Solving fracture problems using an asymptotic numerical method

The present work deals with the use of asymptotic numerical methods (ANM) to manage crack onset and crack growth in the framework of continuum damage mechanics (CDM). More specifically, an application of regularization techniques to a 1D cohesive model is proposed. The standard “triangle” damageable elastic model, which is often used in finite element codes to describe fracture of brittle materials, was chosen. Results associated with the load–unload cycle showed that ANM is convenient for numerically taking this specific irregular behavior into account. Moreover, the present paper also shows that the chosen damageable interface model can be introduced in the generalized standard material formalism, thus unabling us to define a complete energy balance associated with the damage process. In such a framework, the damage state is described by a new displacement variable. Finally, a 1D finite element application to a simple elastic damageable structure is shown to highlight the potential of this approach.     

Limit load analysis of thick-walled concrete structures - a finite element approach to fracture

The paper illustrates the interaction of constitutive modelling and finite element solution techniques for limit load prediction of concrete structures.On the constitutive side, an engineering model of concrete fracture is developed in which the Mohr-Coulomb criterion is augmented by tension cut-off to describe incipient failure. Upon intersection with the stress path the failure surface collapses for brittle behaviour according to one of three softening rules — no-tension, no-cohesion, and no-friction. The stress transfer accompanying the energy dissipation during local failure is modeled by several fracture rules which are examined with regard to ultimate load prediction.On the numerical side the effect of finite element idealization is studied first as far as ultimate load convergence is concerned. Subsequently, incremental tangential and initial load techniques are compared together with the effect of step size.Limit load analyses of a thick-walled concrete ring and a lined concrete reactor closure conclude the paper along with engineering examples.     

Reliability investigations in micromechanical devices

Fatigue limited lifetime of micromechanical structures has been investigated. To determine the maximum cycle number up to failure a modified Paris equation has been used to model crack growth under load. Test structures (cantilever beams) with well-defined pre-cracks were externally loaded at resonance frequency. Single crystalline silicon as functional material (bulk micromachining) was investigated. Measured and simulated critical stress intensity factors are strongly correlated for all investigated test structures and for different crack lengths showing the validity of the used model. Lifetime decreases exponentially for loads approaching a critical stress intensity. Using the experimental results determined at test structures and the simulation model, fatigue limited lifetime of micromechanical device with typical, process induced crack distribution can be extrapolated.     

Hybrid-modelling of compact tension energy in high strength pipeline steel using a Gaussian Mixture Model based error compensation

In material science studies, it is often desired to know in advance the fracture toughness of a material, which is related to the released energy during its compact tension (CT) test to prevent catastrophic failure. In this paper, two frameworks are proposed for automatic model elicitation from experimental data to predict the fracture energy released during the CT test of X100 pipeline steel. The two models including an adaptive rule-based fuzzy modelling approach and a double-loop based neural network model, relate the load, crack mouth opening displacement (CMOD) and crack length to the released energies during this test. The relationship between how fracture is propagated and the fracture energy is further investigated in greater detail. To improve the performances of the models, a Gaussian Mixture Model (GMM)-based error compensation strategy which enables one monitor the error distributions of the predicted result is integrated in the model validation stage. This can help isolate the error distribution pattern and to establish the correlations with the predictions from the deterministic models. This is the first time a data-driven approach has been used in this fashion on an application that has conventionally been handled using finite element methods or physical models.     

A Phenomenological Discrete Brittle Damage-Mechanics Model for Fatigue of MEMS Devices With Application to LIGA Ni

Fatigue initiation and failure of various microelectromechanical systems (MEMS) is of significant importance as they gain widespread acceptance in sensors and electronics. This paper presents an approach for utilizing available experimental fatigue data to evaluate the fatigue lives of MEMS components. The approach is based on a phenomenological discrete material representation in which a domain is represented by a collection of rigid elements that interacts via springs along their boundaries. The principles of continuum damage mechanics are used to degrade the spring stiffnesses as brittle damage occurs when the domain is subjected to fatigue loading. The model utilizes experimental stress–life data for LIGA Ni to identify the material properties used in the model. The proposed model captures the statistical distribution of material properties and geometrical randomness of the microstructure commonly observed in a wide variety of MEMS. Consequently, simulations that account for the variability in fatigue life can be readily performed. The model is applied to a dog-bone-shaped specimen to evaluate the influence of material heterogeneity and material flaws on fatigue crack initiation life and scatter. The ability of the model to predict the fatigue life of different types of MEMS devices and loading conditions is also demonstrated by simulating the fatigue stress–life behavior of a MEMS resonator support beam. $hfill$[2008-0087]      

