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The main goal of this paper is presentation of a computational approach todamage evolution within the composite pipe adhesive joint subjected to constant amplitudetension. This approach uses the average shear stress criterion to simulate defectpropagation within adhesive layer. The numerical procedures are carried out thanks to thecommercial Finite Element Method displacement-based program ANSYS. The prediction ofcomposite pipe joint life is described in terms of defect growth rate and load cycles number.Finally, a relation between the mean cycle load and defect growth rate is obtained fromcomputational studies.