5土木工程外文翻译外文文献英文文献混凝土应力实.doc

1、混凝土应力实验一、实验介绍直径很小的钢纤维用于混凝土结构可以大大的提高混凝土的抗拉承载能力。 在一般 情况下混凝土中掺钢纤维的体积比例在 0.2%2.0%之间。在很小比例下，钢筋混凝土 的张拉响应可假设为不硬化的类型，它有加大单个裂缝扩展性质很像无钢筋的素混凝 土，钢纤维对混凝土开裂之后性能的改善作用更加明显，可以通过控制裂缝的开展从而 较大幅度地提高混凝土的韧性。然而它对其它性质的改进很小，因此在正常实验方法下 如此低得的纤维含量很难难得到钢纤维混凝土轴拉应力 应变曲线的平稳段。 为了找 到一个合适易行的方法来研究SFRC轴拉性能人们做了很多工作并且有报告称可通过添 加刚性组件方法来获得轴拉

2、全曲线。在这篇文章中 ,我们将用不同类型的纤维来做钢筋混凝土的单轴拉伸试验。钢筋混凝土的抗拉特型首钢纤维的强度和含量影响。 另外，在强力作用下，钢筋混凝土的应力 应变曲线受多种因素的影响。对纤维混凝土增强机理进行研究，要获得钢纤维混凝土的 受拉全过程曲线，采用轴拉方法最为适宜，但是要在试验方法上作一定改进，并且试验 机要有足够的刚度，来保证试验过程的稳定。众所周知，在工程实践过程中，由于施工 技术及经济条件的限制，SFRC中纤维体积掺率一般不超过2%,而大部分工程实例中， 纤维掺量都在1%左右。为此，本文设计了轴拉 SFRC材料试验，纤维掺量取1%,并采 用不同种类的纤维增强形式，进行对比分析

3、。二、实验内容试验在 60 吨万能试验机上进行。在试验装置中添加了四个高强钢杆以增大试件的 卸载刚度，并通过在试件两端添加球铰来消除试件的初始偏心率。通过调节连接试件和横梁的四个高强螺栓来保证试件的轴心受拉。 试件相对两侧面 之间的拉应变值之差不得大于其平均值的 15%。当钢纤维掺量很低（为零或 0.5%时）， 在荷载峰值采用低周反复加载曲线的外包络线来获得轴拉应力 应变全曲线 .。2.1 材料 由四种不同类型的钢纤维用于该试验，这些纤维中三种是带钩的（和）一种是光滑的。见于表一。 在基体强度等级为 C60 和DK 一 5型减水剂和瑞士 Sika公司生C30,C60,C80混凝土被制成的试件，

4、试验中所采用的三种混凝土配合比用于研究，C80 钢纤维混凝土中分别加入了大连建科院生产的 产的液体减水剂。这些被用来研究钢纤维混凝土的在标准情况下养护 28 天。三种试件的平均强度见于表一。水泥采用大连小野田水泥厂 生产的 32.5级和 52.5级普通硅酸盐水泥。细骨料采用细度模数 26的河砂。粗骨料采 用 5 20 石灰岩碎石。2.2、试件水泥强度(ISO)水泥Kg/m3沙的比率u/c沙屈服强度Kg/m3碱水剂Kg/m3压缩强度MpaC3032.54500.440.36667118532.07C6052.55000.350.336121223DK-567.59C8052.5：6000.290

5、.315351191Sika82.96用建筑结构胶将轴拉试件粘贴于两端的钢垫板上。22组共110个试件的具体参数。2.3、补充经过28天，普通混凝土和钢纤维混凝土分别被用来做抗拉强度试验。张拉应力一一应变曲线由此获得。对于高强度钢纤维混凝土诸如抗拉能力等拉伸特性也由此得到。增 强类钢纤维混凝土比增韧类钢纤维混凝土的强度平均提高13%;而由基本开裂至裂缝宽度为0.5mm区间(相应的应变约2000卩的断裂能积分则显示：增韧类钢纤维混凝土比增 强类钢纤维混凝土的断裂能平均提高 20%.由表3还可以看出，大部分SFRC第一峰值对 应的极限拉应变值与素混凝土相当，在 100卩左右，这说明低含率纤维的掺入

