纤维缠绕壳体应力变形及损伤研究
|
摘要
随着复合材料在各个领域的广泛应用，作为××××发动机燃烧室的纤维缠绕复合材料壳体在航天领域中越来越受到人们的重视。本文以某发动机技术研究院的“纤维缠绕××××发动机壳体的应力变形及损伤研究”项目为研究背景。由设计方案A研制的××××发动机壳体称为A壳体。为满足弹头质量增加的需要，在设计方案A的基础上研制了B壳体，但B壳体在试验中发生了低压爆破。针对××××发动机B壳体发生低压爆破的问题，应用复合理论、网格理论和非线性有限元法对B壳体进行了宏观应力应变分析，从而确定了B壳体低压爆破的原因是由于损伤所致。在此基础上，深入地研究了壳体损伤发生概率最大、而危害又相当明显的典型损伤类型——基体开裂和分层损伤，分别采用能量法和剪切滞后方法建立基体开裂和分层损伤的模型，对损伤的机理和损伤对壳体性能的影响进行了深入的研究。
首先，采用网格理论、复合理论和非线性有限元方法对××××发动机壳体的应力和变形情况进行分析与计算。在非线性有限元建模过程中，对壳体缠绕角度和厚度进行了修正，针对××××发动机这样的大型结构，首次采用一种四边形复合材料单元，实现了能够在单元内部沿厚度方向进行离散化，使得在划分单元总数较少的情况下，计算结果比较精确。通过对网格理论、复合理论和非线性有限元方法计算结果与试验值之间的相互比较，可以看出：非线性有限元计算结果介于网格理论和复合理论之间，且有限元计算结果与复合理论结果更加接近，表明在水检压力下壳体筒段确实存在着基体开裂等损伤。在最大压力为水检压力的作用下，应用有限元计算出壳体的整体变形以及不同部位的各种应力(不同应力分量)和位移分量，与试验结果均比较吻合，证明采用大变形方法分析壳体宏观应力和变形是合理的，A壳体与B壳体的应力、变形情况基本相同，B壳体发生低压爆破不是由于结构参数的调整造成，而是由于各种试验导致的累积损伤造成的。
哈尔滨工程大学博士学位论文
其次，采用能量法建立了纤维缠绕壳体筒段同时受到均匀内压和轴向拉
伸载荷作用时的表面分层损伤临界分层屈曲分析模型，探讨了壳体筒段表面
分层损伤屈曲扩展的机理。研究结果表明:壳体筒段受轴向拉伸和内压载荷
作用时，轴向和环向载荷的比率不同，母层和子层可能发生拉伸屈曲，也可
能发生收缩屈曲，或者同时发生拉伸和压缩屈曲;母层与子层各向异性存在
差异，即泊松比与剪切模量不匹配时，将使子层板的边界上承受压缩和剪切
作用，当分层达到临界状态则发生屈曲，当母层与子层的各向异性差异越大，
则发生分层屈曲的可能性越大;分层损伤的屈曲应变值与子层自身的弹性模
量、分层子层的形状、厚度以及圆柱半径等因素有关。
第三，研究了在应力较高时横向开裂裂纹的裂尖引发的分层损伤现象。
建立了包含分层损伤的完全抛物线分析模型，依此模型计算材料的宏观刚度
性能，并与没有考虑分层损伤的不完全抛物线模型和完全抛物线模型进行了
比较。结果表明，在应力较高的情况下，考虑了分层的完全抛物线模型与试
验结果符合程度最好。
The filament-wound case (FWC) plays a more and more important role in the solid rocket motor chamber structure (SRMCS) with composite material widely used in spaceflight fields. The work of this thesis is under the engineering background of project -Study on distortion and damage of filament-wound SRMCS. Case A we called here is a type of SRMCS based on designing method A. Case B was redesigned based on Case A in order to meet the needs of enhancive warhead mass, but it burst under low pressure. In order to find out the reason of bursting under low pressure, macro stress and strain of SRMCS were analyzed by using compound theory, netting theory and nonlinear finite element method (FEM). It was concluded that the damages of the SRMCS led to the bursting of Case B under low pressure. Then it was necessary to study the matrix crack and delamination damages in detail, which occurred with the maximum probability and played the most important role on FWC failure. Two models about damage analysis were established b
y using energy method and shear lag method. The mechanism of damage and the effect to structure performance caused by damage are studied further.
First, three kinds of analytical methods including netting theory, compound theory and nonlinear FEM were performed to obtain the stresses and deformations of SRMCS. Based upon the facts that parameters were unequal in thickness and winding angle along the meridional direction, some fitting formulations were proposed in the FEM model. This FEM model could also represent geometrical nonlinear behavior by considering large displacements. A kind of quadrilateral composite element was firstly used in large structures such as SRMCS, in which at least five layers can be contained in one element along thickness direction, thus
the calculation results will be more precise although divided the structure into less elements. By way of comparing the results obtained from netting theory, compound theory, nonlinear FEM and experimental test, the conclusion could be drawn that matrix crack damage surely existed in the cylinder part of structure. When the structure was subject to internal pressure up to 6.8MPa, which was the maximum loading of hydrostatic test, the deformation of the global structure and stress and strain distributed in any parts of structure were obtained. A fairly good agreement was obtained between the analysis and the test results. And it was proved that it is reasonable to analyze the FWC using nonlinear FEM. The results of case A and case B were about the same, thus it was displayed that modifying structure did not cause the bursting under low pressure but the damages of the structure.
Second, an analytical model was developed to assess the critical buckling problem of near surface interlaminar rectangular defects in the cylindrical part of SRMCS under axis and interior pressure loads. The relationships between critical strain value and the parameters of geometry and radius of cylindrical were discussed. With the different loading ratio of parallel to axis and normal to axis direction, damage defects will occur bulking problem. By varying the degree of material anisotropy relative to the loading axis such as Poisson's ratio and shear modulus, crack growth bulking strain value parallel to or normal to the loading axis is different. The parameters controlling the growth or arrest of the delamination damage are identified as the geometry and the depth of defects and radius of cylindrical etc.
