The semianalytic finite-element method is used to develop a method for solving problems of creep and continuous fracture of complex spatial bodies. The method allows modeling the variation of the stress-strain state during creep, accompanying accumulation of dispersed microdamages, and development of macroscopic effects-continuous fracture process zones. The growth of a continuous fracture process zone is modeled. A criterion is formulated for determination of the applicability limits of continuum damage mechanics. The method is exemplified by the problem of deformation and continuous fracture of a gas turbine blade Keywords: creep, damage, continuous fracture process zone, spatial bodies, semianalytic finite-element method, iterative algorithm, long-term strength Introduction.A typical feature of the deformation of materials under long-term static loads at high temperatures is the accumulation of creep strains accompanied by the nucleation, coalescence, and growth of microscopic discontinuities-damage accumulation. This process is the subject of a number of studies [6-9, 13, 15, 18-21, 25-28, etc.], which represent today a separate division of solid mechanics-continuum damage mechanics.The operating conditions described above are typical for blades and rotors of gas turbines, blade-disk couplings, fragments of casings, and many other crucial elements of engineering structures whose long-term strength is mainly determined by creep strains. These elements are complex spatial bodies. To determine their lifetime under distributed external forces, it is necessary to solve three-dimensional problems of continuum creep-damage mechanics. The shape of the above-mentioned and many other elements is such that they can be generated by moving a plane figure of complex configuration along a rectilinear generatrix (Fig. 1).Bodies of this kind will be called inhomogeneous prismatic bodies. An efficient means of solving three-dimensional elastic problems for such bodies is the semianalytic finite-element method (SFEM) [4,23].According to [5,7], the lifetime of an element is meant the time interval between the commencement of operation and the occurrence of a limit state defined as the moment at which operation is suspended or terminated because of reduced safety. The lifetime includes the period of concealed damaging due to the nucleation and accumulation of microdamages (time to failure or no-failure lifetime) and the period of growth of macrodefects (continuous fracture process zones (FPZs))-additional lifetime-until total loss of load-bearing capacity or formation of a crack-like defect. The moment this defect occurs determines an applicability limit for continuum damage mechanics.Most publications that address the creep-rupture problem solved within the framework of continuum damage mechanics analyze the deformation process only up to the moment of rupture. However, continuum damage mechanics allows us to model the behavior of the continuous fracture process zone. The solution of this problem involves severe mathematical dif...

Based on the semi-analytic finite element method and relationships of the continuum fracture mechanics, a numerical investigation on the creep and extension of the continuum fracture zone in a gas turbine blade is performed. The value of life prior to the formation of a crack-like defect and applicability limits of the relationships of continuum fracture mechanics are determined.Ensuring the safety of gas turbine units (GTU) during long periods of service usage requires the availability of data on the variation in the load-carrying capacity of their critical parts and assemblies. Under loading after exposure to elevated temperatures, the life of GTU blades is largely determined by the accumulation of creep strains, which necessitates the long-term strength calculation. The problems concerning the determination of the stress-strain state of GTU blades taking into account the creep strains were considered by the authors of works [1-3] and others. In this connection, it is noted in [4] that the simulation of the deformation processes in elements of stationary GTU whose design life is about 50 to 100 thousand years requires the use of physical equations that take into account the material damage accumulation accompanying the creep. The necessity of predicting the occurrence of defects in a material at the initial stage of their development is also noted in [5].In work [6], the life assessment prior to the beginning of fracture and determination of the location of a macroscopic defect (initial zone of fracture) in a GTU blade was made using the procedure of numerical simulation of the stress-strain state, creep and continuum fracture of three-dimensional bodies developed on the basis of the semi-analytic finite element method (SAFEM). It was shown that the life assessment problem should be solved in three-dimensional formulation taking into account the stress redistribution in the process of creep and the temperature dependence of the material physicomechanical properties. However, the question as to the value of the additional life related to the extension of the zone of continuum fracture is of importance.The goal of the present work is to develop the procedure for simulating the extension of the zones of fracture in three-dimensional bodies, to estimate the value of the additional life related to the extension of the fracture zone, and to determine the applicability limits of the relationships of continuum fracture mechanics (CFM) for the type of objects under consideration. For solving this problem, it is required to develop the finite element base that enables simulating both the variable geometry of the blade along the vertical axis and the presence of the zones of fracture, to derive efficient algorithms for simulating the extension of fracture zones and solving sets of nonlinear equations of the SAFEM.The creep process description is made on the basis of the strengthening theory using the Kachanov-Rabotnov damage accumulation parameter.A blade is a three-dimensional body of a complex shape due to the variable ...

