Coefficient of Linear Expansion Explained: How Materials Expand with Temperature

What is the Coefficient of Linear Expansion?

The coefficient of linear expansion, also called the thermal expansion coefficient, measures how much an object’s length or volume changes with temperature. It is typically expressed in per Kelvin (/K) or per Celsius (/℃).

Linear expansion refers to changes in length, while volume expansion refers to changes in volume. Linear expansion is more commonly used in engineering and design.

The coefficient is not a fixed value. It is usually expressed as an average over a specific temperature range. For wide temperature ranges, separate coefficients may be used for ranges before and after the glass transition temperature.

Relationship Between Coefficient of Linear Expansion and Coefficient of Volume Expansion

The coefficient of linear expansion α for a solid is defined as:

α = (1/l) * (Δl/Δt)

Where l: length of the object, Δl: change in length, t: temperature of the object, Δt: change in temperature.

The coefficient of volume expansion β is defined as:

β = (1/V) * (ΔV/Δt)

Where V: volume of the object, ΔV: change in volume, t: temperature of the object, Δt: change in temperature.

For most common objects, both coefficients are very small and can be considered nearly constant regardless of temperature.

By substituting the formula for volume V = l × l × l:

β ≈ 3α

Meaning that the volume expansion β is approximately three times the coefficient of linear expansion α.

Calculating Dimensional Change Value

The dimensional change value Δl can be expressed as: Δl = α × l × Δt.

Therefore, it can be calculated with: (Coefficient of linear expansion) × (Original length) × (Amount of temperature change: Final temperature - Original temperature)

Example: For a Teflon (PTFE) material of 100×100×100 (mm), when the temperature changes from 15℃ to 25℃: Assuming the coefficient of linear expansion for PTFE is 100 (10⁻⁶/℃), the calculation is:

(100 × 10⁻⁶) × (100) × (25 - 15) = 0.1

Therefore, the new dimensions will be 100.1 × 100.1 × 100.1 (mm).

If the length of each side is different, calculate each one separately.

Coefficient of Linear Expansion for Major Materials

Below are the coefficients of linear expansion for representative materials.

Metal Materials

Plastic Materials

Pay Attention to the Units of the Coefficient of Linear Expansion

Metals generally have smaller coefficients of linear expansion than plastics, meaning they experience less dimensional change with temperature fluctuations. Among plastics, high-performance engineering plastics such as PEEK, PBT, PPS, and PAI have relatively small coefficients of linear expansion.

It is important to note the units used for the coefficient of linear expansion. Depending on the material, the units can vary between 10⁻⁴/℃, 10⁻⁵/℃, and 10⁻⁶/℃. Metals often use 10⁻⁶/℃, plastics use 10⁻⁵/℃, and rubbers use 10⁻⁴/℃. Since each of these represents a tenfold difference, always confirm the units when comparing values.

For plastics, the coefficient of linear expansion can be reduced by adding glass or carbon fibers, or through treatments that modify the crystalline structure. For products requiring high dimensional accuracy, it is also necessary to account for moisture and water absorption effects in addition to thermal expansion.

Shrink Fitting and Cold Fitting

Thermal expansion is sometimes used in assembly for mating machined metal parts through techniques called shrink fitting or cold fitting.

• Shrink fitting: The female part (hole) is heated to expand it before inserting the male part.

• Cold fitting: The male part is cooled to shrink it before insertion.

In both cases, the parts become fixed once they return to ambient temperature. These principles can also be applied to machined plastic parts.

Resins and rubbers with large coefficients of linear expansion may undergo significant dimensional changes even with normal air temperature variations. This can occasionally lead to parts that fit perfectly during machining or winter inspection failing to mate during assembly. In such cases, warming the female part in hot water can often restore a proper fit.

The direction of a hole's expansion when heated depends on the size of the hole relative to the face area. Small holes compared to the face area may contract as they expand. Ring-shaped or large holes relative to the face area will expand, making the hole larger.

Step Up Your Project with Yumoto Electric

Yumoto Electric delivers high-quality components fast, worldwide. We provide precision machining for a wide range of metals and engineering plastics. We have experience with over 200 materials including metals such as aluminum alloys, stainless steel, molybdenum, and titanium, and engineering plastics including PEEK, PPS, MC Nylon, and POM.

If you’re unsure about material selection or machining methods, we offer complimentary consultations to help optimize your design and production. For any questions, please feel free to contact us.