Elastic-plastic Finite Element Analysis Research Articles

Probabilistic Modeling Geometric Tolerance and Low Cycle Fatigue Life of Gas Turbine Compressor Blade

Abstract This paper presents a probabilistic low cycle fatigue (LCF) assessment for geometric tolerances on high load contact surfaces of gas turbine compressor blades. The typical patterns of the geometric deviations for the root contact flank of the compressor blades are identified and characterized according to coordinate measurement machine (CMM) measurements of the blade root. These typical patterns are closely related to the root form manufacture tools and process. Finite element (FE) models for the typical geometric deviation patterns are created based on nodal coordinates transformation of the surface nodes on the blade root contact flanks and radius. An optimized blade root profile tolerance is established, which enables significant cost saving. The elastic-plastic FE analysis with nonlinear contact model, material strain-life test, response surface, and constrained Monte Carlo simulation are used to create a probabilistic LCF life model for the optimized tolerance. The model quantifies the effect of the geometric deviations, blade mass, and material property on the blade LCF life. The result shows that with the optimized tolerance, the probability of blade LCF failure is very low and acceptable. It is also shown that the strain life material property is the most critical factor for the LCF failure. The root profile tolerance and blade mass are seen to have a much weaker effect on the blade LCF life.

Detectability of residual stress anomalies in railway wheels with different geometries subjected to thermal overload based on back gauge change

Temperature increases of railway wheels due to frictional braking on the running surface (wheel tread) can lead to maintenance challenges such as tread wear and thermal cracking. While heating within the anticipated design range should not adversely affect the structural safety of the wheels, excessive temperature rises resulting from brake system failures can induce tensile residual stresses in the rim, potentially leading to wheel fracture. Detecting wheels with abnormal residual stresses is therefore crucial for railway safety, and monitoring residual displacements in the rim due to changes in circumferential residual stresses is an implementable approach. However, the shape of the wheel web varies, and the displacement response to thermal input differs depending on the wheel geometries. This study aims to explore general deformation behaviours related to wheel shape and elucidate the relationship between shape and heat resistance. The elastic-plastic finite element analysis employing simplified intense thermal input revealed that residual deformation after excessive thermal loading consistently results in back gauge expansion, although the deformation and stress responses differ based on the web geometry. Differences in heat resistance are indicated by the variation in the temperature at which compressive yielding due to thermal stress occurs, depending on the web shape. The residual stress detectability of each wheel is determined based on the principle that greater residual displacement at lower stress indicates higher anomaly detectability.

Influence of welding sequences and boundary conditions on residual stress and residual deformation in DH36 steel T-joint fillet welds

This paper aims to investigate the influence of welding sequences and boundary conditions on welding-induced residual stress and residual deformation of DH36 steel T-joint fillet welds through experimental and numerical methods. A series of typical experiments of successive and simultaneous double-sided welding conditions are conducted to explore both the magnitude and distribution of temperature field, residual stress and residual deformation. Meanwhile, thermal elastic-plastic finite element analysis based on a double ellipsoidal heat source model is performed to investigate the heat transfer and deformation mechanism during the welding process. The influencing factors are further explored to determine and quantify the residual stress and residual deformation induced by different welding sequences and boundary conditions. There is generally well agreement between the experimental and numerical results in terms of temperature field, residual stress, residual deformation and molten pool morphology. The results show that the welding sequences have an important influence on the magnitude and distribution of residual stress and residual deformation. Continuous simultaneous double-sided welding can significantly reduce residual stress and residual deformation to obtain better-quality welds. Boundary conditions have a significant effect on the distribution and magnitude of residual deformation and little effects on residual stress. Tightening the ends of the flange plate with bolts during the welding process can significantly reduce the deformation.

Local relaxation of residual stress in high-strength steel welded joints treated by HFMI

This research studies the influence of high-peak loads on local relaxation of residual stress and fatigue damage in high-strength steel welded joints treated by high-frequency mechanical impact (HFMI) treatment. The joint behavior is simulated with elastic–plastic finite element analyses that account for the combined effect of geometry, residual stress, and material properties. This simulation uses two treated geometry models: with or without surface roughness on HFMI groove, and two material properties: S690QL and AH36 structural steels. The results show that surface roughness and load history, including high-peak loads, significantly influence fatigue response. It is revealed that the model neglecting the surface roughness cannot represent the amount of residual stress change and fatigue damage at less than 100 µm depth from the surface. In addition, the local yield strength in the HFMI-treated zone affects the plasticity behavior near the surface imperfection under the high-peak loads, which provides comparatively different fatigue damage between S690QL and AH36 in some cases. As a result, this study provides the further understanding needed to develop a robust modeling approach to the fatigue life estimation of HFMI-treated welds subjected to high-peak loads.