At last, it was investigated that the delamination damage is often induced by the tip of matrix damage under higher stress. A complete parabolic shear-lag analysis containing delamination damage induced by transverse cracks was
proposed and applied to predict the global properties of materials. The predictions from the complete parabolic shear-lag analysis without containing the delamination, incomplete parabolic shear-lag model and the complete parabolic shear-lag analysis proposed in this paper have been compared. The results show the complete parabolic sh
首先，采用网格理论、复合理论和非线性有限元方法对××××发动机壳体的应力和变形情况进行分析与计算。在非线性有限元建模过程中，对壳体缠绕角度和厚度进行了修正，针对××××发动机这样的大型结构，首次采用一种四边形复合材料单元，实现了能够在单元内部沿厚度方向进行离散化，使得在划分单元总数较少的情况下，计算结果比较精确。通过对网格理论、复合理论和非线性有限元方法计算结果与试验值之间的相互比较，可以看出：非线性有限元计算结果介于网格理论和复合理论之间，且有限元计算结果与复合理论结果更加接近，表明在水检压力下壳体筒段确实存在着基体开裂等损伤。在最大压力为水检压力的作用下，应用有限元计算出壳体的整体变形以及不同部位的各种应力(不同应力分量)和位移分量，与试验结果均比较吻合，证明采用大变形方法分析壳体宏观应力和变形是合理的，A壳体与B壳体的应力、变形情况基本相同，B壳体发生低压爆破不是由于结构参数的调整造成，而是由于各种试验导致的累积损伤造成的。
哈尔滨工程大学博士学位论文
其次，采用能量法建立了纤维缠绕壳体筒段同时受到均匀内压和轴向拉
伸载荷作用时的表面分层损伤临界分层屈曲分析模型，探讨了壳体筒段表面
分层损伤屈曲扩展的机理。研究结果表明:壳体筒段受轴向拉伸和内压载荷
作用时，轴向和环向载荷的比率不同，母层和子层可能发生拉伸屈曲，也可
能发生收缩屈曲，或者同时发生拉伸和压缩屈曲;母层与子层各向异性存在
差异，即泊松比与剪切模量不匹配时，将使子层板的边界上承受压缩和剪切
作用，当分层达到临界状态则发生屈曲，当母层与子层的各向异性差异越大，
则发生分层屈曲的可能性越大;分层损伤的屈曲应变值与子层自身的弹性模
量、分层子层的形状、厚度以及圆柱半径等因素有关。
第三，研究了在应力较高时横向开裂裂纹的裂尖引发的分层损伤现象。
建立了包含分层损伤的完全抛物线分析模型，依此模型计算材料的宏观刚度
性能，并与没有考虑分层损伤的不完全抛物线模型和完全抛物线模型进行了
比较。结果表明，在应力较高的情况下，考虑了分层的完全抛物线模型与试
验结果符合程度最好。
The filament-wound case (FWC) plays a more and more important role in the solid rocket motor chamber structure (SRMCS) with composite material widely used in spaceflight fields. The work of this thesis is under the engineering background of project -Study on distortion and damage of filament-wound SRMCS. Case A we called here is a type of SRMCS based on designing method A. Case B was redesigned based on Case A in order to meet the needs of enhancive warhead mass, but it burst under low pressure. In order to find out the reason of bursting under low pressure, macro stress and strain of SRMCS were analyzed by using compound theory, netting theory and nonlinear finite element method (FEM). It was concluded that the damages of the SRMCS led to the bursting of Case B under low pressure. Then it was necessary to study the matrix crack and delamination damages in detail, which occurred with the maximum probability and played the most important role on FWC failure. Two models about damage analysis were established b
y using energy method and shear lag method. The mechanism of damage and the effect to structure performance caused by damage are studied further.
First, three kinds of analytical methods including netting theory, compound theory and nonlinear FEM were performed to obtain the stresses and deformations of SRMCS. Based upon the facts that parameters were unequal in thickness and winding angle along the meridional direction, some fitting formulations were proposed in the FEM model. This FEM model could also represent geometrical nonlinear behavior by considering large displacements. A kind of quadrilateral composite element was firstly used in large structures such as SRMCS, in which at least five layers can be contained in one element along thickness direction, thus
the calculation results will be more precise although divided the structure into less elements. By way of comparing the results obtained from netting theory, compound theory, nonlinear FEM and experimental test, the conclusion could be drawn that matrix crack damage surely existed in the cylinder part of structure. When the structure was subject to internal pressure up to 6.8MPa, which was the maximum loading of hydrostatic test, the deformation of the global structure and stress and strain distributed in any parts of structure were obtained. A fairly good agreement was obtained between the analysis and the test results. And it was proved that it is reasonable to analyze the FWC using nonlinear FEM. The results of case A and case B were about the same, thus it was displayed that modifying structure did not cause the bursting under low pressure but the damages of the structure.
Second, an analytical model was developed to assess the critical buckling problem of near surface interlaminar rectangular defects in the cylindrical part of SRMCS under axis and interior pressure loads. The relationships between critical strain value and the parameters of geometry and radius of cylindrical were discussed. With the different loading ratio of parallel to axis and normal to axis direction, damage defects will occur bulking problem. By varying the degree of material anisotropy relative to the loading axis such as Poisson's ratio and shear modulus, crack growth bulking strain value parallel to or normal to the loading axis is different. The parameters controlling the growth or arrest of the delamination damage are identified as the geometry and the depth of defects and radius of cylindrical etc.
At last, it was investigated that the delamination damage is often induced by the tip of matrix damage under higher stress. A complete parabolic shear-lag analysis containing delamination damage induced by transverse cracks was
proposed and applied to predict the global properties of materials. The predictions from the complete parabolic shear-lag analysis without containing the delamination, incomplete parabolic shear-lag model and the complete parabolic shear-lag analysis proposed in this paper have been compared. The results show the complete parabolic sh
引文
[1] 沈观林．复合材料力学．清华大学出版社．1996：40-78页，184-199页
[2] 蒋咏秋，陆逢升，顾志建．复合材料力学．西安交通大学出版社．1990，14-43页，58-87页
[3] 郭艳阳．复合材料细观损伤实验研究及剩余强度预报．哈工大博士论文．1997
[4] 孙雪坤，郭艳阳等．纤维缠绕固体火箭发动机壳体的应力及强度分析．复合材料学报．1997，14(1)：97-102P
[5] 潘燕环，陈汝训．层合复合材料的损伤刚度分析．宇航学报，2000，21(3)：88-93P
[6] 钱林方，袁人枢等．火箭发动机复合材料壳体爆破压力的计算．兵工学报．1997，18(4)：316-320P
[7] 杜善义，王彪．复合材料细观力学．科学出版社．1998，184P
[8] 王铮，胡永强．《固体火箭发动机》，宇航出版社，1993，165-229页
[9] 稽醒．玻璃纤维缠绕火箭发动机壳体的基体选择准则的研究．固体力学及其工程应用．：403-409页
[10] 卢天健．树脂基体对纤维缠绕固体火箭发动机壳体强度影响机理的力学分析和试验研究．西安交通大学硕士论文．1987
[11] S. Adali, et al. Optimisation of laminated cylindrical pressure vessels under strength criterion, Composite Structures. 1993,25:305-312P.