6、对提高混 凝土的极限拉应变作用不很明显。而增韧类 SFRC第二峰值对应的应变则大大提高，可 达1000卩罗由此可知第二峰值的出现大大提高了材料的韧性。DRAMIX型纤维因为长度是其它三种纤维长度的2倍，其断裂韧性更好，在试验曲线中可以看出在应变达到后， 其荷载强度仍然保持较高水平，直到10000卩应变时荷载仍可保持其峰值水平的 50%左 右。三、试验结果和分析3.1劈拉强度和轴拉极限强度不同试件的劈拉强度和轴拉极限强度查表，在混凝土中增加钢纤维的量可以提高它 的劈拉强度和轴拉极限强度，两种不同参数的钢纤维钢筋混凝土和普通混凝土(它们的 混合比例相同)的比率也可查表。从上我们可以看出钢纤维对初裂

7、强度的增强作用受基体强度变化的影响很小。也就是说在掺人同种钢纤维时，随着基体强度的增加，钢纤维混凝土与同配比素混凝土的初 裂强度的比值基本恒定然而，不同情况下的极限抗拉强度是不一样的，当基体强度增加时，对于不同类型 的钢纤维，极限抗拉强度的分配量是不同的。另外它的增加量比劈拉恰强度大F1型钢纤维作为基体的极限抗拉强度很高，这是因为这类型的钢纤维的强度很高(大于1100MPa)试验过程中没有纤维拔断的现象出现而且当基体强度较高时(C80)，钢纤维的端部弯钩被完全拉直。由于黏结强度的提高，基体强度越高，该纤维对高强混 凝土轴拉极限强度的增强效果越好。F2和F3型钢纤维的强度较高，二者均有端部弯钩，

8、 并且表面较为粗糙，当基体强度较高时 (C80)，出现纤维拔断现象，该现象的出现对这 两种钢纤维的增强效果产生了消极影响，因此为了最大限度的发挥这两种钢纤维的增强作用，应将其应用于中高强度混凝土中。F4型纤维为长直型，其与基体问的粘结力较小，因此它的增强效果耍弱于其他二 种。因为其与基体问的粘结力较小因此在试验过程中没有纤维拔断现象出现。并且随着基体强度升高，由于黏结力的增大，该纤维增强效率有持续提高。试验中重点针对F3型钢纤维研究了纤维掺量的变化对钢纤维高强混凝土轴拉初裂 强度和极限强度的影响。试验中钢纤维体积掺率变化范围为 0.5-1.5。可见随着纤维掺量 增大，轴拉初裂强度和极限强度均有

9、提高。两图中曲线的上升趋势很相似。也就是说纤 维掺量在整个拉伸过程中对钢纤维混凝土内拉应力的影响是积极的和稳定的。纤维序号F10.642F20.862F30.794F40.589钢纤维钢筋混凝土轴拉极限强度可以用下式来计算：吳=/ x （I + o'严）（1）式中：fft为钢纤维钢纤维轴拉极限强度轴拉极限强度；ft为同配比素混凝土轴拉极限强度； 纤维类型系数有表四给出/为钢纤维体积掺率，l/d为钢纤维长径比。M3.2轴拉变形性能和韧性初裂拉应变和峰值荷载拉应变对试件四周四个夹式位移计测得的应变值进行平均获得试件的拉应变值。若试验中试件相对侧面的拉应变差大于平均值的 15%，该试件作废。

10、高强SFRC的初裂拉应变和峰值拉应变要远大于同配比素混凝土（见表5），随着基体强度或者纤维掺量增大，这个差值有所增长，钢纤维对峰值应变的提高作用要比初裂 应变更加明显。拉伸功和轴拉韧性指数拉伸功为位移0-0. 5 mm轴拉荷载位移全曲线下面积（图5中阴影面积）。另外，引 入轴拉韧性指数。其定义为：Re05 = 100 x |（2）式八/I中:fft为钢纤维混凝土轴拉极限强度；A为轴拉试件的破坏横截面面积。两参数均用来评价钢纤维高强混凝土在轴拉过程中的韧性。轴拉韧性指数为无量纲系数，与轴拉功相比，在评价轴拉韧性时可在一定程度上消除轴拉极限强度的差别所带 来的影响。从上我们可以发现，基体强度和纤维

