CFRP防撞梁低速碰撞渐进损伤及优化

黄德明; 朱孙科; 王秋林; 孙永刚; 郑佳秋

doi:10.13801/j.cnki.fhclxb.20210702.002

CFRP防撞梁低速碰撞渐进损伤及优化

doi: 10.13801/j.cnki.fhclxb.20210702.002

1.
重庆交通大学　机电与车辆工程学院，重庆 400074
2.
成都航空职业技术学院，成都 610100
3.
桂林电子科技大学　机电工程学院，桂林 541010

基金项目: 重庆市自然科学基金(cstc2016jcyjA0467；cstc2017jcyjAX0248)；重庆市教委科学技术研究项目(KJQN201800718)

详细信息

通讯作者:
朱孙科，博士，副教授，研究方向为复合材料结构损伤　E-mail：suncobest@163.com

中图分类号: TH113.2；TB33
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出版历程
- 收稿日期: 2021-05-24
- 修回日期: 2021-06-22
- 录用日期: 2021-06-27
- 网络出版日期: 2021-07-02
- 刊出日期: 2022-06-01

Progressive damage and optimization of CFRP anti-collision beams in low-speed collision

1.
School of Mechatronics and Vehicle Engineering, Chongqing Jiaotong University, Chongqing 400074, China
2.
Chengdu Vocational and Technical College of Aviation, Chengdu 610100, China
3.
School of Mechanical and Electrical Engineering, Guilin University of Electronic Technology, Guilin 541010, China

摘要

摘要: 为预测和控制低速碰撞中碳纤维增强树脂复合材料(CFRP)防撞梁损伤程度，建立了含CFRP防撞梁的有限元显式动力学碰撞模型，防撞梁层内采用实体复合材料模拟其力学特性，采用Cohesive单元模拟CFRP层间相互作用。发展了基于Tsai-Wu张量理论的VUSDFLD子程序用于判定碰撞过程中复合材料单元6个方向损伤，失效单元按照突降退化模型进行刚度折减，利用Johnson-Cook本构模型模拟铝合金强化层碰撞损伤，其失效单元采用线性连续退化模型进行刚度折减。通过[±45°/45°/0°/0°/90°/−45°/0°/0°/90°]_s和[±45°/45°/0°/0°/0°/−45°/90°/−45°/0°/0°/90°]_s两种CFRP防撞梁铺层结构碰撞结果与含铝合金强化层CFRP防撞梁碰撞结果对比可知，在层内单元数相同的情况下，CFRP防撞梁增设4层复合材料铺层后，失效单元数量降低明显；碰撞过程中含铝合金强化层的多材料混合防撞梁结构在质量基本不变的情况下，失效单元数显著降低。结果表明，所开发的VUSDFLD子程序能够用于复合材料防撞梁的显式动力学碰撞损伤模拟，基于碰撞损伤的计算结果为CFRP防撞梁的结构设计提供参考。
- CFRP /
- 显式动力学 /
- Tsai-Wu失效准则 /
- 铝合金材料 /
- 碰撞损伤
Abstract: In order to predict and control the damage degree of carbon fiber reinforced polymer (CFRP) anti-collision beams in low speed collision, a finite element explicit dynamic collision model of CFRP anti-collision beams was established. Mechanical properties of CFRP anti-collision beams were simulated by solid composite materials, and the interlayer interaction of CFRP was simulated by cohesive element. A VUSDFLD subroutine based on Tsai-Wu tensor theory was developed to determine the damage of composite elements in six directions during the collision process. The stiffness of the failure elements was reduced according to the sudden degradation model. The Johnson-Cook constitutive model was used to simulate the impact damage of reinforced aluminum alloy layers. The stiffness reduction of the failure element was carried out by linear continuous degradation model. The collision results of two CFRP laminates ([±45°/45°/0°/0°/90°/45°/0°/0°/90°]_s and [±45°/45°/0°/0°/0°/45°/90°/45°/0°/0°/90°]_s) were compared with the collision results of CFRP anti-collision beam containing aluminum alloy reinforced layer. It can be seen that when the number of elements in the layer is the same, the number of failure elements decreases obviously by adding four layers of composite laminates to CFRP anti-collision beam. The number of failure elements of the multi-material hybrid anti-collision beam structure with reinforced aluminum alloy layer is significantly reduced under the condition that the mass of the beam is basically unchanged. The results show that the developed VUSDFLD subroutine can be used for the explicit dynamic collision damage simulation of composite anti-collision beams, and the results based on the collision damage simulation can provide a reference for the structural design of CFRP anti-collision beams.
- CFRP /
- explicit dynamics /
- Tsai-Wu failure criterion /
- aluminum alloy material /
- impact damage

