针刺C/C复合材料面内拉伸强度预测

刘文台; 程坤; 周何乐子; 白侠; 廖敦明; 周华民

doi:10.13801/j.cnki.fhclxb.20220310.001

针刺C/C复合材料面内拉伸强度预测

doi: 10.13801/j.cnki.fhclxb.20220310.001

1.
华中科技大学　材料成形与模具技术国家重点实验室，武汉 430074
2.
西安航天复合材料研究所，西安 710025

基金项目: 国家自然科学基金(U20A20288)；校启动经费(2020kfyXJJS001)

详细信息

通讯作者:
周何乐子，博士，讲师，硕士生导师，研究方向为碳纤维复合材料成形及力学　E-mail: helezizhou@hust.edu.cn；

廖敦明，博士，教授，博士生导师，研究方向为复合材料成型过程模拟　E-mail：liaodunming@hust.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2022-01-06
- 修回日期: 2022-02-23
- 录用日期: 2022-03-03
- 网络出版日期: 2022-03-11
- 刊出日期: 2023-02-15

Prediction of in-plane tensile strength of needle punched C/C composites

1.
State Key Laboratory of Materials Processing and Die & Mould Technology, Huazhong University of Science and Technology, Wuhan 430074, China
2.
Xi’an Aerospace Composites Research Institute, Xi’an 710025, China

Funds: National Natural Science Foundation of China (U20A20288); Fundamental Research Funds for the Central Universities (2020kfyXJJS001)

摘要

摘要: 为研究针刺碳纤维增强碳基体复合材料(针刺C/C复合材料)面内拉伸强度与渐进损伤，建立了针刺C/C复合材料代表性体积单元有限元模型。模型包含无纬布层、网胎层、针刺纤维束、界面4类子区域，并考虑了孔隙的影响。采用基于应变的破坏准则及指数型损伤演化规律研究无纬布层及针刺纤维束损伤，采用弹塑性本构研究网胎层损伤，采用内聚力牵引分离定律和二次应力破坏准则分析界面损伤。通过两步法计算了孔隙对材料性能的折减效果，并得到上述4个子区域的力学性能，通过ABAQUS UMAT预测了材料的面内拉伸应力-应变曲线及各子区域损伤起始、演化与失效过程，非线性趋势及拉伸强度数值与试验数值吻合较好，验证了该模型有效性。
- 针刺C/C复合材料 /
- 渐进损伤 /
- 强度预测 /
- 有限元法 /
- 代表性体积单元
Abstract: In order to study the in-plane tensile strength and the progressive damage behavior of needle punched carbon fiber reinforced carbon composites (needle punched C/C composites), a representative volume element finite element model of needle punched C/C composites was established. The model was divided into four sub-regions: non-woven cloth, short cut fiber felt, needling fibers and interface, and the effect of pores was estimated. Based on the failure criterion and exponential damage evolution law, the damage of the non-woven cloth and needling fibers was studied. The damage of the short cut fiber felt was defined by an elastic-plastic constitutive method. A cohesive force traction separation law and a quadratic nominal stress criterion were adopted at the interface. The negative influence of pores on mechanical properties of the material was considered by two steps. Then, mechanical properties of the four sub-regions were calculated. The in-plane tensile stress-strain curve of the material was predicted through ABAQUS UMAT subroutine, and the damage initiation, propagation and failure of the four sub-regions were simulated. The nonlinear trend and tensile strength agree well with experimentally measured data, which verifies the proposed model.
- needle punched C/C composites /
- progressive damage /
- strength prediction /
- finite element method /
- representative volume element

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图 1 针刺碳纤维预制体结构示意图

Figure 1. Schematic diagram of needle punched carbon fiber preform

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图 2 针刺C/C复合材料结构形貌

Figure 2. Structural morphologies of the needle punched C/C composite

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图 3 针刺C/C复合材料代表性体积单元(RVE)网格模型

Figure 3. Geometric model of representative volume element (RVE) for needle punched C/C composites

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图 4 短切纤维毡的网胎层力-位移响应趋势

Figure 4. Force-displacement response trend of the short cut fiber felt

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图 5 拉伸试验

Figure 5. Tensile test

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图 6 针刺C/C复合材料面内拉伸模拟和试验应力-应变曲线对比(A、B、C、D分别为各类损伤出现的时刻)

