We present an efficient Monte Carlo based probabilistic fracture mechanics simulation implementation for heterogeneous high-performance (HPC) architectures including CPUs and GPUs. The specific application focuses on large heavy-duty gas turbine rotor components for the energy sector. A reliable probabilistic risk quantification requires the simulation of millions to billions of Monte Carlo (MC) samples. We apply a modified Runge-Kutta algorithm in order to solve numerically the fatigue crack growth for this large number of cracks for varying initial crack sizes, locations, material and service conditions. This compute intensive simulation has already been demonstrated to perform efficiently and scalable on parallel and distributed HPC architectures including hundreds of CPUs utilizing the Message Passing Interface (MPI) paradigm. In this work, we go a step further and include GPUs in our parallelization strategy. We develop a load distribution scheme to share one or more GPUs on compute nodes distributed over a network. We detail technical challenges and solution strategies in performing the simulations on GPUs efficiently. We show that the key computation of the modified Runge-Kutta integration step speeds up over two orders of magnitude on a typical GPU compared to a single threaded CPU. This is supported by our use of GPU textures for efficient interpolation of multi-dimensional tables utilized in the implementation. We demonstrate weak and strong scaling of our GPU implementation, i.e., that we can efficiently utilize a large number of GPUs/CPUs in order to solve for more MC samples, or reduce the computational turn-around time, respectively. On seven different GPUs spanning four generations, the presented probabilistic fracture mechanics simulation tool ProbFM achieves a speed-up ranging from 16.4x to 47.4x compared to single threaded CPU implementation.

This work presents a temperature-dependent reformulation of a multiscale fracture mechanics-informed matrix damage model previously developed by the authors. In this paper, internal state variable theory, fracture mechanics, and temperature-dependent material properties and model parameters are implemented to account for length scale-specific ceramic matrix composite (CMC) brittle matrix damage initiation and propagation behavior for temperatures ranging from room temperature (RT) to 1200°C. A unified damage internal state variable (ISV) is introduced to capture effects of matrix porosity, which occurs as a result of material diffusion around grain boundaries, as well as matrix property degradation due to matrix crack initiation and propagation. The porosity contribution to the unified damage ISV is related to the volumetric strain, and matrix cracking effects are captured using fracture mechanics and crack growth kinetics. A combination of temperature-dependent material properties and damage model parameters are included in the model to simulate effects of temperature on the deformation and damage behavior of 2D woven C/SiC CMC material systems. Model calibration is performed using experimental data from literature for plain weave C/SiC CMC at RT, 700°C, and 1200°C to determine how damage model parameters change in this temperature range. The nonlinear, temperature-dependent predictive capabilities of the reformulated model are demonstrated for 1000°C using interpolation to obtain expected damage model parameters at this temperature and the predictions are in good agreement with experimental results at 1000°C.

The Gas Turbine (GT) Axial Compressor (AXCO) can absorb up to the 30% of the power produced by the GT, being the component with the largest impact over the performances. The axial compressor blades might undergo the fouling phenomena as a consequence of the unwanted material locally accumulating during the machine operations. The presence of such polluting substances reduces the aerodynamic efficiency as well as the air intake causing the drop of performances and the increase of the fuel consumption. To address the above-mentioned critical issues, several washing strategies have been implemented so far, among the most promising ones, High Flow On-Line Water Washing (HFOLWW) is worth to mention. Exploiting this technique, the performance levels are preserved, whereas the stops for maintenance should be reduced. Nevertheless, this comes at the cost of a long-term erosion exposure caused by the impact of water washing droplets. Hence, it was deemed necessary to carry out a finite element method (FEM) structural analysis of the first rotor stage of the compressor of an aeroderivative GT, integrated into the HFOLWW scheme, in order to evaluate the fatigue strength of the component subjected to the erosion; possibly along with its acceptability limits. The first step requires the determination of the blade areas affected by erosion, using computational fluid dynamics (CFD) simulations, followed by the creation and the 3D modelling of the damaged geometry. The final step consists in the evaluation of the static stress and the dynamic agents, to perform a fatigue analysis through the Goodman relation and carrying out a simulation of damage propagation exploiting the theory of fracture mechanics. This procedure has been extended to the damage-free baseline component to set-up a model suitable for comparison. The structural analysis confirms the design of the blade, moreover dynamic and static evaluation of the eroded profiles haven’t outlined any working, nor mechanical, issue. This entitles the structural choice of HFOLWW as a system which guarantees full performance levels of the compressor.

