Stress-Strain Diagram - Ductile Materials

When a specimen is first loaded, its length increases linearly at a slow rate, creating a steep straight line on the stress-strain diagram. This indicates elastic deformation, where the material will return to its original shape once the load is removed. This linear behavior continues until the material reaches its yield strength.

Yield strength is the stress at which a material begins plastic deformation and no longer returns to its original shape after unloading. Ultimate strength is the maximum stress the material can withstand before necking occurs. Breaking strength, by contrast, is the stress corresponding to material rupture after necking.

As load increases beyond the yield point, the material's diameter decreases at a localized region due to plastic deformation concentrating in that area. This phenomenon is called necking. After necking begins, even small load increments cause significant elongation until the specimen ruptures completely.

Structural steel exhibits constant stress post-yield due to strain-hardening, where the material strengthens as it deforms plastically. Aluminum, however, shows non-linear stress increase after yield, meaning its stress continues to rise as strain increases. Both materials are ductile but respond differently to plastic deformation.

Ductility is measured by percent elongation, which represents the permanent length increase after rupture, or by percent reduction in cross-sectional area at the necked region. These metrics quantify how much plastic deformation a material undergoes before failure, with higher values indicating greater ductility and ability to deform.

Under compression, ductile materials' stress-strain curves diverge at higher strains compared to tension. Unlike tension, necking does not occur during compression, allowing the material to continue deforming without localized diameter reduction. This fundamental difference affects how ductile materials respond to compressive versus tensile loading.

After yielding begins, shearing stresses cause slippage along oblique surfaces within the material, enabling significant plastic deformation with minimal increase in applied load. This shear-driven mechanism is responsible for the material's ability to undergo substantial permanent shape change. Shearing stresses are the primary driver of plastic behavior in ductile materials.