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图 1 复合材料刚度折减方式

Figure 1. Composite material stiffness reduction method

E—Elasticity modulus; σ—Stress vector

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图 2 内聚力单元双线性本构关系

${\sigma }_{\mathrm{C}\mathrm{m}\mathrm{a}\mathrm{x}}$—Maximum traction; $ {\delta }_{0} $—Displacement at the beginning of the damage; $ {\delta }_{\mathrm{m}\mathrm{a}\mathrm{x}} $—Displacement at break; D—Degradation parameter of the cohesion unit

Figure 2. Bilinear constitutive relationship of cohesion unit

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图 3 Johnson-Cook模型的损伤演化规律

Figure 3. Damage evolution law of Johnson-Cook model

U—Displacement; U_max—Maximum displacement; $\bar D $—Damage parameter

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图 4 CFRP试件载荷-时间曲线

Figure 4. Load-time curve of CFRP specimen

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图 5 CFRP试件应力-时间曲线

Figure 5. Stress-time curve of CFRP specimen

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图 6 CFRP防撞梁低速碰撞有限元模型

Figure 6. Finite element model of low-speed collision of CFRP anti-collision beam

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图 7 低速碰撞碰撞器尺寸标准

Figure 7. Low-speed collision collider size standard

R—Radius

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图 8 CFRP防撞梁第1层复合材料FV3方向损伤演化过程

Figure 8. Damage evolution process in FV3 direction of the first layer of composite material of CFRP anti-collision beam

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图 9 CFRP防撞梁第2层复合材料FV3方向损伤演化过程

Figure 9. Damage evolution process in the FV3 direction of the second layer of composite material of CFRP anti-collision beam

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图 10 多材料混合防撞梁第21层复合材料FV3方向损伤演化过程

Figure 10. Damage evolution process in FV3 direction of the 21st layer composite of multi-material hybrid anti-collision beam

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图 11 CFRP防撞梁24层复合材料防撞梁出现损伤时间对比

Figure 11. Comparison of damage time of 24-layer CFRP anti-collision beam

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图 12 嵌入铝合金材料防撞梁出现损伤时间对比

Figure 12. Comparison of damage time of anti-collision beams embedded in aluminum alloy materials

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图 13 三种防撞梁结构碰撞动能曲线对比

Figure 13. Comparison of collision kinetic energy curves of three anti-collision beam structures

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图 14 三种防撞梁结构弧形顶点处变形对比

Figure 14. Comparison of deformations at the arc vertices of three anti-collision beam structures

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表 1 碳纤维/环氧复合材料防撞梁材料参数

Table 1. Material parameters of carbon fiber/epoxy composite anti-collision beam

Elastic modulus/GPa	Poisson’s ratio	Density/(kg·$ {\mathrm{m}}^{-3} $)	Strength/MPa
$ {E}_{1} $=114	$ {\gamma }_{12} $=$ {\gamma }_{13} $=0.3	$ \rho $=1780	$ {X}_{\mathrm{T}} $=2688	$ {Z}_{\mathrm{T}} $=55.5
$ {E}_{2} $=$ {E}_{3} $=8.61	$ {\gamma }_{23} $=0.45		$ {X}_{\mathrm{C}} $=1458	$ {Z}_{\mathrm{C}} $=175
$ {G}_{12} $=$ {G}_{13} $=4.16			$ {Y}_{\mathrm{T}} $=69.5	$ {S}_{12} $=$ {S}_{13} $=136
$ {G}_{23} $=3.0			$ {Y}_{\mathrm{C}} $=236	$ {S}_{23} $=95.6

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表 2 碳纤维增强树脂复合材料(CFRP)性能退化方式

Table 2. Performance degradation methods of carbon fiber reinforced polymer (CFRP)

