Fatigue Crack Growth by FEM-DBEM Approach in a Steam Turbine Blade

This study is concerned with the integrity assessment of cracked steam turbine rotor components, made of steel X20Cr13, that operate under cyclic loading. Damage accumulation and growth occurred on the leading edge of turbine blade starting from part-through surface flaws. Tensile tests are performed for assessment of the main mechanical and fracture steel properties: specimens are cut out from critical zones of turbine blade body after a given operating time. The subject for experimental studies is a steel bar of circular cross-section with straight-fronted edge crack. The optical microscope measurement and the COD method are used to monitor crack growth during the tests. An automatic crack propagation simulation on the blade is performed by a coupled approach which, starting from the results of a global finite element method (FEM) analysis, proceeds through the sub modelling of the cracked volume in a DBEM dual boundary element method (DBEM) environment and subsequent propagation analysis. displacement (COD) method [8-11]. Residual fatigue life of turbine blades could be predicted with reasonable accuracy from knowledge of 3D stress-strain state, SIFs, fracture resistance material properties and in correspondence of different types of operation loadings. In operation, the analysed blades experiences two main types of damage: the first is the erosive and corrosive pitting, with an initial flaw size approximately equal to 0.5 mm; the second is a welding defect introduced during the protective coating application, on the leading edge of the blade, with an initial flaw size approximately equal to 1.5 mm. The former kind of defect is modelled in this work. Critical crack lengths discovered on in service blades were varying from 28 to 32 mm. The analysed blades belongs to the 27th stage of a 200 MW power steam turbine with operation time t=92245 hours. Fatigue failures of blades in rotating turbine disk were detected in service. Their fracture was the result of fatigue crack initiation and propagation up to the formation of a critical crack. In all of these failures, crack propagation started from leading edge as a part-through surface flaw (Figure 1) produced by erosive and corrosive pitting. Experimental Tests Tensile tests were performed for determination of the main mechanical properties of blade materials. Smooth and notched specimens were cut out from critical zones of turbine blade body with given operating time in order to allow for degradation of mechanical properties such as strength and ductility. The material analysed by experimental tests is a steel X20Cr13 bar of circular cross-section with Industrial Engineering & Management I n d u s tri al En gin eering &Mnagem e n t


Introduction
Most components in power plant such as turbine rotors have been in service for more than 20 or even 30 years, which is much longer than their design life of 105 h. Now the power steam turbine elements at heat-power engineering enterprises have exhausted their life span or come closer to their limiting values so that a large and growing portion of electricity is produced by ageing thermal power plants.
Turbine disk and blades are subjected to cyclic loading and the structural integrity assessment of these components, with particular reference to remaining life prediction, are increasingly required to guarantee the safe and economic running of power plant engineering components. Extending the life of steam turbines and ensuring high reliability requires life assessment technology, scheduled repairing, modification and upgrading of components in order to provide a stable power supply.
In this paper, we are interested in low-pressure power steam turbine, experiencing in service fatigue failures due to damage accumulation and growth.
Although high quality materials are used for the steam turbines, various forms of metallurgical degradation, like creep and fatigue, affect the parts and components during long-time operation at medium-high temperature.
There are several kinds of examination methods for damage assessment of steam turbines: destructive methods, non-destructive methods and numerical modelling, but they are not always effective and accurate. In order to predict the residual fatigue life of turbine blades, it is necessary to carry out fatigue life and fracture resistance assessment of given material with allowance for the operating time.
This study is concerned with assessment of damage accumulation and growth occurred on the leading edge of a turbine blade, with the crack propagation starting from part-through surface flaws.
A combined FEM-DBEM approach is adopted to calculate the fracture mechanics parameters useful to assess crack growth rates and lifetime of such turbine blades. In particular, the stress analysis on the global model is performed by FEM [1][2][3] whereas the crack propagation phase is simulated by DBEM [4][5][6][7], with the stress intensity factors (SIFs) values along the crack front calculated using the crack opening displacement (COD) method [8][9][10][11].
Residual fatigue life of turbine blades could be predicted with reasonable accuracy from knowledge of 3D stress-strain state, SIFs, fracture resistance material properties and in correspondence of different types of operation loadings.
In operation, the analysed blades experiences two main types of damage: the first is the erosive and corrosive pitting, with an initial flaw size approximately equal to 0.5 mm; the second is a welding defect introduced during the protective coating application, on the leading edge of the blade, with an initial flaw size approximately equal to 1.5 mm. The former kind of defect is modelled in this work.
Critical crack lengths discovered on in service blades were varying from 28 to 32 mm.
The analysed blades belongs to the 27 th stage of a 200 MW power steam turbine with operation time t=92245 hours. Fatigue failures of blades in rotating turbine disk were detected in service. Their fracture was the result of fatigue crack initiation and propagation up to the formation of a critical crack. In all of these failures, crack propagation started from leading edge as a part-through surface flaw ( Figure 1) produced by erosive and corrosive pitting.