Analysis of secondary makeup characteristics of drill collar joint and prediction of downhole equivalent impact torque of Well SDTK1

Based on the three-dimensional elastic-plastic finite element analysis of the 8” (203.2 mm) drill collar joint, this paper studies the mechanical characteristics of the pin and box of NC56 drill collar joints under complex load conditions, as well as the downhole secondary makeup features, and calculates the downhole equivalent impact torque with the relative offset at the shoulder of internal and external threads. On the basis of verifying the correctness of the calculation results by using measured results in Well GT1, the prediction model of the downhole equivalent impact torque is formed and applied in the first extra-deep well with a depth over 10 000 m in China (Well SDTK1). The results indicate that under complex loads, the stress distribution in drill collar joints is uneven, with relatively higher von Mises stress at the shoulder and the threads close to the shoulder. For 203.2 mm drill collar joints pre-tightened according to the make-up torque recommended by American Petroleum Institute standards, when the downhole equivalent impact torque exceeds 65 kN·m, the preload balance of the joint is disrupted, leading to secondary make-up of the joint. As the downhole equivalent impact torque increases, the relative offset at the shoulder of internal and external threads increases. The calculation results reveal that there exists significant downhole impact torque in Well SDTK1 with complex loading environment. It is necessary to use double shoulder collar joints to improve the impact torque resistance of the joint or optimize the operating parameters to reduce the downhole impact torque, and effectively prevent drilling tool failure.

A finite crack growth energy release rate for elastic-plastic fracture

The concept of energy release rate proposed by Griffith originally used for elastic brittle material was extended for ductile material by Irwin and Orowan using the sum of the surface energy and the work of plastic dissipation as fracture resistance. This fracture resistance, however, depends on the load type and specimen geometry, which hinders its wide application. In contrast, in this paper, a finite crack growth energy release rate is proposed by assuming a finite crack growth, which is conveniently applicable to finite element analysis. The effect of the plastic dissipation on the crack growth is considered in the driving force. Elastic-plastic finite element analysis is used to apply the present energy release rate. Compared to the experiment results, it is shown that for a fixed finite crack growth, a constant critical energy release rate can well predict the stable crack growths and residual strengths of sheets with single and various collinear cracks subjected to different types of loads. The present finite crack growth energy release rate is conceptually simple, has a solid physical foundation, and would be appealing for ductile crack growth analysis.

Numerical Investigation of Residual Stress Formation Mechanisms in Flash-Butt Welded Rail

For the construction of long and continuous railway lines as well as the replacement of defected rails, rails are joined using flash-butt welding. Under various localized temperatures and thermo-mechanical stresses, a residual stress can develop in the flash-butt welded joint. The residual stress can affect the performance and reliability of the welded rail, particularly in terms of progressive structural damage caused by repeated wheel load. In the present work, the mechanisms of residual stress formation in a flash-butt welded rail and the influence of upsetting force (including its temperature range and magnitude) were investigated using the thermal elastic–plastic finite element analysis. The formation mechanisms of residual stress involved the changes in thermal expansion coefficient, strain, and elastic modulus of the welded joint with respect to temperature. The calculated cooling temperatures and residual stresses in the flash-butt welded joint were in good agreement with the measured results. Compressive residual stresses were observed around the rail head and the rail foot (i.e., approximately −648 MPa at the rail head and −495 MPa at the rail foot), while tensile residual stresses were observed at the rail web (i.e., approximately 165 MPa). It was observed that the investigated compressive upsetting force predominantly induced plastic deformation within the welded joint, resulting in minimal alteration of stress. Consequently, the investigated ranges of upsetting temperature and upsetting forces had an insignificant impact on the formation of residual stress.

Effects of angles and shapes of a corner crack on the driving force at a set-in nozzle-cylinder in a PWR pressure vessel

Corner cracks are one of the common forms of flaws in the reactor pressure vessels (RPVs) of nuclear power plants (NPPs). Accurate evaluation of the driving force of such corner cracks is essential and critical for the efficient design and integrity assessment of the RPVs. In this study, the combined effect of the depth, length and angle of a given corner crack under the service loading was analyzed using elastic–plastic finite element analysis (EPFEA). Based on the consideration of the distribution profiles of stress intensity factor (SIF) and J integral as the crack growth along corner crack front, the crack growth stability with various crack shapes and angles was analyzed. Finite element analysis (FEA) results showed that the crack growth driving force is affected by the shape and angle of the initial crack. It is also found that the sliding mode (mode II) crack or tearing mode (mode III) crack should be taken into account in the structural integrity analysis of RPVs.

