Fatigue life prediction under cyclic thermal loads using the boundary elements method for two-dimensional problems

This study describes a sub-domain boundary element procedure for predicting the fatigue life of elastic media under cyclic transient thermal loads. The procedure assumes an initial crack in a two-dimensional medium, and evaluates the crack extension along a path defined by the maximum circumferential stress criterion. Partial closure may occur on the growing crack faces due to thermal loading. Appropriate thermal and mechanical boundary conditions are imposed on the numerical model to account for the contact state. The analysis requires solutions to the equations of quasi-static thermo-elasticity, and uses an iterative procedure to detect the contact region. We investigate cases of pure opening or mixed mode fracture, demonstrating the effects of crack closure on the predicted fatigue life. We compare the obtained results with those of other publications.     

Influence of micro-cracking and contact on the effective properties of composite materials

In the present work a novel micro-mechanical approach to analyze the influence of micro-crack evolution and contact on the effective properties of elastic composite materials is proposed, based on homogenization techniques, interface models and fracture mechanics concepts. By means of the finite element method, enhanced non-linear macroscopic constitutive laws are developed by taking into account changes in micro-structural configuration associated with the growth of micro-cracks and with contact between crack faces. Numerical simulations are carried out for the cases of a porous composite with edge cracks and of a debonded fibre reinforced composite, loaded along extension/compression uniaxial macro-strain paths. Micro-crack propagation is modelled by using an original methodology based on the J-integral technique in conjunction with an interface model taking into account the unilateral contact of crack faces. In the context of a micro-to-macro transition obtained by controlling the macro-deformation of the micro-structure, the effects of adopting three types of boundary conditions on the macroscopic constitutive law, namely linear deformation, uniform tractions and periodic deformations and anti-periodic tractions, are studied. As a consequence, the proposed method can be applied to a large class of problems including periodic, locally periodic and irregular composite materials. Micro-crack and contact evolution result in a progressive loss of stiffness and can lead to failure for homogeneous macro-deformations associated with unstable crack propagation.     

A comparative study on the failure resistance of thermal barrier coatings

A bi-material structure, representing a single layer thermal barrier coating, containing an interfacial crack and subjected to a cooling shock, is investigated using the finite element method. Numerical tests are performed to study the effect of material properties mismatch, between the coating and the substrate, on the failure resistance of the cracked structure, represented by the strain energy release rate. No special care is taken for taking into consideration the singular nature of near tip temperature and displacement fields. The parametric study is based on a quasi-static uncoupled thermo-elasticity assumption and a crack opening displacement formula for obtaining the strain energy release rate. The methodology that is followed has been validated in a previous article by comparison to an analytic solution. Computational results indicate that the strain energy release rate peak, experienced during the thermal shock, is highly dependent on the thermal conductivity and thermal expansion coefficient mismatch, but almost independent from the Young’s modulus mismatch between the two materials. It is concluded that, the failure resistance of the thermal barrier coating decreases, as the insulation provided by the coating and its thermal expansion coefficient increase in relation to the substrate.     

An elastoplastic cracked-beam finite element for structural analysis

A finite element model has been developed in this paper to analyse statically indeterminate skeletal cracked structures. The model is based on elastic-plastic fracture mechanics techniques in order to consider the crack tip plasticity in the analysis. Stiffness matrices for single-edge and double-edge cracked structural elements have been derived using transfer matrix theory. These matrices take into account the effects of axial, flexural and shear deformations due to crack presence. The present model has been applied to investigate the effects of crack size, structure cross-section depth and crack tip plasticity on the redistribution of internal forces in structures. Hence, this analysis can be employed to identify the overstressed regions in cracked structures.     