Breaking mode	Breaking rule	Stiffness reduction
1 direction stretch	$ {\sigma }_{1}>{X}_{\mathrm{T}} $	$ E=0.01\mathrm{\%}E $ $ G=0.01\mathrm{\%}G $ $ v =1\mathrm{\%}v $
1 direction compression	$ -{\sigma }_{1}>{X}_{\mathrm{C}} $	$ E=0.01\mathrm{\%}E $ $ G=0.01\mathrm{\%}G $ $ v =1\mathrm{\%}v $
2 direction stretch	$ {\sigma }_{2}>{Y}_{\mathrm{T}} $	$ {E}_{2}=1\%{E}_{2} $ $ {G}_{12}=20\%{G}_{12} $ $ {G}_{13}=20\%{G}_{13} $
2 direction compression	$ -{\sigma }_{2}>{Y}_{\mathrm{C}} $	$ {E}_{2}=1\%{E}_{2} $ $ {G}_{12}=20\%{G}_{12} $ $ {G}_{13}=20\%{G}_{13} $
3 direction stretch	$ {\sigma }_{3}>{Z}_{\mathrm{T}} $	$ {E}_{3}=1\%{E}_{3} $ $ {G}_{12}=20\%{G}_{12} $ $ {G}_{13}=20\%{G}_{13} $
3 direction compression	$ {-\sigma }_{3}>{Z}_{\mathrm{C}} $	$ {E}_{3}=1\%{E}_{3} $ $ {G}_{12}=20\%{G}_{12} $ $ {G}_{13}=20\%{G}_{13} $
1-2 in-plane shear	$ \left\|{\tau }_{12}\right\|>{S}_{12} $	$ {E}_{2}=1\%{E}_{2} $ $ {G}_{12}=1\%{G}_{12} $
1-3 in-plane shear	$ \left\|{\tau }_{13}\right\|>{S}_{13} $	$ {E}_{3}=1\%{E}_{3} $ $ {G}_{13}=1\%{G}_{13} $
2-3 in-plane shear	$ \left\|{\tau }_{23}\right\|>{S}_{23} $	$ {E}_{2}=1\%{E}_{2}{E}_{3}=1\%{E}_{3} $ $ G=1\mathrm{\%}G $
Notes: E includes $ {E}_{1} $, $ {E}_{2} $ and $ {E}_{3} $; G includes $ {G}_{12} $, $ {G}_{13} $ and $ {G}_{23} $; $ v $ includes $ {v }_{1} $, $ {v }_{2} $ and $ { v }_{3} $.

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表 3 黏结层Cohesive单元材料参数

Table 3. Material parameters of the cohesive element of the bonding layer

Parameter	$ {K}_{1}/(\mathrm{N}·{\mathrm{m}\mathrm{m}}^{-3}) $	$ {K}_{2}/(\mathrm{N}·{\mathrm{m}\mathrm{m}}^{-3}) $	$ {K}_{3}/(\mathrm{N}·{\mathrm{m}\mathrm{m}}^{-3}) $	$ N/\mathrm{M}\mathrm{P}\mathrm{a} $	$ S/\mathrm{M}\mathrm{P}\mathrm{a} $	$ T/\mathrm{M}\mathrm{P}\mathrm{a} $	$ {G}_{1\mathrm{c}}/(\mathrm{N}·{\mathrm{m}\mathrm{m}}^{-1}) $	$ {G}_{2\mathrm{c}}/(\mathrm{N}·{\mathrm{m}\mathrm{m}}^{-1}) $	$ {G}_{3\mathrm{c}}/(\mathrm{N}·{\mathrm{m}\mathrm{m}}^{-1}) $
Value	24000	24000	24000	60	70	70	3.84	3.84	1.88
Notes: K—Stiffness coefficients in different directions; N, S, T—Intensity in different directions; $ {G}_{\mathrm{c}} $—Fracture energies in different directions.

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表 4 6061-T6铝合金材料参数

Table 4. 6061-T6 aluminum alloy material parameters

Parameter	Value	Parameter	Value	Parameter	Value
Density$ \rho $/(t·$ {\mathrm{m}\mathrm{m}}^{-3} $)	2.7×10⁻⁹	Material parameter c	0.2215	Damage parameter $ {D}_{2} $	1.45
Elastic modulus $ E/\mathrm{M}\mathrm{P}\mathrm{a} $	7×10⁴	Material parameter n	0.34	Damage parameter $ {D}_{3} $	−0.47
Poisson’s ratio $ \gamma $	0.33	Material parameter m	1	Damage parameter $ {D}_{4} $	0.011
Material parameter $ A/\mathrm{M}\mathrm{P}\mathrm{a} $	265	Reference strain rate $ {\dot{\epsilon }}_{0}/\mathrm{S} $	1.34	Damage parameter $ {D}_{5} $	1.6
Material parameter B$ /\mathrm{M}\mathrm{P}\mathrm{a} $	426	Damage parameter $ {D}_{1} $	−0.77	Reference strain rate $ {\dot{\epsilon }}_{0}/\mathrm{S} $	1