11、含量两种参数的有规律的改变很相似，因此我 们分析的重点应放在韧性指数上。掺有四种钢纤维及素混凝土试件基体强度与轴拉韧性指数的关系成比例，其中纤维混凝土试件中钢纤维体积掺率均为 1.0%。可见高强SFRC的轴拉韧性要远远优于同配 比素混凝土。钢纤维的抗拉强度的影响是显著的，随着基体强度升高，混凝土脆性明显增加，素 混凝土轴拉韧性明显下降。在掺有 F1和F2型钢纤维的试件中也出现了韧性下降现象。F1 型纤维从基体中拔出其实是一个纤维端钩被拉直，纤维端部周围混凝土被挤碎的过 程。当纤维端钩最终被拉直时，轴拉荷载很快下降。混凝土的强度越高，基体硬度和脆 性越大，上述过程历时也更短。因此当基体强度较高时

12、，轴拉应力 应变曲线下降得更快，轴拉韧性指数也有所下降。在四种类型纤维种F1型纤维的增韧效果最好，F2型纤维长径比最小，基体强度较 高时出现了纤维拔断现象，因此当基体强度增加时韧性指数不断下降。F3 和 F4 型钢纤维韧性指数均随基体强度升高而增大。这两种纤维均为剪切型，表 面较粗糙。在钢纤维和基体之间黏结力的各组分中，摩擦力起主导作用。摩擦力随基体 强度的升高而增大，且该黏结类型的拔出破坏是一个持续过程，因此基体强度升高对掺 有这两种钢纤维的混凝土韧性起积极作用。这两种纤维的不同之处是 F3 型的两端有弯 钩。由于端钩的存在使得在基体强度不太高时 （C30 和 C60）， F3 型钢纤维的增

13、韧作用优 于F4型。当基体强度很高时（C80），由于纤维拔断现象影响了 F3型的增韧效果，F4型 钢纤维的增韧效果叉反过来超过了 F3型钢纤维。3.3 钢纤维钢筋混凝土单轴拉伸应力 应变曲线典型的钢纤维高强混凝土轴拉应力一应变全曲线（为了便于比较，每组试件选出条典型曲线作为代表 ），表述了轴拉曲线随基体强度的变化规律；表述了轴拉曲线随钢纤 维（F3 型）掺量的变化规律。曲线由弹性阶段、弹塑性阶段和下降段（软化段）组成。下降段存在拐点。从上中可以看到，基体强度越高，轴拉应力一应变全曲线下降得越快。另外，钢纤 维掺量的提高可以大大地改善曲线的丰满程度。 钢纤维类型对轴拉应力一应变全曲线的 形状也有

14、一定的影响。 Fl 型纤维的曲线是几种钢纤维中最丰满的， 并且在拉应变为大约 10000个微应变时出现了第二峰值。 该现象体现了 Fl 型纤维良好的增韧效果。 当基体强 度较高时，由于纤维拔断的出现使得F2和F3型钢纤维试件的轴拉曲线下降端呈阶梯状。F4 型纤维的曲线较为平滑，形状与素混凝土曲线相似，但是更为饱满。这是因为长直 形钢纤维的拔出过程是相对连续和柔和的 .四、研究分析由 4 种钢纤维混凝土的典型拉伸应力 -应变曲线可以看出：在轴拉条件下，1%掺量的钢纤维远远没有达到使混凝土材料实现应变强化的地步， 大部分试验曲线都在达到峰 值后，出现荷载骤降段。但是，随着变形的增加，有两条曲线有明

15、显的第二峰值出现， 而另外两条则没有， 正是根据这种现象， 可以将其分为增强和增韧两大类钢纤维混凝土， 有第二峰值的为增韧类，无第二峰值的为增强类。曾经有许多钢纤维混凝土轴拉应力一应变全曲线模型提出大多数为分段函数， 以应 力峰值点为分界点。本文中，全曲线的上升段和下降段采用不同的函数表达式。在公式（ 3）中4.1 上升段的公式上升段的数学模型为：(4)这 里 ：为与基体和钢纤维特性有关的参数。 边界条件为：1) X=0，Y=0 ；2) X=0，dy/dx=E0 /Ep；3) X=1 , Y=1 , dy/dx=0.由边界条件可得公式(5)可以简化为：y - ( 5)系数可a xa + I a

