On the study of the creep damage development in circumferential notch specimens

Numerical calculations with K–R damage law have been performed to study the creep damage development in circular notch specimens under constant loading. The emphasis was placed on the roles of notch radius, material constant- and applied stress. The results show that the distributions of stresses under creep conditions are different from those of previous studies. Creep damage development and life are different for different notch specimens, and the distributions of the maximum creep damage in the minimum cross-section vary with the notch radius. The creep damage is remarkably affected by the applied stress, material parameter- and notch radius. Higher stress and tri-axial stress state parameter- can cause the creep damage to develop faster.     

Anisotropic creep modeling of coated textile membrane using finite element analysis

Coated textile membranes (CTMs) form a class of flexible textile composites undergoing viscoelastic deformation because they consist of a polymeric reinforcement and matrix and are tensioned in service. In most CTMs, woven fabrics are frequently used as a reinforcement structure, causing anisotropic mechanical behavior including time dependent viscoelastic deformation. To describe such anisotropic and nonlinear time dependent deformation, the creep potential with three orthotropic parameters was introduced and incorporated into finite element software through a user material subroutine. The three parameters included in the creep potential were determined by carrying out off-axis coupon creep tests and using various mathematical formulae for the effective creep compliance. To validate the current creep modeling and its implementation in finite element software, off-axis coupon creep tests were re-simulated and compared with the experiments, showing that the present modeling can describe the anisotropic and nonlinear creep deformation of CTM with acceptable accuracy.     

Monte Carlo simulation of polycrystalline microstructures and finite element stress analysis

A two-dimensional numerical model of microstructural effects is presented, with an aim to understand the mechanical performance in polycrystalline materials. The microstructural calculations are firstly carried out on a square lattice by means of a 2-D Monte Carlo (MC) simulation for grain growth, then the conventional finite element method is applied to perform stress analysis of a plane strain problem. The mean grain size and the average stress are calculated during the MC evolution. The simulation result shows that the mean grain size increases with the simulation time, which is about 3.2 at 100 Monte Carlo step (MCS), and about 13.5 at 5000 MCS. The stress distributions are heterogeneous in materials because of the existence of grains. The mechanical property of grain boundary significantly affects the average stress. As the grains grow, the average stress without grain boundary effect slightly decreases as the simulation time, while the one with strengthening effect significantly decreases, and the one with weakening effect increases. The average stress and the grain size agree well with the Hall–Petch relationship.     

Cone bit bearing seal failure analysis based on the finite element analysis

Failure analysis of cone bit bearing seals is important in reducing production cost and preventing in-service component failure. However, a generally accepted criterion for their failure has not yet been established because of complexities in both their material properties and the environment. In this study, a two-dimensional axisymmetric finite element analysis (FEA) numerical model was established. FEA software was developed based on the Mooney–Rivlin constitutive model of the rubber material, and the penalty function contact algorithm. The distributions of stress, strain and contact pressure were analyzed to establish their effect on failure. The locations and causes of the failure and preventive measures were determined by comparison with an actual failure case. It was found that stress concentration and uneven pressure distribution occur at the seal. Rubber rings are highly and unequally compressed. Metal ring structure mainly determines sealing performance. To reduce the occurrence of failure, the structure must be improved by: designing an appropriate angle-tapered metal ring end face structure instead of a plane to change the trend in pressure distribution, increasing the contact area of the metal ring end face to reduce contact pressure and make the contact pressure distribution more uniform to reduce sealing surface wear, reducing the radial thickness to reduce the compression of the rubber ring, and improving back support structures to reduce the stress concentration. Results from the study can prevent and minimize risk for future failures to increase bit life and reduce drilling costs.     

Three-dimensional finite element analysis of finite deformation micromorphic linear isotropic elasticity

A finite deformation micromorphic materially linear isotropic elastic model is formulated and implemented for three dimensional finite element analysis. The model is based on the kinematics, balance equations and thermodynamic equations proposed by Eringen and Suhubi (1964). The constitutive equations are calculated in the reference configuration, and the resulting stresses are mapped to the current configuration. The balance of linear momentum and the balance of first moment of momentum are linearized to construct the consistent tangent for three dimensional finite element implementation for solution by the Newton–Raphson method. Three dimensional numerical examples are analyzed to demonstrate preliminarily the implementation.     