[12] J. Mistry, et al. Failure of composite cylinders under combined external pressure and axial loading. Composite Structures. 1992,22:193-200P.
[13] 徐芝纶，《弹性力学》．高等教育出版社，1984年．
[14] Mindlin, R. D., Influence of rotary inertia and shear deformation
on flexural motions of isotropic elastic plates. J. Appl. Mech. 1951, 18: 31—38P.
[15] K. H. Lo, et al., A high order theory of plate deformation.. Part2:Laminated plates. J. Appl. Mech. 1977,44:669-675P.
[16] 王震鸣编著．复合材料力学和复合材料结构力学．机械工业出版社．1990，305页
[17] 杨光松编著．损伤力学及复合材料损伤．国防工业出版社．1995：247页
[18] Singh G and Rao S. Large deflection behavior of thick composite plates. Comp. Struct. 1987,8: 13-29P
[19] Idelsohn S, ed. Pre-and post-degradation analysis of composite materials with different moduli in tension and compression. Comp. Meth. Appl. Mech. Eng. 1982,30: 133-149P
[20] 贺鹏飞．纤维缠绕固体火箭发动机壳体强度的细观力学研究，西安交通大学博士论文，1992
[21] 段登平等．纤维缠绕壳体材料非线线性及大变形分析计算．复合材料学报．1999，16(1)：142-148P
[22] 稽醒，刘西瑞．固体火箭发动机壳体及裙部的应力分析．第四届全国复合材料学术会议文集．1986：813-817页
[23] Doh Y D and Hong C S. Progressive failure analysis for filament wound pressure vessel. Journal of reinforced plastics and composites. 1995,14(December): 1278-1306P
[24] Garret K W and Bailey J E. Multiple transverse fractrure in 90° cross-ply laminates of a glass fibre-reinforced polyester. J. Mater. Sci. 1977(12):157-161P
[25] Parvizi A, Garret K W and Bailey J E. Constrained cracking in glass fiber-reinforced epoxy cross-ply laminates. J. Mater. Sci. 1978(13): 201-211P
[26] 华玉，王兴国，郦正能．一般各向异性复合材料层板基体开裂损伤性能
衰减研究(I)一分解刚度法建立(θM／90N)s开裂层板本构关系．应用 数学和力学．1998，19(3) ：257-264P
[27] Lim S G & Hong C S. Prediction of transverse cracking and stiffness reduction in cross-ply laminated composites. J. Comp. Mater. 1989(23) : 695-731P
[28] Han Y M, ed. Ply cracking and property degradations of symmetric balanced laminates under general in-plane loading. Comp. Sci. Tech. 1989(35) : 377-97P
[29] Lee J W & Daniel I M. Progressive transverse cracking of cross-ply composite laminates. J. Comp. Mater. 1990(24) :1225-1243P
[30] Zhang J F and Soutis C. Analysis of Multiple Matrix Cracking in [θm/90n]s Composite laminates. Part: In-Plane Stiffness Properties. Composites. 1992, 23(5) : 291-298P
[31] Tay T E & Lim E H. Analysis of stresses loss in cross-ply composite laminates containing distributed transverse cracks. Finite Elements in Analysis and Design. 1994(18) :301-308P
[32] Highsimth A L and Reifnsider K L. Stiffness reduction mechanisms in composite laminates. In 'Damage in Composite Materials' . ASTM STP 775． American Society for Testing and Materials,. Philadelphia. PA. 1982: 103-117P
[33] Hashin Z. Analysis of stiffness reduction of cracked cross-ply laminates. Eng. Fract. Mech. 1986(25) :771-778P
[34] Aboudi J. Stiffness reduction of cracked solids. Eng. Fract. Mech. 1987(26) :637-650P
[35] Nuismer R J and Tan S C. Constitutive relations of a cracked composite lamina. J. Comp. Mater. 1988, 22(4) :306-321P
[36] Lee J H & Hong C S. Refined two-dimensional analysis of cross-ply
laminates with transverse cracks based on the assumed crack opening deformation. Composites Science and Technology 1993, (46) :157-166P
[37] Talreja R. Transverse cracking and stiffness reduction in composite laminates. J. Comp. Mater. 1985(19) :355-375P
[38] Allen D H and Harris C E. A thermo mechanical constitutive theory for elastic composites with distributed damage Ⅱ. application to matrix cracking in laminated composites. Int. J. Solids Structures. 1987, 23 (9) :1319-1338P
[39] Kwon Y W. Calculation of effective modulli of fibrous composites with or without micro-mechanical damages. Composite laminates. 1993(25) : 187-192P
[40] Kwon Y W, Berner J M. Matrix damage of fibrous composites: effects of thermal residual stresses and layer sequences. Computers & Structures. 1997, 64(1-4) :375-382P
[41] Tay T E & Lim E H. Analysis of stiffness loss in cross-ply composite laminates. Comp. Struct. 1993(25) :419-425P
[42] Tay T E, Lim E H. Analysis of composite laminates with transverse cracks. Com. Stru. 1996(34) :419-426P
[43] Tay T E, Lam K Y and Cen Z. Analysis of composite structures with distributed and localized damage by the finite-element method. Comp. Struct. 1997,37:135-143
[44] 邓梁波等．复合材料叠层板横向开裂的研究．复合材料学 报．1997，14(1) ：127-134页
[45] Rebiere J L, ed. Initiation and growth of transverse and longitudinal cracks in composite cross-ply laminates. Cmoposite structures. 2001, 53:173-187
[46] J. varna, R. Joffe, N. V. Akshantala, R. Talreja, Damage in
composite laminates with off-axis plies. Composites science and Technology. 1999,59:2139-2147
[47] Tong J, Ogin F J and Smith P A. On matrix crack growth in quasi-isotropic laminates-experimental investigation. Comop. Sci. and Tech. 1997,57:1527-1535P.
