17 Contribution to Fatigue Striation Phenomenon Analysis by Using Image Processing 121 and X=(x −ξ) cos(α) +(y −γ)sin(α) In this formulation, A, B and ϕare not directly obtained from the optimization process but only C0, C1, C2, C3 and α. ϕ is then obtained by the analytical resolution of the equation system below: ⎧ ⎪⎪⎪⎨ ⎪⎪⎪⎩ C0 =Acos(ϕ) +B C1 =− 2Asin(ϕ)π p C2 =− 2Acos(ϕ)π 2 p2 C3 = 4Asin(ϕ)π 3 3p3 (17.5) and ϕchosen as: ϕ =arctan πC1 pC2 (17.6) As the parameter α ranges between 0 and πduring the optimization process the maps giving the phase field unwrapped is not correctly oriented [8]. The correctly orientated phase field is obtained with the help of unwrapping process applied to α field. During this unwrapping process [10, 11] of α field, ϕfield correctly orientated can be calculated by removing ϕby (2π−ϕ)when πdiscontinuity is detected [8]. 17.1.2 Applying pMPC to SEM Images In a first approach, a single striation pattern SEM image has been processed with the pMPC algorithm. The SEM used for the purpose of the study is a JSM JEOL 7100F. Results are presented in Fig. 17.2. Fig. 17.2 Striation image directly analysed by pMPC
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