5 中英文对照 土木工程 外文翻译 英文文献-混凝土应力实验

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。

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。

试验中所采用的三种混凝土配合比用于研究，见于表一。

在基体强度等级为C60和C80钢纤维混凝土中分别加入了大连建科院生产的DK一5型减水剂和瑞士Sika公司生产的液体减水剂。

这些被用来研究钢纤维混凝土的C30,C60,C80混凝土被制成的试件，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2．6的河砂。

粗骨料采用5～20 石灰岩碎石。

表一
2.2、试件
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——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2000με)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100με左右，这说明低含率纤维的掺入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1000με，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10000με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。

3.1.1基体强度及纤维类型对轴拉强度的影响
从上我们可以看出钢纤维对初裂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，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。

3.1.2钢纤维掺量对轴拉强度的影响
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
F1 0.642
F2 0.862
F3 0.794
F4 0.589
钢纤维钢筋混凝土轴拉极限强度可以用下式来计算：
（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。

3.2 轴拉变形性能和韧性
3.2.1 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。

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。

3.2.2 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：
(2)
式中: 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，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：和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：
（5）
系数可以通过试验数据回归获得
(6)
式中：E0为圆点切线模量；EP 为峰值应力点割线模量(第一峰值)。

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：
（8）
式中：和为与基体和钢纤维特性有关的参数。

下降段表达式中系数值选取1.7。

边界条件x=l和y=1自然满足。

系数的取值通过最小二乘法回归获得：
（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l2所示(以试件F3—6010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，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 test
1 Test Introduction
The tensile properties of concrete can be enhanced substantially by incorporating high strength and small diameter short steel fibers．which leads to the steel fiber reinforced concrete(SFRC)．In conventional SFRC，the steel fiber content is usually within the range of 0．2％—2％by volume．At such a low 6her content．the tensile response of SFRC would assume a nonhardening type．which is characterized by the widening of a single crack，similar to an unreinforced concrete ．The contribution of fibers is apparent in the post—cracking response, represented by an increase in post—cracking ductility due to the work associated with pullout of fibers bridging a failure crack. However，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 methods．Many works have been done to find a suitable and relatively easy way to analyze the tensile characteristics ．And it was reported that the whole curve could be got on a normal testing machine with stiffening components added.
In this article，the stress—strain behavior of SFRC under uniaxial tension Was analyzed for different types of fiber．The tensile characteristics of SFRC influenced by the matrix strength and the steel fiber content were studied also．In addition，the stress—strain curves of high strength SFRC with different factors were well acquired．The mechanism of fiber reinforced concrete to enhance research, to obtain steel fiber reinforced concrete in 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 conditions 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 types of fiber-reinforced forms, were analyzed.
2 Experimental Content
The 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 specimens．．
It was ensured that specimens should be pulled under uniaxial tension by adjusting the four high strength bolts which connect the specimens to the crossbeam．And the difference between the tensile strains of the opposite sides of the specimen should be less than 1 5％of their mean value．When the fiber content was low (0 and 0.5％by volume)，the cyclic quire the whole stress—strain.
2．1 Materials
Four 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 smooth．
Three concrete mixtures，shown in Table 2，were investigated．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 C30，C60，C80 mixes were determined according to “Test Methods Used for Steel Fiber Reinforced Concrete”(CECS 13：89)"8 3 at 28 days using 150 mm×150 mm ×150 mm cube s．Averaged results for 3 specimens are given in Table 2．0rdinary Portland cement(yielded by Dalian 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 crushed limestone coarse aggregates(5—20 Bin) were used．
2．2 Specimen
The tensile specimen was bonded to steel padding plates at both ends by tygoweld．A total of 1 1 0 specimens were divided into 22 groups according to certain parameters．The parameters of these specimens are shown in Table 3．
2．3 Items
At 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 concrete such as tensile work，etc were calculated also. Enhanced class steel fiber reinforced concrete toughness category than the strength of steel fiber reinforced concrete an average of 13%; while cracking from the basic to the crack width of 0.5mm interval (the corresponding strain of about 2000με) showed the fracture energy integral: toughening class steel fiber reinforced concrete enhanced class than the fracture energy of steel fiber reinforced concrete an average of 20%. from Table 3 also shows that most of the SFRC first peak corresponds to the limit of tensile strain value and plain concrete rather, in the 100με around, indicating a low rate of fiber-containing incorporation in improving the role of ultimate tensile strain of concrete is not very obvious. The toughening class SFRC second peak corresponds to a much greater strain, up to 1000με, From this second peak has greatly enhanced the appearance of 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 when the load so as to maintain 10000με its peak level of 50%.