16、,以通过试验数据回归获得割线因此公式(6)可以转换为:(7)4.2下降段公式下降段数学的模型为：下降段表达式中系数值选取 最小二乘法回归获得：式中：E0为圆点切线模量；EP为峰值应力点 模量(第一峰值)。(8)为与基体和钢纤维特性有关的参数。1.7。边界条件x=l和y=1自然满足。系数的取值通过(9)可见基体强度和纤维参量对轴拉曲线下降段的下降速率的影响是相反的。五、理论曲线与试验结果的比较钢纤维高强混凝土轴拉应力一应变理论曲线和试验曲线的比较如图12所示(以试件F36010为例)。可见，理论结果与试验结果符合较好。六、实验结论(1) 试验结果表明：钢纤维高强混凝土劈拉强度略高于轴拉强度，两者

17、有较好的相关性，钢纤维高强混凝土轴拉强度可取为劈拉强度的0.9倍。(2) 在掺入同种同量钢纤维时，随着基体强度的增加，钢纤维高强混凝土与同配比素 混凝土的初裂强度的比值基本不变；轴拉极限强度的比值有所变化，且该变化对不同的 纤维类型有所不同，钢纤维与基体黏结性能好，且破坏时不被拉断，则增强效果好。(3) 提高钢纤维掺量对钢纤维高强混凝土的抗拉强度特性的改善作用比对普通强度 混凝土的改善作用明显。(4) 钢纤维高强混凝土的初裂应变和峰值应变要比素混凝土的增幅随基体强度和纤 维掺量的升高而增大。(5) 引入了轴拉韧性指数来评价钢纤维高强混凝土的韧性，钢纤维混凝土的轴拉韧性要大大优于同配比的索混凝土

18、，并且受基体强度和钢纤维特性和掺量的影响。(6) 基体强度越高，钢纤维高强混凝土的轴拉应力应变曲线在峰值过后下降得越快； 纤维掺量的提高可以大大改善曲线的丰满程度，钢纤维类型对曲线形状也有一定的影 响。通过对实验曲线的分析与回归，给出了考虑上述影响因素的钢纤维高强混凝土轴拉 应力应变全曲线表达式。(7) 综合而言，四种钢纤维中，F3型钢纤维的增强效果最好，而Fl型钢纤维的增韧效果最好。外文翻译原文Concrete stress test1 Test IntroductionThe tensile properties of concrete can be enhanced substantia

19、lly by incorporating high strength and small diameter short steel fiberswhich leads to the steel fiber reinforced concrete(SFRC)In conventional SFRC， the steel fiber content is usually within the range of 022 by volumeAt such a low 6her content the tensile response of SFRC would assume a nonhardenin

20、g typewhich is characterized by the widening of a single crack， similar to an unreinforced concrete The contribution of fibers is apparent in the postcracking response, represented by an increase inpostcracking ductility due to the work associated with pullout of fibers bridging a failure crack. How

21、ever， improvements in some other properties are insignificant Moreover ， the softening segment of the stress strain curve of SFRC with such a low fiber content under uniaxial tension is difficult to be got with normal experimental methodsMany works have been done to find a suitable and relatively ea

22、sy way to analyze the tensile characteristicsAnd it was reported that the whole curve could be got on a normal testing machine with stiffening components added.In this article， the stressstrain behavior of SFRC under uniaxial tension Was analyzed for different types of fiber The tensile characterist

23、ics of SFRC influenced by the matrix strength and the steel fiber content were studied alsoIn addition ， the stress strain curves of high strength SFRC with different factors were well acquiredThe mechanism of fiber reinforced concrete to enhanceresearch,to obtain steel fiber reinforced concrete in

24、tension curve of the whole process, using the most appropriate method of axial tension, but to make sure the testing methods improved, and the testing machine must have enough stiffness to ensure the testing process stability. Is well known in engineering practice, process, technology and economic c

25、onditions due to construction constraints, SFRC-doped fiber volume in the rate of generally not more than 2%, while most of the engineering example, the fiber fraction are about 1%. In this paper the design of the axial tension SFRC material testing, fiber dosage to take 1%, and using different type

26、s of fiber-reinforced forms, were analyzed.2 Experimental ContentThe specimens were tested on a 60 kN universal testing machine Four high steel bars were added to enhance the stiffness of the testing machine In addition ， spherichinges were used to abate the initial axial eccentricity of the specime

27、nsIt was ensured that specimens should be pulled under uniaxial tension by adjusting the four high strength bolts which connect the specimens to the crossbeamAnd the difference between the tensile strains of the opposite sides of the specimen should be less than 15 of their mean value. When the fibe

