Determination of the Thermal Expansion Coefficient of Coatings under Vibration and Combustion Condit

The coefficient of thermal expansion (CTE) of a coating controls the residual stresses, adhesion, and spallation resistance of coated components operating in hot-gas and vibrating environments. This article explains how coating CTE is determined through dilatometry, thermomechanical analysis, high-temperature X-ray diffraction, and combined vibration–combustion (burner rig) testing, covering specimen preparation, applicable standards, measured parameters, and typical industrial applications.

Technical Overview

The coefficient of thermal expansion (CTE) quantifies the fractional dimensional change of a material per unit temperature change. The mean linear CTE between two temperatures is defined as the length change divided by the initial length and the temperature interval, while the instantaneous CTE is the first derivative of length with respect to temperature at a given point. For engineering coatings, this parameter is a primary design input because thermal expansion mismatch between coating and substrate generates interfacial stresses that drive cracking, buckling, and spallation during thermal cycling.

Engineering coatings produced by atmospheric plasma spraying (APS), high-velocity oxy-fuel (HVOF) spraying, electron-beam physical vapor deposition (EB-PVD), or wet chemical routes are porous, microcracked, and often chemically graded. Their effective CTE therefore differs from that of the corresponding dense bulk material and must be measured on the actual coating. As a reference, yttria-stabilized zirconia (YSZ) thermal barrier coatings typically exhibit a CTE of approximately 9 to 11 ppm/K, MCrAlY bond coats approximately 13 to 15 ppm/K, and nickel-base superalloy substrates approximately 14 to 16 ppm/K. The mismatch of several ppm/K, multiplied by elastic modulus and temperature swing, produces stresses on the order of hundreds of megapascals at every start-up and shut-down cycle.

In real service environments such as gas turbine combustors, afterburners, and rocket thrust chambers, coatings are exposed simultaneously to combustion gas heating, steep through-thickness temperature gradients, and mechanical vibration from acoustic and structural excitation. Determination of the thermal expansion coefficient under combined vibration and combustion conditions therefore provides data that reflect true component behavior rather than idealized furnace conditions, and it supports lifetime modeling, coating formulation, and acceptance decisions for safety-critical hardware.

Testing Samples

Freestanding Coating Specimens

Freestanding specimens isolate the intrinsic expansion response of the coating. Coatings are deposited onto sacrificial substrates, typically 1 to 3 mm thick, and subsequently detached by electrochemical dissolution of the substrate, mechanical separation, or controlled heat treatment. The detached strips or cylinders are ground to flat, parallel ends with a typical length of 10 to 25 mm, suitable for push-rod dilatometry. Grinding is performed with light passes and ample coolant to avoid sealing surface porosity or introducing compressive residual stresses that distort the measurement.

Coated Substrate Coupons

Coated coupons are used for temperature-gradient and combined-environment testing. Discs of 25 to 30 mm diameter, rectangular bars, or airfoil-shaped buttons are coated on one face and mounted on a cooled holder so that a controlled temperature gradient is established through the wall, mimicking service conditions. These coupons allow the effective expansion behavior of the coating-substrate system, including interfacial sliding and oxide growth effects, to be evaluated.

Reference and Calibration Specimens

Certified reference materials such as sapphire, fused silica, platinum, and low-expansion alloys are measured under identical conditions to correct for the expansion of the dilatometer fixtures. The reference correction is essential at temperatures above 800 °C, where apparatus expansion can exceed the specimen expansion being measured.

Testing Items

Typical test items reported for coating CTE determination include:

• Mean linear CTE over specified intervals, for example room temperature to 800 °C, 1000 °C, or 1200 °C
• Instantaneous (tangential) CTE as a function of temperature across the full test range
• In-plane versus through-thickness CTE, quantifying expansion anisotropy typical of lamellar thermal spray coatings
• Heating–cooling hysteresis and permanent linear change, indicating sintering shrinkage, microcrack healing, or phase transformation
• Effective expansion behavior of the coating-substrate system under through-thickness temperature gradients
• Dimensional stability and expansion response under simultaneous flame heating and mechanical vibration in burner rig testing
• Supporting properties such as elastic modulus by resonant frequency methods, used with CTE data for mismatch stress calculation

Testing Methods

Push-Rod Dilatometry (ASTM E228)

The freestanding coating specimen is placed between a fused silica support tube and a spring-loaded push rod, and length change is sensed by a linear variable differential transformer during heating at 3 to 5 K/min in air or inert gas. A reference specimen run provides the apparatus correction. With careful specimen preparation and duplicate measurements, accuracy better than 0.5 ppm/K is achievable. This method is the primary route for baseline CTE data on thermal spray and sol-gel coatings.