Application of an interface failure model to predict fatigue crack growth in an implanted metallic femoral stem

A novel computational modelling technique has been developed for the prediction of crack growth in load bearing orthopaedic alloys subjected to fatigue loading. Elastic-plastic fracture mechanics has been used to define a three-dimensional fracture model, which explicitly models the opening, sliding and tearing process. This model consists of 3D nonlinear spring elements implemented in conjunction with a brittle material failure function, which is defined by the fracture energy for each nonlinear spring element. Thus, the fracture energy criterion is implicit in the brittle material failure function to search for crack initiation and crack development automatically. A degradation function is employed to reduce interfacial fracture properties corresponding to the number of cycles; thus fatigue lifetime can be predicted. Unlike other failure modelling methods, this model predicts the failure load, crack path and residual stiffness directly without assuming any pre-flaw condition. As an example, fatigue of a cobalt based alloy (CoCrMo) femoral stem is simulated. Experimental fatigue data was obtained from four point bending tests. The finite element model simulated a fully embedded implant with a constant point load. Comparison between the model and mechanical test results showed good agreement in fatigue crack growth rate.     

大规模并行原子模拟在钛合金界面行为研究中的应用

界面对钛合金的力学性能有至关重要的影响。界面行为的原子模拟涉及的原子数目庞大,必须借助大规模并行计算。本研究组开发了大规模并行分子动力学程序,并将其应用于钛合金中不同种类界面行为的模拟研究。本文以钛铝金属间化合物中的孪晶界和 α 钛中的特殊大角晶界为例,介绍研究组在钛合金晶界行为的计算模拟方面的近期研究成果。所模拟的体系尺寸达到微米级,所需 CPU 核数几十至几百不等。研究发现,钛铝模拟晶胞沿伪孪晶方向剪切变形时,等静压力下可产生 L1₁ 结构的伪孪晶形核长大,而等静张力下剪切可产生真孪晶的形核长大,提出钛铝中一种新的孪晶长大机制。在 α 钛中,特定取向的两个晶粒所形成的晶界与位错发生相互作用,裂纹形核依赖于加载外力的取向而发生在晶界处或硬取向晶粒内,从而可能导致疲劳断裂行为与加载取向相关。这些结果有助于理解钛合金的塑性变形行为,并为更高尺度的模拟研究提供了原子尺度细节。     

Study of elastic behaviour of plates containing cracks by finite element analysis

This work applies finite element analysis very simply to cracked plates. An infinite plate and a finite plate, both with a central crack, are considered to study their elastic behaviour and some fracture mechanics concepts, such as the geometry factor and the fracture toughness. These magnitudes are calculated by means of finite element methods and the results are in very good agreement with the established theory, which proves that the finite element approach is very appropriate. The fracture toughness fraction is defined and calculated for a finite plate to predict its failure.     

A generalised technique for fracture analysis of cracked plates under combined tensile,bending and shear loads

The objective of this paper is to propose a generalized technique called numerically integrated modified virtual crack closure integral (NI-MVCCI) technique for fracture analysis of cracked plates under combined tensile, bending and shear loads. NI-MVCCI technique is used for post-processing the results of finite element analysis (FEA) for computation of strain energy release rate (SERR) components and the corresponding stress intensity factor (SIF) for cracked plates. NI-MVCCI technique has been demonstrated for 4-noded, 8-noded (regular and quarter-point) and 9-noded (regular and quarter-point) isoparametric plate finite elements. These elements are based on Mindlin’s plate theory that considers shear deformation. For all the elements, reduced integration/selective reduced integration techniques have been employed in the studies. In addition, for 9-noded element assumed shear interpolation functions have been used to overcome the shear locking problem. Numerical studies on fracture analysis of plates subjected to tension–moment and tension–shear loads have been conducted employing these elements. It is observed that among these elements, the 9-noded Lagrangian plate element with assumed shear interpolation functions exhibits better performance for fracture analysis of cracked plates.     