3 Results and Discussion
3．1 Crack stress and ultimate tensile strength
The crack stress and ultimate tensile strength of different specimens are listed in Table 3．The addition of steel fibers into concrete increased its crack stress an d ultimate tensile strength．And the ratios of these two parameters of SFRC to those of plain concreue (with the same mix proportion)are given in Table 3，too．
3．1．1 Effect of matrix strength an(1 fiber type
From table 3．It 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 stresses of SFRC ( with the same type of fibers contained)to those of plain concrete ones with the same mix proportion are invariable．
However，the condition for ultimate tensile strength is different．When the matrix strength increases．these ratios of ultimate tensile strengths(shown in Table 3)vary dissimilarly according to the type of steel fiber．Moreover．the increments are bigger than those of crack stress．
The heightening efficiency of fiber F1 for ultimate tensile strength rises as matrix strength increases．It is because that the strength of this kind of fiber is very high(>1 100 MPa)．No fiber broken was observed during 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 stress．The strengths of fibers F2 and F3 are mid—high(>700 MPa)．They all have hooked ends and both of their surfaces are coarse．When the matrix strength was high(C80)．fiber breaking occurred in the test．And this phenomenon impaired the heightening efficiency of these two kinds of steel fiber．So they should be used in middle strength concrete to exert their strengthening effect more efficiently．Fiber F4 is smooth．and its bond stress with matrix is
comparatively low．T}1erefore．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 ultimate tensile strength rises as matrix strength increases．3．1．2 Effect of fiber content
The effect of fiber content on the crack stress and u1．ultimate tensile strength was investigated for SFRC contained fiber F3．And the fiber content varied from 0．5％to 1．5％by volume(shown in Table 3)．It can be seen from Fig．1 and Fig．2 that as the fiber content increases．
The crack stress and ultimate strength of SFRC improve obviously．Moreover．the rising trends of the curves in these two figures are stupendously similar．In other words，the effect of fiber content on the characters of tensile stress of SFRC is positive and consistent．
Table 4 Fiber type factors
Fiber code at
F1 0.642
F2 0.862
F3 0.794
F4 0.589
The tensile strength of SFRC can be calculated with the follow formula：
(1)
where，f ft is the ultimate tensile strength of SFRC；the ultimate tensile strength of plain concrete with the same mixing proportion；a，the fiber type factor，
which is shown Table 4；is the fiber content 0f volume and l/d is the aspect ratio of steel fibers.
3．2 Tensile strain and toughness characters
3．2．1 Crack strain and the strain at peak tensile load
The tensile strains were acquired by averaging the readings of the four displacement sensors fixed around the specimen．In addition，the specimens whose difference between the tensile strains of its opposite sides is larger than 15％of their mean value were blanked out．The crack strain or the strains at peak tensile load of SFRC are much bigger than those of plain concrete(as shown in Table 5)．And the increments go up as the matrix strength or the fiber content increases．Compared to that on crack strain．the increscent effect of steel fiber on the strain at peak tensile load is more remarkable．
3．2．2 Tensile work and toughness modulus
The tensile work was defined as the area under the load-displacement curve from 0 to 0．5 rain．More—over，a tensile toughness modulus was introduced(shown in Table 5)．
It was defined as：
(2)
where，f ft is the ultimate tensile strength of SFRC；A，the area of the cross section of specimen．
Both these two parameters were quoted to evaluate the toughness characters of SFRC under uniaxial tension．The tensile toughness modulus is a dimensionless factor．Compared to what the tensile work does．it can avoid the influence of the ultimate tensile strength when studying the toughness of SFRC．
It call be found from Table 5 that the altering regularities of these two factors along with the changes of matrix strength and fiber content are approximate．Therefore，the emphasis of analysis was put on the toughness modulus．
The relationship between the matrix strength and toughness modulus of SFRC with four kinds of steel fiber are shown in Fig．3．whose fiber contents are all 1．O％by volume．together with that relationship of plain concrete．The tensile toughness of SFRC is much better than that of plain concrete．The tensile toughening effect of steel fiber is remarkable．As the matrix strength rises．The brittleness of concrete increases obviously，and then the tensile toughness of plain concrete falls down．This phenomenon was also found on specimens containing fiber F1and F2．The pulling out of fiber F1 from concrete is in fact a process of hook-end’s being straightened and the matrix’s being crushed around the hook-end．When the hooked end is straightened 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 lasts．Thus．the stress-strain curve falls down more quickly，and then the toughness modulus decreases．However，the toughening effect 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 occurs．Therefore，the toughness modulus falls down continually as the matrix strength rises.
