一种基于复合材料剩余强度的衍生疲劳损伤模型

赵晟; 张继文

doi:10.13801/j.cnki.fhclxb.20191224.002

一种基于复合材料剩余强度的衍生疲劳损伤模型

doi: 10.13801/j.cnki.fhclxb.20191224.002

赵晟,
张继文^,

东南大学　土木工程学院，南京 210096

基金项目: 国家重点研发计划(2017YFC0703006-01)；国家自然科学基金(51378104)

详细信息

通讯作者:
张继文，教授，博士生导师，研究方向为土木工程领域FRP应用技术、防灾减灾及防护工程　E-mail：jiwenzhang_seu@hotmail.com

中图分类号: TB332
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出版历程
- 收稿日期: 2019-10-30
- 录用日期: 2019-12-12
- 网络出版日期: 2019-12-24
- 刊出日期: 2020-10-15

A derivative fatigue damage model based on residual strength of composites

ZHAO Sheng,
ZHANG Jiwen^,

Department of Civil Engineering, Southeast University, Nanjing 210096, China

摘要

摘要: 为了研究纤维增强树脂复合材料在疲劳载荷作用下的损伤发展规律，提出了一种基于复合材料剩余强度的归一化衍生疲劳损伤模型。在该模型中，假定累积损伤与应力水平呈线性关系，可以由拉-拉疲劳试验的应力水平的损伤曲线衍生出未试验的应力水平的损伤曲线。对直径为8 mm的碳纤维增强树脂复合材料(CFRP)索材进行了不同应力幅的疲劳试验，并同时采用了文献中玻璃纤维增强树脂复合材料(GFRP)层合板的试验数据验证模型的可靠性，试验结果表明：损伤模型能较好地反映出三阶段的发展规律，衍生的损伤曲线与试验数据拟合出来的损伤曲线偏离度较小。此外，本文还研究了应力水平对复合材料损伤演化的影响，结果表明随着应力水平的增大，损伤曲线相邻阶段的边界变得不明显。
- 复合材料 /
- 剩余强度 /
- 衍生损伤曲线 /
- 疲劳寿命 /
- 等幅疲劳试验
Abstract: In order to investigate the damage development regularity of composites subjected to fatigue loading, a normalized derivative damage model based on the residual strength was proposed. In this model, it is assumed that the cumulative damage and stress level have a linear relationship, based on which, the damage curves of untested stress levels can be derived from that of tested stress levels with positive stress ratios. Fatigue tests of 8mm-diameter carbon fiber reinforced polymer (CFRP) composite tendons for different stress situations were conducted, and the experimental data of glass fiber reinforced polymer (GFRP) composite laminates from references were adopted to validate the reliability of the proposed damage model. The experimental results show that the damage model can well reflect the three-stage development law of CFRP composite tendons, and the derived damage curves show a good agreement with the damage curves obtained by fitting the experimental data. Besides, this paper investigates the influence of stress level on the damage evolution of composites. As the stress level increases, the boundaries between adjacent stages of damage curves become unobvious.
- composite /
- residual strength /
- derivable damage curve /
- fatigue life /
- constant amplitude fatigue test

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图 1 参数对复合材料疲劳损伤曲线的影响

Figure 1. Influence of parameters on shape of the proposed model for composites

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图 2 复合材料损伤曲线的衍生示意图

Figure 2. Derivation of damage curves of composites

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图 3 夹片式锚固系统示意图

Figure 3. Schematic diagram of wedge-type anchorage system

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图 4 Instron 8800疲劳试验机

Figure 4. Fatigue testing machine Instron 8800

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图 5 碳纤维增强树脂复合材料(CFRP)复合材料索材的拉伸破坏

Figure 5. Tensile failure of carbon fiber reinforced polymer(CFRP) composite tendon

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图 6 三组复合材料试验的损伤曲线及损伤速率

Figure 6. Damage curves and damage development rates of three test composite specimens

