纤维高强混凝土断裂性能的试验研究
|
摘要
随着纤维混凝土的广泛应用和结构分析方法、试验技术、设计方法等的日臻完善，纤维混凝土断裂机理的研究已经引起了广大科技工作者的广泛重视。本文在河南省自然科学基金(0311052800)资助下，主要进行了以下几个方面的研究：
1．通过24组共72个试件尺寸为200mm×170mm×100mm的楔劈拉伸试件的试验，探讨了钢纤维体积率、钢纤维类型、相对切口深度等对高强混凝土断裂性能的影响，建立了钢纤维高强混凝土断裂韧度(K_(IC))、断裂能(G_F)、临界裂缝嘴张开位移(CMOD_C)、临界裂缝尖端张开位移(CTOD_C)等断裂参数与钢纤维含量特征参数的关系式；分析了钢纤维高强混凝土和普通高强混凝土的缺口敏感性以及钢纤维对高强混凝土裂缝前缘应变场分布的影响。试验结果表明：钢纤维的加入可以极大地改善高强混凝土的断裂性能，随着纤维体积率的增加，钢纤维高强混凝土断裂参数均有不同程度的提高；与铣削型和剪切波纹型钢纤维相比，切断弓型钢纤维可以极大地改善高强混凝土的断裂性能；钢纤维高强混凝土断裂韧度和断裂能存在缺口敏感性，钢纤维体积率的变化对高强混凝土缺口敏感性的影响较小；钢纤维的加入可以改善裂缝前缘应变场分布。
2．通过8组共24个试件尺寸为200mm×170mm×100mm楔劈拉伸试件的试验，探讨了聚丙烯纤维掺量对高强混凝土断裂韧度、断裂能和临界裂缝嘴张开位移的影响，研究了聚丙烯纤维高强混凝土裂缝前缘应变场分布。结果表明：在本次试验条件下，聚丙烯纤维对高强混凝土断裂韧度基本没有影响，但可以提高高强混凝土的断裂能和临界裂缝嘴张开位移；随着纤维掺量的增加，断裂能和断裂能增益比都有不同程度的提高，临界裂缝张开位移有减小的趋势，临界裂缝嘴张开位移增益比变化没有明显的规律性；聚丙烯纤维对高强混凝土试件裂缝前缘应变场分布改善不显著；聚丙烯纤维主要改善高强混凝土的裂后行为。
3．通过对14组共42个混杂纤维高强混凝土楔劈拉伸试件的试验，研究了混杂纤维高强混凝土的断裂力学性能和纤维混杂效应。研究结果表明：纤维的加入可以极大地改善高强混凝土的断裂性能，纤维掺量较小的混杂纤维高强混凝土表现了纤维的正混杂效应，随着纤维掺量的增加，纤维的混杂效应逐渐消失；钢纤维在混杂纤维高强混凝土断裂性能的改善方面起着主导作用，聚丙烯纤维对高强混凝土断裂性能的改善有局限性，弓型纤维对混杂纤维高强混凝土断裂性能的改善较为有效。
With the extensive use of fiber reinforced concrete and the development of structural analysis method, experimental technique, design means, the research on the fracture properties of fiber reinforced concrete has been extensively regarded. As the project supported by the Natural Science Foundation of HENAN Province (0311052800), the following research works have been accomplished in this paper:
1 .By the wedge-splitting tensile test on seventy-two specimens of steel fiber reinforced high-strength concrete (HSC) with the size of 200mmxl70mmx 100mm, the impacts of steel fiber volume ratio, notch depth ratio and different types of steel fiber upon the fracture properties, such as critical stress intensity factor (K\c), fracture energy (Gf), critical crack mouth opening displacement (CMODc) as well as critical crack tip opening displacement (CTODc) of HSC have been studied. The correlativity between steel fiber aspect ratio and fracture properties of HSC reinforced with steel fiber has been established. The notch sensitivity of HSC and steel fiber reinforced HSC and the strain field of HSC reinforced with steel fibers ahead of the crack tip have been analyzed. The test results indicated that the addition of steel fiber can significantly improve the fracture properties of HSC. As the increase of steel fiber volume ratio, the fracture parameters of steel fiber reinforced HSC increase differently. In comp
arison with the milled steel fiber and waved steel fiber, the addition of bowed steel fiber to HSC improves its fractural properties more. The HSC and steel fiber reinforced HSC are all have notch sensitivity. The addition of steel fiber to the HSC has extensively improved the strain filed ahead of the crack tip.