Dynamic stress analysis of rail joint with height difference defect using finite element method

A finite element analysis is conducted to study dynamic elastic–plastic stress when a wheel passes a rail joint with height difference between the two sides of a gap. The ANSYS implicit code and LS-DYNA explicit code are coupled to simulate the process of the wheel contacting or impacting the rail joint. Contact elements are used to simulate the interactions between wheel and rails, between rails and joint bars, between joint bars and bolts and between bolts and rails. The effects of train speed, axle load and height difference on the contact forces, stresses and strains at railhead are investigated. Numerical results show that the presence of rail joint with height difference significantly affect the contact force, stress and strains. The results also indicate that the train speed has a larger effect on the contact force, stress and strains than the axle load.     

Effect of stress dependent creep ductility on creep crack growth behaviour of steels for wide range of C*

Abstract

In this work, the effect of stress dependent creep ductility on the creep crack growth (CCG) behaviour of steels has been investigated by finite element simulations based on ductility exhaustion damage model. The relationship between the transition region of creep ductility and the transition behaviour of CCG rate on da/dt-C* curves has been examined and the CCG life assessments of components and CCG resistance of materials for a wide range of C* were discussed. The results show that with increasing the transition region size of creep ductility, the transition C* region size on da/dt-C* curves increases. With moving transition region position of creep ductility to high stress region (increasing transition stress levels), the transition C* region on the da/dt-C* curves also moves to high C* region. Decreasing transition stress levels and transition region sizes of creep ductility and increasing the lower shelf and upper shelf creep ductility values can improve the CCG resistance of materials. If the extrapolation CCG rate data from the high C* region or from the transition C* region are used in life assessments of the components at low C* region, the non-conservative or excessive conservative results may be produced. Therefore, the CCG rate data should be obtained for a wide range of C* by long term laboratory tests or numerical predictions using the stress dependent creep ductility and model.     

Using three-dimensional finite element analysis for simulation of residual stresses in railway wheels

One of the most important issues in railway wheels is residual stresses. It is desirable to produce less residual stresses when possible and to decrease the remaining residual stresses in the wheels. The objective of this paper is to provide an estimation of the residual stresses in the rail wheel caused by the stress field from heat treatment process of a railway wheel. A three-dimensional nonlinear stress analysis model has been applied to estimate stress fields of the railway mono-block wheel in heat treatment process. After forging or casting, railway wheels are heat-treated to induce the desirable circumferential compressive residual stress in the upper rim. Finite element analysis model is presented applying the elastic–plastic finite element analysis for the rail wheel under variable thermal loads. Calculative analysis applying a finite element method (FEM) has been used to predict residual stresses. The quenching and annealing segments of the wheel manufacturing process are simulated using a decoupled heat transfer and stress analysis. Three-dimensional finite element analysis results obtained show good agreement with those achieved in field measurements.     

A finite element approach to anisotropic damage of ductile materials in large deformations Part II: finite element formulation and applications

A finite element analysis model for material and geometrical non-linearities due to large plastic deformations of ductile materials is presented using the continuum damage mechanics approach. To overcome limitations of the conventional plastic analysis, a fourth-order tensor damage, defined in Part I of this paper to represent the stiffness degradation in the finite strain regime, is incorporated. General forms of an updated Lagrangian (U.L.) finite element procedure are formulated to solve the governing equations of the coupled elastic–plastic-damage analysis, and a computer program is developed for two-dimensional plane stress/strain problems. A numerical algorithm to treat the anisotropic damage is proposed in addition to the non-linear incremental solution algorithm of the U.L. formulation. Selected examples, compared with published results, show the validity of the presented finite element approach. Finally, the necking phenomenon of a plate with a hole is studied to explore plastic damage in large strain deformations. This revised version was published online in August 2006 with corrections to the Cover Date.     

Fully plastic analyses for notched bars and plates using finite element limit analysis

In the present work, fully plastic analyses for notched bars and (plane strain) plates in tension are performed, via finite element (FE) limit analysis based on non-hardening plasticity, from which plastic limit loads and stress fields are determined. Relevant geometric parameters are systematically varied to cover all possible ranges of the notch depth and radius. For the limit loads, it is found that the FE solutions for the notched plate agree well with the existing solution. For the notched bar, however, the FE solutions are found to be significantly different from known solutions, and accordingly the new approximation is given. Regarding fully plastic stress fields, it is found that, for the notched plate, the maximum hydrostatic (mean normal) stress overall occurs in the center of the specimen, which strongly depends on the relative notch depth and the notch radius-to-depth ratio. On the other hand, for the notched bar, the maximum hydrostatic stress can occur in between the center of the specimen and the notch tip. The maximum hydrostatic stress for a given notch depth can occur not for the cracked case, but for the notched case with a certain radius. This is true for both bars and plates. For a given notch radius, on the other hand, the maximum hydrostatic stress increases monotonically with the decreasing notch radius.     

Evaluating stress intensity factors due to weld residual stresses by the weight function and finite element methods

This paper presents a study on the application of the weight function and finite element methods to evaluate residual stress intensity factors in welded test samples. Three specimen geometries and various residual stress profiles were studied. Comparisons of the two different methods were made in terms of the accuracy, easiness to use, conditions and limitations. Calculated residual stress intensity factors by the two different methods are in general in good agreement for all the configurations studied. Computational issues involved in executing these methods are discussed. Some practical issues are also addressed, e.g. treatment of incomplete or limited residual stress measurements, influence of transverse residual stresses, and modelling residual stress in short-length specimens. The finite element method is validated by well-established weight functions and thus can be applied to complex geometries following the procedures recommended in this paper.     

Stress recovery in geometrically nonlinear membranes by a Hu-Washizu finite element formulation

A class of mixed finite elements based on the Hu-Washizu functional is introduced as a strategy to reduce the spurious stress phenomena encountered with standard or displacement-based formulations for geometrically exact membranes. Selected examples compare the performance of this class of elements with that of the standard formulation and demonstrate that reduction of spurious stresses is obtained and that the stresses are more accurate than those optimally sampled in the standard formulation.     

Numerical stress and crack initiation analysis of the compressor blades after foreign object damage subjected to high-cycle fatigue

This paper presents results of the complex stress and crack initiation analysis of the PZL-10 W turbo-engine compressor blade subjected to high cycle fatigue (HCF). A nonlinear finite element method was utilized to determine the stress state of the blade during the first mode of transverse vibration. In this analysis, the numerical models without defects and also with V-notches were defined. The quality of the numerical solution was checked by the convergence analysis. Obtained results were next used as an input data into crack initiation (ε–N) analyzes performed for the load time history equivalent to one cycle of the transverse vibration. In the fatigue analysis the different methods such as: Neuber elastic–plastic strain correction, linear damage summation and Palmgreen–Miner rule were utilized. As a result of ε–N analysis, the number of load cycles to the first fatigue crack appearing in the compressor blades was obtained. Moreover, the influence of the blade vibration amplitude on the number of cycles to the crack initiation was analyzed. Values of the fatigue properties of the blade material according to Baumel–Seeger and Muralidharan methods were calculated. The influence of both the notch radius and values of the UTS of the blade material on the fatigue behavior of the structure was also considered. In the last part of work, the finite element results were compared with the results of an experimental vibration HCF tests performed for the compressor blades.     

Stress intensity factor error index for finite element analysis with singular elements

An error index for the stress intensity factor (SIF) obtained from the finite element analysis results using singular elements is proposed. The index was developed by considering the facts that the analytical function shape of the crack tip displacement is known and that the SIF can be evaluated from the displacements only. The advantage of the error index is that it has the dimension of the SIF and converges to zero when the actual error of the SIF by displacement correlation technique converges to zero. Numerical examples for some typical crack problems, including a mixed mode crack, whose analytical solutions are known, indicated the validity of the index. The degree of actual SIF error seems to be approximated by the value of the proposed index.     

Failure analysis of a diesel engine cylinder head based on finite element method

Macro fatigue cracks are expected to occur in valve bridges of cylinder head when engine is operating in normal working condition. In order to determine the causes of these failures, stress analysis is carried out using finite element method with a concern of temperature dependency of material properties. Mechanical and thermal properties of material tested at high temperatures are applied to the finite element analysis. Furthermore, temperatures of the cylinder head in actual working condition are measured to validate the simulation results of finite element analysis. After that, stress computation is performed and the regions of stress concentration on the flame deck surface are obtained. The analysis results of stress show that the regions of stress concentration are in agreement with the actual failure regions of the cylinder head. When analyzing the failures on the flame deck surface of a cylinder head by evaluating stress concentration, temperature’s effect on mechanical strength of material should not be ignored. The methodology of failure analysis proposed in this paper is time-saving and also relatively accurate and predictive in actual engineering practice.     

