聚丙烯纤维增强混凝土断裂韧度及软化本构曲线确定

doi:10.13229/j.cnki.jdxbgxb20180020

摘要/Abstract

摘要：

对粗、细聚丙烯（Polypropylene, PP）纤维不同混掺情况下的混凝土切口梁试件进行三点弯曲试验，基于双K断裂理论探讨了不同尺寸PP纤维混掺方式对试件断裂韧度的影响及其破坏机理，并通过起裂、失稳、黏聚韧度3者之间的定量关系得到实测黏聚韧度、起裂韧度增量和桥接韧度。借鉴3种普通混凝土的双线性软化本构曲线计算得到理论黏聚韧度，并将其与实测黏聚韧度对比，确定适合于不同纤维掺入情况下PP纤维增强混凝土(Polypropylene fiber reinforced concrete, PFRC)的双线性软化本构曲线。研究结果表明，PFRC相对素混凝土有较高的起裂韧度、失稳韧度和断裂能；2或3种尺寸PP纤维混掺时，其桥接应力对桥接韧度的增强效果非常显著；3种尺寸PP纤维在裂缝扩展的不同阶段发挥桥接作用，体现了良好的混掺增强、增韧效应；徐世烺和Reinhardt改进的双线性软化本构曲线，取校正系数λ为6时，可较好地适用于PFRC。

关键词: 土木工程, 聚丙烯纤维增强混凝土, 双K断裂理论, 双线性软化本构曲线

Abstract:

The three?point bending test was carried out on concrete notched beams with different amount of coarse and fine polypropylene(PP) fibers. Based on the double?K fracture theory, the influence of mixing method of PP fibers with different sizes on the fracture toughness and failure mechanism were discussed.The real cohesive toughness, the increment of initiation toughness and the bridge connection toughness were gained by the quantitative relationship between the initiation toughness, the unstable toughness and the cohesive toughness. In addition, The theoretical cohesive toughness was calculated from three kinds of ordinary concrete bilinear softening constitutive curves, which was compared with the real cohesive toughness to determine the bilinear softening traction?separation law of PFRC, which was suitable for different PP fiber incorporation conditions. The results show that PFRC has higher initiation toughness, unstable toughness and fracture energy compared with plain concrete. The enhancement effect of bridge connection toughness from bridging stress is very significant when 2 or 3 sizes of PP fibers are mixed. The 3 sizes of PP fibers play the role of bridging at different stages of crack propagation, and it serves a well function of toughening and strengthening. The bilinear softening traction?separation law proposed by Xu and Reinhardt is well applicable for PFRC when the correction coefficient is 6.

Key words: civil engineering, polypropylene fiber reinforced concrete, double?K fracture model, bilinear softening traction?separation law

中图分类号:

TU528

梁宁慧,缪庆旭,刘新荣,代继飞,钟祖良. 聚丙烯纤维增强混凝土断裂韧度及软化本构曲线确定[J]. 吉林大学学报(工学版), 2019, 49(4): 1144-1152.

Ning⁃hui LIANG,Qing⁃xu MIAO,Xin⁃rong LIU,Ji⁃fei DAI,Zu⁃liang ZHONG. Determination of fracture toughness and softening traction⁃separation law of polypropylene fiber reinforced concrete[J]. Journal of Jilin University(Engineering and Technology Edition), 2019, 49(4): 1144-1152.

图/表 8

图1

图2

表1

表2

图3

表3

双K断裂韧度及断裂能的计算结果"

试件编号	CMOD _c/μm	$C T O D c$ /μm	P _inl/N	$K I c i n i$ /(MPa·m^1/2)	$P m a x$ /N	a _c/mm	$K I c u n$ /(MPa·m^1/2)	G _f /(N·m^-1)
A0	39.9	10	1665	0.561	2017	57	0.869	104.7
A1	48.1	13	1943	0.654	2441	59	1.133	147.6
A2	42.5	12	1503	0.506	1929	61	0.960	113.3
A3	51.1	15	1807	0.608	2265	61	1.132	403.1
A4	51.2	16	1727	0.582	2243	62	1.120	537.9
A5	58.8	21	1850	0.623	2457	63	1.336	562.0
A6	54.7	18	1752	0.590	2276	64	1.285	535.0
A7	54.8	18	1797	0.605	2351	63	1.287	480.7
A8	56.5	19	1755	0.591	2284	64	1.282	544.2
A9	47.2	16	1627	0.548	2177	64	1.272	433.6
A10	44.9	18	1983	0.670	2552	63	1.356	537.7
A11	57.3	20	1930	0.650	2580	64	1.454	608.8

表3

表4

PFRC的 Δ K I c i n i s 和 K I c c s 值"

试件编号	$K I c c s$	$Δ K I c i n i s$
A0	0	0
A1	0.171	0.093
A2	0.146	-0.055
A3	0.216	0.047
A4	0.230	0.021
A5	0.405	0.062
A6	0.387	0.029
A7	0.374	0.044
A8	0.383	0.030
A9	0.416	-0.013
A10	0.378	0.109
A11	0.496	0.089

表4

表5

实测黏结韧度与理论黏聚韧度的比较"