2. By the wedge-splitting tensile test on the twenty-four specimens of polypropylene fiber reinforced HSC with the size of 200mmx170mmx 100mm, the impacts of polypropylene dosage upon the fracture properties, such as stress intensity factor, fracture energy, as well as critical crack mouth opening displacement of polypropylene reinforced HSC have been investigated, and the strain field ahead of the crack tip of polypropylene fiber reinforced HSC has been researched. The test results indicate that the addition of polypropylene has no impacts upon the KIC, but increases the GF and CMODc. With the increase dosage of polypropylene, GV and the increment ratio of GF increase respectively, but CMODc decreased, and the varying of increment ratio of CMODc has no disciplinarian, and the influence of strain field ahead of crack tip is small. Polypropylene improves the properties of HSC at the post-cracking zone.
3. By the wedge-splitting tensile test on the forty-two specimens of hybrid (steel and polypropylene) fiber reinforced HSC with the size of 200mmx 170mmx 100mm, the fracture properties of hybrid fiber reinforced HSC and the synergy effect on HSC have been investigated.
The test results indicate that the addition of fiber has extensively improved the fracture properties of HSC. A positive synergy effect between steel fiber and polypropylene has been observed at low fiber dosage and the synergy effect disappears with the increase of fiber dosage. Steel fiber plays a key role on the improvement of fracture properties of hybrid fiber reinforced HSC. The improvement effect of polypropylene on the fracture properties of hybrid reinforced HSC is small. Bowed steel fiber is more effective on the improvement of fracture properties of hybrid fiber reinforced HSC than other two types of steel fiber.
1．通过24组共72个试件尺寸为200mm×170mm×100mm的楔劈拉伸试件的试验，探讨了钢纤维体积率、钢纤维类型、相对切口深度等对高强混凝土断裂性能的影响，建立了钢纤维高强混凝土断裂韧度(K_(IC))、断裂能(G_F)、临界裂缝嘴张开位移(CMOD_C)、临界裂缝尖端张开位移(CTOD_C)等断裂参数与钢纤维含量特征参数的关系式；分析了钢纤维高强混凝土和普通高强混凝土的缺口敏感性以及钢纤维对高强混凝土裂缝前缘应变场分布的影响。试验结果表明：钢纤维的加入可以极大地改善高强混凝土的断裂性能，随着纤维体积率的增加，钢纤维高强混凝土断裂参数均有不同程度的提高；与铣削型和剪切波纹型钢纤维相比，切断弓型钢纤维可以极大地改善高强混凝土的断裂性能；钢纤维高强混凝土断裂韧度和断裂能存在缺口敏感性，钢纤维体积率的变化对高强混凝土缺口敏感性的影响较小；钢纤维的加入可以改善裂缝前缘应变场分布。
2．通过8组共24个试件尺寸为200mm×170mm×100mm楔劈拉伸试件的试验，探讨了聚丙烯纤维掺量对高强混凝土断裂韧度、断裂能和临界裂缝嘴张开位移的影响，研究了聚丙烯纤维高强混凝土裂缝前缘应变场分布。结果表明：在本次试验条件下，聚丙烯纤维对高强混凝土断裂韧度基本没有影响，但可以提高高强混凝土的断裂能和临界裂缝嘴张开位移；随着纤维掺量的增加，断裂能和断裂能增益比都有不同程度的提高，临界裂缝张开位移有减小的趋势，临界裂缝嘴张开位移增益比变化没有明显的规律性；聚丙烯纤维对高强混凝土试件裂缝前缘应变场分布改善不显著；聚丙烯纤维主要改善高强混凝土的裂后行为。
3．通过对14组共42个混杂纤维高强混凝土楔劈拉伸试件的试验，研究了混杂纤维高强混凝土的断裂力学性能和纤维混杂效应。研究结果表明：纤维的加入可以极大地改善高强混凝土的断裂性能，纤维掺量较小的混杂纤维高强混凝土表现了纤维的正混杂效应，随着纤维掺量的增加，纤维的混杂效应逐渐消失；钢纤维在混杂纤维高强混凝土断裂性能的改善方面起着主导作用，聚丙烯纤维对高强混凝土断裂性能的改善有局限性，弓型纤维对混杂纤维高强混凝土断裂性能的改善较为有效。
With the extensive use of fiber reinforced concrete and the development of structural analysis method, experimental technique, design means, the research on the fracture properties of fiber reinforced concrete has been extensively regarded. As the project supported by the Natural Science Foundation of HENAN Province (0311052800), the following research works have been accomplished in this paper:
1 .By the wedge-splitting tensile test on seventy-two specimens of steel fiber reinforced high-strength concrete (HSC) with the size of 200mmxl70mmx 100mm, the impacts of steel fiber volume ratio, notch depth ratio and different types of steel fiber upon the fracture properties, such as critical stress intensity factor (K\c), fracture energy (Gf), critical crack mouth opening displacement (CMODc) as well as critical crack tip opening displacement (CTODc) of HSC have been studied. The correlativity between steel fiber aspect ratio and fracture properties of HSC reinforced with steel fiber has been established. The notch sensitivity of HSC and steel fiber reinforced HSC and the strain field of HSC reinforced with steel fibers ahead of the crack tip have been analyzed. The test results indicated that the addition of steel fiber can significantly improve the fracture properties of HSC. As the increase of steel fiber volume ratio, the fracture parameters of steel fiber reinforced HSC increase differently. In comp
arison with the milled steel fiber and waved steel fiber, the addition of bowed steel fiber to HSC improves its fractural properties more. The HSC and steel fiber reinforced HSC are all have notch sensitivity. The addition of steel fiber to the HSC has extensively improved the strain filed ahead of the crack tip.
2. By the wedge-splitting tensile test on the twenty-four specimens of polypropylene fiber reinforced HSC with the size of 200mmx170mmx 100mm, the impacts of polypropylene dosage upon the fracture properties, such as stress intensity factor, fracture energy, as well as critical crack mouth opening displacement of polypropylene reinforced HSC have been investigated, and the strain field ahead of the crack tip of polypropylene fiber reinforced HSC has been researched. The test results indicate that the addition of polypropylene has no impacts upon the KIC, but increases the GF and CMODc. With the increase dosage of polypropylene, GV and the increment ratio of GF increase respectively, but CMODc decreased, and the varying of increment ratio of CMODc has no disciplinarian, and the influence of strain field ahead of crack tip is small. Polypropylene improves the properties of HSC at the post-cracking zone.
3. By the wedge-splitting tensile test on the forty-two specimens of hybrid (steel and polypropylene) fiber reinforced HSC with the size of 200mmx 170mmx 100mm, the fracture properties of hybrid fiber reinforced HSC and the synergy effect on HSC have been investigated.
The test results indicate that the addition of fiber has extensively improved the fracture properties of HSC. A positive synergy effect between steel fiber and polypropylene has been observed at low fiber dosage and the synergy effect disappears with the increase of fiber dosage. Steel fiber plays a key role on the improvement of fracture properties of hybrid fiber reinforced HSC. The improvement effect of polypropylene on the fracture properties of hybrid reinforced HSC is small. Bowed steel fiber is more effective on the improvement of fracture properties of hybrid fiber reinforced HSC than other two types of steel fiber.