Analysing the effect of defects on stress concentration and fatigue life of L-PBF AlSi10Mg alloy using finite element modelling

Additive manufacturing (AM) is a developing manufacturing technology, which provides excellent attributes compared to other manufacturing techniques. However, one of the critical challenges is the presence of defects that hinder the mechanical properties of the parts, particularly the fatigue life. Experimental understanding of fatigue is a cumbersome process. Therefore, numerical prediction based on specified conditions (such as porosity and applied load) can be an alternative to experimental analysis at the design stage of AM parts. In this study, elastic–plastic finite element analysis (FEA) is performed to obtain the stress distribution around pores, and their resultant effect on fatigue life for L-PBF (laser powder bed fusion) produced AlSi10Mg alloy samples. The stress field is calculated for both single and multiple pore models, where stress concentration is evaluated as a function of the pore’s location and its size. It is found that both pore location and size affect the stress field; however, location effects dominate over pore size. For the same remote applied stress level, the stress concentration around the pore increases with an increase in pore size, and the local maximum stress occurs near the pores that are closest to the surface. The current study also evaluates the relative effect of porosity fraction, average pore size, and location. It is found that the magnitude and sensitivity of stress concentration are hierarchically controlled by porosity location, pore size, and porosity density. A multi-scale finite element (FE) model is proposed based on inherent porosity data measured using Computed Tomography (CT) to predict overall fatigue life. The fatigue cycles are calculated using the rainflow counting algorithm in FE Safe using the stress–strain data obtained from the proposed FEA model. Using the proposed model, it is possible to generate S–N curves for any loading condition for a given porosity condition (porosity density and average pore size). The S–N curve results obtained from the FE model are compared to the experimental observations. The predicted fatigue life shows approximately 5% error with experimental results at high stress loading conditions. However, the proposed model overpredicts the fatigue life at low stress loading by almost 30%.

Reinforcement of cracked aluminum plates using polymeric composite patches embedded with prestressed SMA wires

Many studies have been performed on composite patches as reinforcement of cracked metal sheets. However, in most previous research, composite patches without prestressing have been used to repair cracks. In the present study, a novel method for repairing cracked aluminum sheets is proposed by using polymer composite patches with embedded prestressed Nitinol shape memory alloy (Ni-Ti SMA) wires. Elastic-plastic finite element analysis of an aluminum plate, with a central crack in the pure mode I and the mixed-mode I/II fracture, repaired with SMA wires reinforced composite patch (SMA-CP) was performed. The peel stress on the adhesive layer between the composite patch and the aluminum plate was calculated to evaluate the performance and efficiency of the repair. The effect of the prestress of the embedded Ni-Ti SMA wires on the efficiency of the composite patch was examined. The results show that embedding prestressed SMA wires in the composite patch reduces the stiffness ratio of the patch. Also, the value of the J-integral and the size of the plastic area compared to the patch without SMA wires were decreased.

Study on the relationship between the root welding residual stress and the root-failure fatigue strength of Plug Welded specimens

It is difficult to examine the relation between the root notch welding residual stress (WRS) and the root-failure fatigue strength because of the difficulty in the direct root WRS measurement. The root WRS can be calculated by thermal elastic-plastic finite element analysis (TEPFEA), but its accuracy has not been fully verified yet. In this study, root-failure fatigue tests, in which direct root WRS measurement can be performed, are carried out. Plug welded (PW) specimens with backing plates are used in those tests, and the root WRS in as-welded (AW) and stress-relieved (SR = PWHT) specimens are measured using X-ray diffraction (XRD) method by cutting off the backing plate. The measured WRSs are compared with those calculated by TEPFEA. It is found that the root WRSs in the PW specimens estimated by TEPFEA become much larger than those measured when creep strain is neglected. The SR specimen’s fatigue strength improvement ratio is estimated by using the mean stress effect formulas developed for toe-failure cases (IIW Fatigue Recommendations and MIL-HDBK-5D). The estimated improvement ratio shows fair agreement with that measured.

