Issue 50

M. Belhamiani et alii, Frattura ed Integrità Strutturale, 50 (2019) 623-637; DOI: 10.3221/IGF-ESIS.50.53 624 The problematic in this work lies in the difficulty of i) finding a global criterion for comparing the state of a cracked pipe to the reference state means uncracked pipe in the first place and a pipe repaired by this technique to the same reference state. ii) The difficulty is how to define precisely the field of the application of stress intensity factor SIF (K 1 ) and J integral criterion. iii) Also, there is a difficulty to specify a referential of the crack front to be studied. iv) The SINTAP procedure cannot estimate the safety status of an uncracked pipe’s find a criterion which can quantify the state of security of a pipe in the presence of several defects at the same time such as a crack, a thermic affected zone, a welding and a loss of material. To deal with this problems, in this work we have chosen to use an additional criterion which is the plastic collapse pressure, this approach raises an important operational problem: by quantifying the state of the structure by a measurable parameter is more efficient and even more exact than to express it by a computable parameter (SIF and integral J ) and which strongly depends on the referential point. Moreover, in technical terms: in industry it is better to value the repair by a parameter that can easily be understood and managed as the limit pressure rather than a computable parameter. There are eight potential modes or mechanisms of failure that must be avoided according to the ASME code criterion between these modes, the excessive plastic deformation under a static load. The ASME Section VIII Div 2 5.2 (ASME Designe by analyses DBA) [2] define the procedure for assessment of plastic collapse based on elastic-plastic analysis methods. In this study, the procedures for limit and elastic-plastic design are considered. E VALUATION CRITERIA First criterion: The J integral n the theory of linear elasticity, a crack introduces a discontinuity in the structure where the stresses tend to infinity in the vicinity of the crack tip. Using the semi-inverse method of Westergaard [3], Irwin [4, 5] related the singular behavior of the stress components to the distance to the crack tip. Based on the deformation theory of plasticity, Rice [6] proposed a new fracture parameter to predict the crack growth, based on path-independent contours that was called J integral and defined as: ( )  i i C u J wdy T ds x     ∮ (1) where C is an arbitrary curve around the tip of a crack, w is the strain energy density, T i is the components of the traction vector, u i is the displacement vector components, ds is the length increment along the contour, x and y are the rectangular coordinates with the y direction taken normal to the crack line and the origin at the crack tip. Kobayashi et al. [7] verified this path independence by the finite element analysis (FEA)For power-law hardening materials, Hutchinson [8] and Rice and Rosengren [9] evaluated independently the character of crack-tip stress fields. Researchers Rice and Rosengren have studied the conditions of plane deformation while Hutchinson studied both the conditions of stress and deformation planes. Rice and Rosengren obtained essentially identical results to Hutchinson’s solutions in a different format. For a power-law hardening material, as pointed out by McClintock [10], Hutchinson obtained the following asymptotic solutions of crack-tip stress and strain fields:    1 1 0 0 0 , n ij ij n J n I r               (2)    1 0 0 0 , n n ij ij n J n I r               (3) where  0 =  0 /E,  0 is a reference stress, n is the strain hardening exponent, I n is an integration constant that depends on n,  ij and  ij are the dimensionless functions of n and h. This solution is called the HRR field. The J-integral and HRR has laid a solid foundation for the EPFM theory. I