[48] Tong J, Ogin F J and Smith P A. On matrix crack growth in quasi-isotropic laminates-finite element analysis. Comop. Sci. and Tech. 1997,57:1537-1545P
[49] Spoofing Hu, ed. On the phenomenon of curved microcracks in [(S)/90_n]_s laminates: their shapes, initiation angles and locations. Composites Science and Technology. 1993,47:321-329P
[50] Herakovich G J and Hyer M W. Damage-induced property changes in composites subjected to cyclic thermal loading, Engineering Fracture Mechanics. 1986,25(5/6):779-791P
[51] 孙先念．含层间分层损伤复合材料层合板压缩破坏行为的研究．大连理工大学博士论文．1998
[52] 宋云莲．纤维增强复合材料层合板壳结构的可靠性研究．哈尔滨工程大学博士论文．2000
[53] 华玉，复合材料层板，北京航空航天大学博士论文．1998
[54] 傅志平，曹志远．复合材料构件性能的细观元分析．复合材料学报．1998，15(1)：108-111页
[55] Wang S S. Fracture Mechanics for Delamination Problems. J. Composite Materials. 1983,17(3):210-22P
[56] Wang J and Karihaloo B L. Matrix crack-induced delamination in comosite laminates under transverse loading. Composite Structures. 1997,38(1-4):661-666P
[57] Debabrata chakraborty and Pradhan B. Effect of ply thickness and fibre orientation on delamination initiation in broken ply
comosite laminates. J. of Reinforced Plastics and composites. 1999,18(8) :735-758P
[58] Pagano NJ and Pipes R B. The influence of sequence on laminate strenngth, J. comp. Mat. 1971, 5:50P
[59] Jen K C and Sun C T. Matrix Cracking and delamination prediction in graphite / epoxy laminates. Technique Publishing Co., Inc. 1992(10) : 1163-1113P
[60] Lesser A J, Filippov A G. Mechanism governing the damage resistance of laminated composites subjected to low velocity impacts. International Journal of damage mechanics. 1994, 3(4) : 408?32P
[61] Choi H Y, Chang F K. A model for predicting damage In graphite epoxy laminated composites resulting from low velocity point impact. J. Comp. Mat. 1992, 26(14) :2134-2167P.
[62] 唐啸东，沈真，陈普会等．带损伤复合材料层压板剩余强度估算方法研 究．航空学报．1997，18(2) ：146～152页
[63] Ozdil F and Carlsson L A. Characterization of mixed mode delamination growth in glass/epoxy composite cylinders. J. of Composite Materials. 2000, Vol. 34(5) :420-441
[64] Sjoblom P 0 and Hartness J T. On low-velocity impact testing of composite materials. J. Com. Mat. 1988,22:30-52
[65] Lee S M and P Zahuta. Instrumented impact and static indentation of composites. J. Com. Mat. 1991, 25:204-222．
[66] Ozdil F and Carlsson L A. Characterization of mode Ⅰ delamination growth in glass/epoxy composite cylinders. J. of Composite Materials. 2000,34(5) :398-419P
[67] Ozdil F and Carlsson LA and Li X. Characterization of mode Ⅱ delamination growth in glass/epoxy composite cylinders. J. of
Composite Materials. 2000,34(4) :274-298P
[68] Hong S and liu L. On the relationship between impact energy and delamination area. Experimental Mechanics. 1989, 13:115-120
[69] Wu H T and Springer G S. Impact induced stresses, strains, and delaminations in composite plates. J. Com. Mat. 1988,22:533-560
[70] Choi H Y, Wu H T and Chang F. A new approach toward understanding damage mechanisms and mechanics of laminated composites due to low-velocity impact: parti-experiments. J. Com. Mat. 1991,25:992-1011
[71] Choi H Y, Wu H T and Chang F. Effect of laminate configuration and impactor's mass on the initial impact damage of graphite/epoxy composite plates due to line-loading impact. J.Com. Mat. 1992,26:804-827
[72] Kamiya S and H Sekine. Prediction of the fracture strength of notched continuous fiber-reinforced laminates by interlaminar crack extension analysis. Comp. Sci. and Tech., 1996,56:11-21
[73] Shoji kamiya , hideki seking and yoshimasa yagishita. Computational simulation of interlaminar crack extension in angle-ply laminates due to transverse loading, J. Com. Mat. 1998,32(8) :745-765P
[74] Ekaterina demianouchko and Jinbo Bai, Stress state analyses of a ±55° filament-wound composite tube with damage effect. Comp. Structures. 1997,37:233-239P
[75] Jinbo Bai, Philippe Seeleuthner and Philippe Bompard. Mechanical behaviour of ±55° filament-wound glass-fiber/epoxy-resin tubes: I microstructural analyses, mechanical behaviour and damage mechanisms of composite tubes under pure tensile loading, pure internal pressure and combined loading. Composites Science and
Technology. 1997,57:141-153P
[76] Jinbo Bai, Gengkai Hu and Philippe Bompard, Mechanical behaviour of ±55° filament-wound glass-fiber/epoxy-resin tubes: Ⅱ.microstructural model of damage initiation and the competition between different mechanisms. Composites Science and Technology. 1997,57:141-153P
[77] SH Q Bai, Murakami S and Kanagawa U. A lamination theory incorporating the effect of interlaminar deformation. J. of Composite Materials. 1997,31(20):2052-2073P
[78] Reifsnider K L and Talug A. Analysis of stress fields in composite laminates with interior cracks Int. J. of Fatigue. 1980,3(1): 3—11P
[79] Daudeville L and Ladeveze P. A damage mechanics tool foe laminate delamination, composite structures. 1993,25:547-555P
[80] Lin Ye. Characterization of delamination resistance in composite laminates, Composites. 1989,20(3):275-281P.
