Problem 34 - An Introduction to the Mechanics of Solids in SI Units

Question

The most commonly quoted results of a tensile test are the yield point or yield strength, the tensile strength, the percentage elongation, and the percentage of reduction of area. How can one tell from these results whether or not any necking occurred before fracture?

Step-by-Step Solution

Answer

From the results of a tensile test, one could infer that necking has occurred before fracture if there is a large percentage of elongation and a significant percentage reduction in area. This signifies that considerable plastic deformation has occurred, which is characteristic of necking.

Step 1: Define necking

Necking in a material under stress is a form of tensile deformation where the cross-section of the sample narrows significantly. This occurs after the material has reached its ultimate tensile strength, meaning it has passed the highest stress that it can withstand without breaking.

Step 2: Understand the implication on the four parameters

After the occurrence of necking, the cross-sectional area starts to decrease. Hence, even if the load might decrease, the stress might increase due to the decrease in cross-sectional area. The elongation continues to increase until fracture occurs. The percentage of reduction in area will be greater when necking occurs.

Step 3: Drawing Conclusion

If there is a significant reduction in area compared to the nominal area or a significant elongation, it is likely that necking occurred before fracture. These are signs of significant plastic deformation which is an indicator of necking.

Key Concepts

Yield Strength

Yield strength is a fundamental concept in materials science, referring to the maximum stress that a material can withstand while still maintaining its shape. Before reaching the yield strength, materials will undergo elastic deformation, where they can return to their original form when the applied stress is removed. It acts as a defining limit between elastic and plastic deformation.
Understanding yield strength is important because:

• It indicates the ability of the material to sustain loads without permanent deformation.
• Helps in choosing appropriate materials for structures that need to endure specific stress levels.

The yield strength is typically determined from a stress-strain curve, found during a tensile test. On this curve, it appears as the point where the curve starts to deviate from linearity. This deviation indicates that permanent, or plastic, deformation begins.
After surpassing the yield strength, any additional stress will result in irreversible deformation. This plastic change does not revert unless further processed or stressed beyond the yield point.

Tensile Strength

Tensile strength, also known as ultimate tensile strength (UTS), is another critical measure in material science. It represents the maximum stress a material can endure while being stretched or pulled before necking starts to occur.
This property is measured in a tensile test by applying a force gradually and recording the stress at which the material ultimately fractures.
Key aspects to remember about tensile strength include:

• It provides a peak measure of a material's resistance to breaking under tension.
• The tensile strength is higher than the yield strength because it includes the plastic deformation ability of the material.
• Materials with high tensile strength are often more suited for applications where high-load resistance is necessary.

During a tensile test, tensile strength can be identified at the highest point on the stress-strain curve. This maximum point provides valuable insights for engineers and designers about a material's capability to withstand various loads before failure.

Necking

Necking refers to the localized decrease in cross-sectional area of a material experiencing tensile stress. This phenomenon occurs after the material has surpassed its tensile strength, where it reaches the ultimate capacity point for sustaining stress.
As the material continues to be pulled, the necking area becomes more pronounced, leading to eventual fracture.
Here are a few relevant details about necking:

• Necking serves as an indicator that the tensile strength has been surpassed. It is the precursor step to fracture.
• Materials that demonstrate significant necking tend to exhibit greater plasticity or ductility.
• In tensile tests, the occurrence of necking can be noted through a sharp drop in the stress level post the ultimate tensile strength.
• Observations during necking include substantial elongation and a notable reduction in the cross-sectional area.

When necking occurs, it is a clear sign of the material's capacity to deform plastically under stress, highlighting its ductility. To determine if necking has taken place, engineers will look for key indicators such as significant elongation and reduced cross-sectional area in test samples.