Stresses in a FR-4 laminate

Rearranging the equation we get .

For l = 0.3m and dT = 50°C, the unit being metres, as for l.

Table 1 gives α for copper as 16.7 ppm/°C, or 16.7 µm/m/°C, so the increase in length of the foils is 15 · 16.7 = 250 µm.

E-glass has a CTE of 54 ppm/°C, but epoxy is quoted as having a wide range of values. This is where we have to make the simplifying assumption that the glass, being more rigid than the epoxy, will be the major influence on the CTE of the whole. The approximate increase in length is given by 15 x 54 = 810 µm, so that a reasonable estimate of the difference in length of foils and core when the laminate is 50°C hotter is 810 – 250 = 560 µm, the core being longer than the foil when the temperature increases (and shorter when the temperature falls).

Note that this differential expansion is a quite measurable half a millimetre! However, real laminates don’t actually show this: instead, internal stresses compensate for the difference in CTE, so that the copper is stretched as the board expands. Provided that the copper is ductile enough, the process of heating and cooling will not result in permanent deformation. If this aspect of metals puzzles you, look at Mechanical properties of metals.

If the copper is patterned, the same thing happens, with the pattern expanding. However, if the pattern is mostly copper, and the surfaces have different percentages of copper, the stresses exerted by copper on laminate will be different on the two sides. This is a major factor in causing board warp.

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