[81] 张铱，温玄玲，陈浩然．含分层复合材料层合板的高阶有限元分析方法．太原工业大学学报．2000，28(1)：23-28P
[82] 陈浩然，温玄玲，左庄太．含分层损伤轴对称复合材料层合壳的高阶理论及有限元分析．大连理工大学学报．1999，39(5)，205-210页
[83] 郭兆璞，陈浩然．含分层损伤复合材料层合板的屈曲特性研究．玻璃钢/复合材料．1999(2)，23-35页
[84] 赵美英，万小朋，张延辉．复合材料含损伤结构剩余强度分析．机械强度2001，23(2)：129～130页
[85] Jianxin Tao and Sun C T. Influence of ply orientation on delamination in composite laminates. J. Comp. Mat. 1998, 32(2): 1933-1947P
[86] Banbury A, Kelly D W and Jain L K. A study of fastener pull-through
failure of composite laminates. Part 2:Failure prediction. Composite Structure. 1999,45:255-270P
[87] Shinji Ogihara & Nobuo Takeda. Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates. Composites Science and Technology. 1995(54): 395-404P
[88] Reifsnider K L and Highsmith A L. Characteristic damage states: a new approach to representing fatigue damage in composite laminates materials: experimentation and design in fatigue. 1981, 246-260P
[89] 贺鹏飞，嵇醒．复合材料由于基体损伤而引起的刚度下降．第六届全国复合材料会议论文集．北京，1990，189-191页
[90] 贺鹏飞，嵇醒．等效夹杂法在纤维增强复合材料细观力学研究中的应用．同济大学学报．1992，12：15—21页
[91] O' Brien T K. Analysis of local delamiantions and influence on composite laminate behavior. Delamination and debonding of materials, ASTM STP 876, Johnson. American Society for Testing and Material Philadelphia, PA, 1985:282-297P
[92] Wang A S D, Kishore N N and Li C A. Crack development in graphite-epoxy cross-ply laminates under uniaxial tension. Comp. Sci. rechnol. 1985(24): 1-31P
[93] Nairn, J.A. and Hu, S., The initiation and growth delaminations induced by matrix microcrack laminated composites. Int. J. Fract., 1992(57): 1-24P
[94] Dharani L R and Tang H. Micromechanics characterization of sublaminate damage. Int. J. Fract 1009: 123-140P
[95] Nobuo Takeda and Shinji Ogihara. Initiation and growth of delamination from the tips of transverse cracks in CFRP cross-ply
laminates. Compos. Sci. And Tech. 1994(52): 309-318P
[96] Steif, P.S. Parabolic shear lag analysis of a [0/90]_s laminate.In 'Transverse ply crack growth and associated stiffness reduction during the fatigue of a simple cross-ply laminate' (Eds S. L. Ogin, P. A. Smith and P.W. R. Beaumont),Report CUED/C/MATS/TR 105. Cambridge University, 1984
[97] Lee J W & Daniel I M. Progressive transverse cracking of cross-ply composite laminates. J. Comp. Mater. 1990(24): 1225-1243P
[98] Berthelot J M, Leblond P, ed. Transverse cracking of cross-ply laminates. Part 1. Analysis. Composites Part A. 1996(9): 989-1001P
[99] 伍天健等．某壳体爆破试验压强偏小的原因调研与分析报告．2000．8(内部资料)
[100] 《纤维缠绕内压容器的力学分析》(内部资料)，1983
[101] 王勖成，邵敏编著．有限元法基本原理与数值方法．北京：清华大学出版社，1988．
[102] 非线性，《纤维增强塑料(玻璃钢)汇编标准》。中国标准出版社，1988年。
[103] 黄启珍等编，《导弹结构，材料，强度》，宇航出版社，1996，第1版．237页
[104] Arruda, E. M. and Boyce, M. C. "A three-dimensional constitutive model or the large stretch behaviour of rubber elastic materials", J. Mech. Phys. Solids, Vol. 41, No. 2, 1993.
[105] Mooney, M. J. Appl Phys., Vol. Ⅱ, p. 582, 1940.
[106] Gent, A. N. "A new constitutive relation for rubber", Rubber Chem. Tech., 69, 1996.
[107] Chai H et al. One dimensional modeling of failure in laminated plates by delammination buckling. J. Solids Structures, 1981,
17(11): 1069
[108]Chai H, Babcock C D. Two-dimensional Modelling of compressive failure in delaminated laminates. J. of Composite Materials.1985,19(1): 67
[109]Yin W L. Axisymmetric buckling and growth of a circular delamination in a compressed laminate. J. Solids structures.1985, 25: 503
[110]陈思秋．复合材料层合板分层屈曲研究。硕士学位论文，上海交通大学，1989
[111]陈思秋，李思简．对称层板二维的分层屈曲研究．上海交通大学学报．1989，23(6)：30-39页
[112]Yeh M K, Tan C M. Buckling of elliptically delaminated composite plate. Composite Structure. 1994, 28(1): 36P
[113]呼延晓智，刘方龙．准各向同性基层上椭圆形子层的屈曲．宇航学报．1990，10页
[114]李思简，万晖．层合圆柱壳体表层矩形分层屈曲分析．上海交通大学学报，1990，24(6)：164-172页
[115]肖道国，王熙，苏丹．层合圆柱壳体表层局部分层屈曲研究．复合材料的现状与发展．第十一届全国复合材料学术会议论文集．中国合肥，2000，10
[116]Shivakumar K N and Whitcomb J D. Buckling of a sublaminate in a quasi-isotropic composite laminate. Journal of composite materials. 1985, 19(1): 2-18 P
[117]李顺林主编．复合材料工作手册．北京：航空工业出版社，1988．
[118]Cox H L. The elasticity and strength of paper and other fibrous materials. Br. J. App. Phys, 1952, (22): 72-79P
[119]Fukunaga. H, Chou T W, Peters P M and Schulte K. Probabilistic failure strength analysis of graphite/epoxy cross-plylaminates.
