## An Introduction to Yield Strength

Yield strength is defined as the stress at which a material ceases elastic deformation and begins plastic deformation. It is one of a material's most important mechanical properties. It helps engineers to understand how a material deforms when subjected to stress, therefore assisting them in picking appropriate materials for different applications. Yield strength is determined by conducting a tensile test on a material specimen. This article will define yield strength, discuss its importance in engineering, and describe how it is plotted on graphs and how it is calculated.

First, identify the linear portion of the graph. This is the portion of the curve where the stress and strain are proportional to each other. Second, identify where the linear portion of the curve ends and the non-linear portion begins.

There are several ways to define a material’s yield strength based on its stress-strain graph. The most common way of characterizing a material's yield strength is called the "0.2% offset yield strength." To determine the 0.2% offset yield strength, a line is drawn on the stress-strain curve parallel to the initial linear, elastic stress-strain loading curve. The origin of this offset line is at zero stress (0 on the y-axis) and 0.2% strain (0.2% on the x-axis). The point where this offset parallel line intersects the actual stress-strain curve is considered the yield strength of the material. For more information, see our guide on the Stress-Strain Curve.

The yield point is just one point on a stress-strain curve. Surrounding that point are other features that can be described and measured from a stress-strain curve. These points of interest and regions are explained in the list below:

#### 1. Yield Point

The yield point is the observed point on the stress-strain curve where plastic deformation begins. The material deforms elastically from the start of the tensile stress to the yield point. The yield point can be estimated by observing where the linear portion of the stress-strain graph ends and where the non-linear portion begins. Some metals, like mild steel, have two yield points.

#### 2. Elastic Limit

The elastic limit is the point on the stress-strain curve that characterizes the maximum amount of strain a material can withstand without permanent deformation. When stress is released, the material returns to its original dimensions. Beyond the elastic limit, deformation is permanent.

#### 3. Proportionality Limit

The proportionality limit is the point at the end of the linear portion of the stress-strain curve. Prior to the proportionality limit, stress is directly proportional to strain in the material. The proportion of the stress to strain is the modulus of elasticity or Young’s modulus of the material. Once the proportionality limit is surpassed, the relationship between stress and strain is no longer linear.

#### 4. True Elastic Limit

The true elastic limit is the lowest stress that allows dislocations in the crystalline structure of materials to move. It is seldom used to describe material yield since dislocations can move at low stress and it is difficult to detect such movements.

#### 5. Upper and Lower Yield Points

The upper yield point indicates the onset of plastic deformation in the test specimen due to the rapid generation of dislocations in the crystal lattice. However, this point occurs at an unstable value which is dependent on strain rate and test equipment and is not a good basis for design work. The lower yield point denotes a period before strain hardening begins, during which localized bands of plastic deformation, called Luders bands, form and spread across the test section at almost constant stress. The lower yield point is both more repeatable and more conservative.

#### 6. Offset Yield Stress (Proof Stress)

The offset yield stress or proof stress is the most common method for describing a material’s yield strength. It is determined by drawing a line parallel to the linear portion of the stress-strain curve. This line is offset 0.2% strain in the positive direction. The point where this offset line intersects the stress-strain curve is taken to be the yield strength of the material.

### Necking and Fracture in the Yield Strength Test

A neck is a region of localized high plastic deformation formed during a tensile test that will inevitably lead to fracture with further application of load. There is a noticeable decrease in the cross-sectional area of the test specimen at the neck perpendicular to the direction of application of the tensile forces. Necking normally occurs in ductile metals after the peak engineering stress (ultimate tensile strength) has been reached. After that point, engineering stress decreases because the neck reduces the sample's cross-sectional area.

## The Formula for Yield Strength

The mathematical formula for yield strength, or stress at yielding, is simply the basic formula for determining stress: force divided by area normal to the force. Yield strength is specifically defined as the applied force when plastic deformation begins divided by the original cross-sectional area of the test sample. This can also be referred to as the engineering stress at the yield point. The formula is given below:

Yield strength formula.

*Where:*

- F is the applied force
- A0 is the original cross-sectional area of the test specimen

The stress used to calculate yield strength can be based upon either the engineering stress at 0.2% offset strain or upon the engineering stress at the lower yield point.

Yield strength is usually expressed in Pascals (Pa), the SI unit for stress, or in pounds per square inch (psi).

The symbol for yield strength is σY. The Greek letter σ is the symbol used for engineering stress, while the subscript “Y” means “yield.” Occasionally, “SY” is also used to denote yield strength.

## Examples of Yield Strength in Key Materials

The yield strength of a material depends on its crystal structure, its chemical composition, and whether it is a fiber-reinforced composite. The yield strengths of some example materials are listed below:

**Steels:**The yield strength of steel ranges from as low as 220 MPa (hot-rolled A36 steel) to as high as 1570 MPa (4140 alloys, oil-quenched and tempered).**Stainless Steels:**Yield strength for stainless steel varies between about 250 MPa (austenitic stainless steel) to 1000 MPa (precipitation-hardened stainless steel).**Aluminum Alloys:**The yield strengths of aluminum alloys range between 24 MPa (1100 aluminum alloy) and 483 MPa (7075 aluminum alloy).**Plastics:**The yield strengths of plastics range from as low as 4 MPa (plasticized PVC) to as high as 300 MPa (carbon-fiber filled PA 66).

These are good things to keep in mind when you're working on your parts before uploading them to the Xometry platform.

Xometry provides a wide range of manufacturing capabilities including CNC machining, 3D printing, injection molding, laser cutting, and sheet metal fabrication. You can get quotes on materials with many different yield strengths. Get your instant quote today.

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