Large gas turbine design and service business are challenged with increased demands towards flexible operations, increasing number of start-stop cycles and intermediate cycles. Probabilistic fracture mechanics (PFM) simulation design tools have matured and became robust and reliable. We present a probabilistic re-evaluation of Siemens E-class turbine disks by the combination of probabilistic two-dimensional axisymmetric part analysis of the disk and a novel probabilistic approach for the three-dimensional blade attachment. The first addresses the risk of inherent forging flaws, the latter combines the risk of surface crack initiation, growth and failure. Both models consider the heterogeneous nature of material properties, flaw geometries and detectability. These novel concepts developed at Siemens allow for an optimization of resource usage and safety, as well as the development of new service and inspection concepts for a variety of service frames and classes.

Prediction of fatigue life based on internal defect data is an important research topic for components built through both traditional welds and modern additive manufacturing. In this work, a systematic approach is taken to investigate application of fracture mechanics principle for this purpose. To this end, fatigue test samples are prepared from TIG-welded titanium alloy sheets and also representative weld repairs of cast plates. Metro-tomography is employed to obtain information about internal defects in the specimens before fatigue testing. After fatigue testing, fractography is used to identify the defect that led to failure and to gather information on its location and size. The information from metro-tomography and fractography are then directly compared to assess the accuracy of the tomography data. Simple fracture mechanics methods are employed to estimate the fatigue life for each specimen, considering separately tomography and fractography data. Such estimates are then compared with fatigue life from tests. Through such quantitative comparisons, the work highlights the advantages and the challenges of the fracture mechanics approach to assess the fatigue life of test specimens with internal defects. A key observation is that life estimates employing a fracture mechanics approach are reasonable when the defect leading to failure is known, but the challenge may lie in a-priori identification of the defect that would eventually lead to failure.

Large gas turbine nickel based superalloys blades are typically manufactured using an investment casting process. In spite of superior processing and quality control, large turbine blades may contain manufacturing induced discontinuities such as porosities, segregation, chemical inhomogeneities, particles, etc in few of the manufactured parts. These manufacturing discontinuities can significantly influence the reliable component life if they are under a load condition where they will form a crack. A typical engineering approach is to treat these discontinuities as a crack from the beginning of the part life. This leads to a conservative life prediction, as crack nucleation and influencing geometrical details of the discontinuities are neglected. This paper presents a framework and path forward for a comprehensive life assessment. It includes computer tomography (CT) analysis, metallographic analysis, local stress analysis, crack formation, as well as state of the art fracture mechanics analysis. For instance, CT and destructive tests reveal details of the geometry of a porous region and thereby enabling the calculation of crack formation life. A subsequent fracture mechanics analysis by engineering tool, FRANC3D can then yield a comprehensive life assessment for comparisons to experimental findings and fleet experience. This approach enables Siemens to diligently ensure that comprehensive life predication assessment has been performed for the components for robust and reliable operation.

We present a probabilistic rotor life prediction framework that combines the forging flaw crack nucleation process and the subsequent crack growth to failure. Experimental fatigue tests of specimens including forging flaws show that the life cycle of a forging flaw can be described by a nucleation phase followed by a fatigue crack growth phase. These results demonstrate that the nucleation phase is a significant fraction of the whole life cycle to failure. However, as there is no engineering method available that describes reliably the nucleation phase, this portion is oftentimes neglected in engineering life prediction frameworks, therefore resulting in a conservative life quantification. In order to improve probabilistic life quantification methods, we introduce a rigorous scheme that convolutes the local crack nucleation probabilities and the local crack growth failure probabilities in order to provide a local failure probability. Integration over the whole component then yields the total probability of failure for the engineering part under a specific load spectrum. A specific direct simulation Monte Carlo numerical implementation is demonstrated. It is applied to fatigue crack nucleation from large gas turbine rotor disk forging flaws followed by crack growth to component failure. For different regions of the analyzed rotor components, the results show the probabilistic interplay of the different temperature and stress dependences of the applied empirical nucleation models and the fatigue crack growth models. The presented probabilistic approach is generic and not restricted to the discussed fatigue nucleation and subsequent crack growth process in large rotor forgings. The framework can be applied to a variety of sequential failure processes including static and fatigue loading phenomena, as well as a multiplicity of failure modes and sequences relevant for engineering components.