J. Comp. Mater. 1984, (18) : 339-356P
[120] Ogin. S., Smith. P. A. and Beaumont. P. W. R. Matrix cracking and stiffness reduction during the fatigure of a (0/90) GFRPlaminate. Compos. Sci. Technol. 1985(22) : 23-31P
[121] Berthelot J M. Analysis of the Transverse Cracking of Cross-Ply Laminates: a Generalized Approach. J. Compos. Mater. 1997, 31(18) : 1780-1805P
[2] 蒋咏秋，陆逢升，顾志建．复合材料力学．西安交通大学出版社．1990，14-43页，58-87页
[3] 郭艳阳．复合材料细观损伤实验研究及剩余强度预报．哈工大博士论文．1997
[4] 孙雪坤，郭艳阳等．纤维缠绕固体火箭发动机壳体的应力及强度分析．复合材料学报．1997，14(1)：97-102P
[5] 潘燕环，陈汝训．层合复合材料的损伤刚度分析．宇航学报，2000，21(3)：88-93P
[6] 钱林方，袁人枢等．火箭发动机复合材料壳体爆破压力的计算．兵工学报．1997，18(4)：316-320P
[7] 杜善义，王彪．复合材料细观力学．科学出版社．1998，184P
[8] 王铮，胡永强．《固体火箭发动机》，宇航出版社，1993，165-229页
[9] 稽醒．玻璃纤维缠绕火箭发动机壳体的基体选择准则的研究．固体力学及其工程应用．：403-409页
[10] 卢天健．树脂基体对纤维缠绕固体火箭发动机壳体强度影响机理的力学分析和试验研究．西安交通大学硕士论文．1987
[11] S. Adali, et al. Optimisation of laminated cylindrical pressure vessels under strength criterion, Composite Structures. 1993,25:305-312P.
[12] J. Mistry, et al. Failure of composite cylinders under combined external pressure and axial loading. Composite Structures. 1992,22:193-200P.
[13] 徐芝纶，《弹性力学》．高等教育出版社，1984年．
[14] Mindlin, R. D., Influence of rotary inertia and shear deformation
on flexural motions of isotropic elastic plates. J. Appl. Mech. 1951, 18: 31—38P.
[15] K. H. Lo, et al., A high order theory of plate deformation.. Part2:Laminated plates. J. Appl. Mech. 1977,44:669-675P.
[16] 王震鸣编著．复合材料力学和复合材料结构力学．机械工业出版社．1990，305页
[17] 杨光松编著．损伤力学及复合材料损伤．国防工业出版社．1995：247页
[18] Singh G and Rao S. Large deflection behavior of thick composite plates. Comp. Struct. 1987,8: 13-29P
[19] Idelsohn S, ed. Pre-and post-degradation analysis of composite materials with different moduli in tension and compression. Comp. Meth. Appl. Mech. Eng. 1982,30: 133-149P
[20] 贺鹏飞．纤维缠绕固体火箭发动机壳体强度的细观力学研究，西安交通大学博士论文，1992
[21] 段登平等．纤维缠绕壳体材料非线线性及大变形分析计算．复合材料学报．1999，16(1)：142-148P
[22] 稽醒，刘西瑞．固体火箭发动机壳体及裙部的应力分析．第四届全国复合材料学术会议文集．1986：813-817页
[23] Doh Y D and Hong C S. Progressive failure analysis for filament wound pressure vessel. Journal of reinforced plastics and composites. 1995,14(December): 1278-1306P
[24] Garret K W and Bailey J E. Multiple transverse fractrure in 90° cross-ply laminates of a glass fibre-reinforced polyester. J. Mater. Sci. 1977(12):157-161P
[25] Parvizi A, Garret K W and Bailey J E. Constrained cracking in glass fiber-reinforced epoxy cross-ply laminates. J. Mater. Sci. 1978(13): 201-211P
[26] 华玉，王兴国，郦正能．一般各向异性复合材料层板基体开裂损伤性能
衰减研究(I)一分解刚度法建立(θM／90N)s开裂层板本构关系．应用 数学和力学．1998，19(3) ：257-264P
[27] Lim S G & Hong C S. Prediction of transverse cracking and stiffness reduction in cross-ply laminated composites. J. Comp. Mater. 1989(23) : 695-731P
[28] Han Y M, ed. Ply cracking and property degradations of symmetric balanced laminates under general in-plane loading. Comp. Sci. Tech. 1989(35) : 377-97P
[29] Lee J W & Daniel I M. Progressive transverse cracking of cross-ply composite laminates. J. Comp. Mater. 1990(24) :1225-1243P
[30] Zhang J F and Soutis C. Analysis of Multiple Matrix Cracking in [θm/90n]s Composite laminates. Part: In-Plane Stiffness Properties. Composites. 1992, 23(5) : 291-298P
[31] Tay T E & Lim E H. Analysis of stresses loss in cross-ply composite laminates containing distributed transverse cracks. Finite Elements in Analysis and Design. 1994(18) :301-308P
[32] Highsimth A L and Reifnsider K L. Stiffness reduction mechanisms in composite laminates. In 'Damage in Composite Materials' . ASTM STP 775． American Society for Testing and Materials,. Philadelphia. PA. 1982: 103-117P
[33] Hashin Z. Analysis of stiffness reduction of cracked cross-ply laminates. Eng. Fract. Mech. 1986(25) :771-778P
[34] Aboudi J. Stiffness reduction of cracked solids. Eng. Fract. Mech. 1987(26) :637-650P
[35] Nuismer R J and Tan S C. Constitutive relations of a cracked composite lamina. J. Comp. Mater. 1988, 22(4) :306-321P
[36] Lee J H & Hong C S. Refined two-dimensional analysis of cross-ply
laminates with transverse cracks based on the assumed crack opening deformation. Composites Science and Technology 1993, (46) :157-166P
[37] Talreja R. Transverse cracking and stiffness reduction in composite laminates. J. Comp. Mater. 1985(19) :355-375P
[38] Allen D H and Harris C E. A thermo mechanical constitutive theory for elastic composites with distributed damage Ⅱ. application to matrix cracking in laminated composites. Int. J. Solids Structures. 1987, 23 (9) :1319-1338P
[39] Kwon Y W. Calculation of effective modulli of fibrous composites with or without micro-mechanical damages. Composite laminates. 1993(25) : 187-192P
[40] Kwon Y W, Berner J M. Matrix damage of fibrous composites: effects of thermal residual stresses and layer sequences. Computers & Structures. 1997, 64(1-4) :375-382P
[41] Tay T E & Lim E H. Analysis of stiffness loss in cross-ply composite laminates. Comp. Struct. 1993(25) :419-425P
[42] Tay T E, Lim E H. Analysis of composite laminates with transverse cracks. Com. Stru. 1996(34) :419-426P
[43] Tay T E, Lam K Y and Cen Z. Analysis of composite structures with distributed and localized damage by the finite-element method. Comp. Struct. 1997,37:135-143
[44] 邓梁波等．复合材料叠层板横向开裂的研究．复合材料学 报．1997，14(1) ：127-134页
[45] Rebiere J L, ed. Initiation and growth of transverse and longitudinal cracks in composite cross-ply laminates. Cmoposite structures. 2001, 53:173-187
[46] J. varna, R. Joffe, N. V. Akshantala, R. Talreja, Damage in
composite laminates with off-axis plies. Composites science and Technology. 1999,59:2139-2147
[47] Tong J, Ogin F J and Smith P A. On matrix crack growth in quasi-isotropic laminates-experimental investigation. Comop. Sci. and Tech. 1997,57:1527-1535P.