Numerical modeling of masonry-infilled RC frames subjected to seismic loads

The behavior of masonry-infilled reinforced concrete frames under cyclic lateral loading is complicated because a number of different failure mechanisms can be induced by the frame-infill interaction, including brittle shear failures of the concrete columns and damage of the infill walls. In this study, nonlinear finite element models have been used to simulate the behavior of these structures. Diffused cracking and crushing in concrete and masonry are described by a smeared-crack continuum model, while dominant cracks as well as masonry mortar joints are modeled with a cohesive crack interface model. The interface model adopts an elasto-plastic formulation to describe the mixed-mode fracture of concrete and masonry. The model accounts for cyclic crack opening and closing, reversible shear dilatation, and joint compaction due to damage. The constitutive models have been validated with experimental data and successfully applied to the dynamic analysis of a three-story, two-bay, masonry-infilled, non-ductile, reinforced concrete frame tested on a shake table. The results have demonstrated the capabilities of the finite element method in capturing the nonlinear cyclic load–displacement response and failure mechanisms of the structure, and indicated the important contribution of infill walls to the seismic resistance of a non-ductile reinforced concrete frame.     

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.     

Prediction of constant amplitude fatigue crack growth life of 2024 T3 Al alloy with R-ratio effect by GP

The objective of this study is to develop a genetic programming (GP) based model to predict constant amplitude fatigue crack propagation life of 2024 T3 aluminum alloys under load ratio effect based on experimental data and to compare the results with earlier proposed ANN model. It is proved that genetic programming can effectively interpret fatigue crack growth rate data and can efficiently model fatigue life of the material system under investigation in comparison to ANN model.     

A two-parameter model for crack growth simulation by combined FEM–DBEM approach

This paper describes the application of a two-parameters crack growth model, based on the usage of two threshold material parameters (ΔK_th and K_max,th) and on the allowance for residual stresses, introduced at the crack tip by a fatigue load spectrum or by material plastic deformations. The coupled usage of finite element method (FEM) and dual boundary element method (DBEM) is proposed in order to take advantage of the main capabilities of the two methods.The procedure is validated by comparison with available experimental results, in order to assess its capability to predict the retardation phenomena, introduced by a variable load spectrum or by a plastic deformation introduced with a tool on the panel (indentation).In particular two different tests are made: the first test involve a CT specimen undergoing a load spectrum and the second one involve a dented panel undergoing a constant amplitude fatigue load. In both cases a satisfactory numerical–experimental correlation will be proved.The main advantages of the aforementioned procedure are: the simplicity of the crack growth law calibration (few constant amplitude tests are sufficient without the need for any non-physical calibration parameters), and the possibility to simulate residual stress effects on crack propagation with a simplified approach, based on linear elastic fracture mechanics.     

Fracture resistance via topology optimization

The fracture resistance of structures is optimized using the level-set method. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension, and is calculated using the virtual crack extension technique. The shape derivative of the fracture-resistance objective function is derived. Two illustrative two-dimensional case studies are presented: a hole in a plate subjected to biaxial strain; and a bridge fixed at both ends subjected to a single load in which the compliance and fracture resistance are jointly optimized. The structures obtained have rounded corners and more material at places where they are in tension. Based on the results, we propose that fracture resistance may be modeled more easily but less directly by including a term proportional to surface area in the objective function, in conjunction with nonlinear elasticity where the Young’s modulus in tension is lower than in compression.     

Crack band model of fracture in irregular lattices

An irregular lattice model is used to simulate mode I fracture in softening materials, such as concrete. Lattice geometry is based on a three-dimensional Voronoi discretization of the material domain. The Voronoi diagram provides scaling rules for the elemental stiffness relations, leading to an elastically uniform representation of the material for simple modes of straining. Fracture is represented using a crack band approach, in which the dimensions of the crack band are also scaled according to the Voronoi diagram. The material is viewed as homogeneous and the energy dissipation mechanisms active at finer scales are lumped into a cohesive crack relation. This energy conserving crack band approach is objective with respect to the irregular geometry of the lattice. Model accuracy and performance are demonstrated through simulated fracture testing of concrete specimens under uniaxial tension and flexural loadings. Basic qualities of the simulation approach, demonstrated here for homogeneous models of concrete, are applicable toward simulating fracture in multi-phase systems where material features are explicitly modeled.     