The numerical simulation of creep, continuum fracture zone evolution and crack propagation in a gas turbine blade uner cyclic loading conditions have been performed using a semianalytic finite-element method. The blade basic life (before fracture zone appearance) and additional resource (concerned with fracture process) of a blade have been determined.Assessment of service life of a stationary gas turbine involves assessment of lifetimes of its components, in particular, rotor blades. Blades operate under high temperature conditions; as a result, the material deformation is accompanied by a creep process and damage accumulation in the material. The blade basic life t * -failure-free operating life -is defined as an instant of time when at a given point in a blade there arises an initial continuum fracture zone that further grows, for a time period Δt I * , to result in a crack-like defect. At the next stage, which lastsΔt II * , the crack grows to a critical size. Thus, the blade total life is given by a sum of the basic life t * , which is represented by a time period to the formation of a continuum fracture zone, and the additional life Δ Δ t t I I I * * + that depends on the propagation of the continuum fracture zone to form a crack-like defect and subsequent growth of the main crack. The values of t * and Δt I * are calculated using the relations of the continuum fracture mechanics. Determination of the additional life Δt II * calls for the relations of the discrete fracture mechanics -the crack mechanics. The investigations for this type of blade [1] demonstrated that the additional resource, i.e., the time period till the formation of crack-like defect, is about 5% of the basic life. For the evaluation of the blade total life it is important to find the second component of the additional resource. Among the factors that cause a blade to fail, the cyclic loading is the main one [2]. The crack growth process under cyclic loading is most commonly described by the Paris formula [3] dl dN C K l b = ( ( )) . I (1)Considering the intricate shape of the crack front and the essentially spatial pattern of the stress-strain state (SSS), the integration of equation (1) in the majority of cases is carried out by numerical methods. Numerical solution of the life assessment problem for cracked bodies involves a discrete representation of the deformation process as a totality of steps in time or external load. At each step, we determine SSS in a cracked body, calculate parameters of the fracture mechanics and define the crack front configuration.The number of nodes of a kinked curve that models a crack front in finite-element (FE) discretization is found from the convergence conditions for the numerical solution of the SSS problem for a cracked body and the conditions for providing a required accuracy of the determination of stress intensity factors (SIF) at the crack front 518 0039-2316/08/4005-0518

We present theoretical approaches and a procedure for the FEM computation of parameters of nonlinear fracture mechanics in prismatic bodies with a crack. The efficiency of the proposed approaches and the veracity of the results obtained have been analyzed.Keywords: fracture mechanics, invariant J-integral, path of integration, finite element method, linear and nonlinear problems.The majority of problems of fracture mechanics can only be tackled using numerical methods, in particular a finite element method (FEM). The most difficult tasks in these cases are to state the problem and elaborate a procedure for solving three-dimensional problems of fracture mechanics. The efficiency of an FEM procedure for solving such problems can be improved through special FEM modifications, among which there is a semi-analytic finite element method (SA-FEM) [1,2]. The method has proved high efficient in solving a wide range of problems of determination of stress intensity factor (SIF) on the basis of a direct method under mechanical [1, 2] and thermomechanical loading conditions [3] as well as the problems of modeling a crack growth in three-dimensional bodies [4]. However, the field of applicability of direct methods the SIF values determined by such methods is limited to the problems of linear fracture mechanics to treat elastic deformation of solids. Meanwhile, considering an unambiguous relation between the J-integral and SIF in elastic deformation, the possibility of performing a parallel computation of parameters of fracture mechanics by both the direct methods and the strain-energy methods permits validation of the results obtained. In the case of significant plastic strains, the bearing capacity of cracked bodies should be assessed by the strain-energy approaches to the determination of fracture-mechanics parameters, in particular, the Cherepanov-Rice J-integral [5, 6] -the most universal parameter that can be used in nonlinear fracture problems.The objective of the present work is to provide a theory for and practically implement the procedure of computation of the contour J-integral for three-dimensional prismatic bodies using SA-FEM and to analyze the veracity of the results obtained, including satisfaction of the fundamental properties of invariance of the J-integral, as well as to compare the efficiency of the proposed procedure versus other available approaches. We also intend to implement a new J-integral calculation procedure which would ensure the integral invariance in the discrete FEM models in both linear and nonlinear three-dimensional problems of fracture mechanics.According to the basic definition of the J-integral [5,6], to calculate this integral at some point of the crack front (point C in Fig. 1) in the vicinity of this point we pick out a surface F F F F k = + + 1 2 of an arbitrary configuration, which covers the crack front and has a characteristic dimension D along the front.

No abstract