This paper proposes an axisymmetric ordinary state-based peridynamic model considering the thermal expansion effect for temperature-induced cracking of linear elastic solids. Both the force state and bond failure criterion of the model are built in axisymmetric domain. The direct calculation for peridynamic bond energy density of the axisymmetric model considering thermal terms is given. The adaptive dynamic relaxation method is adopted for the quasi-static peridynamic simulations. Validity and reliability of the proposed axisymmetric model are illustrated by numerical examples of cold-induced fracture in a pipe with an inner crack. It is shown that the displacement predicted by the proposed peridynamic model is in good agreement with the corresponding finite element method. The critical bond energy density criterion for thermal cracking is verified via comparisons with the critical fracture temperature loads computed from the virtual crack closure technique and released energy based on Griffith’s theory. The sensitivity of the present model on the peridynamic discretization is investigated and discussed in both the continuous deformation and cracking cases. The performance of the peridynamic model is further demonstrated for cold-induced fracture of double-layered pipes with inner cracks, and the cracking behaviors influenced by the interfacial toughness and number of inner cracks are captured, respectively. The present model is capable of solving axisymmetric thermal cracking problems of linear elastic solids effectively, and it can be applied in more advanced axisymmetric structures which involve more complicated cracking issues.

考虑温度膨胀引起的线性弹性固体开裂的热膨胀效应，本文提出了一种基于轴对称常态的周向动力学模型。模型的受力状态和粘结破坏准则都建立在轴对称域中。给出了考虑热项的轴对称模型绕动力键能密度的直接计算。准静态周动力模拟采用自适应动态松弛方法。数值模拟的例子说明了所提出的轴对称模型的有效性和可靠性。结果表明，所提出的绕动力学模型预测的位移与相应的有限元方法吻合良好。通过与虚拟裂纹闭合技术计算的临界断裂温度载荷以及基于格里菲斯理论的释放能量进行比较，验证了热裂纹的临界结合能密度标准。在连续变形和开裂的情况下，都研究并讨论了本模型对绕动离散的敏感性。进一步证明了该蠕动模型在具有内部裂纹的双层管冷诱导断裂中的性能，并分别记录了受界面韧性和内部裂纹数影响的裂纹行为。该模型能够有效解决线性弹性固体的轴对称热裂纹问题，