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表 1 CFRP复合材料试件的力学性能

Table 1. Mechanical properties of CFRP composite specimens

Material	Longitudinal modulus/GPa	Tensile strength/MPa
CFRP tendon	159.0	2 103.9
GFRP laminate I^[1]	24.8	448
GFRP laminate II^[13]	25.2	333

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表 2 本文模型中相关参数值

Table 2. Parameter values of the presented model

Material	Stress level $ \sigma $/MPa	N_f/cycle	a	b	R²
CFRP tendon	${ {\sigma }_{ {\rm{m} }{\rm{a} }{\rm{x} } }=0.6{\sigma }_{ {\rm{u} } },\sigma }_{{\rm{a}}}=900$	6 895	0.996	−0.071	0.959
	${ {\sigma }_{ {\rm{m} }{\rm{a} }{\rm{x} } }=0.6{\sigma }_{ {\rm{u} } },\sigma }_{{\rm{a}}}=800$	7 654	0.868	−0.339	0.902
	${ {\sigma }_{ {\rm{m} }{\rm{a} }{\rm{x} } }=0.6{\sigma }_{ {\rm{u} } },\sigma }_{{\rm{a}}}=600$	13 758	0.751	−0.614	0.943
	${ {\sigma }_{ {\rm{m} }{\rm{a} }{\rm{x} } }=0.6{\sigma }_{ {\rm{u} } },\sigma }_{{\rm{a}}}=500$	32 558	0.586	−0.451	0.968
GFRP laminate Ⅰ^[1]	$ {\sigma }_{{\rm{m}}{\rm{a}}{\rm{x}}}=386,R=0.05 $	493	0.22487	−2.478	0.999
	$ {\sigma }_{{\rm{m}}{\rm{a}}{\rm{x}}}=338,R=0.05 $	2 471	0.69607	−1.417	0.999
	$ {\sigma }_{{\rm{m}}{\rm{a}}{\rm{x}}}=290,R=0.05 $	14 706	0.63714	−1.096	0.999
	$ {\sigma }_{{\rm{m}}{\rm{a}}{\rm{x}}}=241,R=0.05 $	172 186	0.40554	−1.996	0.999
GFRP laminate Ⅱ^[13]	$ {\sigma }_{{\rm{m}}{\rm{a}}{\rm{x}}}=174,R=0.1 $	11 162	0.714	−1.213	0.998
	$ {\sigma }_{{\rm{m}}{\rm{a}}{\rm{x}}}=147,R=0.1 $	44 010	0.637	−1.390	0.997
	$ {\sigma }_{{\rm{m}}{\rm{a}}{\rm{x}}}=120,R=0.1 $	377 012	0.582	−1.999	0.989
Notes：${N}_{{\rm{f}}}$—Fatigue life of FRP specimens; $ {\sigma }_{{\rm{m}}{\rm{a}}{\rm{x}}} $—Peak stress of fatigue loading; $ {\sigma }_{{\rm{u}}} $—Ultimate strength of FRP specimens; ${\sigma }_{{\rm{a}}}$—Stress amplitude of fatigue loading; $ R $—Stress ratio; a, b—Relevant parameters of the proposed model; R²—Correlation coefficient.

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表 3 对CFRP复合材料拉-拉疲劳试验损伤曲线的预测值与拟合值的比较($ {\sigma }_{{\rm{a}}} $=800 MPa)

Table 3. Comparison of predicted results and fitting results of tension-tention fatigue damage curve for CFRP composite ($ {\sigma }_{{\rm{a}}} $=800 MPa)

n/N_f	Prediction of 900-500 MPa	Prediction of 900-600 MPa	Damage curve	Deviation (900-500 MPa)/ %	Deviation (900-600 MPa)/ %
0.1959	0.2358	0.2185	0.2292	2.89	4.70
0.2613	0.2982	0.2793	0.2897	2.97	3.57
0.3266	0.3585	0.3380	0.3467	3.40	2.50
0.3919	0.4173	0.3952	0.4013	3.99	1.52
0.5879	0.5895	0.5624	0.5577	5.70	0.84
0.7839	0.7638	0.7336	0.7194	6.17	1.97
0.9145	0.8905	0.8636	0.8509	4.65	1.49
0.9861	0.9747	0.9601	0.9577	1.77	0.25
Notes：n—Number of cycles that have been performed; Prediction of 900-500 MPa is the fatigue damage prediction D(x) derived from damage curves of 900 MPa and 500 MPa; Deviation (900-500 MPa) is the deviation between the fitting value and the prediction value derived from damage curves of 900 MPa and 500 MPa.

