The properties of fiber composites change with increasing the temperature, which generates the different thermal stresses and thermal expansion coefficients for fiber and matrix. The existence of a force makes the fiber and matrix maintain a bonding state in the process of expansion, and this force is fundamental for the equation of stress and strain. For a flexible substrate, the shear stress of matrix is inversely proportional to the distance to fiber, and the internal axial shear stress equation is obtained in this study. The deformation compatibility condition of interface could be also defined if the fiber and matrix are without debonding. Because the residual stress is a kind of balance of internal stress, the balance formula is proposed, and then the thermal residual stress expression could be finally obtained. It is found that the value of thermal residual stress varies with the length of fiber, and the effect of fiber length-diameter ratio on thermal residual stress is also discussed.

纤维复合材料的性能随温度的升高而变化，从而对纤维和基体产生不同的热应力和热膨胀系数。力的存在使纤维和基体在膨胀过程中保持粘结状态，该力对于应力和应变方程式至关重要。对于柔性基底，基体的切应力与到纤维的距离成反比，并且在此研究中获得了内部轴向切应力方程。如果纤维和基体没有脱粘，也可以定义界面的变形相容条件。由于残余应力是内应力的一种平衡，因此提出了平衡公式，从而最终得到了热残余应力的表达式。