Coefficient of Linear Thermal Expansion (CLTE)

Under the effects of increasing temperature, any material will expand. This can lead to: 
 

• significant changes in the dimensions
• unequal shrinkage (warpage), or
• internal stress
  
   

The coefficient of linear thermal expansion is a material property that:
 

• Characterizes the ability of a plastic to expand when the temperature increases.
• Estimate the dimensional stability of a developed part when temperature varies.

It is abbreviated as CLTE.

 

The CLTE is referred to as "α." It is obtained by dividing the linear expansion per unit length by the change in temperature. The formula for the linear coefficient for plastic and polymer materials is: 
 

where,

• α is the coefficient of linear thermal expansion per degree Celsius.
• ΔL is the change in length of test specimen due to heating or cooling.
• L0 is the original length of specimen at room temperature.
• ΔT is the temperature change in °C, during the test.

When reporting the mean coefficient of thermal expansion specify the temperature ranges. 

 

The units of coefficient of linear expansion are: 
 

• Degree Celcius (°C^-1)
• Kelvin (K^-1)
• Degree Fahrenheit(°F^-1)

Fibers and Fillers

Fibers and other fillers significantly reduce thermal expansion. The factors that pose a great impact on the linear coefficient of thermal expansion are:
 

• degree of anisotropy of the filler and the
• orientation of the filler

Temperature

The temperature is directly proportional to CLTE. The magnitude of CTE increases with rising temperature. 
 

Graph showing the CLTE vs. Temperature of plastics 

Molecular Orientation

Molecular orientation also affects the thermal expansion of plastics. It is often affected by the cooling time during processing. This is especially true with semi-crystalline polymers whose crystallization process requires time.

 

The thermal expansion difference develops internal stresses and stress concentrations in the polymer. This allows premature failure to occur. Find out the top 3 roots causes to avoid plastic failure » 

CLTE is important for the economics of production. It is also necessary for the quality and functioning of products. It determines the:
 

• Design to predict shrinkage in injection molded parts.
• Dimensional behavior of structures subject to temperature changes.
• Thermal stresses that can occur and cause the failure of a solid artifact composed of different materials. This failure is subjected to a temperature excursion. For example, to predict efficient material bonding or while using plastics with metals.

The standards to measure the CLTE of thermoplastics and thermosets are as follows. These plastics can be either in filled or unfilled form or in sheet or molded form. 

 

Dilatometry Technique

It is the widely used technique in which the specimen is heated in a furnace. The displacement of the ends (lengths) of the specimen are transmitted to a sensor by means of push rod. Push rods may be of several types such as:
 

• the vitreous silica type,
• the high-purity alumina type, or
• the isotropic graphite type.

Standards to calculate CLTE of plastics using Dilatometry:
 

1. ASTM D696 – This method determines the CLTE for plastics having values greater than 1 µm/(m.°C). This method uses a vitreous silica dilatometer. The nature of most plastics and the construction of the dilatometer make −30 to +30°C (−22°F to +86°F) a convenient temperature range. This range covers the temperatures in which plastics are most commonly used.
    
2. ASTM E228 – This standard covers a temperature range other than −30°C to 30°C. It determines the CLTE of solid materials with a push-rod dilatometer.

Thermomechanical Analysis (TMA)
 

The linear thermal coefficient is measured using a thermomechanical analyzer. This instrument consists of: 
 

• a specimen holder
• a probe
• a transducer

The probe transmits changes in length to a transducer that translates the movements of the probe into an electrical signal. 

Standards to calculate CLTE of plastics using TMA:
 

1. ASTM E831 (and ISO 11359-2) –These methods are applicable to solid materials that exhibit sufficient rigidity. It is applicable from −120 to 900°C. This range can be extended depending on the instrumentation and calibration materials used. The lower limit for CTE with this method is 5 × 10^-6/K (2.8 × 10^-6/°F), but it may be used at lower or negative expansion levels with decreased accuracy and precision.

Interferometry Technique

The displacement of the specimen ends is measured with optical interference techniques. This is done in terms of the number of wavelengths of monochromatic light. The precision of this instrument is greater than with dilatometry. Interferometry is not used much above 700°C (1290°F) as it relies on the optical reflectance of the specimen surface. 
 

The Displacement of the Specimen Ends is Measured with Optical Interference Techniques (Source: Researchgate)

Standards to calculate CLTE using Interferometry technique:
 

1. ASTM E289 determines the CLTE of rigid solids with interferometry from –150 to 700°C (–240 to 1290°F). It is more applicable to materials:
   • Having low or negative CTE in the range of < 5 × 10^-6/K (2.8 × 10^-6/°F).
   • Where only limited thickness lengths of other higher expansion coefficient materials are available. 

In the service temperature range, the coefficient of linear thermal expansion lies between:

• Ca. 0.6 x 10^-4 to 2.3 x 10^-4 K^-1 for most of the thermoplastics
• Ca. 0.2 x 10^-4 to 0.6 x 10^-4 K^-1 for most of the thermosets

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