引文
[1] 尹双增．断裂判据与在混凝土中的应用[M]．北京：北京科学出版社，1996
[2] 刘佳毅．混凝土双K断裂参数及其尺寸效应[D]．大连：大连理工大学硕士学位，2000
[3] Mel Vin F. Kanninen, Carl H. Popelar. 著，洪其麟，郑光华等译．高等断裂力学[M]．北京：北京航空学院出版社，1987
[4] 杨卫．宏观断裂力学[M]．北京：国防工业出版社，1995
[5] 尹双增．断裂·损伤理论及应用[M]．北京：清华大学出版社，1992
[6] 胡传忻．断裂力学及其工程应用[M]．北京：北京工业大学出版社，1989
[7] 赵志方，徐世烺．混凝土软化本构曲线形状对双K断裂参数的影响[J]．土木工程学报，2001，34(5)：29-34
[8] 易成，谢和平，孙华飞．钢纤维混凝土疲劳断裂性能与工程应用[M]．北京：科学技术出版社．2003：29-32
[9] 郭少华．混凝土破坏理论研究进展[J]．力学进展，1993，23(4)：520-529
[10] 丁遂栋．断裂力学[M]．北京：机械工业出版社，1997
[11] A. Hillerborg. The theoretical basis of a method to determine the fracture energy G_F of concrete[J]. Material and Construction, 2003,18(106): 291-296
[12] 王慧．混凝土及纤维混凝土的断裂分析[J]．合肥工业大学学报(自然科学版)，1996，19(4)：64-68
[13] 钱觉时，王智，罗晖．混凝土应变软化关系及其确定[J]．大连理工大学学报，1997，37(增刊1)：62-67
[14] 徐艳秋，高伟．混凝土软化本构关系研究的发展[J]．石家庄铁道学院学报，2000，13(2)：34-38
[15] 高丹盈，王占桥．钢纤维高强混凝土断裂性能的试验研究[J]．郑州大学学报(工学版)，2004，25(1)：1-5
[16] G. V. Guinea, J. Planas, M. Elices. A general bilinear fit for the softening curve of concrete [J]. Material and Structures, 1994, 27: 99-105
[17] 段树金，李云峰，李彦军，王书报，彭成山，章美文．测定混凝土应变软化曲线的J积分法[J]．工程力学，1998，15(4)：108-114
[18] 王宝庭，徐道远．混凝土拉伸软化曲线折线近似的逆解方法[J]．力学学报，2001，33(4)：535-541
[19] H. Ananthan, B.K. Raghuprasad, K.T. Sundara Rajaiyengar. Influence of softening on the fracture of plain concrete [J]. International Journal of Fracture, 1990 (45): 195-219,
[20] A. Carpinteri, A. R. Ingraffea著，杨煜惠，黄政宇，万良芬等译．混凝土断裂力学—材料
特性与试验[M]．长沙：湖南大学出版社，1988
[21] 王新友．钢纤维混凝土的断裂模型研究[J]．广西水利水电，1992，(3)：2-7
[22] 高丹盈，刘建秀．钢纤维混凝土基本理论[M]．北京：科学技术文献出版社．1994
[23] Norihiko Kurihara, Minoru Kunieda, Toshiro Kamada, Yuichi Uchida, Keitetsu Rokugo. Tension softening diagrams and evaluation of properties of steel fiber reinforced concrete[J]. Engineering Fracture Mechanics , 2000, (65): 235-245
[24] M. Wecharatana, S.P. Shah. A model for predicting fracture resistance of fiber reinforced concrete[J]. Cement and Concrete Research, 1983, (13): 819-829
[25] K. Visalvanich and A. E. Naaman. Fracture model for fiber reinforced concrete[J]. Journal of the American Concrete Institute, 1983,80(2): 128-138
[26] K. Visalvanich and A. E. Naaman. Fracture methods in cement composite[J]. Proceedings. ASCE, 1981,107:1155-1171
[27] A. E. Naaman. A fracture model for fiber reinforced cementitious materials[J]. Cement and Concrete Research. 1973, (3):397-411
[28] A.-B. Eissa, G. Batson. Model for predicting the fracture process zone and R-curve for high strength FRC[J]. Cement and Concrete Research 1996, (18):125-133
[29] M. Wecharatana and S. P. shah. Double tension test for studying slow crack growth of Portland cement mortar[J]. Cement and Concrete Research. 1980,10(5): 832-844
[30] M. Wecharatana and S. P. shah. A model for predicting fracture resistance of fiber reinforced concrete[J]. Cement and concrete research. 1983,13(6):819-829
