13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- the inverse educing method. For mode I crack, the expression of stress intensity factor range ΔK is a K Y π σ Δ = Δ , (21) where, Δ σ is external stress range, a is crack dimension parameter, Y is shape factor which relates to structure shape, crack location and dimension as well as load condition. Substituting Eq. (9) into Eq. (21), the expression of external stress range Δ σ is derived as m N a Y a C 1/ d 1 d π 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ Δ =σ , (22) It can be found from Eq. (22) that if the values of crack propagation rate are measured, then the external stress range acted on the sample can be calculated using the inverse educing method. For standard compact tension sample (Fig. 2), the expression of stress intensity factor range ΔK is ( )α F B W P K Δ Δ = , 14.72 5.6 ) (0.886 4.46 13.32 (1 ) 2 ( ) 4 3 2 3/ 2 α α α α α α α − + − + × − + = F , (23) where, ΔP is external load range, Β is thickness, W is width, and α is the ratio of crack length a to width W. Substituting Eq. (9) into Eq. (22), the expression of external load range ΔP is derived as ( ) d 1 d 1/ α F N a C P B W m ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ⋅ Δ = , (24) For example, in the case of R=0.4, the fracture surface morpologies in the steady propagation region at various stress intensity factors are shown in Fig. 6. Measuring the widths of damage striations on the fracture surface, and recording the corresponding number of loading cycles, thus the crack propagation rates are calculated. Using Eq. (23) and Eq. (24), the stress intensity factor ranges and external loads relating with crack propagation rates are derived. 4 m (b) Figure 6. Fracture surface morpology: (a) ΔK=60.69MPa·m1/2; (b) ΔK=80.53MPa·m1/2 According to Eq. (16), the regression analysis on the calculated data obtained from the fractography is performed, and the inverse deduced equations on fatigue crack propagation are derived. In the cases of stress ratio R=0.02, 0.1, 0.2, 0.4, the inverse deduced equations are individually as 11.842) lg( 7.633 2.619 d d lg ⎟ =− + × Δ − ⎠ ⎞ ⎜ ⎝ ⎛ K N a , (25) 11.313) lg( 7.544 2.498 d d lg ⎟ =− + × Δ − ⎠ ⎞ ⎜ ⎝ ⎛ K N a , (26) 9.773) lg( 7.595 2.500 d d lg ⎟ =− + × Δ − ⎠ ⎞ ⎜ ⎝ ⎛ K N a , (27) 7.440) lg( 8.003 2.647 d d lg ⎟ =− + × Δ − ⎠ ⎞ ⎜ ⎝ ⎛ K N a , (28)
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