28、r content was low (0 and 0.% by volume), the cyclic quire the whole stress strai n.2. 1 MaterialsFour types of steel fibers shown in Table were chosen for this test Three of these fibers (F1, F2 and F3) were hooked-end and the other one(F4)was smoothThree concrete mixtures shown in Table 2, were inv

29、estigated. Water reducing agents were used in C60 and C80 mixes(DK 一 5 made by Dalian Structure Research Institute and Sika made in Switzerland respectively). The compressive strengths of these C3,0 C60, C80 mixes were determined according to “ TestMethods Used for Steel Fiber Reinforced Concrete ”(

30、CECS:：39)"8 3 at 28 days using 150 mm 150 mm X50 mm cube s Averaged results for 3 specime ns are give n in Table 2. Ordinary Portla nd ceme nt(yielded by Dalia n Huaneng Onoda Cement Company)of 32. 5 and 52. 5 (according to China standard) were chosen . River sand(modulus of fineness is 2.6)and

31、 crushed limestone coarse aggregates(5- 20 Bi n) were used.TableMatrix codeStre ngth gradeOf ceme nt(ISO)Ceme ntKg/m2 SpecimenThe ten sile specime n was bon ded to steel padd ing plates at both ends by tygoweldA total of 1 1 0 specime ns were divided in to 22 groups accordi ng to certa in parameters

32、The parameters of these specime ns are show n in Table.32. 3 ItemsAt the age of 28 days, plain concrete and steel fiber concrete specimens were tested for tensile strength, respectively .The tensile stress strain curves were acquired. Many other tensile characters of the high strength steel fiber co

33、ncrete such as tensile work , etc were calculated also. Enhan ced class steel fiber rein forced con crete tough ness category tha n the stre ngth of steel fiber rein forced con crete an average of 13%; while crack ing from the basic to the crack width of 0.5mm interval (the corresponding strain of a

34、bout 2000 showed the fracture en ergy in tegral: toughe ning class steel fiber rei nforced con crete enhan ced class tha n the fracture en ergy of steel fiber rein forced con crete an average of 20%. from Table 3 also shows that most of the SFRC first peak correspondsto the limit of tensile strain v

35、alue and plain concrete rather, in the 100 caround, indicating a low rate of fiber-containing incorporation in improving the role of ultimate tensile strain of concrete is not very obvious. The toughe ning class SFRC sec ond peak corresp onds to a much greater stra in, up to 1000 From this second pe

36、ak has greatly enhancedthe appearanceof toughness. DRAMIX Fiber because of the length of other three kinds of fiber length of 2 times the fracture toughness and better in the test curve can be seen in the strain is attained, the load continues to maintain a high level of intensity, until the strain

37、when the load so as to maintain 10000 卩& its peak level of 50%.3 Results and Discussi on 1 Crack stress and ultimate ten sile stre ngthu/c rati oSand ratioSandKg/m3CrushedStrneKg/m3Water reduc ingCompressiveStre ngthMpaC3032.54500.440.36667115537.07C6052.55000.350.336021223DK-567.59C8052.56000.2

38、90.315351190Sika82.96The crack stress and ultimate tensile strength of different specimens are listed in Table 3The addition of steel fibers into concrete increased its crack stress an d ultimate tensile strengthAnd the ratios of these two parameters of SFRC to those of plain concreue (with the same

39、 mix proportion)are given in Table 3，too 31 1 Effect of matrix strength an(1 fiber typeFrom table 3It can be seen that the effects of steel fibers 0n crack stress are little influenced by the matsix strength That is to say When the matrix strength increases, the ratios of crack stressesof SFRC ( wit

40、h the same type of fibers contained)to those of plain concrete ones with the same mix proportion are invariableHowever，the condition for ultimate tensile strength is different When the matrix strength increasesthese ratios of ultimate tensile strengths(shown in Table 3)vary dissimilarly according to

41、 the type of steel fiber Moreoverthe increments are bigger than those of crack stressThe heightening efficiency of fiber F1 for ultimate tensile strength rises as matrix strength increases It is becausethat the strength of this kind of fiber is very high(>1 100 MPa)No fiber broken was observed du

42、ring the test and the hooked ends of the fibers were straightened when the matrix strength was high(C80) The higher the matrix strength this kind of steel fiber takes on its strengthening effect more efficiently for the increasing of bond stressThe strengths of fibers F2 and F3 are midhigh(>700 M

