Fiber Bragg Grating (FBG) strain dependence
The strain dependence of a fiber Bragg grating is given by the expression:
k– k factor of the Bragg grating
Fiber Bragg Grating (FBG) temperature dependence
The temperature dependence of a fiber Bragg grating is:
– coefficient of thermal expansion of the fiber
ζ – thermo-optic coefficient (dependence of the index of refraction on temperature)
Temperature dependence of a fixed Fiber Bragg Grating (FBG)
If the optical strain gauge is fixed to a rigid strain free structure, the temperature may change the index of refraction of the fiber, but its expansion is fixed by the structure. This is equivalent to consider the thermal expansion of a fixed fiber as =0. The temperature dependence of a fiber Bragg grating measuring strain is:
When measuring strain this temperature induced wavelength change is confused with strain. The measured strain that is actually caused by temperature is:
The cross-sensitivity to temperature (TCS) is therefore given by:
The effective strain should be calculated from the strain sensor as the strain measured by the strain sensor minus the effect of temperature on the strain FBG:
This correction of the deformation does not take into account the effect of temperature on the deformation of the structure where the sensor is fixed on.
Temperature dependence of a Fiber Bragg Grating (FBG) fixed to a structure
To compensate also for the deformation of the structure due to temperature effects, the computation should be done considering the coefficient of thermal expansion (CTE) of the structure.
The total strain variation of a structure is:
The wavelength variation of a sensor fixed to a structure that is subjected to load and temperature is given by:
Meaning that to compensate the deformation of the structure due to temperature effect it is necessary to know the CTE value of the material of the structure where the sensor is fixed on.