聚丙烯纤维混凝土断裂韧度试验与数值分析

doi:10.13229/j.cnki.jdxbgxb.20221551

摘要/Abstract

摘要：

本文采用9组不同配合比的聚丙烯纤维增强混凝土（Polypropylene fiber reinforced concrete，PPFRC）进行预制裂缝梁三点弯曲试验，以聚丙烯纤维掺量和长径比为控制变量，基于双K断裂模型和四阶段断裂模型分别探讨了聚丙烯纤维对混凝土不同断裂韧度的影响，得到了PPFRC的粘聚力-裂缝张开位移双线性软化曲线，引入影响系数解决了经验计算公式的修正问题，利用ABAQUS的扩展有限元法模拟断裂过程，通过参数分析验证模型分析梁断裂行为的可行性。本文结果表明：四阶段断裂模型更适用于作为PPFRC结构失效的判定准则，模型中的宏观裂缝起裂韧度与纤维掺量成正比，与长径比成反比，结构失效韧度与掺量和长径比均呈正相关。掺入12 kg/m³、20 mm长聚丙烯纤维的混凝土宏观裂缝起裂韧度和结构失效韧度分别为9.80、55.32 MPa·m^1/2。双线性软化本构经验公式中引入的聚丙烯粗纤维β_p=0.849；聚丙烯细纤维β_p在0.409~0.552，取值随长径比增大而上升。

关键词: 建筑材料, 聚丙烯纤维, 断裂韧度, 扩展有限元法, 双线性软化曲线

Abstract:

Nine groups of notched PPFRC beam with different proportions are tested for three-point bending test to study the control variable as polypropylene fiber dosage and length/diameter ratio. Based on double-K fracture model and four-stage fracture model， the influence of polypropylene fiber on different fracture toughness is discussed respectively. The bilinear softening curve of PPFRC is concluded， The influence coefficient is introduced to solve the problem of modifying the empirical calculation formula. The XFEM（Extended finite element method）of ABAQUS was used to simulate the fracture process， and the feasibility of the model was verified by parameter analysis. The results show that the four-stage fracture model is more suitable for judging the failure of PPFRC structure. The macro-crack initiation toughness in the model is positively correlated with the fiber dosage and negatively correlated with the length/diameter ratio. The structural failure toughness is positively correlated with the fiber dosage and length/diameter ratio. The macro crack initiation toughness and structural failure toughness of 12 kg/m³ and 20 mm polypropylene fiber concrete are 9.80 MPa·m^1/2 and 55.32 MPa·m^1/2. The β_p of macro fiber introduced in bilinear softening constitutive equation is 0.849； The value of β_p of micro fiber is in the range of 0.409-0.552 and increases with the increase of aspect ratio.

Key words: architecture material, polypropylene fiber, fracture toughness, extended finite element method（XFEM）, bilinear softening curve

中图分类号:

TU528

许颖,樊悦,王青原,张振宇. 聚丙烯纤维混凝土断裂韧度试验与数值分析[J]. 吉林大学学报(工学版), 2024, 54(10): 2884-2896.

Ying XU,Yue FAN,Qing-yuan WANG,Zhen-yu ZHANG. Experiment and numerical analysis on fracture toughness of polypropylene fiber reinforced concrete[J]. Journal of Jilin University(Engineering and Technology Edition), 2024, 54(10): 2884-2896.

图/表 22

表1

表2

表3

图1

图2

图3

图4

表4

双K断裂韧度计算结果"

编号	CMOD_c/mm	CTOD_c/mm	P_ini/N	$K I C i n i$ /（MPa·m^1/2）	$σ I C i n i$	P_max/N	$K I C u n$ /（MPa·m^1/2）	$σ I C u n$
SU	0.063	0.032 8	2 210.8	0.613	0.018	3 335.9	1.666	0.087
P-6	0.047	0.025 8	2 430.7	0.683	0.019	3 298.9	1.753	0.052
P-9	0.052	0.028 2	2 761.1	0.788	0.023	3 587.0	2.242	0.100
P-12	0.057	0.029 1	2 430.4	0.685	0.024	3 502.3	1.999	0.123
T20-6	0.058	0.029 2	2 584.2	0.737	0.048	3 203.6	2.050	0.155
T20-9	0.047	0.033 3	2 726.9	0.809	0.014	3 558.6	2.413	0.103
T20-12	0.044	0.036 4	2 561.4	0.731	0.037	3 815.4	2.171	0.262
T16-9	0.056	0.036 7	2 388.3	0.688	0.049	3 502.9	2.467	0.168
T10-9	0.059	0.037 4	1 898.9	0.509	0.062	3 970.1	2.980	0.368