43、Pa) They all have hooked ends and both of their surfaces are coarseWhen the matrix strength was high(C80) fiber breaking occurred in the testAnd this phenomenon impaired the heightening efficiency of these two kinds of steel fiberSo they should be used in middle strength concrete to exert their stre

44、ngthening effect more efficiently Fiber F4 is smoothand its bond stress with matrix is comparatively low T1erefore its strengthening effect is 1ess notable than those of other kinds of fiber Because of the low bond stress no fiber broken was found during the test and its heightening efficiency for u

45、ltimate tensile strength rises as matrix strength increases 31 2 Effect of fiber contentThe effect of fiber content on the crack stress and u1ultimate tensile strength was investigated for SFRC contained fiber F3And the fiber content varied from 0 5 to 15 by volume(shown in Table 3)It can be seen fr

46、om Fig1 and Fig2 that as the fiber content increasesThe crack stress and ultimate strength of SFRC improve obviouslyMoreoverthe rising trends of the curves in these two figures are stupendously similarIn other words，the effect of fiber content on the characters of tensile stress of SFRC is positive

47、and consistent Table 4 Fiber type factorsFiber codeatF10.642F20.862F30.794F40.589The tensile strength of SFRC can be calculated with the follow formula：where，fft is the ultimate tensile strength of SFRC; the ultimate tensile strength of plain concrete with the same mixing proportion； a，the fiber typ

48、e factor，Iwhich is shown Table 4；is the fiber content 0f volume and l/d is the aspectratio of steel fibers.3. 2 Tensile strain and toughness characters3. 2. 1 Crack strain and the strain at peak tensile loadThe tensile strains were acquired by averaging the readings of the four displacement sensors

49、fixed around the specimen In addition, the specimens whose difference between the tensile strains of its opposite sides is larger than 1% of their mean value were blanked outThe crack strain or the strains at peak tensile load of SFRC are much bigger than those of plai n con crete(as show n in Table

50、 5). And the in creme nts go up as the matrix stre ngth or the fiber content in creases Compared to that on crack strain the in cresce nt effect of steel fiber on the stra in at peak ten sile load is more remarkable3. 2. 2 Tensile work and toughness modulusThe ten sile work was defi ned as the area

51、un der the load-displaceme nt curve from 0 to 0. 5 rain. Moreover, a tensile toughness modulus was introduced(shown in Table 5) It was defined as(2) where， fft is the ultimate tensile strength of SFRC； A，the area of the cross section of specimenBoth these two parameters were quoted to evaluate the t

52、oughness characters of SFRC under uniaxial tensionThe tensile toughness modulus is a dimensionless factorCompared to what the tensile work doesit can avoid the influence of the ultimate tensile strength when studying the toughness of SFRCIt call be found from Table 5 that the altering regularities o

53、f these two factors along with the changes of matrix strength and fiber content are approximateTherefore，the emphasis of analysis was put on the toughness modulusThe relationship between the matrix strength and toughness modulus of SFRC with four kinds of steel fiber are shown in Fig 3 whose fiber c

54、ontents are all 1 Oby volumetogether with that relationship of plain concreteThe tensile toughness of SFRC is much better than that of plain concreteThe tensile toughening effect of steel fiber is remarkableAs the matrix strength risesThe brittleness of concrete increases obviousl，y and then the ten

55、sile toughness of plain concrete falls downThis phenomenon was also found on specimens containing fiber F1and F2The pulling out of fiber F1 from concrete is in fact a process of hook-end' sbeing straightened and the matrix 'bseing crushed around the hook-end When the hooked end is straighten

56、ed at last the tensile load falls down quickly The higher the concrete strength. the larger the rigidity of the matrix and the shorter the time that the process mentioned above lastsThusthe stress-strain curve falls down more quickly ，and then the toughness modulus decreasesHowever，the toughening ef

57、fect of fiber F1 is the best among these four kinds of steel fiber The aspect ratio of fiber F2 is the least and when the matrix strength is high， fiber breaking occursTherefore，the toughness modulus falls down continually as the matrix strength rises.The toughness modului of fibers F3 and F4 rise together with the matrix strengthr Both the two kinds of fiber are snipped and their surfaces are coarser Thereforer the friction is dominant in the proportions of bond stressr Because the friction between fiber and matrix increases along with the matrix strength，and the whole