SINGULAR p-VERSION FINITE ELEMENTS FOR STRESS INTENSITY FACTOR COMPUTATIONS

The finite element analysis of linear elastic fracture mechanics problems is complicated by the presence of the singular and finite non-singular stress distributions in the crack tip region. The availability of a constant stress term in addition to the singular term in the standard h-version singular finite elements is insufficient to model the finite nonsingular stress zone. A p-version singular finite element capable of modelling the higher-order non-singular stress terms in addition to the singular term and the constant term is presented. The formulation for the displacement substitution technique for computing the stress intensity factors using singular p-version triangular finite elements is developed. Unlike the standard h-version formulation, the stress intensity factors computed using the p-version displacement substitution technique do not depend on the specific arrangement and length of the quarter point elements, and require simple mesh designs as well as fewer number of degrees of freedom. Numerical studies comparing the convergence of the stress intensity factors computed by the p-version method against other available alternatives such as the h-version method and the contour integral method are presented to demonstrate the effectiveness of the present developments. © 1997 by John Wiley & Sons, Ltd.     

Finite‐element analysis of a combined fine‐blanking and extrusion process

This paper presents the characteristics of the combined fine‐blanking and extrusion process and gives a detailed analysis of the process with the finite‐element method. To carry out the simulation step by step and avoid the tendency to diverge in the calculations, the remeshing, tracing and golden section methods were developed and introduced into the finite‐element program. Different boundary conditions were used in the simulation; the mesh distortion, field of material flow, and the stress and strain distributions were obtained. From the simulated results, the deformation characteristics under different boundary conditions were revealed. An experiment was also carried out to verify the simulated results. A large strain analysis technique was chosen to determine the effective strain distribution based on the experiment. The effective strain distributions from the simulation are in accordance with the effective strain distributions and the hardness distributions from the experiment. Copyright © 2005 John Wiley & Sons, Ltd.     

Micromechanical elastic cracktip stresses in a fibrous composite

This paper presents elastic stress distributions near a cracktip in a continuous fiber composite. The material heterogeneity is explicitly accounted for by using the finite element method and a new Mesh Superposition Technique. This new technique superposes a fine mesh with heterogeneous material properties over a coarse mesh with homogeneous ones. The results indicate that the load transferred by fibers near a cracktip may be well described by the homogeneous orthotropic elastic K ₁ field. A technique to postprocess the K ₁ field to accurately obtain the detailed stress distributions within the fiber and matrix is also presented.     

Two- and three-dimensional elastic-plastic stress analysis for a double edge notched tension specimen

This paper describes an elastic-plastic stress analysis for a double edge notched tension specimen, a specimen used for the determination of the microscopic cleavage fracture stress. The analysis was performed numerically using the finite element method. First, a study of the finite element modelling is presented in order to demonstrate the requirements on a three-dimensional finite element structure leading to accurate stress distributions in the whole specimen. On the other hand possible restrictions are shown, if only a certain parameter, e.g. the maximum tensile stress has to be evaluated. Then the global response of the three-dimensional structure is compared with results of two-dimensional calculations assuming plane stress and plane strain, respectively. Subsequently the most interesting stress and strain distributions are discussed. The maximum value of stress concentration in front of the notch is given as a function of the applied stress. Additionally the state of deformation at fracture load is characterized by the plastic zone size, too. All three-dimensional results are compared with results of a plane strain model.     

A Theoretical Analysis on Elastic and Elastoplastic Stress Solutions for Functionally Graded Materials Using Averaging Technique of Composites

Functionally Graded Materials (FGMs) are being used in an everexpanding set of applications. For better applications, an analytical methodology using averaging technique of composites is developed to describe the thermo-elastic and thermo-elastoplastic behaviors of a three-layered FGM system subjected to thermal loading Solutions using averaging technique of composites for the stress distributions in a generic FGM system subjected to arbitrary temperature loading conditions are presented. The power-law strain hardening behaviour is assumed for the FGM metallic phase and the stress of the metallic phase are calculated to judge the plastic in this work The stress distributions within the FGM systems are compared with accurate numerical solutions obtained from finite element analyses and good agreement is found.     