[48] Tong J, Ogin F J and Smith P A. On matrix crack growth in quasi-isotropic laminates-finite element analysis. Comop. Sci. and Tech. 1997,57:1537-1545P
[49] Spoofing Hu, ed. On the phenomenon of curved microcracks in [(S)/90_n]_s laminates: their shapes, initiation angles and locations. Composites Science and Technology. 1993,47:321-329P
[50] Herakovich G J and Hyer M W. Damage-induced property changes in composites subjected to cyclic thermal loading, Engineering Fracture Mechanics. 1986,25(5/6):779-791P
[51] 孙先念．含层间分层损伤复合材料层合板压缩破坏行为的研究．大连理工大学博士论文．1998
[52] 宋云莲．纤维增强复合材料层合板壳结构的可靠性研究．哈尔滨工程大学博士论文．2000
[53] 华玉，复合材料层板，北京航空航天大学博士论文．1998
[54] 傅志平，曹志远．复合材料构件性能的细观元分析．复合材料学报．1998，15(1)：108-111页
[55] Wang S S. Fracture Mechanics for Delamination Problems. J. Composite Materials. 1983,17(3):210-22P
[56] Wang J and Karihaloo B L. Matrix crack-induced delamination in comosite laminates under transverse loading. Composite Structures. 1997,38(1-4):661-666P
[57] Debabrata chakraborty and Pradhan B. Effect of ply thickness and fibre orientation on delamination initiation in broken ply
comosite laminates. J. of Reinforced Plastics and composites. 1999,18(8) :735-758P
[58] Pagano NJ and Pipes R B. The influence of sequence on laminate strenngth, J. comp. Mat. 1971, 5:50P
[59] Jen K C and Sun C T. Matrix Cracking and delamination prediction in graphite / epoxy laminates. Technique Publishing Co., Inc. 1992(10) : 1163-1113P
[60] Lesser A J, Filippov A G. Mechanism governing the damage resistance of laminated composites subjected to low velocity impacts. International Journal of damage mechanics. 1994, 3(4) : 408?32P
[61] Choi H Y, Chang F K. A model for predicting damage In graphite epoxy laminated composites resulting from low velocity point impact. J. Comp. Mat. 1992, 26(14) :2134-2167P.
[62] 唐啸东，沈真，陈普会等．带损伤复合材料层压板剩余强度估算方法研 究．航空学报．1997，18(2) ：146～152页
[63] Ozdil F and Carlsson L A. Characterization of mixed mode delamination growth in glass/epoxy composite cylinders. J. of Composite Materials. 2000, Vol. 34(5) :420-441
[64] Sjoblom P 0 and Hartness J T. On low-velocity impact testing of composite materials. J. Com. Mat. 1988,22:30-52
[65] Lee S M and P Zahuta. Instrumented impact and static indentation of composites. J. Com. Mat. 1991, 25:204-222．
[66] Ozdil F and Carlsson L A. Characterization of mode Ⅰ delamination growth in glass/epoxy composite cylinders. J. of Composite Materials. 2000,34(5) :398-419P
[67] Ozdil F and Carlsson LA and Li X. Characterization of mode Ⅱ delamination growth in glass/epoxy composite cylinders. J. of
Composite Materials. 2000,34(4) :274-298P
[68] Hong S and liu L. On the relationship between impact energy and delamination area. Experimental Mechanics. 1989, 13:115-120
[69] Wu H T and Springer G S. Impact induced stresses, strains, and delaminations in composite plates. J. Com. Mat. 1988,22:533-560
[70] Choi H Y, Wu H T and Chang F. A new approach toward understanding damage mechanisms and mechanics of laminated composites due to low-velocity impact: parti-experiments. J. Com. Mat. 1991,25:992-1011
[71] Choi H Y, Wu H T and Chang F. Effect of laminate configuration and impactor's mass on the initial impact damage of graphite/epoxy composite plates due to line-loading impact. J.Com. Mat. 1992,26:804-827
[72] Kamiya S and H Sekine. Prediction of the fracture strength of notched continuous fiber-reinforced laminates by interlaminar crack extension analysis. Comp. Sci. and Tech., 1996,56:11-21
[73] Shoji kamiya , hideki seking and yoshimasa yagishita. Computational simulation of interlaminar crack extension in angle-ply laminates due to transverse loading, J. Com. Mat. 1998,32(8) :745-765P
[74] Ekaterina demianouchko and Jinbo Bai, Stress state analyses of a ±55° filament-wound composite tube with damage effect. Comp. Structures. 1997,37:233-239P
[75] Jinbo Bai, Philippe Seeleuthner and Philippe Bompard. Mechanical behaviour of ±55° filament-wound glass-fiber/epoxy-resin tubes: I microstructural analyses, mechanical behaviour and damage mechanisms of composite tubes under pure tensile loading, pure internal pressure and combined loading. Composites Science and
Technology. 1997,57:141-153P
[76] Jinbo Bai, Gengkai Hu and Philippe Bompard, Mechanical behaviour of ±55° filament-wound glass-fiber/epoxy-resin tubes: Ⅱ.microstructural model of damage initiation and the competition between different mechanisms. Composites Science and Technology. 1997,57:141-153P
[77] SH Q Bai, Murakami S and Kanagawa U. A lamination theory incorporating the effect of interlaminar deformation. J. of Composite Materials. 1997,31(20):2052-2073P
[78] Reifsnider K L and Talug A. Analysis of stress fields in composite laminates with interior cracks Int. J. of Fatigue. 1980,3(1): 3—11P
[79] Daudeville L and Ladeveze P. A damage mechanics tool foe laminate delamination, composite structures. 1993,25:547-555P
[80] Lin Ye. Characterization of delamination resistance in composite laminates, Composites. 1989,20(3):275-281P.