试件编号		$K I c, T c$	$K I c, E c$ （Petersson)	$K I c, E c$ （CEB?FIP Model Code 1990)	$K I c, E c$ （徐世烺和Reinhardt)
试件编号		$K I c, T c$	$K I c, E c$ （Petersson)	$K I c, E c$ （CEB?FIP Model Code 1990)	λ=5	λ=6	λ=7	λ=8	λ=9	λ=10
$∑ i = 1 11 η i$			0.601	0.594	0.274	0.149	0.161	0.220	0.279	0.305
A0?1		0.287	0.479	0.344	0.328	0.299	0.283	0.272	0.265	0.260
A0?2		0.335	0.510	0.366	0.348	0.317	0.299	0.288	0.280	0.274
A0?3		0.304	0.415	0.298	0.283	0.259	0.245	0.236	0.230	0.225
$η 0$			0.08	0.004	0.002	0.0025	0.005	0.007	0.009	0.010
A1?1		0.489	0.525	0.523	0.494	0.445	0.442	0.431	0.419	0.411
A1?2		0.523	0.622	0.620	0.587	0.532	0.529	0.508	0.493	0.483
A1?3		0.424	0.538	0.536	0.506	0.460	0.458	0.441	0.429	0.420
$η 1$			0.024	0.023	0.011	0.003	0.003	0.0038	0.006	0.008
A2?1		0.588	0.730	0.725	0.692	0.624	0.619	0.594	0.577	0.564
A2?2		0.419	0.630	0.627	0.596	0.540	0.536	0.515	0.501	0.490
A2?3		0.355	0.555	0.552	0.524	0.475	0.474	0.456	0.443	0.434
$η 2$			0.105	0.101	0.07	0.031	0.029	0.02	0.015	0.012
A3?1		0.493	0.547	0.546	0.509	0.461	0.458	0.441	0.428	0.419
A3?2		0.549	0.837	0.836	0.773	0.692	0.689	0.653	0.631	0.616
A3?3		0.526	0.678	0.677	0.630	0.568	0.563	0.539	0.523	0.512
$η 3$			0.109	0.108	0.06	0.023	0.02	0.013	0.011	0.01
A4?1	0.517		0.617	0.616	0.571	0.516	0.512	0.491	0.476	0.466
A4?2	0.931		1.06	1.05	0.972	0.863	0.848	0.807	0.779	0.759
A4?3	0.405		0.632	0.632	0.585	0.527	0.523	0.501	0.486	0.475
$η 4$			0.077	0.051	0.037	0.019	0.021	0.025	0.031	0.037
A5?1		0.791	0.803	0.802	0.743	0.667	0.658	0.630	0.610	0.595
A5?2		0.628	0.771	0.770	0.712	0.639	0.632	0.604	0.586	0.571
A5?3		-	-	-	-	-	-	-	-	-
$η 5$			0.020	0.020	0.009	0.015	0.017	0.026	0.031	0.041
A6?1		0.649	0.759	0.757	0.701	0.630	0.623	0.596	0.578	0.564
A6?2		0.740	0.893	0.892	0.823	0.735	0.724	0.691	0.668	0.651
A6?3		0.695	0.845	0.843	0.781	0.699	0.689	0.659	0.638	0.622
$η 6$			0.058	0.057	0.017	0.0004	0.0001	0.006	0.013	0.02
A7?1		0.713	0.828	0.828	0.763	0.683	0.673	0.644	0.623	0.607
A7?2		0.836	0.960	0.958	0.885	0.788	0.776	0.740	0.715	0.697
A7?3		0.681	0.783	0.781	0.726	0.652	0.644	0.616	0.598	0.583
$η 7$			0.040	0.038	0.007	0.004	0.007	0.018	0.03	0.04
A8?1		0.805	1.038	1.037	0.952	0.846	0.831	0.791	0.764	0.744
A8?2		0.628	0.741	0.739	0.687	0.617	0.611	0.585	0.567	0.553
A8?3		0.691	0.833	0.832	0.768	0.687	0.678	0.648	0.627	0.612
$η 8$			0.087	0.086	0.031	0.002	0.001	0.004	0.009	0.016
A9?1		0.541	0.677	0.676	0.630	0.568	0.563	0.540	0.523	0.512
A9?2		0.794	0.943	0.942	0.868	0.773	0.761	0.726	0.701	0.683
A9?3		0.724	0.880	0.879	0.811	0.725	0.715	0.682	0.660	0.643
$η 9$			0.065	0.064	0.021	0.001	0.0016	0.006	0.013	0.019
A10?1		0.716	0.767	0.766	0.708	0.635	0.628	0.610	0.582	0.568
A10?2		0.783	0.864	0.863	0.797	0.713	0.703	0.671	0.650	0.633
A10?3		0.688	0.755	0.754	0.699	0.627	0.621	0.594	0.576	0.562
$η 10$			0.014	0.013	0.0004	0.015	0.019	0.034	0.048	0.06
A11?1		0.789	0.774	0.773	0.716	0.643	0.635	0.608	0.589	0.575
A11?2		0.806	0.848	0.847	0.781	0.699	0.689	0.659	0.637	0.621
A11?3		-	-	-	-	-	-	-	-	-
$η 11$			0.002	0.002	0.006	0.032	0.037	0.054	0.068	0.080

表5

参考文献 20

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参数	FF1	FF2	CF1
直径/mm	0.026	0.100	0.800
长度/mm	19	19	50
抗拉强度/MPa	641	322	706
弹性模量/GPa	4.5	4.9	7.4
断裂伸长率/%	40	15	10
密度/(g·cm^-3)	0.91	0.91	0.95
推荐掺量/(kg·m^-3)	0.9	0.9	6.0

试件编号	纤维种类	纤维掺量/(kg·m^-3)
A0	无	0
A1	FF1	0.9
A2	FF2	0.9
A3	CF1	6.0
A4	FF1+CF1	0.6+5.4
A5	FF1+CF1	0.9+5.1
A6	FF1+CF1	1.2+4.8
A7	FF2+CF1	0.6+5.4
A8	FF2+CF1	0.9+5.1
A9	FF2+CF1	1.2+4.8
A10	FF1+FF2+CF1	0.45+0.45+5.1
A11	FF1+FF2+CF1	0.6+0.6+4.8

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