13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- singularity intensity of HRR field [12-13]. Begley and Landes [14-15] first recognized that the J integral and its critical value can be evaluated experimentally from the interpretation of J as the energy release rate. A method for estimating the J from a single load-displacement record was proposed first by Rice et al. [16]. For a bending specimen with different sized cracks, Sumpter and Tuner [17] proposed a general expression of J integral. A total Δ can be separated into an elastic component el Δ and a plastic component pl Δ , so the J integral would be expressed as el pl J J J = + (1) where el J is the elastic component of J integral, pl J is the plastic component of J integral. The elastic component of J can be directly calculated from the stress intensity factor K, as used in ASTM E1820-11 for a plane strain crack ( ) 2 2 1 el K J E ν − = (2) in which E is the Young’s modulus and νis the Poisson ratio. The plastic component of J is determined as 0 0 1 1 P pl pl pl pl P J dP d B a B a A Bb η Δ Δ Δ ∂Δ ∂ = =− Δ ∂ ∂ = ∫ ∫ (3) where P is the total generalized load or force of the component, B is the thickness, b is the remaining ligament, a is the crack size, pl Δ is a plastic component of load-point or load line displacement, ηΔ is the plastic factor of load line compact tension specimen, pl A Δ is the plastic component of area under the measured P−Δ curve. All expressions introduced above are valid only for stationary cracks. For a growing crack, the J integral should consider the crack growth correction. J integral is independent of the loading path, so J value is a function of two independent variables: Δ and a according the deformation theory. From Eq 3, Ernst et al. [18] derived the complete differential of pl J as pl pl pl P dJ d J da Bb b η γ Δ Δ = Δ − (4) In which γ Δ is the geometry factor of load line compact tension specimen. The γ Δas follows ' 1 b W η γ η η Δ Δ Δ Δ = − − (5) Where the prime denotes the partial differential with respect to a/W, i.e. ( ) ' / / a W η η Δ Δ =∂ ∂ .
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