13th International Conference on Fracture June 16–21, 2013, Beijing, China -4- For additional information on the development and implementation of the CHM see the following references [4,9,11]. However, two equations have to be fulfilled to determine the material properties from the CHM: 0 and 0 ext hinge obs WST M M CMOD CMOD − = − = (11) where Mext is the external bending moment and Mhinge stands as bending moment transferred by hinge. The CMODobs represents the observed CMOD and CMODWST is computed CMOD. The external bending moment, Mext can be calculated as follow: ( ) 2 0 1 1 1 2 2 ext sp v M P d y Pd mge = − + + (12) where 2tan 1 tan w c v sp c w P P α μ μ α + = − (13) refers to splitting load, Psp, and vertical load Pv; αw stands for wedge angle, μc for friction in the roller bearing, m denotes mass of the specimen, g is the acceleration of gravity and e represents the horizontal distance between the axis of symmetry of the specimen and the centre of gravity of one half of the specimen. The bending moment transferred by hinge, Mhinge is computed by: ( )( )0 0 h hinge M y y y dy σ = − ∫ (14) where σ stands for cohesive law from Eq. (1). The CMODWST is defined as sum of elastic deformation of the specimen, δe; deformation due to presence of the crack opening, δw; and deformation caused by geometrical amplification, δg. WST e w g CMOD δ δ δ = + + (15) The evaluation of the elastic deformation, δe can be found in Tada et al. [15] as 2 sp e P v Et δ = (16) where t = specimen thickness and v2 is a function of the ratio between the length of the initial notch and the distance from the loading line to the bottom of the specimen. ( ) ( )2 2 2 38.2 55.4 33.0 1 x v x x x = − + − (17) The ratio is given by x = 1 – h/b (See Fig.3). The deformation due to presence of the crack opening, δw can be directly computed from Eq. (9) at y = h. Finally, deformation caused by geometrical amplification, δg is derived as ( ) 2 2 1 el w g i b h d δ ϕ δ β ⎛ ⎞ = − ⎜ − ⎟ − ⎝ ⎠ (18)
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