Missing layer replacement method and parameterized analysis of mode Ⅱ inter-layer fracture toughness of additive manufacturing CFRP
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摘要: 为实现增材制造碳纤维增强树脂基复合材料(Carbon fiber reinforced polymer-CFRP)Ⅱ型层间断裂韧性的测试分析，并量化打印参数对Ⅱ型层间断裂韧性的影响规律，推进增材制造CFRP技术在桥梁结构中的应用，本文分别从试验及仿真分析两方面展开了相关研究。首先，对打印工艺进行优化并提出了一种新型层间预制裂纹制备方法，即缺层置换法，并利用该方法探索了两类关键打印参数(打印温度、打印速度)对增材制造CFRP-Ⅱ型层间断裂韧性的影响规律。其次，基于内聚区理论建立了不同打印工况下预制裂纹试件端部缺口梁三点弯曲(End notched flexure-ENF)试验的仿真模型，并完成了仿真结果与试验数据的对比分析。结果表明：两类关键打印参数对增材制造CFRP-Ⅱ型层间断裂韧性的影响明显，且打印温度的影响更强。当打印温度从245℃提升至285℃，试验荷载峰值的变化幅度范围为18%~27%，层间断裂韧性的变化幅度范围为14%~32%；当打印速度从20 mm/s提升至60 mm/s，试验荷载峰值的变化幅度范围为4%~31%，层间断裂韧性的变化幅度范围为4%~16%。同时，仿真结果与试验数据的相对误差均控制在10%以内，表明本次所获试验数据合理且稳定，故缺层置换法可用于制备增材制造CFRP预制裂纹试件，且传统工艺复合材料仿真方法同样适用于增材制造CFRP的仿真分析。因此，本研究可为后续增材制造CFRP桥梁结构层间力学性能的量化分析提供技术支撑。Abstract: In order to test and analyze the mode Ⅱ inter-layer fracture toughness of additive manufacturing carbon fiber reinforced polymer (CFRP), and quantitatively evaluate the influence of printing parameters on the mode Ⅱ fracture toughness, then promote the application of additive manufacturing CFRP technology in bridge structure, experimental and simulation methods were used to carry out the relevant explorations, during this study. Firstly, the printing process was optimized and a novel method for preparing inter-layer pre-cracks was proposed, namely missing layer replacement method. Meanwhile, the influence of two types of key printing parameters (Printing temperature and printing speed) on the mode Ⅱ inter-layer fracture toughness of additive manufacturing CFRP was studied. Secondly, based on the cohesive zone theory, simulation models of the end notched flexure (ENF) test specimens with pre-cracks under various printing conditions were established. In addition, a comparative analysis between simulation results and test data was carried out. The results indicate that the influence of two key printing parameters on the mode II inter-layer fracture toughness of additive manufacturing CFRP are significant, and the influence of printing temperature is stronger. When the printing temperature increases from 245℃ to 285℃, the variation range of peak force test data is 18%~27%, and the variation range of inter-layer fracture toughness is 14%~32%. When the speed increases from 20 mm/s to 60 mm/s, the variation range of peak force test data is 4%~31%, and the variation range of inter-layer fracture toughness is 4%~16%. Moreover, the relative errors between simulation results and test data are controlled within 10%, which indicates that the test data in this study is reasonable and stable, so the missing layer replacement method has strong practicality for preparing additive manufacturing CFRP specimens with pre-cracks. In addition, the simulation method of traditional process composites is also suitable for the simulation analysis of additive manufacturing CFRP. Therefore, this method can provide technical support for the subsequent quantitative evaluation of inter-layer mechanical properties of additive manufacturing CFRP bridge structures.
