Stress-Strain Diagram

The stress-strain diagram is a fundamental tool in material science and mechanical engineering that illustrates how a material responds to applied stress, showing the relationship between stress (force per unit area) and strain (relative deformation). This graph is typically generated from a tensile test, where a sample is gradually stretched until failure, capturing key mechanical properties.

The horizontal axis represents strain (ε), indicating how much the material deforms, while the vertical axis represents stress (σ), showing the internal resistance to deformation. The shape of the curve varies by material, but common features include an initial linear region where stress and strain are proportional, followed by a yield point, plastic deformation, and ultimately fracture.

By analyzing the stress-strain diagram, engineers can determine critical properties such as elasticity, yield strength, ultimate tensile strength, and ductility, which help in selecting appropriate materials for structural and mechanical applications. The curve also distinguishes between brittle and ductile materials, as brittle materials tend to fracture without significant plastic deformation, while ductile materials exhibit extensive elongation before failure.

Stress-Strain Diagram

Young’s Modulus

Young’s Modulus
Young’s modulus is a material property that measures a material's stiffness—its ability to resist deformation under tensile or compressive stress. It quantifies the relationship between stress and strain in the elastic region of a material’s stress-strain curve (it is the slope of the linear part of the curve), where deformation is reversible. The formula for...

Ultimate Strength

Ultimate Strength
Ultimate strength refers to the maximum stress a material can withstand before failure, regardless of whether the failure occurs due to fracture or significant plastic deformation. It represents the peak stress value on a stress-strain diagram and is a key property in material selection and mechanical design. When discussing ultimate strength, the most common reference...

Yield Strength

Yield Strength
Yield strength is the stress level at which a material begins to deform plastically, meaning that beyond this point, deformation is permanent and the material will not return to its original shape when the load is removed. It marks the end of the elastic region and the beginning of the plastic region on a stress-strain...

Strain Hardening

Strain Hardening
Strain hardening, also known as work hardening, is the phenomenon where a material becomes stronger and harder as it undergoes plastic deformation. It occurs after the yield point, in the plastic region of the stress-strain curve, where the material continues to deform under increasing stress. After yielding, if the material is further loaded, it does...

Necking

Necking
Necking is a localized reduction in cross-sectional area that occurs in ductile materials after they reach their ultimate tensile strength (UTS) during a tensile test. As the material is stretched beyond the UTS, plastic deformation becomes concentrated in one region, causing a visible narrowing, or "neck," in the specimen. This phenomenon signals the transition from...

Fracture

Fracture
Fracture is the final stage of material failure, occurring when a material can no longer withstand applied stress and breaks apart. The nature of fracture depends on the material’s ductility and loading conditions, and it is broadly classified into ductile fracture and brittle fracture. Ductile Fracture Ductile fracture occurs after significant plastic deformation, often involving...

Elastic Recovery (Springback)

Elastic Recovery (Springback)
Elastic recovery refers to the tendency of a material to partially return to its original shape after a load is removed, even if some plastic deformation has occurred. While the elastic portion of the deformation is fully recovered, any plastic deformation remains permanent. This behavior is observed in both purely elastic loading and in cases...

Proportional Limit

Proportional Limit
The proportional limit is the maximum stress at which a material maintains a linear relationship between stress and strain, meaning it strictly follows Hooke’s Law (σ = E × ε). Up to this point, stress is directly proportional to strain, and the material behaves elastically, meaning it will return to its original shape once the...
Young's Modulus

Young's Modulus

Young’s modulus is a material property that measures a material's stiffness—its ability to resist def...

Other Moduli of Elasticity

There is a subtle but meaningful distinction between Young’s modulus and the modulus of elasticity ,...
Ultimate Strength

Ultimate Strength

Ultimate strength refers to the maximum stress a material can withstand before failure, regardless...
Yield Strength

Yield Strength

Yield strength is the stress level at which a material begins to deform plastically , meaning that...
Upper & Lower Yield Strength

Upper & Lower Yield Strength

Some materials, particularly mild steels and certain low-carbon alloys , exhibit both an upper yield...
Strain Hardening

Strain Hardening

Strain hardening , also known as work hardening , is the phenomenon where a material becomes stronger...
Necking

Necking

Necking is a localized reduction in cross-sectional area that occurs in ductile materials after they...
Fracture

Fracture

Fracture is the final stage of material failure, occurring when a material can no longer withstand...
Elastic Recovery (Springback)

Elastic Recovery (Springback)

Elastic recovery refers to the tendency of a material to partially return to its original shape after...
Proportional Limit

Proportional Limit

The proportional limit is the maximum stress at which a material maintains a linear relationship between...