ratio, yield stress, and ultimate tensile strength. These properties help engineers select materials for applications where load-bearing capability is critical.

What Is the Stress-Strain Curve of a Ductile Material? 

The engineering stress-strain curve for a ductile material is characterized by an increasing straight line until the yield point is reached. After the yield point, the function of stress and strain increases non-linearly and peaks when the ultimate tensile strength is reached. Afterward, the engineering stress non-linearly decreases as the strain continues to increase. Eventually, once the material’s strain has become so large, the material fractures. For more information, see our guide on Ductility.

Figure 1 below is an example of a stress-strain curve of a ductile and brittle material: