Stress Strain Curve For Mild Steel

Mild steel is one of the most widely used ductile materials in construction due to its affordability and strength. Understanding the behavior of mild steel under loading, specifically how it reacts when forces are applied is crucial for engineers and architects. This behavior can be best understood through the stress-strain curve for mild steel. By studying the curve, professionals can determine the material’s actual limits, strength, and behavior under various conditions, which ultimately helps them in making informed decisions for various construction projects.

What is a Concept of Stress-Strain Curve?

A stress-strain curve is a graphical representation of how a material deforms under various levels of stress. On the x-axis, we have strain (the amount of deformation) while on the y-axis, we have stress (the force per unit area). The curve helps to understand the mechanical properties of materials like mild steel and is essential in material selection, design, and safety calculations.

Stress-Strain Curve for Mild Steel

The stress strain curve for mild steel consists of strain along the x-axis and stress along the y-axis. Stress strain curve for mild steel consists of various stages such as:

• Proportional Limit
• Elastic Limit
• Upper Yield
• Lower Yield
• Ultimate Stress
• Breaking Point

Proportional Limit

At the initial stage, as stress is applied to the mild steel rod, the strain increases in direct proportion to the applied stress. This is represented as point A in the graph. At this stage, the material obeys Hooke’s Law, meaning the stress is proportional to the strain. When the stress is removed, the material returns to its original shape, and the strain returns to zero. This portion is known as the proportional limit. Thus the ‘0’ to ‘A’ points is called as ‘proportional limit‘.

At the start of the curve, as stress is applied to the mild steel, the strain increases in direct proportion to the stress. This region is represented by point A on the stress-strain graph. In this elastic region, the material follows Hooke’s Law, meaning that stress is directly proportional to strain. The relationship is given by the formula:

where:

• σ is the stress,
• E is the Young’s Modulus (modulus of elasticity)
• e is the strain.

At this stage, if the applied stress is removed, the material returns to its original shape, and the strain returns to zero. This is why the region from point 0 to A is referred to as the proportional limit. The material behaves elastically and fully recovers from deformation when the stress is removed.

Elastic Limit

As the stress increases beyond point A, the mild steel enters the elastic limit, represented by point B. The elastic limit is the maximum stress the material can withstand while still returning to its original shape when the stress is removed. If the stress exceeds this limit, the material begins to undergo permanent deformation. This stage indicates when the material shifts from elastic to plastic behavior.

It is essential to recognize the elastic limit in applications where material recovery is important. For example, in structural steel used in buildings, knowing the elastic limit helps structural engineers ensure that the material will not deform permanently under normal loads.

Yield Points: Upper and Lower

Beyond the elastic limit, mild steel enters a plastic deformation region. The yield point marks the onset of permanent deformation, where the material starts to stretch without returning to its original form. There are two key points in this region: the upper yield point (point C) and the lower yield point (point D).

• The upper yield point (point C) is the point at which the material requires the maximum stress to begin plastic deformation. Once this stress is exceeded, the material will continue to deform at a reduced stress level.
• The lower yield point (point D) is the minimum stress required for continued deformation. After the upper yield point is surpassed, the material starts to deform more easily, even with lower stress.

These two yield points are significant because they indicate the material’s transition from elastic to plastic behavior. In practical terms, mild steel is used in scenarios where some plastic deformation is acceptable, such as in beams or structural components that must absorb shock loads.

Ultimate Stress

As stress increases further, the material enters the strain-hardening phase, which is represented by point E on the curve. This point is known as ultimate stress or ultimate tensile strength (UTS). At this stage, the material is undergoing plastic deformation, but the stress required to cause further deformation continues to increase, reaching its peak at the ultimate stress point.

The ultimate stress is the maximum stress the material can withstand before the beginning of necking. Beyond this point, the material begins to experience reduction in cross-sectional area, which leads to the necking stage.

Necking and Breaking Point

After the ultimate stress point, the material undergoes necking, where the cross-sectional area begins to narrow. This narrow reduction in cross-sectional area occurs because the material has become weaker at certain points, often due to microscopic flaws or stress concentration. Eventually, the necked region reaches the breaking point (point F), where the material breaks. This is the final stage in the stress-strain curve, marking the failure of the material under stress.

The breaking point is important in understanding the limits of a material’s performance in real-world applications. For example, mild steel used in structural beams must be carefully designed to prevent failure due to necking and fracture. Engineers must ensure that the material stays within its elastic limit or operates safely below the ultimate stress.

What is a Ductile Material?

Ductile materials are materials that can stretch or deform a lot before breaking. Examples include mild steel, aluminum, copper, and gold. These materials are strong and can absorb a lot of energy during deformation. Their stress-strain curves have two clear parts: an elastic region where they return to their original shape and a plastic region where they stay deformed permanently. Mild steel is a common ductile material, known for its strength and use in construction and manufacturing.

Stress-Strain Curve for Ductile Materials

The stress-strain curve for ductile materials is generally similar to the curve observed for mild steel, with similar elastic and plastic regions. However, slight differences can occur depending on the type of ductile material. For example:

• Aluminum: It does not have same upper and lower yield points like mild steel. Instead, the transition from elastic to plastic deformation is smoother.
• Copper: It shows a higher degree of elongation and strain before breaking, showing a more extended plastic region.
• Gold: It has a much lower yield strength but deforms significantly before fracture, making its curve flatter in the elastic region.

In all ductile materials, the elastic region is where stress is proportional to strain, and the material returns to its original shape if the stress is removed. Beyond the elastic limit, the plastic region begins, where the material undergoes permanent deformation. This behavior, common to all ductile materials, is key to their widespread use in construction and manufacturing.

Elastic Deformation vs. Plastic Deformation

The table below compares elastic and plastic deformation based on their behavior under stress.

Elastic Deformation	Plastic Deformation
Temporary deformation where the material returns to its original shape once the stress is removed.	Permanent deformation where the material does not return to its original shape after the stress is removed.
It occurs in the elastic region of the stress-strain curve.	It occurs in the plastic region of the stress-strain curve.
Stress is proportional to strain, following Hooke’s Law.	Stress and strain are no longer proportional; the material deforms plastically.
The material recovers its original shape once the load is removed.	The material does not recover its original shape after the load is removed.
Example: Stretching a rubber band within its limit.	Example: Bending a metal bar beyond its elastic limit.

How is the Stress-Strain Curve for Concrete Different from Mild Steel?

The stress-strain curve for mild steel shows a clear elastic region where the material stretches and returns to its original shape, followed by a plastic region where it deforms permanently before breaking. In contrast, the curve for concrete behaves differently. Concrete, being a brittle material, has a much steeper curve in the elastic region, meaning it doesn’t stretch as much before it fractures. Unlike mild steel, concrete fractures suddenly with very little plastic deformation. To learn more about how concrete behaves under stress and its stress-strain characteristics, check out our detailed article on the stress-strain curve for concrete.