【正文】 )． 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 loaddisplacement 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， fft 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 hookend’s being straightened and the matrix’s being crushed around the hookend． 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 stressstrain 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。. 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 in the formula of falling section 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 parison 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．