[31] Sameer A. Hamoush, M. Reza Salami, Elias G Abu-Saba. Fracture model to predict intensity in fiber reinforced concrete[J]. ACI Material Journal, 1991, 88(5):504-507
[32] Parviz Soroushian, Hafez Elyamany, Atef Tlili, Ken Ostowari. Mixef-Mode Fracture Properties of Concrete Reinforcef with Low Volume Fractions of Steel and Polypropylene fibers. Cement and Concrete Composites. 1998, (20):67-78
[33] 胡倍雷，赵国藩，宋玉普．钢纤维混凝土断裂能与断裂韧性试验研究[J]．中南水力发电，1994，3：50-52
[34] 邓宗才，杨秀元．钢纤维高强混凝土试件的断裂韧度[J]．工业建筑，1995，25(10)：36-38
[35] 李方元，赵人达．高强混凝土和钢纤维高强混凝土断裂性能试验研究[J]．混凝土，2002，(8)：29-32
[36] 高丹盈，王占桥，朱海堂．钢纤维高强混凝土断裂性能的试验研究[J]．郑州大学学报(工学版)，2004，25(1)：1-5
[37] 罗章，李夕兵，凌同华．钢纤维混凝土的增强机理与断裂力学模型研究[J]．矿业研究与开发，2003，23(4)：18-22
[38] 姚武，蔡江宁，陈兵，吴科如．混杂纤维增韧高性能混凝土的研究[J]．三峡大学学报(自然科学版)，2002，24(1)：42-44
[39] Guo Hong ding, Qian Chunxiang, Piet Stroeven. Fracture Properties of Cement Composite Reinforced with Steel Polypropylene Hybrid Fibers. Journal of Southeast University (English Edition) Dce. 1999, 15(2):55-62
[40] Chunxiang Qian, Piet Stroeven. Fracture properties of concrete reinforced with steel-polypropylene hybrid fibers[J]. Cement and concrete composites, 2000,(22): 343-351
[41] 李光伟，杨元慧．聚丙烯纤维混凝土性能的试验研究[J]．水利水电科技进展，2001，21(5)：14-17
[42] 王成启，吴科如．不同弹性模量的纤维对高强混凝土力学性能的影响[J]．混凝土与水泥制品，2002，(3)：36-37
[43] 蔡敏，蔡四维．混凝上、纤维混凝上的Ⅰ型断裂[J]．工程力学，1999，16(4)：54-58
[44] 郭晓辉，李珠，孙钰．纤维增强混凝土拉伸软化本构方程的实验确定方法[J]．太原工业大学学报，1995，26(3)：35-38
[2] 刘佳毅．混凝土双K断裂参数及其尺寸效应[D]．大连：大连理工大学硕士学位，2000
[3] Mel Vin F. Kanninen, Carl H. Popelar. 著，洪其麟，郑光华等译．高等断裂力学[M]．北京：北京航空学院出版社，1987
[4] 杨卫．宏观断裂力学[M]．北京：国防工业出版社，1995
[5] 尹双增．断裂·损伤理论及应用[M]．北京：清华大学出版社，1992
[6] 胡传忻．断裂力学及其工程应用[M]．北京：北京工业大学出版社，1989
[7] 赵志方，徐世烺．混凝土软化本构曲线形状对双K断裂参数的影响[J]．土木工程学报，2001，34(5)：29-34
[8] 易成，谢和平，孙华飞．钢纤维混凝土疲劳断裂性能与工程应用[M]．北京：科学技术出版社．2003：29-32
[9] 郭少华．混凝土破坏理论研究进展[J]．力学进展，1993，23(4)：520-529
[10] 丁遂栋．断裂力学[M]．北京：机械工业出版社，1997
[11] A. Hillerborg. The theoretical basis of a method to determine the fracture energy G_F of concrete[J]. Material and Construction, 2003,18(106): 291-296
[12] 王慧．混凝土及纤维混凝土的断裂分析[J]．合肥工业大学学报(自然科学版)，1996，19(4)：64-68
[13] 钱觉时，王智，罗晖．混凝土应变软化关系及其确定[J]．大连理工大学学报，1997，37(增刊1)：62-67
[14] 徐艳秋，高伟．混凝土软化本构关系研究的发展[J]．石家庄铁道学院学报，2000，13(2)：34-38
[15] 高丹盈，王占桥．钢纤维高强混凝土断裂性能的试验研究[J]．郑州大学学报(工学版)，2004，25(1)：1-5
[16] G. V. Guinea, J. Planas, M. Elices. A general bilinear fit for the softening curve of concrete [J]. Material and Structures, 1994, 27: 99-105
[17] 段树金，李云峰，李彦军，王书报，彭成山，章美文．测定混凝土应变软化曲线的J积分法[J]．工程力学，1998，15(4)：108-114
[18] 王宝庭，徐道远．混凝土拉伸软化曲线折线近似的逆解方法[J]．力学学报，2001，33(4)：535-541
[19] H. Ananthan, B.K. Raghuprasad, K.T. Sundara Rajaiyengar. Influence of softening on the fracture of plain concrete [J]. International Journal of Fracture, 1990 (45): 195-219,
[20] A. Carpinteri, A. R. Ingraffea著，杨煜惠，黄政宇，万良芬等译．混凝土断裂力学—材料
特性与试验[M]．长沙：湖南大学出版社，1988