Application of genetic algorithm in crack detection of beam-like structures using a new cracked Euler–Bernoulli beam element

In this paper, a crack identification approach is presented for detecting crack depth and location in beam-like structures. For this purpose, a new beam element with a single transverse edge crack, in arbitrary position of beam element with any depth, is developed. The crack is not physically modeled within the element, but its effect on the local flexibility of the element is considered by the modification of the element stiffness as a function of crack's depth and position. The development is based on a simplified model, where each crack is substituted by a corresponding linear rotational spring, connecting two adjacent elastic parts. The localized spring may be represented based on linear fracture mechanics theory. The components of the stiffness matrix for the cracked element are derived using the conjugate beam concept and Betti's theorem, and finally represented in closed-form expressions. The proposed beam element is efficiently employed for solving forward problem (i.e., to gain accurate natural frequencies of beam-like structures knowing the cracks’ characteristics). To validate the proposed element, results obtained by new element are compared with two-dimensional (2D) finite element results as well as available experimental measurements. Moreover, by knowing the natural frequencies, an inverse problem is established in which the cracks location and depth are identified. In the inverse approach, an optimization problem based on the new beam element and genetic algorithms (GAs) is solved to search the solution. The proposed approach is verified through various examples on cracked beams with different damage scenarios. It is shown that the present algorithm is able to identify various crack configurations in a cracked beam.     

A doubly iterative BEM for solving crack closing in an elastic body

An algorithm for the two-dimensional elastic bodies with closed crack and defects loaded by a moving contact elastic body is proposed using a sub-regional boundary element method. Since the extent and status of the contact surface of two elastic bodies and the crack within the body are all not known in advance, a doubly iterative contact algorithm has been presented. The BEM program for solving the closed crack cases has been developed, some numerical examples have been calculated, and the results of the center crack cases are in good agreement with the analytical solution in classical fracture mechanics. In the condition of friction and non-friction, some coupling computational results of the SIF for the closed crack cases, which have different angles and loaded by a moving contact elastic body, have also been obtained by numerical computation. The cracked plate subjected to the moving contact elastic body has been analyzed under the conditions of drilling hole near the crack.     

Subcritical crack growth in silicon MEMS

New experimental techniques need to be developed to address fundamental materials issues in MEMS. Experimental protocols developed for macroscale testing are not necessarily applicable, and an understanding of the behavior of macroscale specimens cannot necessarily be relied upon to predict the behavior of microscale MEMS structures. An experimental protocol for studying slow crack growth in MEMS materials has been developed, and this protocol has been used to show that polycrystalline silicon (polysilicon) MEMS are susceptible to stress corrosion cracking. Using a model of the nonlinear dynamics of a specimen allowed an estimation of crack length and crack closure from the frequency response of the specimen. The procedure can resolve 1-nm crack extensions and crack growth rates below 10^-13 m/s. Crack closure, which has a pronounced effect on the dynamics of this nonlinear system, may be associated with the native oxide that grows on the faces of the crack. The data show that subcritical crack growth in polysilicon MEMS is driven by the synergistic effects of water and stress. In contrast to macroscale stress corrosion cracking behavior, a clear relationship between crack growth rate, stress intensity and humidity has not been found. Micrographs suggest that the crack path is transgranular     

A two-scale extended finite element method for modelling 3D crack growth with interfacial contact

3D fatigue crack growth problems are nowadays handled using X-FEM coupled with level set techniques. It is also well established that such an approach allows mesh-independent crack modelling and no remeshing during crack propagation. However, when contact and friction occur along the crack faces, a discretization of the internal variables linked to the interface law is necessary. The interface discretization is generally constructed from the finite elements cut by the crack. As a consequence, a mesh dependency between the bulk discretization and the interface discretization is introduced. However, the dimension of the possible non-linearities arising at the crack interface (like confined plasticity or unilateral contact with friction) may be several orders of magnitude finer than the crack size. A finer discretization is thus required to accurately capture these non-linearities. The aim of the present paper is to develop a method considering the 3D cracked structure and the crack interface as two independent global and local problems characterized by different length scales and different behaviors. Here, the interface is seen as an autonomous entity with its own discretization, variables and constitutive law. A formulation involving three-fields is used. The interface is linked to the global problem in a weak sense in order to avoid instabilities in the contact solution. Two iterative strategies are considered to solve the contact problem. Two-dimensional and three-dimensional numerical examples are presented to demonstrate the ability of the model to solve the contact at the crack interface with or without propagation at a given level of accuracy.     