Quartz resonator frequency shifts computed using the finite element method

A new solution technique has been developed to calculate the frequency shifts arising from mechanical stresses in the case of quartz resonators. This solution technique utilizes finite element analysis as an initial step to calculate mechanical stress distributions in quartz resonators. Output from the finite element solution is used in a recently developed program to calculate resonator frequency shifts as the final step. Frequency shifts are calculated via numerical integration of the perturbation integral derived by Tiersten.³⁶ The solution technique is general in that any combination of mount and resonator geometries may be modelled. Any crystallographic orientation may be chosen and any load or combination of loads may be applied to the resonator. The frequency perturbation calculation includes movement of the mode to any position in the general vicinity of the resonator centre. Experimental results for AT- and SC-cut quartz resonators subjected to diametric forces and inertial loading verify the accuracy of frequency shifts calculated using the new solution technique.     

Optimization of a crankshaft rolling process for durability

A crankshaft is often designed with a small fillet radius. The crankshaft fillet rolling process is one of the commonly adopted methods in engineering to improve fatigue life of the crankshaft. Compressive residual stresses on and below the fillet radius surface are induced through the fillet rolling operation. Consequently, fatigue life of the crankshaft is improved. An analytical technique is used to optimize the crankshaft rolling process to comply with a crankshaft design criterion for durability. A nonlinear finite element analysis is implemented to approximate the stress distributions induced by the crankshaft rolling process, and a crack modeling technique is developed to calculate the equivalent stress intensity factor ranges based on the combined residual and operational stress distributions along various crack growth planes. The threshold equivalent stress intensity factor range is obtained from previous staircase testing on crankshaft sections. The durability design criterion is met if the threshold equivalent stress intensity factor range exceeds the largest calculated equivalent stress intensity factor range. Due to the complexity of the modeling techniques in simulating the rolling process and calculating the equivalent stress intensity factors, a meta-model is generated based on the uniform design method for the choice of sample points and the quadratic polynomial fitting technique for a response surface generation. In the meta-model optimization process, rolling force, rolling angle, and fillet radius are the control factors, while the variations of the threshold equivalent stress intensity factor range, rolling force, rolling angle, and fillet radius are considered as the noise factors. By using the Hooke–Jeeves direct pattern search method and the Monte Carlo simulation technique, the optimal design is obtained for the highest reliability and the smallest coefficient of variation (COV).     

Dynamic analysis of multi-layered filament-wound composite pipes subjected to cyclic internal pressure and cyclic temperature

Based on the three-dimensional anisotropic elasticity, the stress analysis of multi-layered filament-wound composite pipes subjected to cyclic internal pressure and temperature loading is conducted in this article. The time-dependent stress, strain and deformation distributions are numerically obtained by the use of the finite difference technique. The pressure and temperature are considered to be symmetrical about the axis of the cylinder and independent of the axial coordinate. Each layer of the pipes is made of a homogeneous, anisotropic and linearly elastic material and it is assumed that the material properties do not change with increasing the temperature. The shear extension coupling is also considered because of lay-up angles. Numerical results obtained from the present model are compared with other published results and good agreement has been achieved.     

Stress distribution in damaged composite laminates under transverse impact

Studies on damage in composite laminates subjected to central and normal impact are conducted by a 3-D finite element analysis. The stress analysis is carried out by developing a constitutive equation of composite laminates coupled with the damage. Effects of the damage on the stress distribution in the laminates are investigated in details. The obtained contact force history correlates well with the results reported in literatures. Stress distributions across the thickness of the elastic non-damaged laminate show a probable distribution of delamination. The simulated result for delamination is coincided with the observation of experiments. Stress distributions for the damaged laminates show that the damage releases strain energy and lessens stress concentration.     

Stress intensity factors and weight functions for deep semi-elliptical surface cracks in finite-thickness plates

ABSTRACT Three-dimensional finite element analyses have been conducted to calculate the stress intensity factors for deep semi-elliptical cracks in flat plates. The stress intensity factors are presented for the deepest and surface points on semi-elliptic cracks with a/t -values of 0.9 and 0.95 and aspect ratios ( a/c ) from 0.05 to 2. Uniform, linear, parabolic or cubic stress distributions were applied to the crack face. The results for uniform and linear stress distributions were combined with corresponding results for surface cracks with a/t = 0.6 and 0.8 to derive weight functions over the range 0.05 ≤  a/c  ≤ 2.0 and 0.6 ≤  a/t  ≤ 0.95. The weight functions were then verified against finite element data for parabolic or cubic stress distributions. Excellent agreements are achieved for both the deepest and surface points. The present results complement stress intensity factors and weight functions for surface cracks in finite thickness plate developed previously.     