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图 1 增材制造碳纤维增强树脂基复合材料(Carbon fiber reinforced polymer-CFRP)试件的几何特征
Figure 1. Geometric characteristics of additive manufacturing carbon fiber reinforced polymer (CFRP)
图 3 增材制造CFRP预制裂纹试件打印原理
Figure 3. Printing principles of additive manufacturing CFRP pre-crack specimen
图 5 增材制造CFRP细观结构几何模型
Figure 5. Meso-structures geometric model of additive manufacturing CFRP
图 6 增材制造CFRP试件校准位置
Figure 6. Calibration locations of additive manufacturing CFRP specimen
图 9 增材制造CFRP-Ⅱ型层间断裂加载过程
Figure 9. Mode Ⅱ inter-layer fracture loading process of additive manufacturing CFRP
图 7 增材制造CFRP试件加载特征
Figure 7. Loading characteristics of additive manufacturing CFRP specimen
图 8 增材制造CFRP试件柔度校准试验
Figure 8. Compliance calibration test of additive manufacturing CFRP specimen
图 11 增材制造CFRP预制裂纹试件ENF试验仿真模型
Figure 11. ENF experiment simulation model of additive manufacturing CFRP pre-crack specimen
图 13 不同网格尺寸的计算结果对比
Figure 13. Comparison of calculation results with different mesh sizes
图 14 打印速度40 mm/s下增材制造CFRP荷载-位移曲线：(a) 打印温度245℃；(b) 打印温度255℃；(c) 打印温度265℃；(d) 打印温度275℃；(e) 打印温度285℃
Figure 14. Load displacement curve of additive manufacturing CFRP with printing speed of 40 mm/s: (a) Printing temperature of 245℃; (b) Printing temperature of 255℃; (c) Printing temperature of 265℃; (d) Printing temperature of 275℃; (e) Printing temperature of 285℃
图 15 打印速度40 mm/s下增材制造CFRP层间力学性能变化规律：(a) 荷载峰值；(b) 断裂韧性值
Figure 15. Variation of inter-layer mechanical properties of additive manufacturing CFRP with printing speed of 40 mm/s: (a) Peak load; (b) Fracture toughness
图 16 打印速度40 mm/s下增材制造CFRP的细观结构
Figure 16. Meso-structures of additive manufacturing CFRP with printing speed of 40 mm/s
图 17 打印温度275℃下增材制造CFRP荷载-位移曲线：(a) 打印速度20 mm/s；(b) 打印速度30 mm/s；(c) 打印速度40 mm/s；(d) 打印速度50 mm/s；(e) 打印速度60 mm/s
Figure 17. Load displacement curve of additive manufacturing CFRP with printing temperature of 275℃: (a) Printing speed of 20 mm/s; (b) Printing speed of 30 mm/s; (c) Printing speed of 40 mm/s; (d) Printing speed of 50 mm/s; (e) Printing speed of 60 mm/s
图 18 打印温度275℃下增材制造CFRP层间力学性能变化规律：(a) 荷载峰值；(b) 断裂韧性值
Figure 18. Variation of inter-layer mechanical properties for additive manufacturing CFRP with printing temperature of 40 mm/s: (a) Peak load; (b) Fracture toughness
图 19 打印温度275℃增材制造CFRP的细观结构
Figure 19. Meso-structures of additive manufacturing CFRP with printing temperature of 275℃
图 20 打印速度40 mm/s下增材制造CFRP荷载-位移曲线仿真结果与试验数据对比：(a)打印温度245℃；(b)打印温度255℃；(c)打印温度265℃；(d) 打印温度275℃；(e) 打印温度285℃
Figure 20. Comparison between simulation results and test data of load displacement curve of additive manufacturing CFRP with printing speed of 40 mm/s: (a) Printing temperature of 245℃; (b) Printing temperature of 255℃; (c) Printing temperature of 265℃; (d) Printing temperature of 275℃; (e) Printing temperature of 285℃
图 21 打印温度275℃下增材制造CFRP荷载-位移曲线仿真结果与试验数据对比：(a)打印速度20 mm/s；(b)打印速度30 mm/s；(c)打印速度40 mm/s；(d)打印速度50 mm/s；(e)打印速度60 mm/s
Figure 21. Comparison between simulation results and test data of load displacement curve of additive manufacturing CFRP with printing temperature of 275℃: (a) Printing speed of 20 mm/s; (b) Printing speed of 30 mm/s; (c) Printing speed of 40 mm/s; (d) Printing speed of 50 mm/s; (e) Printing speed of 60 mm/s
表 1 增材制造碳纤维增强树脂基复合材料(Carbon fiber reinforced polymer-CFRP)的物理性能
Table 1. Physical properties of additive manufacturing carbon fiber reinforced polymer (CFRP)
Test condition Properties Values ASTM D792[20] Density /(g·cm−3) 1.17 DSC[21], 10℃/min Vitrification temperature /℃ 56.6 300℃, 2.16 kg Melt index /(g·min−1) 205 DSC[21], 10℃/min Melting point /℃ 220 DSC[21], 10℃/min Crystallization temperature /℃ 186.6 ISO 75[22] 1.8 MPa Thermal deformation /℃ 196 Notes: g/cm3 is a density unit and g/(10 min) is the unit of melt index. 