The increased installation of renewable energy resources results in a requirement for higher steam turbine cycling capabilities. In addition, there is a strong demand to save our environment by improved efficiency, as well as acceptable life-cycle costs whilst keeping a high level of reliability and availability. Optimization using state of the art deterministic methods for dimensioning of components is the traditional way addressing such challenges. The use of more advanced methods like fracture mechanics, assisted by probabilistic design are innovative alternatives that have been pushed significantly in recent years. However, to fully exploit the latest developments of advanced engineering methods, acceptance criteria are essential. Due to the lack of specific steam-turbine standards for several calculation tasks, today acceptance criteria are often based on OEM internal standards and are part of the specific OEM know-how. New methods require the definition or modification of existing acceptance criteria. In case of lack of acceptance criteria one option is to refer to available standards for industries dealing with comparable components, materials and loading conditions. An example is the adaption of acceptance criteria from pressure-vessel codes for high-pressure steam turbine components. The obvious advantage is the ease of use, but the drawback might be an unnecessary conservatism in the design. Another option is the development of acceptance criteria for advanced methods. The main intent of the paper is to contribute to the discussion of acceptance criteria for the application of advanced design methods for steam turbine components. A selected steam-turbine example is discussed, acceptance criteria are compared with available standards and the need for the development of component specific criteria are highlighted.

In this paper, the thermomechanical fatigue (TMF) of fiber-reinforced ceramic-matrix composites (CMCs) is investigated using the hysteresis-based damage parameter. The micro stress field of the damaged CMCs of matrix cracking and fiber/matrix interface debonding is obtained considering the temperature-dependent fiber/matrix interface shear stress. The fiber/matrix interface debonded length and unloading/reloading slip length are determined using the fracture mechanics approach. Based on the damage mechanisms of fiber sliding relative to the matrix in the interface debonded region, the TMF hysteresis loops models and hysteresis-based damage parameters are developed for the partially and completely debonding to analyze the damage evolution inside of fiber-reinforced CMCs. The effects of temperature, phase angle and loading sequences on the damage development of SiC/SiC composite are discussed. When TMF temperature range increases, the fatigue hysteresis loops area, residual strain increase, and the hysteresis modulus decreases, due to the increase of the fiber/matrix interface slip length. Under TMF loading, the phase angle affects the interface debonding and sliding range, and the hysteresis loops shape, location and area of the fiber-reinforced CMCs. The experimental TMF damage evolution of 2D SiC/SiC and cross-ply SiC/MAS composites are predicted.

Fatigue life assessment of turbine rotating components is usually performed taking into account the presence of potential defects and their propagation, together with an accurate description of the stress/strain fields acting at components critical regions. In this work, such an approach was applied on a radial outflow turbine: the component investigated in this paper is the tie-rod. An axisymmetric FEM model of the whole turbine was implemented to evaluate the stress field acting at the root of tie-rod thread, the component most critical region. Three different preload procedures were investigated, in order to evaluate the effects of plastic strains on fatigue cycles. It was found that an initial overtightening, performed before machine assembly, induces a larger plastic zone at the root of the thread, which lowers the peak stress and lessens the stress ratio of the fatigue cycle. Stress gradients for the three different preloading conditions were the starting point of a crack propagation model, which calculated crack advancement as a function of service time. The model, which considered crack closure and stress ratio effects, allowed structural integrity assessment and showed that the initial overtightening had also the effect of crack growth rates reduction.