Figure 6. Comparisons of stress-strain curves between in-plane tensile simulation and test for needle punched C/C composites (A, B, C and D indicate the occurrence of various injuries, respectively)

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图 7 针刺C/C复合材料90°无纬布层基体损伤演化

SDV2—Matrix damage

Figure 7. Damage evolution of matrix in 90° non-woven cloth for needle punched C/C composites

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图 8 针刺C/C复合材料不同90°无纬布层最终时刻基体损伤

Figure 8. Matrix damage of different 90° non-woven cloths at the final moment for needle punched C/C composites

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图 9 针刺C/C复合材料0°无纬布层纤维/基体损伤演化

SDV1—Fiber damage

Figure 9. Damage evolution of fiber and matrix in 0° non-woven cloth for needle punched C/C composites

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图 10 针刺C/C复合材料网胎层应力变化

S—Von-mises stress

Figure 10. Stress variation of short cut fiber felt for needle punched C/C composites

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图 11 针刺C/C复合材料无纬布层与网胎层间界面损伤演化

SDEG—Interfacial damage

Figure 11. Damage evolution of the interface between non-woven cloth and short cut fiber felt for needle punched C/C composites

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表 1 针刺碳纤维增强碳基体(C/C)复合材料各区域成分体积分数

Table 1. Ingredient volume fraction of needle punched carbon fiber reinforced carbon (C/C) composites in different region

Region	Fiber volume fraction V_f /%	Matrix volume fraction V_m/%	Pore volume fraction V_p /%
Needle punched C/C composite	33.3	47.4	19.3
Non-woven cloth (Needling fibers)	35.6	59.5	4.9
Short cut fiber felt	31.7	38.7	29.6

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表 2 针刺C/C复合材料RVE模型几何参数

Table 2. Geometric parameters of the RVE model for needle punched C/C composites

Region	Length/ mm	Width/ mm	Height/ mm	Radius/ mm
Needle punched C/C composite	2.5	2.5	4.80	–
Non-woven cloth	2.5	2.5	0.25	–
Short cut fiber felt	2.5	2.5	0.35	–
Needling fibers	–	–	3.60	0.20

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表 3 T700碳纤维力学性能^[11,22]

Table 3. Mechanical properties of T700 carbon fiber^[11,22]

$ {E}_{1}^{\mathrm{f}} $/GPa	$ {E}_{2}^{\mathrm{f}} $/GPa	$ {v }_{12}^{\mathrm{f}} $	$ {G}_{12}^{\mathrm{f}} $/GPa	$ {G}_{23}^{\mathrm{f}} $/GPa	$ {X}_{1}^{\mathrm{f}} $/MPa
230	18.22	0.27	36.59	7.01	4900
Notes: $ {E}_{1}^{\mathrm{f}} $ and $ {E}_{2}^{\mathrm{f}} $—Longitudinal and transverse tensile modulus of the carbon fiber; $ {v }_{12}^{\mathrm{f}} $−Longitudinal Poisson’s ratio of the carbon fiber; $ {G}_{12}^{\mathrm{f}} $ and $ {G}_{23}^{\mathrm{f}} $—Longitudinal and transverse shear modulus of the carbon fiber; $ {X}_{1}^{\mathrm{f}} $—Longitudinal tensile strength of the carbon fiber.

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表 4 碳基体力学参数^[15]

Table 4. Mechanical properties of carbon matrix^[15]

$ {E}^{\mathrm{m}}/{\rm{GPa}} $	$ {v }^{\mathrm{m}} $	$ {\sigma }_{\mathrm{t}}^{\mathrm{m}} $/MPa	$ {\sigma }_{\mathrm{c}}^{\mathrm{m}} $/MPa	$ {\sigma }_{\mathrm{s}}^{\mathrm{m}} $/MPa
15	0.23	14.7	67.8	19.1
Notes: $ {E}^{\mathrm{m}} $ and $ {v }^{\mathrm{m}} $—Modulus and Poisson’s ratio of the carbon matrix; $ {\sigma }_{\mathrm{t}}^{\mathrm{m}} $, $ {\sigma }_{\mathrm{c}}^{\mathrm{m}} $, $ {\sigma }_{\mathrm{s}}^{\mathrm{m}} $—Tensile, compressive and shear strength of the carbon matrix.

