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We present an approximation result for Barenblatt's cohesive fracture energies in the case of antiplane shear.The regularizing functionals are damage energies of Ambrosio–Tortorelli type and the approximation is obtained in the sense of Gamma-convergence.We also discuss how the phase field convergence scheme can be applied to approximate different special fracture models,like Griffith's model,Dugdale's model,and models with surface energy density having a power-law growth at small openings.