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表 2 增材制造CFRP固定打印参数
Table 2. Fixed printing parameters of additive manufacturing CFRP
Paremeters Values Layer height /mm 0.2 Heated build platform temperature /℃ 90 Filling rate /% 99 Filling shape Linear Filling overlap rate /% 5 Nozzle diameter /mm 0.4
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表 3 增材制造CFRP变量打印参数
Table 3. Variable printing parameters of additive manufacturing CFRP
Temperature /℃ Speed /(mm/s) 245/255/265/275/285 20/30/40/50/60
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表 4 不同工况下的界面刚度$ {K_0} $及界面强度$ {\sigma _0} $
Table 4. Interface stiffness $ {K_0} $ and interface strength $ {\sigma _0} $ with different working conditions
Printing temperature /
℃Printing speed /
(mm·s−1)$ {K_0} $/
(MPa·mm−1)$ {\sigma _0} $ /
MPaPrinting temperature /
℃Printing speed /
(mm·s−1)$ {K_0} $/
(MPa·mm−1)$ {\sigma _0} $ /
MPa245 40 1.8×103 16 275 20 1.7×103 17 255 2.6×103 19 30 2.4×103 21 265 2.7×103 22 50 3.3×103 26 275 3.0×103 24 60 3.7×103 28 285 3.3×103 28 — — — —
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表 5 不同网格尺寸下的计算用时及最大荷载对比
Table 5. Comparison of calculation time and maximum load with different mesh sizes
Mesh size /mm Number of units CPU calculation time /s Maximum load /N 4 3472 1218 1105.031 3 3640 1390 1111.864 2 7680 2334 1116.225
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表 6 不同打印温度下试件荷载峰值
Table 6. Peak load of specimens with different printing temperatures
Printing temperature /℃ Peak load /N 245 255 265 275 285 Specimen I 674.043 736.153 853.720 1083.141 1211.012 Specimen Ⅱ 504.145 696.142 809.258 1044.133 1324.143 Specimen Ⅲ 557.234 736.214 933.317 1207.024 1406.043 Average value 578.474 722.836 865.432 1111.433 1313.733 Standard deviation 70.968 18.876 50.220 69.444 79.961
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表 7 不同打印温度下试件峰值力位移
Table 7. Peak load displacement of specimens with different printing temperatures
Printing temperature /℃ Peak load displacement /mm 245 255 265 275 285 Specimen I 29.365 29.988 27.953 31.683 35.158 Specimen Ⅱ 25.232 27.474 30.841 33.293 34.436 Specimen Ⅲ 28.773 30.695 26.279 30.136 33.596 Average value 27.790 29.284 28.358 31.704 34.397 Standard deviation 1.825 1.429 1.675 1.289 0.638
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表 8 不同打印温度下试件断裂韧性值
Table 8. Fracture toughness of specimens with different printing temperatures
Printing temperature /℃ Fracture toughness /(mJ·mm−2) 245 255 265 275 285 Specimen I 0.983 1.086 1.459 1.850 2.098 Specimen Ⅱ 0.814 1.041 1.287 1.876 2.138 Specimen Ⅲ 0.772 1.250 1.518 1.905 2.231 Average value 0.856 1.126 1.421 1.877 2.156 Standard deviation 0.091 0.090 0.098 0.022 0.056
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表 9 不同打印速度下试件荷载峰值