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表 5 6个CFRP试件的数据

Table 5. Data of 6 experimental CFRP specimens

Number	Maximum load/kN	Residual strength/MPa
1	56.92	419
2	54.39	400
3	57.22	421
4	55.87	406
5	61.04	441
6	54.19	399

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表 6 20层CFRP防撞梁复合材料层失效单元数统计

Table 6. Statistics on the number of failure units of 20 composite material layers of CFRP anti-collision beam

Concrete layer number	FV1	FV2	FV3	FV4	FV5	FV6	Total	Angle/(°)
1	0	187	213	0	5	202	607	45
2	0	147	227	0	5	178	557	−45
3	0	129	164	0	7	187	487	45
4	0	184	54	7	2	106	353	0
5	0	178	52	7	2	108	347	0
6	0	0	236	42	57	41	376	90
7	0	102	198	0	0	151	451	−45
8	0	181	91	13	5	108	398	0
9	0	184	102	14	4	90	394	0
10	0	0	122	44	56	119	341	90
11	0	0	134	45	54	133	366	90
12	0	136	103	10	6	97	352	0
13	0	129	97	10	6	105	347	0
14	0	138	236	0	11	193	578	−45
15	0	0	171	38	47	141	397	90
16	0	86	103	8	10	109	316	0
17	0	90	104	8	8	109	319	0
18	0	85	116	0	8	207	416	45
19	0	68	183	0	13	235	499	−45
20	0	112	159	0	15	218	504	45

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表 7 24层CFRP防撞梁复合材料层失效单元数统计

Table 7. Statistics on the number of failure units of 24 layers of composite material of CFRP anti-collision beam

Concrete layer number	FV1	FV2	FV3	FV4	FV5	FV6	Total	Angle/(°)
1	0	171	221	0	0	175	567	45
2	0	176	197	0	1	197	571	−45
3	0	145	171	0	2	177	495	45
4	0	226	65	9	6	20	326	0
5	0	207	51	8	8	21	295	0
6	0	185	36	9	4	20	254	0
7	0	152	143	0	2	87	384	−45
8	0	0	143	14	0	58	215	90
9	0	125	134	0	3	58	320	−45
10	0	184	42	5	7	25	263	0
11	0	178	52	3	7	28	268	0
12	0	0	106	15	0	112	233	90
13	0	0	15	13	0	155	183.	90
14	0	374	138	6	3	11	532	0
15	0	149	99	5	8	28	289	0
16	0	80	28	0	2	100	210	−45
17	0	0	12	6	0	153	171	90
18	0	66	20	0	0	123	209	−45
19	0	170	21	3	11	35	240	0
20	0	181	34	2	12	32	261	0
21	0	225	58	2	11	32	328	0
22	0	77	33	0	3	205	318	45
23	0	79	24	0	0	192	295	−45
24	0	90	53	0	3	213	359	45

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表 8 铝合金层和CFRP层失效单元数统计

Table 8. Statistics of the number of failure units of the aluminum alloy layer and the CFRP layer

Concrete layer number	FV1	FV2	FV3	FV4	FV5	FV6	Total	Angle/(°)
1	0	0	0	0	0	0	0(SDEG)	Aluminum alloy
2	0	0	0	0	0	0	0(SDEG)	Aluminum alloy
3	0	0	0	0	0	0	0(SDEG)	Aluminum alloy
4	0	103	5	4	2	23	137	0
5	0	17	1	4	2	20	44	0
6	0	1	1	4	2	20	28	0
7	0	36	26	0	0	30	92	−45
8	0	0	0	0	0	62	62	90
9	0	43	33	0	0	70	146	−45
10	0	71	41	0	4	17	133	0
11	0	80	0	1	5	17	103	0
12	0	0	0	0	0	173	173	90
13	0	0	0	0	0	176	176	90
14	0	0	0	0	0	0	0(SDEG)	Aluminum alloy
15	0	134	4	1	6	16	161	0
16	0	51	10	0	0	139	200	−45
17	0	0	5	0	0	198	203	90
18	0	55	13	0	0	140	208	−45
19	0	224	126	0	6	20	376	0
20	0	226	129	0	5	21	381	0
21	0	262	133	0	8	20	423	0
22	0	58	30	0	3	155	246	45
23	0	61	78	0	0	164	303	−45
24	0	73	47	0	3	197	320	45
Note: SDEG—Scalar stiffness degradation, when SDEG>1, the material fails.

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