A parametric finite element study for determining burst strength of thin and thick-walled pressure vessels

To accurately predict the burst strength of both thin and thick-walled pressure vessels (PVs), a parametric study of PV burst strength was performed for a wide range of vessel geometries and materials using elastic-plastic finite element analysis (FEA). A valid FEA model was established through a detailed study of 2D versus 3D FEA models, the critical stress failure criterion versus the limit load criteria, and the thick-wall effect on the FEA simulations. The results show that the stresses and strains at the mean diameter, rather than outside diameter, determines a more accurate burst strength for both thin and thick-walled PVs. On this basis, a parametrized FEA script using the ABAQUS Python application programming interface (API) was used to create a large database of PV burst strengths for a variety of vessel geometries and materials, demonstrating that Python scripting is a powerful technique for performing parametric studies or generating large databases. From the FEA results, using the regression method, a new burst pressure model was developed as a function of the vessel geometry (D/t ratio) and material properties (UTS and n). As validated by a large number of full-scale burst test data, the proposed burst model can very accurately predict the burst strength for both thin and thick-walled PVs.

Elastic–Plastic Numerical Analysis of the Spinning Process of SA-372 Steel Used in High-Pressure Hydrogen Storage Cylinders (≥100 MPA)

Elastic-plastic numerical analysis of the spinning process of SA-372 steel is used in high-pressure hydrogen storage to analyze high-pressure hydrogen storage cylinders with high precision and excellent hydrogen embrittlement resistance. The spinning process of SA-372 steel used to form such a cylinder with a pressure of 100 MPa is investigated through elastic-plastic finite element analysis. The variations in the stress, strain, pressure, temperature, and wall thickness during the spinning processes are comprehensively examined, and the optimized processing parameters are determined based on the numerical analysis results. Finally, these optimal parameters are used to conduct actual spin-forming experiments. The numerical results are found to be in excellent agreement with the experimental results, which verifies the feasibility and effectiveness of the proposed elastic-plastic numerical analysis model for the optimization of spinning process parameters. Furthermore, the hydrogen embrittlement test based on ISO 11114-4:2005 method A proves that the cylinder shoulder has a good hydrogen embrittlement resistance.

The role of plasticity-induced crack closure in the non-propagation prediction of surface defect-initiated cracks near fatigue limit

The purpose of present work is to deepen the understanding of crack propagation, non-propagation, and fatigue limit. Quantitative prediction of fatigue crack non-propagation in constant amplitude loading is attempted through extensive 3D elastic–plastic finite element analysis of near-threshold propagation of short cracks nucleating from surface defects. Level of plasticity-induced crack closure is used to estimate the effective stress intensity factor range, which is evaluated in terms of non-propagation potential. It is shown that plasticity-induced crack closure alone is adequate in producing a local minimum in the development of effective stress intensity factor range, which gives a prerequisite to crack arrest.

A simple method to determine opening stress for the cracked plate considering thickness effect

In this paper, an approach is proposed to determine crack opening stress (COS) based on the variable quantity of maximum crack opening displacement (VMCOD) considering thickness effect. Based on the three-dimensional elastic-plastic finite element analysis of center cracked tension (CCT) specimens and single-edge cracked tension (SET) specimens, the explicit expressions of relationship between COS and VMCOD are put forward, considering the effect of specimen thickness, crack length, stress ratio, Young's modulus, yield stress and strain hardening. These expressions avoid adopting parameters around crack tip and are applicable to different specimen thicknesses. Further studies show these relationships can be applied to calculate the effective stress intensity factor range and predict crack growth rates for plates of different thicknesses, which correlate well with experimental results.

Effects of large plastic deformation and residual stress on the path independence of J-integral for cracks in ductile materials

Large plastic deformation and residual stress exist in the oil and gas transmission pipelines with mechanical damages that often contain a gouge or crack. Residual stresses can alter the mechanics behavior of the crack, and cause the standard J-integral to become path-dependent and unable to describe the crack driving force.This paper investigated the effects of large plastic deformation and residual stress on the path independence of the J-integral for a crack in ductile materials. The basic conditions required for the path independence of the standard J-integral were first reviewed, and the major factors that affect the path independence were then analyzed. This includes the theory of plasticity, finite strain formulation, and residual stresses. Then, a residual stress modified J-integral was introduced for ensuring the path independence. After that, the elastic–plastic finite element analyses were performed for a notched beam in terms of the incremental plasticity to create residual stresses and to simulate a crack at the notch root subject to three-point bending. The path independence of the standard and modified J-integrals was numerically evaluated for each of the major factors. Results showed that the modified J-integral is path-independent and able to describe the crack driving force for a crack in a residual stress field, but the standard J-integral cannot do so because of its nature of path dependence when residual stresses are present. Thus, the modified J-integral can be used as an appropriate fracture parameter to assess the pipeline integrity for line pipes containing cracks and residual stresses.