Thermomechanical Analysis (ASTM E831, ISO 11359-2)

Thermomechanical analysis applies a small static force through a miniature probe and measures dimensional change on specimens only a few millimeters in size, making it well suited to thin coatings and layered systems. It is particularly useful for organic, polymer, and paint-type coatings over the range of approximately −100 °C to 600 °C, and for rapid screening of ceramic coatings at moderate temperatures.

High-Temperature X-Ray Diffraction

High-temperature X-ray diffraction tracks the lattice parameters of the crystalline coating phases as a function of temperature, yielding the intrinsic lattice CTE free from microcrack closure and sintering artifacts. It is applied to YSZ and other ceramic coatings up to approximately 1500 °C and helps separate reversible lattice expansion from irreversible structural densification.

Combined Vibration–Combustion (Burner Rig) Testing

Burner rig testing reproduces the coupled service environment. An oxy-fuel or kerosene combustor impinges a hot gas stream on the coated face of a specimen mounted on a back-side cooled holder, establishing a controlled through-thickness gradient in line with the temperature-gradient cycling concept of ISO 13123. An electromagnetic exciter or shaker table superimposes sinusoidal or random vibration in accordance with IEC 60068-2-6 type procedures, with controlled frequency range and acceleration level. Surface temperature is mapped by pyrometry and embedded thermocouples, while in-situ laser extensometry or digital image correlation records the expansion and dynamic strain of the coating surface in real time. Post-exposure dilatometry of the cycled coating quantifies irreversible length change and the evolved CTE after sintering and oxidation, and defines the number of cycles to coating spallation as a function of expansion mismatch and vibration amplitude.

Applications

CTE determination of coatings under vibration and combustion conditions supports qualification and development across multiple industries:

• Gas turbine hot-section hardware, including blade, vane, and combustor liner thermal barrier coatings, where CTE mismatch controls spallation life
• Aerospace afterburner components, flame holders, and rocket engine combustion chambers and nozzles with thermal protection coatings
• Automotive diesel piston crowns, exhaust manifolds, and turbocharger components exposed to cyclic heating and engine vibration
• Boiler waterwall and furnace tube coatings in power generation, subject to combustion gas corrosion and thermal cycling
• Coating formulation and process optimization, where porosity, phase composition, and lamellar structure are tuned to balance insulation and expansion compatibility
• Lifetime prediction models combining CTE mismatch strain, thermally grown oxide growth kinetics, and dynamic mechanical loading

FAQ

Why must freestanding specimens be used for baseline coating CTE?

When the coating remains attached to the substrate, the much stiffer and thicker substrate dominates the composite expansion response. Detaching the coating isolates its true expansion behavior, which can then be compared directly with substrate data to compute mismatch stress.

What temperature range can be covered?

Push-rod dilatometry with alumina systems routinely covers room temperature to 1400 °C for ceramic coatings, while high-temperature X-ray diffraction extends to approximately 1500 °C. Thermomechanical analysis covers polymer coatings from −100 °C to 600 °C.

How does vibration enter the expansion measurement?

Baseline CTE is measured statically by dilatometry. Vibration is introduced in burner rig testing, where simultaneous combustion heating and controlled mechanical excitation reveal whether dynamic stress accelerates mismatch-driven damage and modifies the effective expansion response of the coating system.

How many specimens are required and what is a typical turnaround?

Freestanding dilatometry generally requires a minimum of three parallel specimens to assess scatter, and typical turnaround at accredited third-party laboratories is five to ten working days, extended when burner rig cycling of several hundred to several thousand cycles is included.

What acceptance criteria are commonly applied?

Criteria are specification driven. For brittle ceramic coatings on metallic substrates, the mismatch with the substrate is commonly limited to approximately 1 to 2 ppm/K, and combined-environment testing must demonstrate no spallation within the specified number of thermal and vibration cycles.

What is the difference between mean and instantaneous CTE?

Mean CTE is the averaged expansion coefficient over a stated temperature interval and is used for engineering stress calculations. Instantaneous CTE is the tangent value at each temperature and reveals features such as phase transitions, sintering onset, and glass transitions that an averaged value conceals.