Strain energy release rate determination of prescribed cracks in adhesively-bonded single-lap composite joints with thick bondlines

An analytical model for determining the strain energy release rate due to a prescribed crack in an adhesively-bonded, single-lap composite joint with thick bondlines and subjected to axial tension is presented. An existing analytical model for determining the adhesive stresses within the joint is used as the foundation for the strain energy release rate calculation. In the stress model, the governing equations of displacements within the adherends are formulated using the first-order laminated plate theory. In order to simulate the thick bondlines, the field equations of the adhesive are formulated using the linear elastic theory to allow non-uniform stress distributions through the thickness. Based on the adhesive stress distributions, the equivalent crack tip forces are obtained and the strain energy release rate due to the crack extension is determined by using the virtual crack closure technique (VCCT). The specimen geometry of ASTM D3165 standard test is followed in the derivation. The system of second-order differential equations is solved to provide the adherend and adhesive stresses using the symbolic computational tool, Maple 7. Finite element analyses using J-integral as well as VCCT are performed to verify the developed analytical model. Finite element analyses are conducted using the commercial finite element analysis software ABAQUS™. The strain energy release rates determined using the analytical method correlate well with the results from the finite element analyses. It can be seen that the same prescribed crack has a higher strain energy release rate for the joints with thicker bondlines. This explains the reason that joints with thick bondlines tend to have a lower load carrying capacity.     

A predictive model for particulate-filled composite materials

A predictive model for particulate-filled composite materials has been developed. The model uses a combination of finite element analysis and spatial statistical techniques; this combination allows the results from finite element analysis to be applied to real materials. The model is applied to epoxy resin filled with glass spheres. Predicted values of stiffness are compared with experimental measurements, and excellent agreement is found. The model is used to investigate stress distributions and the results are compared with experimental observations of fracture under varying conditions; the fracture behaviour of these materials is significantly elucidated.     

Damage in composite laminates: Effects of transverse cracks

Two different methods of solution are used to study the effects of transverse cracks in cross-ply composite laminates. The results of an approximate analytical solution are compared with those obtained using a finite element analysis in order to study the effects of transverse cracks on the degradation of elastic and thermal coefficients as well as stress distributions. In particular, it is shown that transverse cracks cause significant degradation of the Poisson's ratio and shear modulus of the laminates, and also affect some stress distributions in a peculiar manner. Theoretical results are compared with existing experimental results where appropriate.     

Voronoi cell finite element model based on micropolar theory of thermoelasticity for heterogeneous materials

In this paper, a new ‘Voronoi cell finite element model’ is developed for solving steady-state heat conduction and micropolar thermoelastic stress analysis problems in arbitrary heterogeneous materials. The method is based on the natural discretization of a multiple phase domain into basic structural elements by Dirichlet Tessellation. Tessellation process results in a network of polygons called Voronoi polygons. In this paper, formulations are developed for treating these polygons as elements in a finite element mesh. Furthermore, a composite Voronoi cell finite element model is developed to account for the presence of a second phase inclusion within a polygonal element. Various numerical examples are executed for validating the effectiveness of this model in the analysis of the temperature and stress fields for micropolar elastic materials. Effective material properties are derived for microstructures containing different distributions of second phase.     

50th Anniversary Article: The Origin and Management of Residual Stress in Heat‐treatable Aluminium Alloys

The presence of macroscopic residual stresses in heat‐treatable aluminium alloys can give rise to machining distortion, dimensional instability and increased susceptibility to in‐service fatigue and stress corrosion cracking. This paper presents and reviews details about the residual stress magnitudes and distributions introduced into wrought aluminium alloys by the thermal operations associated with heat treatment. Experimental measurement data and the results of finite element analysis are presented and discussed. The available technologies by which residual stresses in aluminium alloys can be relieved are reviewed. The limitations of these techniques are described, and recommendations are made as to selecting the most appropriate technique to manage residual stresses. Opportunities for the future optimisation of these techniques are also presented.     

