A rigorous, comprehensive, and thermodynamically consistent theory has been developed for the fused deposition modelling (FDM) of semi-crystalline polymers. It is sufficiently general in that it can accommodate multiple phase transition mechanisms (crystallization, glass transition, and melting) during the heating and cooling cycles of the process encountered during FDM. The theory predicts the residual stresses and the resulting warpage in the polymer part due to the temperature-dependent, spatially varying specific volumes of each phase, precipitated by the inhomogeneous distribution of temperature. The theory treats the semi-crystalline polymer as a constrained mixture of multiple phases, where glass is assumed to be a new phase of the polymer. The statistically based Avrami kinetics for crystallization, modified for non-isothermal processes, is recovered as a particular case of our non-equilibrium thermodynamic analysis. Moreover, the theory predicts the temperature corresponding to the local free energy minima as the ideal glass transition temperature analogous to that of Franz and Parisi’s mean field theory with a statistical basis.

已经为半结晶聚合物的熔融沉积建模 (FDM) 开发了一个严格、全面且热力学一致的理论。它具有足够的通用性，因为它可以在 FDM 过程中遇到的过程的加热和冷却循环期间适应多种相变机制（结晶、玻璃化转变和熔化）。该理论预测了聚合物部件中的残余应力和由此产生的翘曲，这是由于温度的不均匀分布引起的每个相的随温度变化的、空间变化的特定体积。该理论将半结晶聚合物视为多相的受限混合物，其中玻璃被假定为聚合物的新相。基于统计的 Avrami 结晶动力学，针对非等温过程进行了修改，被恢复为我们的非平衡热力学分析的一个特例。此外，该理论预测对应于局部自由能最小值的温度是理想的玻璃化转变温度，类似于具有统计基础的 Franz 和 Parisi 的平均场理论。