During rapid engine throttling operations, turbine airfoils can experience very rapid heating and cooling, particularly at take-off conditions. These rapid transient events lead to the generation of high thermal gradients and non-uniform stress distributions through the thermal barrier coating, environmental barrier/bond coating and substrate. This in turn can lead to coating delamination, overheat of the substrate materials, creep and thermo-mechanical fatigue of the part. We present the process and computer modeling methodology for a physics-based prediction of deformation, damage, crack propagation and local failure modes in coated turbine airfoils and other parts operating at hot section turbine environment conditions as a function of engine operational regimes, with a particular emphasis on rapid transient events. The overall goal is to predict the effects and severity of the cooling and heating thermal rates on transient thermal mechanical fatigue life of coated hot parts (turbine airfoils, blade outer air seals and combustor liners). The computational analysis incorporates time-accurate, coupled aerothermodynamics with non-linear deformation thermal-structural finite element modeling and fracture mechanics modeling for high rate thermal transient events. Thermal barrier coating thermal failure and spallation are introduced by the use of interface fracture toughness and interface property evolution as well as dissipated energy rate. The spallation model allows estimations of the part remaining life as a function of the heating/cooling rates. Applicability of the developed model is verified using experimental coupons and calibrated against burner rig test data for high flux thermal cycles. Our results show a decrease in TBC spall life due to high rate transient events.

In the development of heavy duty gas turbines for the energy sector oftentimes the majority of the design work is performed in either the 50 Hz or the 60 Hz size. Many aspects of the designed engine for one market (50 Hz as an example) can then be used to design with significantly reduced effort for the other market (i.e. 60 Hz). For example, most dimensions of rotor components can be geometrically scaled such that centrifugal forces in those massively rotating parts are conserved. This article investigates the transferability of probabilistic fracture mechanics results from one market to the other one. Or in other words: can we perform probabilistic fracture mechanics for the 50 Hz rotor design and deduce the risk of failure for the scaled 60 Hz design (or vice versa)? Multiple challenges must be considered in the transferability including the different volume, surface to volume ratio, as well as the different transient behavior for the smaller 60 Hz design. We address that challenge by building up complexity for a generic rotor design in order to separate the different effects and associated design features. We then discuss several Siemens rotor designs with respect to transferability of probabilistic fracture mechanics results and correlations to deterministic approaches. This work enables the creation of design rules to avoid unnecessary work for scaled 50 Hz/60 Hz market engines and therefore supports the reduction of product development costs.

High velocity oxygen fuel (HVOF) sprayed stellite coating is often adopted on contact surfaces of the shrouds and stubs of titanium turbine blades, in order to increase fretting fatigue strength and reduce fretting wear. To confirm the effectiveness of the sprayed stellite coating, we conducted friction-type fretting tests originally developed to simulate the load condition of shrouds and stubs, vibratory force was carried only by friction force. We also investigated the fretting fatigue mechanism of coated materials by observing non-propagating cracks in the tested specimens and analyzed crack propagation behavior at the interface using fracture mechanics. The fretting fatigue tests confirmed that the sprayed stellite coating could double the fretting fatigue strength of Ti-6A1-4V. The fretting fatigue mechanism of Ti-6A1-4V with a sprayed stellite coating was revealed as follows: Final fracture was led by a newly initiated micro-crack at the interface as cracks initiated on the coating surface did not continuously propagate into the substrate but mainly propagated along the interface. The micro-crack propagation at the substrate depends on the length of interface crack. The longer interface crack delays micro-crack propagation to the substrate because the lines of force are less concentrated at the crack tip. Hence, the interface crack makes the fretting fatigue strength of coated Ti-6A1-4V higher than that of uncoated specimens. This finding was supported by the cross-sectional observations of non-propagating cracks in the tested specimens, and by FE analysis which revealed that Δ K of the substrate crack initiated at the interface decreases with an increase in delaminated crack length. Ti-6A1-4V with a sprayed stellite coating offers better wear resistance than uncoated Ti-6A1-4V because the coating’s friction coefficient is lower than that of Ti-6Al-4V, although the wear rates of coated and uncoated materials against the consumption energy per cycle were almost the same.

In 2013, with the operation of 1000MW steam turbine unit in a power plant, the exhaust steam temperature of intermediate pressure (IP) steam turbine exceeded the normal value. After overhaul of the IP steam turbine, a long crack was found through the drain hole of the IP inlet diffuser. The reheat steam leaked out from inside the diffuser to the exhaust cavity. It caused the exhaust temperature to exceed the design value, and reduced the efficiency of the units. Also, if the high temperature steam, which is close to 600°C, came into contact with the outer casing, a significant reduction in life would be obtained. In order to find the root cause of the crack, many efforts have been done within each department of the shanghai turbine plant (STP). Such as material detection, design, manufacture, assembling, etc. In this paper, a three-dimensional finite element diffuser model was built and the stress state during startup and operation was obtain. It was found that the drain hole at the inside and the groove at the outside of the diffuser are dangerous regions because of the stress concentration. That’s the primary reason for causing the diffuser crack. Then the fracture mechanics software ZenCrack was used to analyze the diffuser crack route. This crack route consistently matched the actual diffuser crack.

