This case study shows how thermomechanical analysis (TMA) was used to measure the coefficient of thermal expansion (CTE) of a multilayer printed circuit board in three directions: two in-plane and one through the thickness.
Test specimens were cut from the board with a diamond wire saw and run on a TA Instruments Discovery TMA 450 EM. Each was heated from -50°C to 100°C at 3°C/min under a 0.05 N load, using a method adapted from ASTM E831. Before testing, the instrument was checked against a certified aluminum reference standard.
In-plane, both orientations measured a CTE of about 17 to 18 µm/m·°C across the full temperature range, with no meaningful difference between them. The woven glass fiber reinforcement runs in the plane of the board and limits expansion equally in both directions.
Through the thickness, CTE started around 42 µm/m·°C near room temperature, already more than double the in-plane value. It rose as the temperature climbed, more steeply above about 60 to 70°C, and reached 67.5 µm/m·°C at 90°C, roughly four times the in-plane rate.
Because through-thickness expansion is both higher and nonlinear, a designer working from a single average CTE would underestimate how much this board moves at elevated temperatures. Measuring CTE by direction and by temperature gives thermomechanical models better inputs. This is especially important for automotive, aerospace and AI data center hardware, where CTE mismatch drives solder joint fatigue and via cracking.