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表 4 对CFRP复合材料拉-拉疲劳试验损伤曲线的预测值与拟合值的比较($ {\sigma }_{{\rm{a}}} $=600 MPa)

Table 4. Comparison of predicted results and fitting results of tension-tention fatigue damage curve for CFRP composite ($ {\sigma }_{{\rm{a}}} $=600 MPa)

n/N_f	Prediction of 900-500 MPa	Prediction of 800-500 MPa	Damage curve	Deviation (900-500 MPa)/ %	Deviation (800-500 MPa)/ %
0.2181	0.3389	0.3365	0.2852	18.84	18.00
0.3271	0.4321	0.4281	0.3706	16.60	15.53
0.4361	0.5144	0.5079	0.4446	15.70	14.25
0.5815	0.6163	0.6058	0.5354	15.11	13.16
0.6542	0.6664	0.6540	0.5807	14.76	12.63
0.7433	0.7295	0.7152	0.6397	14.04	11.81
0.8722	0.8310	0.8164	0.7439	11.70	9.75
0.9813	0.9524	0.9457	0.9029	5.48	4.74

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表 5 对CFRP复合材料拉-拉疲劳试验损伤曲线的预测值与拟合值的比较($ {\sigma }_{{\rm{a}}} $=338 MPa)

Table 5. Comparison of predicted results and fitting results of tension-tention fatigue damage curve for CFRP composite ($ {\sigma }_{{\rm{a}}} $=338 MPa)

n/N_f	Prediction of 386-241 MPa	Prediction of 386-290 MPa	Damage curve	Deviation (386-241 MPa)/ %	Deviation (386-290 MPa)/ %
0.2	0.4743	0.4071	0.2572	84.42	58.28
0.4	0.4462	0.4368	0.3472	28.52	25.83
0.6	0.3957	0.4401	0.4028	1.75	9.26
0.8	0.3571	0.4544	0.4641	23.07	2.11
0.9	0.3579	0.4851	0.5228	31.54	7.21

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表 6 对CFRP复合材料拉-拉疲劳试验损伤曲线的预测值与拟合值的比较($ {\sigma }_{{\rm{a}}} $=290 MPa)

Table 6. Comparison of predicted results and fitting results of tension-tention fatigue damage curve for CFRP composite ($ {\sigma }_{{\rm{a}}} $=290 MPa)

n/N_f	Prediction of 386-241 MPa	Prediction of 338-241 MPa	Damage curve	Deviation (386-241 MPa)/ %	Deviation (338-241 MPa)/ %
0.2	0.4323	0.3235	0.3001	44.08	7.82
0.4	0.4280	0.3779	0.4093	4.56	7.66
0.6	0.3964	0.4000	0.4851	18.28	17.55
0.8	0.3738	0.4278	0.5688	34.29	24.78
0.9	0.3833	0.4666	0.6394	40.05	27.03

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表 7 对CFRP复合材料拉-拉疲劳试验损伤曲线的预测值与拟合值的比较($ {\sigma }_{{\rm{a}}} $=147 MPa)

Table 7. Comparison of predicted results and fitting results of tension-tention fatigue damage curve for CFRP composite ($ {\sigma }_{{\rm{a}}} $=147 MPa)

n/N_f	Prediction of 174-147 MPa	Damage curve	Deviation (174-147 MPa)/ %
0.1242	0.2189	0.2280	3.99
0.3854	0.3419	0.3690	7.34
0.6416	0.3932	0.4369	9.98
0.7822	0.4257	0.4786	11.05
0.9012	0.4800	0.5437	11.71
0.9271	0.5021	0.5691	11.77

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