邹坤^a， 曹国栋^a， 邓代强^a， 姜胜强^b

湘潭大学 a.土木工程学院， b.机械工程与力学学院， 湖南 湘潭 411105

引用格式：

邹坤，曹国栋，邓代强，等. 时间依赖性对水泥基材料可打印性影响的数值研究［J］. 中国粉体技术， 2026， 32（5）： 1-10.

Zou Kun，Cao Guoqiang，Deng Daiqiang，， et al. Numerical study on influence of time dependence on printability of cement⁃based materials［J］. China Powder Science and Technology， 2026， 32（5）： 1-10.

摘要：【目的】研究时间依赖性对于3D打印水泥基材料可打印性的影响。【方法】采用离散元法（discrete element method，DEM）研究有、无时间依赖性下的水泥基材料3D打印过程；使用JKR接触模型（Hertz-Mindlin with Johnson-Kendall-Roberts contact model，JKR）描述颗粒间的相互作用，通过调节JKR表面能参数来表征流变性能的时间依赖性；通过静置不同时间下的水泥基材料坍落度试验标定JKR接触模型参数。【结果】对于3D打印水泥基材料，考虑时间依赖性会降低挤出速度并缩短开放时间，3D打印水泥基材料的抗变形能力与湿坯强度显著提高。【结论】3D打印水泥基材料的流动性越好，可挤出性越强，较快的凝结硬化速率有助于改善挤出后性能。

关键词：离散元法；接触模型；水泥基材料；3D打印；时间依赖性

Abstract

Objective This study aims to investigate the influence of time dependence on the printability of 3D-printed cement-based materials （3DPC） and to establish a quantitative evaluation method for their printability.

Methods A simulation method for the extrusion and deposition processes in 3DPC was established based on the discrete element method. The rheological properties of the 3DPC were adjusted by designing mix proportions. The slump test results were compared with the simulation results to calibrate the surface energy parameters corresponding to the Hertz–Mindlin with JKR contact model. When time dependence was considered， the contact model parameters varied with the resting time. When time dependence was not considered， the contact model parameters were fixed at the values obtained from the slump test without resting. The influence of time dependence on the printability of 3DPC was analyzed by testing their extrudability and buildability. The open time of 3DPC was used to evaluate the extrudability， and their buildability was evaluated using the deformation resistance of multi-layer printed filaments and the green strength.

Results and Discussion When time dependence was considered， the uniformity of the printed filaments gradually deteriorated with increasing resting time. For group PS₁ （the mix proportion with 0.1% polycarboxylate superplasticizer）， the non-uniform open time was 10 min， and the fracture open time was 20 min. For groups PS₂ （the mix proportion with 0.2% polycarboxylate superplasticizer） and PS₃ （the mix proportion with 0.3% polycarboxylate superplasticizer）， both the non-uniform open time and the fracture open time exceeded 20 min. Moreover， the average extrusion velocity of the 3DPC gradually decreased with increasing resting time. The average extrusion velocity of group PS₁ after 20 min of resting was the lowest at 0.039 m·s⁻¹， and it was also the only group where filament fracture occurred. In contrast， group PS₃ without resting exhibited the highest average extrusion velocity at 0.282 m·s⁻¹. It was observed that the average extrusion velocity of the non-uniform and fractured filaments was lower than that of the continuous filaments. The deformation rate of the multi-layer printed structures increased with increasing PS （polycarboxylate superplasticizer） content. Under the same mix proportion， the deformation rate of the multi-layer 3DPC structures when considering time dependence was consistently lower than that in the simulations without considering time dependence. In the simulations without time dependence， group PS₃ exhibited the highest deformation rate at 14.7%， while group PS₁ showed the lowest at 9.8%. A similar trend was observed in the simulations with time dependence， where group PS₃ still had the highest deformation rate at 8.6%， and group PS₁ had the lowest at 5.4%. For the three-layer green strength， the values with time dependence were on average 32% higher than those without time dependence. With increasing PS content， the green strength decreased in both cases （with and without time dependence）. Without time dependence， group PS₃ had the minimum three-layer green strength at 226 Pa， while group PS₁ had the maximum at 450 Pa. With time dependence， group PS₃ had the minimum three-layer green strength at 304 Pa， and group PS₁ had the maximum at 605 Pa. The faster the setting and hardening rate of the 3DPC， the greater the difference in green strength between the cases with and without time dependence. As shown in Tab.3 for the slump results， group PS₁ had the fastest setting and hardening rate， and the difference in green strength between the two cases was 178 Pa. Group PS₃ had the slowest setting and hardening rate， with a difference of 78 Pa in green strength between the two cases.

Conclusion The extrudability of 3DPC without considering time dependence is greater than that when time dependence is considered. When time dependence is considered， the average particle extrusion velocity decreases and the extrudability becomes poorer with increasing resting time for all groups. The lower the extrusion velocity， the more likely the filaments are to exhibit discontinuity and fracture. Therefore， the 3DPC should be used and extruded as soon as possible after preparation. When it is necessary to extend the open time of the 3DPC， the PS content can be increased. The buildability of 3DPC with time dependence is significantly stronger than that without time dependence. The faster the slump loss rate， the greater the difference in deformation rate between the two cases. Increasing PS content significantly increases the deformation rate of printed filaments and weakens the deformation resistance of the cement-based materials. The green strength with time dependence is greater than that without time dependence， and the faster the slump loss rate， the greater the difference between the two cases. In addition to the significant influence of setting and hardening rate on the increase of green strength over time， the resting time also greatly affects the green strength. For the same mix proportion， the longer the resting time， the greater the green strength. When designing mix proportions， excessively high PS content should be avoided， as it severely slows the slump loss rate and is unfavorable for strength development.

Keywords： discrete element method； contact model； cement-based material； 3D printing； time dependence

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