Experimental Tests
Tensile tests were performed for determination of the main mechanical properties of blade materials. Smooth and notched specimens were cut out from critical zones of turbine blade body with given operating time in order to allow for degradation of mechanical properties such as strength and ductility. The material analysed by experimental tests is a steel X20Cr13 bar of circular cross-section with The optical microscope measurement and the COD (crack opening displacement) method are used to monitor and calculate both crack depth and superficial crack length during the tests. The validity of effective crack length approximation, estimated by continuous measurements of COD data for each fatigue crack path under cyclic loading, is considered.
Growth rate tests were performed with an harmonic test-cycle and as a result, the Paris law calibration was obtained.
In order to determine the influence of operating time on the main mechanical properties of blade material, smooth specimens were cut out from the considered turbine blades.
Experimental study of the material mechanical properties was performed on the uniaxial 25 kN servo-hydraulic tension test machine at room temperature. As a result, the material mechanical property changes were determined as a function of the operating time.
The reference mechanical properties of the blade material with zero operating time and main mechanical properties obtained from tensile tests are listed in Table 1.
Variable amplitude or block tests were realized by repeatedly applying the same loading history on a servo-hydraulic push-pull testing machine with frequency 10 Hz.

Load sequence
The load sequence used for the fatigue tests on simple specimens has been defined in such a way to be representative of the load history of turbine disk at operation.
It is found that in service, during one year, variable-amplitude fatigue cycles may be approximately clustered in four constant amplitude blocks (Table 2 and Figure 2). The load changes showed in Figure 3 mainly originates from fluid pressure fluctuations but, due to confidential reasons, the real values of stress ratio R in each stage were not disclosed so for experiments and calculation a common (to all stages) value R=0.1 was adopted.
For comparison purposes, fatigue tests were divided into three parts: • constant amplitude (harmonic) loading; • variable amplitude loading (block loading when the load history includes four stages on each block); • spectrum loading with random sequence of the block stages.
The three tests were conducted on a steel bar of circular crosssection with straight-fronted edge notch (Figures 3a and 3b), with load levels such as to cover the crack growth rate range 10 -8 -10 -6 m/cycle. Table 2 gives the max nominal stress and number of cycles per sequence. Each loading history includes N=198 170 cycles and it is repeated iteratively up to failure.
The random sequence was applied by the testing machine by recalling to a random number generator technique. The algorithm for the generation of the signal is such that the same sequence can be     reproduced as many times as desired. Thus the sequence of N=198 170 cycles can be considered as representative of one year operating time for crack growth analysis purpose. Maximum five sequences of about 10 6 cycles were realized using round bar specimens under pure tension.

Crack size assessment procedure
Crack growth assessment was performed for the round bar specimens with the straight-fronted edge notch with initial depth h 0 =0.5 mm [12]. The geometric parameters of specimen test section and growing crack are shown in Figures 3a and 3b. In this Figure 3b is the current crack depth, with the crack front approximated by an elliptical curve with major axis 2c and minor axis 2b. The depth of the initial straight edge notch is denoted by h and the initial notch length by L.
All cylindrical specimens were tested under uniaxial loading with the same stress ratio R=0.1. The tests were carried out under load control and sinusoidal loading form. The crack opening displacements were measured on the free surface of cylindrical specimen by using COD gauge, in the central plane of symmetry as shown in Figure 3b. Thus, the growth rate of the semi-elliptical-fronted edge crack during the fatigue tests was determined using COD measurements and experimental data obtained by using optical microscope. The measured data are reported on a diagram with crack length in the deepest point b of the crack front versus accumulated number of cycles N. To this end the following approximate equations were used, where b/D and c/D are the dimensionless crack depth and crack chord respectively: -random loading.

