三维打印碳纤维增强聚合物复合材料热残余解析解

三维打印碳纤维增强聚合物（CFRP）复合材料因层间材料失配和打印过程中梯度降温而产生热残余现象，影响工件成形质量。本文取代简单的同步降温假设，提出了符合实际制备工艺的梯度降温概念，据此建立了三维打印正交铺层复合材料板和梁的热残余变形和应力的解析解。为反映三维打印过程中随时序动态变化的制备和降温过程，考虑每层制备轮次的降温梯度并进行热残余分析，最后合成得到热残余变形和应力。讨论了4种梯度降温模式，覆盖了所有可能的三维打印工艺。以CFRP复合材料三维打印为例，验证了本文解析解的精度和可靠性，显示了同步降温假设会产生显著的误差，表明热残余水平与降温梯度成正比，讨论了铺层方式对热残余的影响。为优化三维打印CFRP复合材料的结构设计和制备工艺、降低热残余水平提供了可靠的分析方法。 

Thermal residual solutions of carbon fiber reinforced polymer composites by 3D printing

Thermal residual phenomena occurrs in carbon fiber reinforced polymer (CFRP) composite laminates by 3D printing due to the material mismatch among layers and the gradient cooling during printing, and affects the forming quality. Instead of the simple assumption of synchronous cooling, the concept of gradient cooling was introduced to characterize real manufacturing processes. The analytical solutions of thermal residual deformations and stresses of cross-ply composite plates and beams were established. To characterize time-dependent forming and cooling processes during 3D printing, a through-thickness cooling gradient was considered in each layer forming turn. The thermal residual responses in each turn were deduced. The total thermal residual deformations and stresses were obtained in an accumulative way. Four gradient cooling models were summarized to cover various 3D printing techniques. The accuracy and reliability of the present solutions are proved in the example of CFRP composite by 3D printing. It is illustrated that the assumption of synchronous cooling would lead to big errors. Thermal residual level is proportional to the cooling gradient. The effects of ply-up patterns on thermal residual responses are discussed. This work provides reliable methods to optimize structures and techniques and decrease thermal residual level of CFRP composites in 3D printing.