# Principles and Application of Polyimide Fiber Bragg Gratings for Surface Strain Measurement
## 1 Introduction
It provided a method to rectify [PERSON]'s strain transfer model when the interlayer is a stiff layer. [PERSON] et al. [PERSON] et al. (2017) presented the strain transfer mechanism and the error modification theory of an embedded FBG sensor. Similarly, [PERSON] et al. [PERSON] et al. (2018) established a four-layer core-coating bonding layer substrate model of strain transfer by taking the structural differences among fibers into consideration. [PERSON] et al. [PERSON] et al. (2019) proposed a method in which small-diameter fiber Bragg grating (FBG) sensors were applied for the monitoring of delamination induced by low-velocity impact. [PERSON] et al. [PERSON] et al. (2010, 2011) detected transverse cracks in Carbon Fiber Reinforced Polymer (CFRP) composites using uncoated fiber Bragg grating sensors and polyimide FBGs. Based on a strain transfer model of bare FBG, [PERSON] et al. [PERSON] et al. (2012) proposed a method to obtain surface strain on a Carbon Fiber Reinforced Polymer (CFRP)-reinforced concrete arch with bare FBGs, as shown in Figure 2. Based on the Hilbert-Huang transform, the cracking time of the concrete arch can be calculated accurately. [PERSON] et al. [PERSON] et al. (2013) proposed an approach to measure the internal strain of similar material based on embedded bare fiber Bragg gratings. In this research, the impact of substrate modulus to strain transfer ratio is considered carefully because the similar material is a type of low modulus material. Its modulus is always hundreds MPa. The investigation indicates that embedding bare FBG into a specimen can measure the constitutive relation precisely, and it is more accurate than the traditional approach. All these classical strain transfer models demonstrate that polymeric coating can reduce the strain transfer ratio and that more strain transfer layers mean less strain transfer effectiveness. A new experiment with distributed technology can also obtain these conclusions. In the experiment, an encapsulated fiber was bonded to the cantilever beam by an epoxy adhesive and a glue stripe. Above the beam, the two sections of the fiber were covered by epoxy resin together with another section, and were covered by a glue stripe under the beam. The distributed interrogator was the ODISI OBR 4600 (Luna, Inc, Roanoke, VA, USA). Its minimum sensor spacing is 1 cm. The experiment and result is shown in Figure 3. It is concluded that the strain transfer ratio can be clearly reduced by a multi-layer between the fiber and substrate. Figure 2: Samples of polyimide FBGs. (**a**) Cracking monitoring with bare FBGs; (**b**) A similar material sensor with bare FBGs. In contrast with other works in the literature, polyimide fiber Bragg gratings are investigated in this paper. Bare fibers are not fragile when covered by epoxy adhesive. The adhesive-fiber composite material sensors are stiff and durable, even in some strict experiments or Structure Health Monitoring (SHM) cases. On the basis of prior research, in this paper the structural differences of the fibers are considered and a three-layer core-bonding layer-substrate model of strain transfer by using the bare polyimide FBG is established. The proposed model was used to investigate the key factors impacting strain transfer. A calibration experiment was conducted to validate the accuracy and applicability of the strain transfer model. The results of this experiment demonstrated the advantages of polyimide FBG in measuring strain. In order to verify the practicality and ability of measuring surface strain field, the polyimide FBGs are used to get the strain in a concrete specimen with the interrogator SM130-700. The experiment shows that polyimide FBGs can be used in any surface strain measurement even in dynamic measurements, such as explosion measurements. It can be more sensitive and accurate than encapsulated optical fiber sensors.