[21] 王新友．钢纤维混凝土的断裂模型研究[J]．广西水利水电，1992，(3)：2-7
[22] 高丹盈，刘建秀．钢纤维混凝土基本理论[M]．北京：科学技术文献出版社．1994
[23] Norihiko Kurihara, Minoru Kunieda, Toshiro Kamada, Yuichi Uchida, Keitetsu Rokugo. Tension softening diagrams and evaluation of properties of steel fiber reinforced concrete[J]. Engineering Fracture Mechanics , 2000, (65): 235-245
[24] M. Wecharatana, S.P. Shah. A model for predicting fracture resistance of fiber reinforced concrete[J]. Cement and Concrete Research, 1983, (13): 819-829
[25] K. Visalvanich and A. E. Naaman. Fracture model for fiber reinforced concrete[J]. Journal of the American Concrete Institute, 1983,80(2): 128-138
[26] K. Visalvanich and A. E. Naaman. Fracture methods in cement composite[J]. Proceedings. ASCE, 1981,107:1155-1171
[27] A. E. Naaman. A fracture model for fiber reinforced cementitious materials[J]. Cement and Concrete Research. 1973, (3):397-411
[28] A.-B. Eissa, G. Batson. Model for predicting the fracture process zone and R-curve for high strength FRC[J]. Cement and Concrete Research 1996, (18):125-133
[29] M. Wecharatana and S. P. shah. Double tension test for studying slow crack growth of Portland cement mortar[J]. Cement and Concrete Research. 1980,10(5): 832-844
[30] M. Wecharatana and S. P. shah. A model for predicting fracture resistance of fiber reinforced concrete[J]. Cement and concrete research. 1983,13(6):819-829
[31] Sameer A. Hamoush, M. Reza Salami, Elias G Abu-Saba. Fracture model to predict intensity in fiber reinforced concrete[J]. ACI Material Journal, 1991, 88(5):504-507
[32] Parviz Soroushian, Hafez Elyamany, Atef Tlili, Ken Ostowari. Mixef-Mode Fracture Properties of Concrete Reinforcef with Low Volume Fractions of Steel and Polypropylene fibers. Cement and Concrete Composites. 1998, (20):67-78
[33] 胡倍雷，赵国藩，宋玉普．钢纤维混凝土断裂能与断裂韧性试验研究[J]．中南水力发电，1994，3：50-52
[34] 邓宗才，杨秀元．钢纤维高强混凝土试件的断裂韧度[J]．工业建筑，1995，25(10)：36-38
[35] 李方元，赵人达．高强混凝土和钢纤维高强混凝土断裂性能试验研究[J]．混凝土，2002，(8)：29-32
[36] 高丹盈，王占桥，朱海堂．钢纤维高强混凝土断裂性能的试验研究[J]．郑州大学学报(工学版)，2004，25(1)：1-5
[37] 罗章，李夕兵，凌同华．钢纤维混凝土的增强机理与断裂力学模型研究[J]．矿业研究与开发，2003，23(4)：18-22
[38] 姚武，蔡江宁，陈兵，吴科如．混杂纤维增韧高性能混凝土的研究[J]．三峡大学学报(自然科学版)，2002，24(1)：42-44
[39] Guo Hong ding, Qian Chunxiang, Piet Stroeven. Fracture Properties of Cement Composite Reinforced with Steel Polypropylene Hybrid Fibers. Journal of Southeast University (English Edition) Dce. 1999, 15(2):55-62
[40] Chunxiang Qian, Piet Stroeven. Fracture properties of concrete reinforced with steel-polypropylene hybrid fibers[J]. Cement and concrete composites, 2000,(22): 343-351
[41] 李光伟，杨元慧．聚丙烯纤维混凝土性能的试验研究[J]．水利水电科技进展，2001，21(5)：14-17
[42] 王成启，吴科如．不同弹性模量的纤维对高强混凝土力学性能的影响[J]．混凝土与水泥制品，2002，(3)：36-37
[43] 蔡敏，蔡四维．混凝上、纤维混凝上的Ⅰ型断裂[J]．工程力学，1999，16(4)：54-58
[44] 郭晓辉，李珠，孙钰．纤维增强混凝土拉伸软化本构方程的实验确定方法[J]．太原工业大学学报，1995，26(3)：35-38