Abstract: The application of boundary effect model (BEM) and size effect model (SEM) on fracture behavior of materials were compared. A theory and the associated method for determining the material constants (fracture toughness K_IC and tensile strength f_t) were proposed using experimental peak loads P_max from three-point-bend (3-p-b) specimens with quasi-brittle fracture controlled. The ratio of 3-p-b concrete specimens size W to maximum aggregate size d_max under laboratory conditions is around 5 to 20. These concrete specimens are heterogeneous, where quasi-brittle fracture is dominant. In contrast to the fracture mechanical models those are based on continuum mechanics and applied to quasi-brittle fracture, the maximum aggregate size d_max was introduced in the analytical formula of the proposed fracture model. The stable crack growth corresponding to the peak load of these specimens can be evaluated based on parameter combination β d_max, and precisely predict results can be obtained by using different values of discrete number β. The validity of the theory and the proposed method has been confirmed by test results from different scholars, including mortar, concrete and granite material (d_max=1.2 mm to 40 mm), linked with same specimen size W but with different initial crack length a₀ and geometrically similar or with a same ratio of initial crack length to specimens size a₀/W but different W.