Short Answer:

The yield point is the point on the stress-strain diagram at which a material begins to deform permanently. It is defined as the stress at which the material starts to yield, meaning it undergoes plastic deformation even without an increase in the applied load.

In simple words, the yield point is the limit between elastic and plastic behavior of a material. Below this point, the material returns to its original shape when the load is removed. Beyond it, the material experiences permanent deformation and cannot fully regain its original dimensions.

Detailed Explanation:

Yield Point

Definition and Meaning:
When a material is subjected to increasing stress, it first deforms elastically, meaning the deformation disappears completely once the load is removed. However, beyond a certain level of stress, the material begins to deform permanently, and the deformation does not fully disappear even after removing the load.

The stress corresponding to this point — where the material starts to deform plastically — is known as the yield point.

Thus, the yield point is the transition point between elastic and plastic behavior of a material. It represents the beginning of permanent deformation, which is extremely important in engineering design because it defines the safe working limit for materials.

Explanation of Yield Point

When a load is applied to a material, the atoms inside the material are displaced slightly from their original positions. Initially, these atomic bonds stretch but remain intact, and the material returns to its original shape once the load is removed — this is the elastic region.

However, as the load increases, the bonds between atoms begin to slip or rearrange permanently, and the material yields. At this stage, the material continues to deform even if the load is not increased further. This behavior is represented by the yield point on the stress-strain curve.

In the case of ductile materials such as mild steel, the yield point is very clear and distinct. In contrast, brittle materials like cast iron do not show a well-defined yield point.

Yield Point in Stress-Strain Diagram

In the stress-strain diagram of a ductile material (like mild steel), the yield point is located between the elastic limit and the plastic region.

The material initially obeys Hooke’s law in the straight portion of the curve, where stress is proportional to strain. After the elastic limit, a small increase in stress causes a large increase in strain — this marks the yield point.

For mild steel, two yield points are observed:

1. Upper Yield Point:
   • It is the point where yielding starts suddenly with a small increase in load.
   • It represents the maximum stress before the material begins to deform plastically.
   • Beyond this point, the stress drops slightly even though strain increases.
2. Lower Yield Point:
   • It is the point where the material continues to deform at a nearly constant stress.
   • It represents the stable stage of plastic deformation before strain hardening begins.

After the lower yield point, the material enters the plastic region, where it can deform significantly without much increase in stress.

Mathematical Representation

If  is the yield stress, then:

Where:

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

This yield stress helps engineers determine how much stress a material can withstand before permanent deformation begins.

Physical Meaning of Yield Point

The yield point indicates the start of plastic flow in a material. Below this point, deformation is fully recoverable (elastic deformation). Beyond it, deformation becomes irreversible (plastic deformation).

Physically, it means that the internal structure of the material has started to rearrange. The movement of dislocations (imperfections in crystal structure) increases rapidly, allowing atoms to slide over each other, causing permanent deformation.

This property is especially important for ductile materials, which can withstand large plastic deformations before failure, unlike brittle materials that fracture suddenly.

Factors Affecting Yield Point

1. Material Composition:
   • The presence of alloying elements or impurities can change the yield point. For example, adding carbon increases the yield strength of steel.
2. Heat Treatment:
   • Processes like annealing, quenching, and tempering can alter the yield point by changing the internal structure of the material.
3. Temperature:
   • At higher temperatures, materials generally have a lower yield point because they become softer.
   • At lower temperatures, yield stress increases, and materials become more brittle.
4. Strain Rate:
   • The rate at which load is applied affects the yield point. A rapid load application increases the yield stress.
5. Previous Working (Cold Working):
   • Materials that have been plastically deformed earlier (cold-worked) have a higher yield stress due to strain hardening.

Engineering Importance of Yield Point

The yield point is one of the most important mechanical properties in material science and engineering because it defines the safe load-carrying capacity of materials.

1. Design of Components:
   • Engineers always design structures and machine parts to work within the elastic region, below the yield point.
2. Determination of Working Stress:
   • The working stress or allowable stress is usually a fraction of the yield stress, calculated using a factor of safety (FOS).

1. Material Selection:
   • The yield point helps in choosing appropriate materials for construction, machinery, and load-bearing applications.
2. Study of Plastic Deformation:
   • It helps in analyzing how materials behave under long-term loading, metal forming, or shaping operations like forging and rolling.
3. Predicting Failure:
   • By knowing the yield point, engineers can predict when a material will start to deform permanently under real working conditions.

Behavior of Materials Based on Yield Point

• Ductile Materials:
  Such as mild steel, aluminum, and copper show a clear yield point, making them suitable for forming and shaping processes.
• Brittle Materials:
  Materials like cast iron, glass, and ceramics do not exhibit a distinct yield point; they fracture soon after the elastic limit is reached.

In such cases, a property known as 0.2% proof stress is used to define an approximate yield point — it represents the stress that produces 0.2% permanent strain.

Practical Applications of Yield Point

1. Design of Steel Structures and Bridges:
   Yield stress is used as a key design parameter to ensure that steel members do not deform permanently under load.
2. Manufacturing and Metal Forming:
   Knowing the yield point helps in determining the pressure required for forming operations like extrusion, drawing, and rolling.
3. Automotive and Aerospace Engineering:
   Materials are selected based on their yield point to ensure safety and durability under varying load conditions.
4. Testing and Quality Control:
   The yield point is used in tensile testing to verify material properties and ensure compliance with standards.

Conclusion:

The yield point is the stress at which a material starts to deform plastically and cannot return to its original shape after the removal of load. It marks the transition between elastic and plastic behavior and is a key parameter in determining the material’s mechanical strength. For ductile materials, two yield points — upper and lower — are often observed. The concept of yield point is vital in engineering design, material selection, and structural safety, ensuring that materials operate safely within their elastic limit under real-life loading conditions.