An Efficient Adaptive Procedure for Three-Dimensional Fragmentation Simulations

We present a simple set of data structures, and a collection of methods for constructing and updating the structures, designed to support the use of cohesive elements in simulations of fracture and fragmentation. Initially, all interior faces in the triangulation are perfectly coherent, i.e. conforming in the usual finite element sense. Cohesive elements are inserted adaptively at interior faces when the effective traction acting on those faces reaches the cohesive strength of the material. The insertion of cohesive elements changes the geometry of the boundary and, frequently, the topology of the model as well. The data structures and methods presented here are straightforward to implement, and enable the efficient tracking of complex fracture and fragmentation processes. The efficiency and versatility of the approach is demonstrated with the aid of two examples of application to dynamic fracture.     

A robust and consistent remeshing-transfer operator for ductile fracture simulations

This paper addresses the numerical simulation of quasi-static ductile fracture. The main focus is on numerical and stability aspects related to discrete crack propagation. Crack initiation and propagation are taken into account, both driven by the evolution of a discretely coupled damage variable. Discrete ductile failure is embedded in a geometrically nonlinear hyperelasto-plastic model, triggered by an appropriate criterion that has been evaluated for tensile and shear failure. A crack direction criterion is proposed, which is validated for both failure cases and which is capable of capturing the experimentally observed abrupt tensile–shear transition. In a large strain finite element context, remeshing enables to trace the crack geometry as well as to preserve an adequate element shape. Stability of the computations is an important issue during crack propagation that can be compromised by two factors, i.e. large stress redistributions during the crack opening and the transfer of variables between meshes. A numerical procedure is developed that renders crack propagation considerably more robust, independently of the mesh fineness and crack discretisation. A consistent transfer algorithm and a crack relaxation method are proposed and implemented for this purpose. Finally, illustrative simulations are compared with published experimental results to highlight the features mentioned.     

Characterizing mechanical behaviors of a flexible AMOLED during the debonding process

The stress distribution of a flexible active-matrix organic light-emitting diode (AMOLED) display during the debonding process was investigated using finite element analysis. During the fabrication of an AMOLED display, an AMOLED with a polyimide (PI) substrate is detached from a glass carrier; this is a critical process and generally results in failure of the AMOLED. To enhance the yielding rate of AMOLEDs, their stress states generated during the debonding process must be reduced. The interfacial fracture behavior between the PI substrate and glass carrier was characterized on the basis of bimaterial fracture mechanics, and the fracture toughness associated with mode mixity determined through peeling tests was considered a criterion for detaching the AMOLED from the glass carrier. The stress distribution of the AMOLED at the inception of debonding crack extension was evaluated according to fracture toughness. In addition, the parameters possibly influencing the stress states of the AMOLED in the debonding process are discussed.     

Finite element analysis of crack closure in plate bending

The effect of crack closure in plate bending is studied using the finite element method. Elastic plates containing through-wall-thickness stationary cracks under transverse pressure loading are considered with different plate thicknesses and boundary conditions, respectively. Crack closure on the compression side is modeled two different ways: line closure and surface closure models. A plate bending element degenerated from a three-dimensional solid element is used to model such crack closure. Effects of crack closure are compared using the line or surface closure model for different plate thicknesses and boundary conditions, respectively.     