Results
In Figures 4a and 4b experimental relations between crack opening displacements and crack length on the free surface or cycles are presented; the crack growth curves are obtained under three different test conditions: constant amplitude, variable amplitude and random loading. It is found that the crack growth rates along the external surface direction are similar for different loading conditions.
On the base of this experimental data, polynomial functions were calibrated to express COD as a function of the superficial crack length. Figure 5b shows that variable amplitude cyclic loading leads to an increase of the total fatigue life with respect to constant amplitude cyclic loading.
It is well known that total fatigue life can be divided into two stages -crack initiation and growth, therefore, looking at the second stage in Figure 4b and considering the changes in the general durability of the specimens undergoing pure harmonic rather than variable-amplitude loading, significant differences in the crack growth rate in the depth direction b under the above types of loading conditions are expected.
where C and m are the experimental parameters of the fatigue fracture diagrams that characterize the material resistance to crack growth under cyclic loading.
The results from block loading are compared with those from constant amplitude cycles in terms of varying Paris law calibration (Table 3): this table shows the experimental values of the constants of Eqn. 1 for the cylindrical specimens with initial crack depth equal to 0.5 mm, tested under different loading history. The results of Table 3 indicate that the constant C and m do not coincide with each other for constant and variable amplitude loading. From this table, it appears that, as expected, loading history affects crack growth rate.

FEM analysis
The crack propagation simulation is performed by using a combined approach that, starting from the results of a global FEM analysis applied to a whole blade sector (ANSYS code is adopted [13]), proceeds through the submodelling of the cracked volume in a DBEM environment (BEASY code is adopted [14]) and subsequent automatic crack propagation.
In this work, a FEM elastic-plastic stress analysis was performed for a turbine disk with blades undergoing operating loading conditions. In Figures 6a and 6b the FE model related to a segment of the turbine rotor, including disk, blades and rivets, is showed. In Figure 6c the contour plot of Von Mises stresses points out the most stressed areas, on the leading edge at the blade root as a consequence of the main centrifugal load; such resultant stress state is related to the 27 th stage of turbine rotor undergoing operative regime loading conditions. A picture of a single blade is showed in Figures 6d and 6e.
In operation, turbine disk and blades are subjected to inertia loading caused by rotation of the turbine rotor and stresses due to thermal gradients. Surface-to-surface contact finite elements were used at the contact surfaces between blades, rivets and disk. Bending moment induced by steam pressure was neglected as the value of the bending stresses represent only 0.15% of the stress caused by the inertia loading. The elastic-plastic material behavior was described by a bilinear kinematic hardening model.

DBEM analyses
From Figure 7 it is possible to see the position and geometry of the initial crack to be introduced in the DBEM submodel (Figure 8a) that is extracted from the global blade FEM model by a skinning procedure [15][16]. In Figures 8b-8d the Von Mises stresses on the cracked plate subdomain are showed on the deformed plot: it is clear the blade bending and the typical stress gradients at the crack tips.
Then the Paris law (this time ∆K rather than K max is adopted with consistent variation of the C value): with the C and m constants provided by a calibration based on constant amplitude tests on the simple specimens (Table 3) and consistent with crack growth rates expressed by m/cycle and K values by Pa × m 0.5 .
The results referred to the surface point A were used because more reliable (the point A advance is directly measured whereas the point B position is reconstructed with a consequent loss of accuracy). SIFs are calculated by the Crack Opening Displacement method because the J-integral approach [17][18] in BEASY code is disabled when centrifugal loads are present.
After 30 steps of crack propagation, using a stress ratio R=0, with a variable average advance in each step (0.2 mm at the beginning and 0.5 mm in the final stage of crack propagation) an unstable condition is reached based on the conservative value of fracture toughness equal to 80 MPa × m 0.5 (Figures 9a and 9b): the propagation proceeds under pure mode I conditions and that is the reason for only showing the graph with just K I values ( Figure 10). The latter graph shows some irregular fluctuation of K I values in those parts of crack front close  to breakthrough points: this is normal when using COD for SIFs assessment because such technique is highly sensitive to mesh "quality" along the crack front (e.g. quadrilateral elements are better conditioned than triangular…).
In Figure 11 the crack depth vs. Number of cycles is plotted: it clearly shows the sharp acceleration in crack advance in the final stage, when approaching the instability condition.

Conclusions
In this paper full range of fatigue and fracture resistance characteristics of the turbine blade material was obtained with allowance for the operating time and the accumulated damages. Numerical and experimental results provide the opportunity to predict the residual fatigue life of the power steam turbine blades. The real operational load spectrum acting on the blade was not available so in this work simple switch on/off cycles were considered for the simulation.
It can be emphasized the reduced calculation times of the FEM approach, in comparison with the DBEM approach, the latter providing relevant advantages in the preprocessing phase because the crack insertion and the whole crack propagation is fully automatic, with repeated remeshing realized at each crack step nearly without user intervention.
For the cases analyzed, the functionality of the proposed procedure can be stated.