表4

图5

表5

四阶段断裂韧度计算结果"

编号	CMOD_macro/mm	P_macro/N	$K I C m a c r o$ /（MPa·m^1/2）	$σ I C m a c r o$	P_failure/N	$K I C f a i l u r e$ /（MPa·m^1/2）	$σ I C f a i l u r e$
SU	0.263	1 474.7	3.25	0.528	667.2	4.24	0.345
P-6	0.201	1 616.7	5.68	0.144	421.8	10.19	1.271
P-9	0.199	1 929.8	6.27	0.838	591.3	14.30	1.080
P-12	0.197	2 052.3	6.85	0.905	947.8	52.82	1.211
T20-6	0.215	1 983.5	4.81	0.855	748.6	19.44	3.777
T20-9	0.213	2 126.6	6.46	0.715	892.8	29.08	3.509
T20-12	0.203	2 694.9	9.80	0.875	1 098.5	55.32	0.625
T16-9	0.181	2 311.3	7.66	0.576	756.5	20.12	2.834
T10-9	0.162	2 630.8	8.47	0.818	688.1	13.85	1.935

表5

图6

图7

图8

表6

双线性软化曲线控制参数"

编号	$G f i n i$ / （N·m^-1）	$ψ k$	$w 1$ /mm	$w s$ /mm	σ_s/MPa	$w 0$ /mm
SU	92.7	0.313	0.046	0.033	1.27	0.329
P-6	97.4	0.458	0.048	0.029	1.85	0.429
P-9	176.2	0.683	0.087	0.032	2.77	0.374
P-12	176.3	0.666	0.087	0.034	2.70	0.551
T20-6	185.7	0.677	0.092	0.034	2.74	0.456
T20-9	188.6	0.637	0.093	0.038	2.58	0.557
T20-12	159.7	0.537	0.079	0.040	2.18	0.817
T16-9	211.2	0.648	0.104	0.041	2.62	0.481
T10-9	337.1	0.767	0.166	0.043	3.11	0.397

表6

图9

表7

图10

图11

图12

图13

表8

断裂韧度模拟结果"

编号	双K断裂模型/ （MPa·m^1/2）		四阶段断裂模型/ （MPa·m^1/2）
编号	$K I C i n i$	$K I C u n$	$K I C m a c r o$	$K I C f a i l u r e$
SU	0.753	2.047	3.38	4.08
T10-9	0.887	3.013	7.85	13.86
T16-9	0.788	2.046	6.22	21.81
T20-9	0.791	2.688	5.74	31.18

表8

图14

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符号	l/mm	d/mm	ρ/（g·cm^-3）	f_t/MPa	E/GPa
T	10、16、20	0.15	0.91	750	8
P	40	0.6	0.91	650	7

编号	配合比/（kg·m^-3）						纤维
编号	水泥	水	粉煤灰	沙	石	减水剂	长/mm	用量/（kg·m^-3）
SU	445	153	67	642	1 071	6.2	/	0
P-6	445	153	67	642	1 071	6.2	40	6
P-9	445	153	67	642	1 071	6.2	40	9
P-12	445	153	67	642	1 071	6.2	40	12
T10-9	445	153	67	642	1 071	6.2	10	9
T16-9	445	153	67	642	1 071	6.2	16	9
T20-6	445	153	67	642	1 071	6.2	20	6
T20-9	445	153	67	642	1 071	6.2	20	9
T20-12	445	153	67	642	1 071	6.2	20	12

编号	抗压强度/MPa			抗压强度平均值/MPa	变异系数	强度比
编号	1	2	3	抗压强度平均值/MPa	变异系数	强度比
SU	68.0	70.1	67.4	68.5	0.0169	1
P-6	66.4	70.5	68.1	68.3	0.0246	1.00
P-9	71.8	76.3	65.0	71.0	0.0654	1.04
P-12	70.3	69.0	67.5	68.9	0.0166	1.01
T20-6	68.2	61.8	58.7	62.9	0.0629	0.92
T20-9	75.4	76.6	78.4	76.8	0.0161	1.12
T20-12	75.0	81.1	82.1	79.4	0.0395	1.16
T16-9	70.1	71.9	70.7	70.9	0.0106	1.03
T10-9	73.3	68.0	75.8	72.4	0.0449	1.06

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