Component Tests and Numerical Investigations to Determine the Lifetime and Failure Behavior of End Stage Blades

Abstract The paper focuses on experimental and numerical fatigue assessment procedures to evaluate the influence of multi-axial stress state caused by high centrifugal forces superimposed with bending loads due to blade vibrations on the lifetime of end stage blades from steam turbines. The experimental investigations on original-sized end stage blades were carried out on a test rig specially developed for high forces and multicomponent force application. This was based on detailed numerical simulations by the MPA University of Stuttgart. During the fractographic postexaminations of the tested blades using magnetic particle inspection, light and scanning electron microscopes, two competing damage mechanisms were identified that occurred at different locations. Numerical investigations by means of elastic–plastic finite element analyses were carried out to estimate the local stress conditions acting in the blade root. The local stresses and strains were postprocessed using the critical plane approach and advanced multi-axial fatigue damage parameters. Due to the high stress gradients at the edge of contact, over-conservative predictions may result if their effects are not taken into account. Based on the critical plane method in conjunction with fatigue damage parameters, an approach taking the stress gradient into consideration was developed to predict the fatigue life of the end stage blades. The approach is verified by the component tests on original-sized blades.

Study on thermal deformation of hybrid printed circuit heat exchanger for advanced nuclear reactor

The intermediate heat exchanger (IHX) is one of the key components in advanced nuclear reactor power generation system. Printed circuit heat exchanger (PCHE) with mini-channels is a good candidate for the IHX. But the whole PCHE with tens of thousands of mini-channels is hard to be modeled and calculated at high temperature. Thus, the homogenization method, which can calculate the thermal deformation of the whole hybrid mini-channel PCHE, is conducted in this study and both the elastic and elastic-plastic finite element analysis methods are used. Here, the performance of the PCHE is assumed to be isotropic in the simulation. The results show that the macroscopic thermal deformation of the whole PCHE follows a gradually downward trend from hot side to cold side, while obvious thermal stress concentration is observed around the junctions between the PCHE core and cover plate. The stress and strain calculated by elastic and elastic-plastic methods under different constraints show quite different patterns. For the thermal deformation analysis of PCHE under weak constraint or small temperature difference conditions, the stress and strain results by elastic analysis and elastic-plastic analysis are similar so that the elastic analysis can be used. Under the strong condition, the stress of PCHE calculated by elastic analysis is much higher than that of elastic-plastic analysis, while the strain is lower than that of elastic-plastic analysis. The relative deviations of stress are 100.883% and 120.786% along path 1 and path 2 respectively. And the relative deviations of strain are 6.987% and 10.139% along path 1 and path 2 respectively. The elastic-plastic analysis should be used instead of the elastic analysis.

Effects of yield point and plastic anisotropy on results of elastic–plastic finite element analysis of tension leveling

Tension leveling is an important industrial process to eliminate the flatness defects and residual stresses of metal strips to provide high-quality sheet metals for subsequent sheet metal forming. The finite element (FE) method can be applied to elucidate the effects of process parameters on the quality of sheets after tension leveling for various materials. In our previous investigation, an accurate FE model has been established for the elastic–plastic FE analysis of tension leveling. In this study, we further studied the effects of the yield point and plastic anisotropy on tension leveling using the FE model established in our previous investigation. Aiming at improving the accuracy of simulation, a modified constitutive model was developed to describe the anisotropic hardening of materials under cyclic loading. The modified constitutive model was implemented into Abaqus/Standard as a user-defined material subroutine to simulate the development of the anisotropy in materials during tension leveling. The modified model was also applied to the FE analysis of sheet metal forming processes to demonstrate its simulation capability and accuracy.

Elastic-Plastic Finite Element New Method for Lower Bound Shakedown Analysis

Shakedown analysis methods have been well developed to determine the shakedown limit load of structures under various repeated loading situations. However, to take the limited kinematic hardening, geometric effect, and deformation into account, further research is required. A new numerical method is proposed for the lower bound shakedown analysis that applies the extended static shakedown theorem for limited kinematic hardening. The new method determines the shakedown limit load with two kinds of elastic-plastic finite element (FE) analyses: (1) the elastic-plastic loading and unloading analysis is carried out using the hardening model with the actual material parameters and (2) the elastic-perfectly plastic model with ultimate stress as the yield stress is used for the limit analysis. An incremental FE technique for finite strain plasticity is utilized to take the geometric effect into account. Furthermore, the deformation of the structure is monitored by checking the calculated deformation parameters. The method is applied to a square plate with a small central hole subjected to cyclic tensile load. The corresponding physical shakedown experiment of the above square plate was conducted for verification. The numerical result shows a good agreement with the experimental result. The new method provides a valid method for the structural lower bound shakedown analysis taking into account limited kinematic hardening, geometric effect, and deformation.