Mechanical properties of glass frit bonded micro packages

Frit glass bonding is a widely used technology for encapsulation of surface micro-machined structures like inertial sensors or gyroscopes on wafer level. Since for sensors in automotive applications, a lifetime of 15–20 years has to be guaranteed for, a reliable lifetime prediction is necessary. Different material parameters have to be known for a lifetime estimation based on stress corrosion cracking, which determines the long-term strength behaviour of most bonded interfaces of microsystems. Parameters needed for lifetime prediction have to describe the material’s resistance against crack propagation (fracture toughness K _IC), the stress situation in a micro package and the long-term strength behaviour. Results for fracture toughness investigations presented in this paper were determined by the micro chevron test. The stress situation in a micro package was calculated by a thermo-mechanical Finite Element Analysis. Furthermore the residual stress in the glass layer and the linear thermal expansion coefficient were determined by a crack width measurement in an environmental scanning electron microscope.     

Free transverse vibration analysis of size dependent Timoshenko FG cracked nanobeams resting on elastic medium

In the present study, free transverse vibration of a cracked functionally graded (FG) size dependent Timoshenko nanobeam which is resting on polymer elastic foundation is investigated. It is supposed that the material properties of the FG nanobeam are varying continuously across the thickness according to the power-law distribution. To considering the small scale effect, the Eringen’s nonlocal theory is used and for accounting the effect of polymer elastic foundation, the Winkler model is proposed. For this purpose, the equations of motion of the FG Timoshenko nanobeam and boundary conditions are obtained by using Hamilton’s principle. To find the analytical solutions for equations of motion of FG nanobeam, the separation of variable method is employed. Two cases of boundary conditions i.e., simply supported-simply supported (SS) and clamped–clamped (CC) are investigated in the present work. Numerical results are demonstrating the good agreement between the results of present article and some cases available in the literature. The emphasis of the present study is based on investigating the effect of various parameters such as crack severity, crack position, gradient index, mode number, nonlocal parameter, elastic foundation parameter and nanobeam length. It is clearly revealed that the vibrational behavior of a FG nanobeam is significantly depending on these effects. Also, these numerical results can be serving as benchmarks for future studies of FG nanobeams.

     

Inelastic dynamic response of reinforced concrete infilled frames

An inelastic finite element model to simulate the behaviour of reinforced concrete frames infilled with masonry panels subjected to static load and earthquake excitation has been presented. Under the loads, the mortar may crack causing sliding and separation at the interface between the frame and the infill. Further, the infill may get cracked and/or crushed which changes its structural behaviour and may render the infill ineffective, leaving the bare frame to take all the load which may lead to the failure of the framing system itself. In this study, a mathematical model to incorporate this behaviour has been presented.     

An application for the fracture characterisation of quasi-brittle materials taking into account fracture process zone influence

The paper introduces a Java application programmed for the advanced determination of the fracture characteristics of silicate-based materials failing in a quasi-brittle manner. The tool reconstructs the progress of a quasi-brittle fracture from the measured load–displacement curve and the knowledge of basic mechanical properties of the material. The main contribution of the proposed approach is that it takes the characteristics of the Fracture Process Zone (FPZ, particularly its extent, i.e. its size and shape) evolving at the tip of the propagating crack during the failure process into account and incorporates them into the fracture-mechanical parameter evaluation procedure(s). This approach is expected to substantially diminish the influence of the test specimen’s size/shape and the test geometry on the values of the parameters of nonlinear fracture models determined from the records of fracture tests on laboratory specimens. The application implements a developed technique for estimation of the size and shape of the FPZ. The technique is based on an amalgamation of several modelling concepts dealing with the failure of structural materials, i.e. multi-parameter linear elastic fracture mechanics, classical nonlinear fracture models for concrete (equivalent elastic crack and cohesive crack models), and the plasticity approach. The knowledge of the FPZ’s extent is employed for the relation of a part of the entire work of fracture to its characteristics within the presented approach. The verification and validation of the developed technique is performed via numerical simulations using the authors’ own computational code based on physical discretization of continuum and selected sets of experimental evidence published in the literature. Reasonable agreement is observed between the outputs of the presented semi-analytical technique and both the simulation results and the experimental data.