List of Terms related to Strain Measurement with Optical Sensors

λ Wavelength

Wavelength is the measured peak wavelength of a fiber Bragg grating sensor. It is normally expressed in nanometers (nm).

λ0 Reference wavelength

The reference wavelength is the peak wavelength of a fiber Bragg grating sensor at a reference condition (zero strain, at reference temperature, and so forth.. It is normally expressed in nanometers (nm).

Δλ Wavelength variation

The wavelength variation (also commonly referred to as shift or as change) is the difference between the wavelength and the reference wavelength (reference value): Δλ= λ- λ0. It is normally expressed in nanometers (nm).

k k-factor The gauge factor k (also referred to as k-factor) of an optical strain gauge is the proportional change in the Bragg wavelength (Δλ/λ0) and the strain variation Δε. Is is being measured as: Δλ/λ0 = k.Δε. This value is a dimensionless number and depends on the characteristically used optical fiber and sensor encapsulation. In the case of HBM optical strain sensors, the k-factor is identified on the data- and calibration sheets that are individually delivered with each sensor.
ε Strain

Strain is a dimensionless value that represents the relative change in the length of a material to its initial length. It is normally of a very small value, and hence is represented by µm/m, ppm or 10-6.

S Sensitivity

The sensitivity of an optical strain sensor is the direct ratio between the measured strain and the change in the Bragg wavelength: Δε/Δλ= S. It is normally stated as value in micro-strain per nanometer [(µm/m)/nm)] and is different for every sensor, as it depends on its initial base wavelength, that is: S=1/(k. λ0).

 TCS Temperature cross-sensitivity

The temperature cross-sensitivity is a sensor measurement drift caused by temperature variation. It is the strain that is wrongly measured when there is a change of 1ºC (or 1ºK) in temperature. The value is given in (µm/m)/ºC [or (µm/m)/ºK] and can be used to compensate the effect of temperature on the optical strain sensor (not considering the compensation for the thermal expansion of the specimen).

σ Stress

Mechanical stress is expressed by the quotient of the force F and the cross-sectional area A of the stressed material, σ=F/A. It is normally represented in KPa.

E Elastic modulus

The modulus of elasticity, or Young’s modulus, is the ratio between stress and strain in a linear elastic material. It is given by Hooke’s Law (σ=E.ε). It is normally represented in GPa (109 Pa) to correlate strain in µm/m (10-6) with stress in KPa (103 Pa).

v Poisson's ratio

Poisson's ratio is defined by the division of the transverse strain εt and the longitudinal strain εl. For aluminum alloys, ν = 0.33, for example.

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