Thermoelastic analysis of a layered slab subjected to a moving line heat source

Abstract

This paper reports a theoretical study of the transient thermal stress distributions of a layered slab which is composed of two different materials. The layered slab is heated by a moving line heat source on its upper surface and cooled convectively on the lower surface. In order to solve the initial and boundary value problem, a general hybrid Laplace transform/finite element method is utilized. Finally, a numerical procedure, the Fourier series technique, is used to obtain the inversion of the Laplace transform. The effect of the number of mesh elements in the X‐direction is also investigated to verify the accuracy and convergence of the finite element method. In addition, a typical result is compared with the analytic solution. The numerical results of the transient temperature and thermal stress distribution of the layered slab are presented to demonstrate the effect of the physical properties.     

基于遗传算法和有限混合分布的应力谱多模态建模

该文提出了一种基于遗传算法(genetic algorithm, GA)的有限混合分布参数估计方法, 应用该方法对青马大桥典型焊接节点的应力谱进行多模态建模。首先, 采用小波变换消除原始应变监测数据中的温度影响, 利用雨流计数法将应变时程曲线转化为日应力谱, 考虑到交通荷载(包括汽车荷载和火车荷载)和台风的影响, 建立标准日应力谱。然后, 采用三种不同的有限混合分布函数(有限混合正态分布函数、有限混合对数正态分布函数和有限混合威布尔分布函数)以及基于遗传算法的混合参数估计方法对应力幅进行多模态建模, 根据赤池信息准则(Akaike’s information criterion, AIC)确定最佳的有限混合模型。最后, 采用双变量有限混合分布和基于遗传算法的混合参数估计方法建立了应力幅和平均应力二维随机变量联合概率密度函数。结果表明, 该文提出的基于遗传算法的有限混合分布参数估计方法可以有效应用于二维随机变量的概率建模。     

An investigation on strain/stress distribution around the overlap end of laminated composite single-lap joints

The damages of laminated composite single-lap joints often begin from their overlap ends because strain/stress concentrations often occur at the overlap ends. This paper presents the results of a combined experimental and finite element (FE) investigation on the strain/stress distributions around the overlap ends of laminated composite single-lap joints. Digital image correlation (DIC) technique is used to measure the strain fields near the overlap ends. A three-dimensional geometrically nonlinear FE model based on the submodel technique is developed to predict the deformation of single-lap joints. A reasonable agreement is achieved between the results from experimental measurements and FE analysis. Additionally, some FE models are built to investigate the effects of the mesostructures at the overlap ends on the stress concentrations around the overlap ends.     

STRESS INTENSITY FACTORS FOR CORNER CRACKS AT A HOLE BY A 3-D WEIGHT FUNCTION METHOD WITH STRESSES FROM THE FINITE ELEMENT METHOD

Abstract— Stress intensity factors for quarter-elliptical corner cracks emanating from a circular hole are determined using a 3-D weight function method combined with a 3-D finite element method. The 3-D finite element method is used to analyze uncracked configurations and provide stress distributions in the region where a crack is likely to occur. Using this stress distribution as input, the 3-D weight function method is used to determine stress intensity factors. Three different loading conditions, i.e. remote tension, remote bending and wedge loading, are considered for a wide range of geometrical parameters. The significance of using 3-D uncracked stress distributions is studied. Comparisons are made with solutions available in the literature.     

Three-dimensional stress analysis of rotating composite beams due to material discontinuities

Material discontinuity could cause in-plane stress gradients that it arises out-of-plane stresses in regions of sudden transition of material properties. A layerwise laminated plate theory is adapted to laminated beams to analyze analytically the three-dimensional stress field at material discontinuities in rotating composite beams. Equations of motion are obtained by using Hamilton’s principle. The beam is divided into two regions with different layups which are joined together to model the region of material discontinuity. The predicted stress distributions at the ply interfaces are shown to be in good agreement with comparative three-dimensional finite element analysis.