Fatigue crack closure determination by means of finite element analysis

Plasticity-induced crack closure is an observed phenomenon during fatigue crack growth. However, accurate determination of fatigue crack closure has been a complex task for years. It has been approached by means of experimental and numerical methods. The finite element method (FEM) has been the principal numerical tool employed. In this paper the results of a broad study of fatigue crack closure in plane stress and plane strain by means of FEM are presented. The effect of three principal factors has been analysed in depth, the maximum load, the crack length and the stress ratio. It has been found that the results are independent of maximum load and the crack length, and there exists a direct influence of the stress ratio. This relation has been numerically correlated and compared with experimental results. Differences have also been established between opening and closure points and between the different criteria employed to compute crack closure.     

Discrete cohesive zone model for mixed-mode fracture using finite element analysis

The discrete cohesive zone model (DCZM) is implemented using the finite element (FE) method to simulate fracture initiation and subsequent growth when material non-linear effects are significant. Different from the widely used continuum cohesive zone model (CCZM) where the cohesive zone model is implemented within continuum type elements and the cohesive law is applied at each integral point, DCZM uses rod type elements and applies the cohesive law as the rod internal force vs. nodal separation (or rod elongation). These rod elements have the provision of being represented as spring type elements and this is what is considered in the present paper. A series of 1D interface elements was placed between node pairs along the intended fracture path to simulate fracture initiation and growth. Dummy nodes were introduced within the interface element to extract information regarding the mesh size and the crack path orientation. To illustrate the DCZM, three popular fracture test configurations were examined. For pure mode I, the double cantilever beam configuration, using both uniform and biased meshes were analyzed and the results show that the DCZM is not sensitive to the mesh size. Results also show that DCZM is not sensitive to the loading increment, either. Next, the end notched flexure for pure mode II and, the mixed-mode bending were studied to further investigate the approach. No convergence difficulty was encountered during the crack growth analyses. Therefore, the proposed DCZM approach is a simple but promising tool in analyzing very general two-dimensional crack growth problems. This approach has been implemented in the commercial FEA software ABAQUS^® using a user defined subroutine and should be very useful in performing structural integrity analysis of cracked structures by engineers using ABAQUS^®.     

Elastic property prediction by finite element analysis with random distribution of materials for heterogeneous solids

In the present paper, finite element method is employed to predict the effective material properties of heterogeneous materials via random distributions of the constituent materials. With the random distributing strategy, massive parametric analysis via finite element becomes feasible for multi-phase heterogeneous solids. Using a two-phase bi-continuous material as an example, the effects of the specimen size with respect to the characteristic size of the micro-structural size and the element density on the predicted effective properties are considered. The numerical predictions of the effective properties are checked by two analytical bounds which were proposed by Hashin and Shtrikemn (1963) through the principle of variation and the matrix-fiber model. Some discussions on the finite element prediction are also made to clarify the status of the present work in the composite mechanics research.     

Influence of minimum element size to determine crack closure stress by the finite element method

Measuring opening or closure stress is a complex process that influences the low accuracy of obtained data. Finite element models have been one of the available ways to deal with this problem. The difficulty of modelling the whole process of crack growth (due to the great number of cycles implied) as the great complexity of the phenomenon itself (with a high plastic strain concentrated in a small area, with elevated stress gradients) has made the results to be quite varied, being influenced by a great number of modelling parameters. Of those parameters, the minimum size of the element used to mesh the area around the crack tip vicinity presents a great influence on the results.In this work, a detailed analysis of the influence of this parameter in the results in terms of closure or opening stress is presented. The effect that different meshing criteria can have on the result is complex and it has been necessary to reduce the element size around the crack tip to a size that had not been reached before. Procedures and modelling criteria stricter than the ones shown in the current bibliography are proposed. A methodology for the correct interpretation of the results is also established.     

Combined plasticity and creep analysis in 2D by means of the boundary element method

This work presents a formulation to make a combined analysis of plasticity and creep in two-dimensional (2D) using the Boundary Element Method. This new approach is developed to combine the constitutive equation for time hardening creep and the constitutive equation for plasticity, the latter based on the Von Misses criterion and the Prandtl–Reuss flow. The implementation of creep strain in the formulation is achieved through domain integrals. The creep phenomenon takes place in the domain which is discretized into quadratic quadrilateral continuous and discontinuous cells. The creep analysis is applied to metals with a power law creep for the secondary creep stage. The results, obtained with reference to three models, show a good agreement when compared to those published in the literature. This finding shows that the Boundary Element Method is a suitable tool to deal with combined nonlinear problems.