Fracture mechanics analysis is essential for demonstrating structural integrity of gas turbine components. Usually, analyses based on simpler 2D stress intensity solutions provide reasonable approximations of crack growth. However, in some cases, simpler 2D solutions are too-conservative and does not provide realistic crack growth predictions; often due to its inability to account for actual 3D geometry, and complex thermal-mechanical stress fields. In such cases, 3D fracture mechanics analysis provides extra fidelity to crack growth predictions due to increased accuracy of the stress intensity factor calculations. Improved fidelity often leads to benefits for gas turbine components by reducing design margins, improving engine efficiency, and decreasing life cycle costs. In this paper, the application of 3D fracture mechanics analysis on a gas turbine blade for predicting crack arrest is presented. A comparison of stress intensity factor values from 3D and 2D analysis is also shown. The 3D crack growth analysis was performed by using FRANC3D in conjunction with ANSYS.

We developed and successfully applied a direct simulation Monte-Carlo scheme to quantify the risk of fracture for heavy duty rotors commonly used in the energy sector. The developed Probabilistic Fracture Mechanics high-performance computing methodology and code ProbFM routinely assesses relevant modes of operation for a component by performing billions of individual fracture mechanics simulations. The methodology can be used for new design and life-optimization of components, as well as for the risk of failure quantification of in service rotors and their re-qualifications in conjunction with non-destructive examination techniques, such as ultrasonic testing. The developed probabilistic scheme integrates material data, ultra-sonic testing information, duty-cycle data, and finite element analysis in order to determine the risk of failure. The methodology provides an integrative and robust measure of the fitness for service and allows for a save and reliable operation management of heavy duty rotating equipment.

U.S. Department of Energy (DOE) has recently sponsored research programs to develop Megawatt scale supercritical CO2 (sCO2) turbine for use in concentrated solar power (CSP) and fossil based applications. From rotordynamics perspective, the extremely high power densities associated with this sCO2 turbine (similar to those of rocket turbo pump) and the long shaft of the turbine require mid-span support from bearings to achieve the high rotational speeds needed to achieve desired turbine efficiency targets. The mid-span bearings, if oil lubricated, need two sets of seals to isolate the working fluid from lubricating oil and represent a combined parasitic load of as much as 5% of the power plant output. These parasitic loads can be avoided by the use of hybrid gas bearing (HGB) which uses turbine working fluid itself as the lubricant for generating hydrostatic + hydrodynamic pressure and hence can operate in a high temperature, high pressure sCO2 environment. A successful and reliable implementation of HGB is expected to provide significant efficiency improvement in the sCO2 turbine for modular plants in 10MW scale. However, the behavior of hybrid gas bearing with supercritical CO2 as the working fluid has never been studied before. Hence a careful investigation of its hydrodynamic and rotordynamic characteristics with perturbations associated with sCO2 fluid and sCO2 turbine is warranted. In this paper the use of HGB to bring the critical speed ratio of highly power dense 10 MW sCO2 turbine into a manageable regime is investigated. Further, the performance characteristics of HGB in high pressure, high temperature sCO2 are investigated with a coupled fluid-structure interaction model. Differences between load capacity and stiffness characteristics for traditional operation in air versus operation in highly dense and viscous sCO2 are highlighted. Using Bayesian probabilistic models, insights into key design parameters needed to optimize HGB performance are obtained. A 3D fracture mechanics and crack propagation model is also developed to predict life of HGB under typical sCO2 turbine mission cycle for CSP application.

