PSI - Issue 48

Mersida Manjgo et al. / Procedia Structural Integrity 48 (2023) 155–160 Manjgo et al/ Structural Integrity Procedia 00 (2023) 000–000

156 2

pressure equipment are made, such as casing, flanges, and flanges, predicting their behavior is relatively simple because they are materials whose properties are mostly uniform in all directions. However, predicting the behavior of welded joints due to structural inhomogeneity, changes in the geometry of the wall at the location of the welded joint, due to residual stresses and seam formation errors is much more difficult and therefore less reliable [2]. The assessment of integrity in dynamically loaded structures and welded joints is the focus of numerous authors [3]. Considering that the conditions of exploitation affect the integrity and life of the welded structure, the

determination of the exploitation life is imposed as a necessity. 2. Assessment of the remaining working life of the structure

During exploitation, cracks appear in structural elements or they are present as errors within the material already after production itself. These cracks are often not large enough to cause an immediate loss of load-bearing capacity of the element, but during exploitation they can grow and cause breakage, thus significantly shortening the life of the structure compared to the expected one. Therefore, in the last fifty years, methods of estimating the service life of structures have been developed based on parameters of fracture mechanics, which assume the presence of such defects within the structure. These methods predict the durability of the structure, i.e., the time required for the cracks to reach a critical size that threatens the load-bearing capacity and safety of the structure [4]. Fatigue crack growth up to the critical size depends on the load and crack growth rate, as defined by the Paris law for metals and alloys, which establishes a relationship between fatigue crack growth da/dN and the range of the stress intensity factor ΔK [5]. The application of Paris's law [6] for the calculation of the crack length depending on the number of cycles is simple with the application of numerical integration to consider the change of the geometric parameter Y due to the increase in the depth of the surface crack. The concept of local deformations is used to evaluate the number of cycles Ni required for crack initiation, and the concept of fracture mechanics is used to evaluate the share of the crack growth phase N p . Although loads with a constant amplitude are rare in practice, the largest number of experimental data in the form of the dependence da/dN = f (ΔK, R) is given precisely for such load changes. This means that the changes in ΔK during the crack growth during the test are gradual, to minimize the possible interaction effect of the load. Empirical models, with more or less success, describe crack growth for such conditions, with the corresponding material constants C and m adjusted to satisfy experimental results. Therefore, these idealized models can be used to predict the fatigue life of components subjected to loads with approximately constant values of range ΔK and range R . Assuming that the change is known [7]:     , that is , da da f K R dN dN f K R     (1) integration gives the century:

d a

da

  

N  

(2)



, f K R

a

0

Since the function f (ΔK, R) is often complex, the solution of this integral can rarely be given in a closed form, so the integration must be carried out numerically. The simplest form of the function f (ΔK, R) is in the Paris model, so the previous expression takes the form:

1 d a

da



(3)

N  

m

0 C a Y  a



a            W  

where ΔN is the number of cycles necessary for crack growth from initial a 0 to critical a c or permissible crack length a d , Y=Y(a/W) - correction factor for a crack in the component, most often it is in the form of a long polynomial or it is given in a tabular form, and under the condition that ∆σ = const and that it does not depend on a, solving the