Short Answer:

Yield stress is the amount of stress at which a material begins to deform permanently. It represents the transition point between elastic and plastic behavior. When stress is below the yield stress, the material returns to its original shape after removing the load, but once it exceeds the yield stress, the deformation becomes permanent.

In simple words, yield stress defines the limit of elasticity of a material. It is a critical property used in engineering design to ensure that materials and components operate safely without undergoing permanent deformation under working loads.

Detailed Explanation:

Yield Stress

Definition and Meaning:
When a material is subjected to an external load, it experiences deformation. Initially, this deformation is elastic, meaning the material returns to its original shape once the load is removed. However, as the load increases, the material reaches a point beyond which deformation becomes permanent even after removing the load.

The stress corresponding to this point is known as yield stress or yield strength.

Mathematically,

Where:

• σy = Yield stress (N/m² or MPa)
• Py = Load at yield point (N)
• A₀ = Original cross-sectional area (m²)

The yield stress indicates the beginning of plastic deformation, which is irreversible. This value is crucial for designing safe and reliable mechanical components.

Explanation of Yield Stress

The behavior of a material under stress can be understood using a stress-strain diagram. As the applied load increases, the material passes through several regions — elastic, yielding, plastic, and fracture. The yield stress marks the end of the elastic region and the beginning of the plastic region.

1. Elastic Region (Before Yield Stress):
   In this region, stress is directly proportional to strain, following Hooke’s Law:

The material behaves elastically, meaning once the load is removed, it returns to its original dimensions.

1. At the Yield Point (Yield Stress):
   When stress reaches the yield stress, the material starts to yield — that is, it undergoes permanent deformation. This deformation continues without any significant increase in stress.
2. Plastic Region (Beyond Yield Stress):
   In this region, the material deforms permanently even if the load is removed. The strain increases significantly while the stress remains almost constant or increases slightly.

Thus, yield stress is the dividing line between elastic and plastic deformation. It defines how much stress a material can withstand before it begins to deform permanently.

Physical Meaning of Yield Stress

The yield stress represents the stress level at which atomic bonds within the material begin to break or rearrange. Below this stress level, the atomic structure of the material only stretches, and when the load is removed, the atoms return to their original positions.

However, when the applied stress exceeds the yield stress, the atomic bonds start to slip and rearrange permanently, resulting in plastic deformation. This process is known as yielding.

Therefore, yield stress provides an accurate indication of a material’s elastic strength and the beginning of its plastic behavior.

Typical Values of Yield Stress for Common Materials

• Mild Steel: 250 – 350 MPa
• Copper: 70 – 100 MPa
• Aluminum: 40 – 80 MPa
• Brass: 100 – 200 MPa
• Cast Iron: 100 – 150 MPa
• Rubber: 10 – 20 MPa

The yield stress varies widely depending on the type of material and its treatment. Ductile materials such as steel and copper show a clear yield point, while brittle materials like cast iron do not have a distinct yield stress.

Types of Yield Stress

1. Upper Yield Stress:
   • It is the maximum stress at which a material begins to yield.
   • Seen in ductile materials like mild steel where stress rises slightly before dropping.
   • It represents the point at which yielding starts suddenly.
2. Lower Yield Stress:
   • It is the minimum stress at which the material continues to deform plastically after yielding begins.
   • This occurs just after the upper yield point.
   • It remains almost constant during the plastic flow of the material.

In many materials, particularly brittle ones, the yield stress is not well-defined. In such cases, a proof stress is used instead.

Proof Stress (Alternative to Yield Stress)

For materials that do not show a clear yield point, such as aluminum or high-strength alloys, an arbitrary offset strain (usually 0.2%) is chosen. The stress corresponding to this strain is called the 0.2% proof stress.

Thus, the proof stress represents the stress that causes 0.2% permanent strain in the material. It serves as an approximate value of yield stress for materials without a distinct yield point.

Factors Affecting Yield Stress

1. Material Composition:
   Alloying elements and impurities affect the yield strength. For example, adding carbon to steel increases its yield stress.
2. Heat Treatment:
   Heat treatment processes such as quenching, annealing, or tempering can alter yield stress by changing the internal structure of materials.
3. Temperature:
   • As temperature increases, yield stress decreases because materials become softer and more ductile.
   • At low temperatures, yield stress increases, making materials stronger but more brittle.
4. Strain Rate:
   Yield stress increases with faster application of load since materials have less time to deform plastically.
5. Cold Working:
   Plastic deformation at room temperature (cold working) increases yield stress by strain hardening.

Engineering Importance of Yield Stress

1. Safe Design of Components:
   Engineers design mechanical components to operate below the yield stress to prevent permanent deformation.
2. Calculation of Working Stress:
   The working or permissible stress is derived from yield stress using a factor of safety (FOS).

1. Material Selection:
   Yield stress helps engineers choose suitable materials for components that need to resist high stresses without deforming.
2. Structural Integrity:
   It ensures that parts like beams, rods, or shafts do not deform permanently under load, maintaining their shape and functionality.
3. Quality Control:
   In manufacturing, the yield stress is used to verify that materials meet required mechanical strength standards.

Example Calculation

A mild steel rod has a cross-sectional area of 100 mm² and begins to yield under a load of 30,000 N.

Hence, the yield stress of the material is 300 MPa, meaning the rod will begin to deform permanently if the stress exceeds this limit.

Conclusion:

The yield stress is the stress at which a material begins to deform plastically and can no longer return to its original shape when the load is removed. It defines the limit between elastic and plastic behavior and is a vital property for determining the safe working load of materials. By keeping operating stresses below the yield stress, engineers ensure that machines and structures remain safe, efficient, and reliable during service. Therefore, yield stress is a fundamental concept in material strength and mechanical design.