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The toughness moduli 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 impairer 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 plumiest of them al1．The second peak was observed in the curves of fiber F1 at the strain of about 10 000 ur．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. Analytic al 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 pided 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 pisional 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：