Understanding Ultimate Stress in Mild Steel

The question asks about the relationship between the ultimate tensile stress and the ultimate compressive stress of mild steel.

Let's first understand what ultimate stress means.

• Ultimate Tensile Stress: This is the maximum stress a material can withstand under tensile loading before necking starts (a localized reduction in cross-sectional area). It is calculated as the maximum load sustained during a tensile test divided by the original cross-sectional area of the specimen.
• Ultimate Compressive Stress: This is the maximum stress a material can withstand under compressive loading. For ductile materials like mild steel, it is often considered the stress at which the material yields significantly or begins to deform plastically under compression, although the concept of "ultimate" compressive stress can be less clearly defined than in tension because ductile materials tend to bulge or barrel rather than fracture cleanly. However, it generally represents the maximum load carried per original unit area in compression.

Behavior of Mild Steel Under Tension and Compression

Mild steel is a ductile material. Its behavior under tensile and compressive loads is different, particularly in the post-yield region leading up to the ultimate stress.

• Under tension, mild steel exhibits yielding, strain hardening, and then necking before fracture. The ultimate tensile stress corresponds to the peak load before necking.
• Under compression, mild steel also yields. However, instead of necking, it tends to bulge or barrel due to lateral expansion. For short specimens where buckling is prevented, the material can withstand significant compressive strain and the stress may continue to rise after initial yielding due to strain hardening. Defining a clear "ultimate" point akin to the peak in tension can be complex, but engineers often use the stress at which significant plastic flow occurs or a specific amount of strain is reached as a practical limit.

Comparing Ultimate Tensile and Compressive Strength

For ductile materials like mild steel, the ultimate tensile strength is typically considered to be higher than the ultimate compressive strength. This is partly due to the way failure occurs in tension (necking) versus compression (barreling/yielding).

In a tensile test, the stress is calculated based on the original area, but the material actually supports the load over a decreasing cross-sectional area during necking. The ultimate tensile stress is the maximum load divided by the original area, which represents the peak of the engineering stress-strain curve.

In a compression test, the cross-sectional area typically increases as the material bulges. The stress is also calculated based on the original area. While the material can sustain very large loads and strains in compression (if buckling is prevented), the concept of an "ultimate" failure point analogous to tensile fracture is less distinct. Often, the yield strength in compression is similar to that in tension, but the ultimate strength values differ.

Experimental data and material properties generally show that the ultimate tensile strength of mild steel is greater than its ultimate compressive strength.

Therefore, the ultimate tensile stress of mild steel compared to ultimate compressive stress is more.