## 2 Internal Energy Storage Calculation Model of Defect Evolution Process  
Energy cannot be absorbed by large plastic deformations, because the residual strain of the blade material with defects under fatigue load is small. Part of the mechanical energy is stored in the material in the form of internal energy storage, and most of the remaining energy is dissipated as heat [25]. According to the law of the conservation of energy, with the mechanical energy \(W\), the heat dissipation \(Q\) and the internal energy storage \(E\) that is generated during the material loading, we can express the energy balance equation as follows [26]:  
\[W=E+Q,\]where \(E\) is the internal energy storage, and \(Q\) is the heat source intensity caused by the internal friction, that is, the heat dissipation. The accumulation of the internal energy storage during defects evolution causes irreversible changes in the microstructure of the material. The mechanical energy \(W\) at the continuous and uniform position can be expressed as follows:  
\[W=\sigma\varepsilon V, \tag{2}\]  
where \(\sigma\) is the stress in a cycle, \(\varepsilon\) is the strain in a cycle and \(V\) is the volume of material within the measurement range. According to [PERSON]'s law of heat conduction [27]:  
\[Q+\lambda\
abla^{2}T=\rho c\frac{\partial T}{\partial t}, \tag{3}\]  
where \(\
abla\) represents the Laplace operator, \(\rho\) represents the density of the material (kg/m\({}^{3}\)), \(\lambda\) represents the thermal conductivity (W/(m\({}^{\text{-}\circ}\)C)), and \(c\) represents the specific heat capacity (J/(kg\({}^{\text{-}\circ}\)C)). According to the law of energy and the Gauss theorem, Equation (3) can be transformed as follows [28]:  
\[Q-\
abla\cdot\overset{\rightarrow}{q}=\rho c\frac{\partial T}{\partial t}, \tag{4}\]  
As the GFRP composite is anisotropic, its thermal conductivity is also anisotropic. The thermal conductivity is no longer a constant, but a second-order tensor consisting of nine components \(\lambda_{ij}\), \(i\), \(j=1\), 2, 3. Therefore, the linear combination of the temperature gradients of the heat fluxes in the Cartesian coordinate system along the three coordinate axes is as follows [29]:  
\[\left\{ \begin{array}{l}-q_{x}\!\!=\lambda_{11}\frac{\partial T}{\partial x} \!+\!\lambda_{12}\frac{\partial T}{\partial y}\!+\!\lambda_{13}\frac{\partial T }{\partial z},\\ -q_{y}\!\!=\lambda_{21}\frac{\partial T}{\partial x}\!+\!\lambda_{22}\frac{ \partial T}{\partial y}\!+\!\lambda_{23}\frac{\partial T}{\partial z}\end{array}  \right., \tag{5}\]  
By substituting (5) into (4), we obtain the following:  
\[Q+\lambda_{11}\frac{\partial^{2}T}{\partial x^{2}}+\lambda_{22}\frac{\partial^ {2}T}{\partial y^{2}}+\lambda_{33}\frac{\partial^{2}T}{\partial z^{2}}+( \lambda_{12}+\lambda_{21})\frac{\partial^{2}T}{\partial x\partial y}+( \lambda_{13}+\lambda_{31})\frac{\partial^{2}T}{\partial x\partial z}+(\lambda_ {23}+\lambda_{32})\frac{\partial^{2}T}{\partial y\partial z}=\rho c\frac{ \partial T}{\partial t}, \tag{6}\]  
According to the Onsager principle of the thermodynamics of irreversible processes, the phenomenological coefficients in Equation (5) have the following reciprocal relationship:  
\[\lambda_{ij}\!\!=\lambda_{ji}\;\;\;i,\;j=1,\;2,\;3,\;i\;\
eq\;j,\;\lambda_{ii} \lambda_{jj}>\;0, \tag{7}\]  
The axes are \(x\), \(y\) and \(z\) as the coordinate system shown in Figure 1. Axis \(x\) is in the longitude direction of the fibers, axis y is in the transverse direction and axis \(z\) is the thickness direction of the laminate.