Materials engineering and damage tolerance assessment have traditionally been performed as disjoint processes involving repeated tests that can ultimately prolong the time required for certification of new materials. Computational advances have been made both in the prediction of material properties and probabilistic damage tolerance analysis, but have been pursued primarily as independent efforts. Integrated computational materials engineering (ICME) has the potential to significantly reduce the time required for development and insertion of new materials in the gas turbine industry. A manufacturing process software tool called DEFORM™ has been linked with a probabilistic damage tolerance analysis (PDTA) software tool called DARWIN ® to form a new capability for ICME of gas turbine engine components. DEFORM simulates rotor manufacturing processes including forging, heat treating, and machining to compute residual stress and strain, track anomaly location, and predict microstructure including grain size and orientation. DARWIN integrates finite element stress analysis results, fracture mechanics models, material anomaly data, probability of anomaly detection, and inspection schedules to compute the probability of fracture of a gas turbine engine rotor as a function of operating cycles. Previous papers have focused on probabilistic modeling of residual stresses in DARWIN based on manufacturing process training data from DEFORM. This paper describes recent efforts to extend the probabilistic link between DEFORM and DARWIN to enable modeling of residual strain, average grain size, and ALA (unrecrystalized) grain size as random variables. Gaussian Process modeling is used to estimate the relationship among model responses and material processing parameters. These random variables are applied to microstructure-based fatigue crack nucleation and growth models for use in probabilistic risk assessments. The integrated DARWIN-DEFORM capability is demonstrated for a representative engine disk model which illustrates the influences of manufacturing-induced random variables on component fracture risk. The results provide critical insight regarding the potential benefits of integrating probabilistic computational material processing models with probabilistic damage tolerance-based risk assessment.

The demand for higher plant cycling operation and reduced life-cycle costs are the main drivers for the design and assessment of turbine components today. Heavy cyclic loading increases the potential of fully utilizing the fatigue capabilities of the material which might lead to crack initiation and subsequent crack propagation. Fracture mechanics methods and evaluation concepts are widely applied to assess the integrity of components with defects or crack-like findings. The realistic modelling of the failure mechanism plays a key role for the accurate prediction of crack sizes at failure state. A basic treatment of material toughness typically leads to conservative assessments for components with sufficient ductility. A standard approach to describe material behavior with high ductility is to use the start of stable crack extension as a dimensioning parameter for the analysis. By definition a critical condition for a component is reached when the crack driving force is equal to the characteristic material parameter. On the other hand, advanced analysis methods allow determination of the instability point (ductile tearing analysis). This paper will discuss two cases for practical analysis from steam turbine design showing clear advantages for service application by using advanced analysis methods.

Heavy duty gas turbine blades and vanes are operated at high temperatures and high stresses, condition where several damage mechanisms can simultaneously be present. For example creep, fatigue and oxidation play an important role in the propagation of existing cracks. Crack growth models are employed for assessment criteria, interpretation of the field feedback and non-conformities management and they are required to be as accurate as possible when predicting crack propagation under the combined effect of all the three phenomena. In this work, a Linear Elastic Fracture Mechanics (LEFM) model based on isothermal experimental tests and validated by Thermo-Mechanical-Fatigue Crack Growth tests (TMFCG), is employed to predict crack propagation of a cast Ni-base superalloy used in gas turbine blades and vanes. When calculating the individual propagation fractions of creep and fatigue crack growth, the model accounts for the instantaneous stress state and temperature in transient regime (i.e. a complete cycle of start-up, base-load and shut-down). The loss of γ’- precipitates at the crack tip due to surface oxidation is interpreted as environmental damage fraction. A complete workflow for the systematic use of the approach, comprising an in-house software, has been defined and developed. Stress intensity factors used for LEFM calculations are determined either using tabulated weight functions or with the aid of Finite Element Analysis (FEA). This flexible approach is consistent with the industrial need of a given fracture mechanics calculation, which might require different levels of accuracy and resources/time consumption case by case. The software identifies the fraction of propagation caused by oxidation, creep crack growth or fatigue crack growth. This allows checking the physical realism of the results by comparing to metallographic analysis of fracture surfaces from broken TMFCG test specimen and/or real component damage information from field. Besides, this feature can be helpful to support the engineer in residual life evaluation under damage tolerant approach because it allows the identification of the type of operational regime that minimizes crack propagation. The software also allows the execution of sensitivity analyses via Monte-Carlo calculations, identifying for a given component and operational condition the more relevant calculation inputs. This feature also quantitatively supports the engineers in the identification of the most appropriate safety margins.