[81] 张铱，温玄玲，陈浩然．含分层复合材料层合板的高阶有限元分析方法．太原工业大学学报．2000，28(1)：23-28P
[82] 陈浩然，温玄玲，左庄太．含分层损伤轴对称复合材料层合壳的高阶理论及有限元分析．大连理工大学学报．1999，39(5)，205-210页
[83] 郭兆璞，陈浩然．含分层损伤复合材料层合板的屈曲特性研究．玻璃钢/复合材料．1999(2)，23-35页
[84] 赵美英，万小朋，张延辉．复合材料含损伤结构剩余强度分析．机械强度2001，23(2)：129～130页
[85] Jianxin Tao and Sun C T. Influence of ply orientation on delamination in composite laminates. J. Comp. Mat. 1998, 32(2): 1933-1947P
[86] Banbury A, Kelly D W and Jain L K. A study of fastener pull-through
failure of composite laminates. Part 2:Failure prediction. Composite Structure. 1999,45:255-270P
[87] Shinji Ogihara & Nobuo Takeda. Interaction between transverse cracks and delamination during damage progress in CFRP cross-ply laminates. Composites Science and Technology. 1995(54): 395-404P
[88] Reifsnider K L and Highsmith A L. Characteristic damage states: a new approach to representing fatigue damage in composite laminates materials: experimentation and design in fatigue. 1981, 246-260P
[89] 贺鹏飞，嵇醒．复合材料由于基体损伤而引起的刚度下降．第六届全国复合材料会议论文集．北京，1990，189-191页
[90] 贺鹏飞，嵇醒．等效夹杂法在纤维增强复合材料细观力学研究中的应用．同济大学学报．1992，12：15—21页
[91] O' Brien T K. Analysis of local delamiantions and influence on composite laminate behavior. Delamination and debonding of materials, ASTM STP 876, Johnson. American Society for Testing and Material Philadelphia, PA, 1985:282-297P
[92] Wang A S D, Kishore N N and Li C A. Crack development in graphite-epoxy cross-ply laminates under uniaxial tension. Comp. Sci. rechnol. 1985(24): 1-31P
[93] Nairn, J.A. and Hu, S., The initiation and growth delaminations induced by matrix microcrack laminated composites. Int. J. Fract., 1992(57): 1-24P
[94] Dharani L R and Tang H. Micromechanics characterization of sublaminate damage. Int. J. Fract 1009: 123-140P
[95] Nobuo Takeda and Shinji Ogihara. Initiation and growth of delamination from the tips of transverse cracks in CFRP cross-ply
laminates. Compos. Sci. And Tech. 1994(52): 309-318P
[96] Steif, P.S. Parabolic shear lag analysis of a [0/90]_s laminate.In 'Transverse ply crack growth and associated stiffness reduction during the fatigue of a simple cross-ply laminate' (Eds S. L. Ogin, P. A. Smith and P.W. R. Beaumont),Report CUED/C/MATS/TR 105. Cambridge University, 1984
[97] Lee J W & Daniel I M. Progressive transverse cracking of cross-ply composite laminates. J. Comp. Mater. 1990(24): 1225-1243P
[98] Berthelot J M, Leblond P, ed. Transverse cracking of cross-ply laminates. Part 1. Analysis. Composites Part A. 1996(9): 989-1001P
[99] 伍天健等．某壳体爆破试验压强偏小的原因调研与分析报告．2000．8(内部资料)
[100] 《纤维缠绕内压容器的力学分析》(内部资料)，1983
[101] 王勖成，邵敏编著．有限元法基本原理与数值方法．北京：清华大学出版社，1988．
[102] 非线性，《纤维增强塑料(玻璃钢)汇编标准》。中国标准出版社，1988年。
[103] 黄启珍等编，《导弹结构，材料，强度》，宇航出版社，1996，第1版．237页
[104] Arruda, E. M. and Boyce, M. C. "A three-dimensional constitutive model or the large stretch behaviour of rubber elastic materials", J. Mech. Phys. Solids, Vol. 41, No. 2, 1993.
[105] Mooney, M. J. Appl Phys., Vol. Ⅱ, p. 582, 1940.
[106] Gent, A. N. "A new constitutive relation for rubber", Rubber Chem. Tech., 69, 1996.
[107] Chai H et al. One dimensional modeling of failure in laminated plates by delammination buckling. J. Solids Structures, 1981,
17(11): 1069
[108]Chai H, Babcock C D. Two-dimensional Modelling of compressive failure in delaminated laminates. J. of Composite Materials.1985,19(1): 67
[109]Yin W L. Axisymmetric buckling and growth of a circular delamination in a compressed laminate. J. Solids structures.1985, 25: 503
[110]陈思秋．复合材料层合板分层屈曲研究。硕士学位论文，上海交通大学，1989
[111]陈思秋，李思简．对称层板二维的分层屈曲研究．上海交通大学学报．1989，23(6)：30-39页
[112]Yeh M K, Tan C M. Buckling of elliptically delaminated composite plate. Composite Structure. 1994, 28(1): 36P
[113]呼延晓智，刘方龙．准各向同性基层上椭圆形子层的屈曲．宇航学报．1990，10页
[114]李思简，万晖．层合圆柱壳体表层矩形分层屈曲分析．上海交通大学学报，1990，24(6)：164-172页
[115]肖道国，王熙，苏丹．层合圆柱壳体表层局部分层屈曲研究．复合材料的现状与发展．第十一届全国复合材料学术会议论文集．中国合肥，2000，10
[116]Shivakumar K N and Whitcomb J D. Buckling of a sublaminate in a quasi-isotropic composite laminate. Journal of composite materials. 1985, 19(1): 2-18 P
[117]李顺林主编．复合材料工作手册．北京：航空工业出版社，1988．
[118]Cox H L. The elasticity and strength of paper and other fibrous materials. Br. J. App. Phys, 1952, (22): 72-79P
[119]Fukunaga. H, Chou T W, Peters P M and Schulte K. Probabilistic failure strength analysis of graphite/epoxy cross-plylaminates.
J. Comp. Mater. 1984, (18) : 339-356P
[120] Ogin. S., Smith. P. A. and Beaumont. P. W. R. Matrix cracking and stiffness reduction during the fatigure of a (0/90) GFRPlaminate. Compos. Sci. Technol. 1985(22) : 23-31P
[121] Berthelot J M. Analysis of the Transverse Cracking of Cross-Ply Laminates: a Generalized Approach. J. Compos. Mater. 1997, 31(18) : 1780-1805P
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |