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．论文网 混凝土应力英文文献和中文翻译(6):http://www.751com.cn/fanyi/lunwen_15707.html