Table 9. Peak load of specimens with different printing speed
Printing speed /(mm·s−1) Peak load /N 20 30 40 50 60 Specimen I 1045.134 868.359 1083.021 1167.156 1271.056 Specimen Ⅱ 880.102 919.665 1044.359 1101.876 1378.168 Specimen Ⅲ 784.413 751.864 1207.189 1206.341 1189.058 Average value 903.216 846.629 1111.523 1158.458 1279.427 Standard deviation 107.687 70.806 69.463 43.089 77.430
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表 10 不同打印速度下试件峰值力位移
Table 10. Peak load displacement of specimens with different printing speed
Printing speed /(mm·s−1) Peak load displacement /mm 20 30 40 50 60 Specimen I 31.302 31.711 31.683 31.899 34.281 Specimen Ⅱ 26.290 30.126 33.293 33.451 32.507 Specimen Ⅲ 29.075 32.883 30.136 30.541 35.929 Average value 28.889 31.573 31.704 31.964 34.239 Standard deviation 2.050 1.130 1.289 1.189 1.397
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表 11 不同打印速度下试件断裂韧性值
Table 11. Fracture toughness of specimens with different printing speed
Printing speed /(mm·s−1) Fracture toughness /(mJ·mm−2) 20 30 40 50 60 Specimen I 1.473 1.727 1.850 1.920 2.018 Specimen Ⅱ 1.491 1.678 1.876 2.155 2.038 Specimen Ⅲ 1.555 1.826 1.905 1.905 2.258 Average value 1.506 1.744 1.877 1.993 2.105 Standard deviation 0.035 0.062 0.022 0.114 0.109
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表 12 变温度工况下增材制造CFRP力学性能仿真结果与试验数据的对比分析
Table 12. Comparison between simulation results and test data of additive manufacturing CFRP mechanical properties with variable temperature conditions
Working conditions and parameters
/(℃-mm/s)Peak load /N Relative errors /% Peak load displacement /mm Relative errors /% 245-40 Test date 674.043 1.173 29.365 4.734 Simulation result 685.920 27.975 255-40 Test date 736.214 0.626 29.988 3.645 Simulation result 740.854 28.895 265-40 Test date 853.720 1.7145 27.953 8.664 Simulation result 839.083 25.531 275-40 Test date 1083.141 3.745 31.683 9.245 Simulation result 1125.282 28.754 285-40 Test date 1211.012 2.057 35.158 8.283 Simulation result 1236.447 32.246
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表 13 变速度工况下增材制造CFRP力学性能仿真结果与试验数据的对比分析
Table 13. Comparison between simulation results and test data of additive manufacturing CFRP mechanical properties with variable speed conditions
Working conditions and parameters
/(℃-mm/s)Peak load /N Relative errors /% Peak load displacement /mm Relative errors /% 275-20 Test date 880.102 1.477 29.075 2.102 Simulation result 893.294 28.464 275-30 Test date 868.359 0.678 31.711 4.055 Simulation result 874.284 30.425 275-40 Test date 1083.021 3.756 31.683 9.245 Simulation result 1125.282 28.754 275-50 Test date 1167.156 2.895 31.899 8.483 Simulation result 1201.949 29.193 275-60 Test date 1271.056 3.095 34.281 6.677 Simulation result 1311.648 31.992
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