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表 5 针刺C/C复合材料各区域材料参数^[27]

Table 5. Material parameters in each region of needle punched C/C composites^[27]

Non-woven cloth (Needling fibers)	$ {E}_{11}^{\mathrm{L}} $/GPa	$ {E}_{22}^{\mathrm{L}} $/GPa	$ {G}_{12}^{\mathrm{L}} $/GPa	$ {G}_{23}^{\mathrm{L}} $/GPa	$ {v }_{12}^{\mathrm{L}} $	$ {X}_{\mathrm{T}}^{\mathrm{L}} $/MPa
	57.801	15.950	11.227	6.334	0.234	670.284
	$ {X}_{\mathrm{C}}^{\mathrm{L}} $/MPa	$ {Y}_{\mathrm{T}}^{\mathrm{L}} $/MPa	$ {Y}_{\mathrm{C}}^{\mathrm{L}} $/MPa	$ {S}_{12}^{\mathrm{L}} $/MPa	$ {G}^{\mathrm{f}} $/(N·mm⁻¹)	$ {G}^{\mathrm{m}} $/(N·mm⁻¹)
	335.142	10.791	49.772	11.896	8	1
Short cut fiber felt	$ {E}^{\mathrm{S}} $/GPa	${v }^{{\rm{S}}}$	$ {\sigma }^{\mathrm{S}} $/MPa
Short cut fiber felt	11.243	0.146	20.7
Interface	$ {K}_{\mathrm{n}} $/(N·mm⁻³)	$ {K}_{\mathrm{s}} $/(N·mm⁻³)	$ {t}_{\mathrm{n}} $/MPa	$ {t}_{\mathrm{s}} $/MPa	$ {G}_{\mathrm{n}} $/(N·mm⁻¹)	$ {G}_{\mathrm{s}} $/(N·mm⁻¹)
Interface	10⁶	10⁶	13.8	18.0	1	1
Notes: $ {E}_{11}^{\mathrm{L}} $ and $ {E}_{22}^{\mathrm{L}} $—Longitudinal and transverse tensile modulus of the non-woven cloth (needling fibers); $ {G}_{12}^{\mathrm{L}} $ and $ {G}_{23}^{\mathrm{L}} $—Longitudinal and transverse shear modulus of the non-woven cloth (needling fibers); $ {v }_{12}^{\mathrm{L}} $—Longitudinal Poisson’s ratio of the non-woven cloth (needling fibers); $ {X}_{\mathrm{T}}^{\mathrm{L}} $ and $ {X}_{\mathrm{C}}^{\mathrm{L}} $—Longitudinal tensile and compressive strength of the non-woven cloth (needling fibers); $ {Y}_{\mathrm{T}}^{\mathrm{L}} $ and $ {Y}_{\mathrm{C}}^{\mathrm{L}} $—Transverse tensile and compressive strength of the non-woven cloth (needling fibers); $ {S}_{12}^{\mathrm{L}} $—Longitudinal shear strength of the non-woven cloth (needling fibers); $ {G}^{\mathrm{f}} $ and $ {G}^{\mathrm{m}} $—Fracture energy of the fiber and the matrix; $ {E}^{\mathrm{S}} $—Tensile modulus of the short cut fiber felt; $ {v }^{{\rm{S}}} $—Poisson’s ratio of the short cut fiber felt; ${\sigma }^{\rm{S} }$—Tensile strength of the short cut fiber felt; $ {K}_{\mathrm{n}} $ and $ {K}_{\mathrm{s}} $—Stiffness of the interface in normal and tangential direction; $ {t}_{\mathrm{n}} $ and $ {t}_{\mathrm{s}} $—Strength of the interface in normal and tangential direction; $ {G}_{\mathrm{n}} $ and $ {G}_{\mathrm{s}} $−Fracture energy of the interface in normal and tangential direction.

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表 6 针刺C/C复合材料模拟结果和拉伸试验结果对比

Table 6. Result comparison of the finite element method with the tensile test for needle punched C/C composites

Property	Modulus	Strength
Experimental result/MPa	23783	88.62
Predicted value/MPa	21736	82.83
Error/%	8.61	6.53

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