The toughness modului of fibers F3 and F4 rise together with the matrix strength．Both the two kinds of fiber are snipped and their surfaces are coarse．Therefore．the friction is dominant in the proportions of bond stress．Because the friction between fiber and matrix increases along with the matrix strength，and the whole pulling out of these kinds of bond status is a continuous process，the rising of matrix strength plays a positive role in improving the toughness of SFRC containing these two kinds of fiber．The difference between the two kinds of fibers is that fiber F3 has hooked ends，which makes fiber F3 have better toughening effects than fiber F4 when the matrix strength is comparatively low(C30 and C60)．When the matrix strength is high(C80)，fiber breaking impaires the toughening effect of fiber F3．And the function of fiber F4 exceeds that of fiber F3 in reverse．
3．3 Stress-strain curves of SFRC under uniaxial tension
The typical stress--strain curves of SFRC under uniaxial tension are shown in Figs．4—11(one curve is chosen for each group of specimen to keep the graphs orderly)．Figs．4—8 express the variation of curves along with the increasing of the matrix strength，and Figs．9一l1 express the variation along with the change of the fiber content of fiber F3．The curve consists of elastic section．elastic—plastic section and falling section(softening section)．Points of contra flexure exit in the falling section of the curve．It can be seen from these figures that the matrix strength is higher，the stress—strain curves fall down faster，and the rising of the fiber content can much improve the chubbiness of these curves．Moreover，the type of steel fiber has some effect on the shape of the stress—strain curve．The curves of fiber F1 are the plumpiest of them al1．The second peak was observed in the curves of fiber F1 at the strain of about 10 000 ue．This phenomenon expresses a good toughening effect of fiber F1．The curves of fibe1s F2 and F3 are ladder—like when the matrix strength is high because of fiber breaking．The curves of fiber F4 ale smooth and like those of plain concrete in shape ．That is because the pullout process of smooth steel fiber is rather gentle．
4 Analytical Investigation
Four kinds of typical steel fiber concrete tensile stress - strain curves can be seen: in axial tension conditions, the 1% dosage of the steel fiber is far short of strain hardening of the concrete materials to the point where most of the experimental curves are in reach After the peak, there loads sag section. However, as deformation increases, there are two curves have a clear second peak appeared, while the other two do not, it is the basis of this phenomenon can be divided into two major categories of strengthening and toughening of steel fiber reinforced concrete, there is a second peak for the toughening class, no second peak to enhance the class. Many tensile stress—strain models have been brought forward一1、2、4、6、9、10，Most of their formats are sectiona1．taking the peak load as the divisional point．In this paper，the formula of the rising section and that of the fa11ing section are different．
In the formulas：
（3）
4．1 Formula of rising section
The digital model for the rising section is
（4）
where，are parameters related to the characters of matrix an d steel fibers．
The boundary conditions are as following：
1) X=0，Y=0；
2) X=0，dy／dx=E0 ／Ep；
3)X=1，Y=1，dy／dx=0．
It can be drawn from the boundary'.
Formula(4)can be simplified as：
(5)
And the value of can be calculated from experimental data as ：
(6)
where，Eo is the origin tan gent modulus；E p，secant modulus at peak load(the first peak) Thus，Formula(5)Call be inverted as：
(7)
4．2 Formula of falling section
The digital model for the falling section is：
(8)
where，are parameters related to the characters of matrix an d steel fibers ．
The value of is chosen as 1.7 in the formula of falling section 9、10．the boundary condition X= 1，y= 1 is satisfied inherently．In addition．the value of a could be regressed with the method of least squares as：
(9)
it can be seen from the expression that the effects of the matrix strength and fiber content on the curve’s falling rate are opposite．
5. Comparison of Predictions and Experimental Results
The comparison of predictions and experimental results for stress—strain curves are shown in Fig．1 2 (take the curves of F3—6010 as an example)．The theoretical curve and the experimental ones fit wel1．
6. Conclusions
a)When the matrix strength increases，the ratios of crack stresses of SFRC (with the same type of fiber)to those of plain concrete ones with the saii3e mix proportion are invariable．These ratios of ultimate tensile strengths vary dissimilarly according to the type of steel fiber．Moreover，the increments ale bigger than those of crack stress and are influenced by fiber type．
b)As the fiber content increases．the crack stress and ultimate tensile strength of SFRC improve obviously and the effect of the fiber content on the characters of tensile strength of SFRC is positive an d consistent．
c)The crack strain or the strains at peak tensile load 0f SFRC are much bigger than these of plain concrete．In addition，the increments go up as the matrix strength or the fiber content increases．
d)A tensile toughness modulus was introduced to evaluate the toughness characters of SFRC under uniaxial tension．The tensile toughness of SFRC is much better than that of plain concrete．In addition．it is influenced by the matrix strength and characters of steel fiber．e)The matrix strength is higher，the stress—strain curves fall down faster．Otherwise，the rising of the fiber content can much improve the chubbiness of these curves．Moreover．the type of steel fiber has some effect on the shape of the stress—strain curve．
f)The formula of the tensile stress—strain curve of SFRC was regressed．The theoretical curve and the experimental ones fit wel1．T}1is model may be helpful in the further research of SFRC under uniaxial tension．。