A global model reduction approach for 3D fatigue crack growth with confined plasticity

It has been known for decades that fatigue crack propagation in elastic–plastic media is very sensitive to load history since the nonlinear behavior of the material can have a great influence on propagation rates. However, raw computations of millions of nonlinear fatigue cycles on tridimensional structures would lead to prohibitive calculation times. In this respect, we propose a global model reduction strategy, mixing both the a posteriori and a priori approaches in order to drastically decrease the computational cost of these types of problems.     

High-cycle fatigue of single-crystal silicon thin films

When subjected to alternating stresses, most materials degrade, e.g., suffer premature failure, due to a phenomenon known as fatigue. It is generally accepted that in brittle materials, such as ceramics, fatigue can only take place in toughened solids, i.e., premature fatigue failure would not be expected in materials such as single crystal silicon. The results of this study, however, appear to be at odds with the current understanding of brittle material fatigue. Twelve thin-film (~20 μm thick) single crystal silicon specimens were tested to failure in a controlled air environment (30±0.1°C, 50±2% relative humidity). Damage accumulation and failure of the notched cantilever beams were monitored electrically during the "fatigue life" test. Specimen lives ranged from about 10 s to 48 days, or 1×106 to 1×1011 cycles before failure over stress amplitudes ranging from approximately 4 to 10 GPa. A variety of mechanisms are discussed in light of the fatigue life data and fracture surface evaluation     

Numerical–experimental crack growth analysis in AA2024-T3 FSWed butt joints

This paper deals with a numerical and experimental investigation on the influence of residual stresses on fatigue crack growth in AA2024-T3 friction stir welded butt joints. The computational approach is based on the sequential usage of the Finite Element Method (FEM) and the Dual Boundary Element Method (DBEM). Linear elastic FE simulations are performed to evaluate the process induced residual stresses, by means of the contour method. The computed stress field is transferred to a DBEM environment and superimposed to the stress field produced by a remote fatigue traction load applied on a friction stir welded cracked specimen; the crack propagation is then simulated according to a two-parameter growth model. Numerical results have been compared with experimental data showing good agreement and evidencing the predictive capability of the proposed method. The obtained results highlight the influence of the residual stress distribution on crack growth.     

Nonlinear finite element analysis of reinforced concrete plates and shells under monotonic loading

Plane stress constitutive models are proposed for the nonlinear finite element analysis of reinforced concrete structures under monotonic loading. An elastic strain hardening plastic stress-strain relationship with a nonassociated flow rule is used to model concrete in the compression dominating region and an elastic brittle fracture behavior is assumed for concrete in the tension dominating area. After cracking takes place, the smeared cracked approach together with the rotating crack concept is employed. The steel is modeled by an idealized bilinear curve identical in tension and compressions. Via a layered approach, these material models are further extended to model the flexural behavior of reinforced concrete plates and shells. These material models have been tested against experimental data and good agreement has been obtained.     

Meshless Animation of Fracturing Solids

We present a new meshless animation framework for elastic and plastic materials that fracture. Central to our method is a highly dynamic surface and volume sampling method that supports arbitrary crack initiation, propagation, and termination, while avoiding many of the stability problems of traditional mesh-based techniques. We explicitly model advancing crack fronts and associated fracture surfaces embedded in the simulation volume. When cutting through the material, crack fronts directly affect the coupling between simulation nodes, requiring a dynamic adaptation of the nodal shape functions. We show how local visibility tests and dynamic caching lead to an efficient implementation of these effects based on point collocation. Complex fracture patterns of interacting and branching cracks are handled using a small set of topological operations for splitting, merging, and terminating crack fronts. This allows continuous propagation of cracks with highly detailed fracture surfaces, independent of the spatial resolution of the simulation nodes, and provides effective mechanisms for controlling fracture paths. We demonstrate our method for a wide range of materials, from stiff elastic to highly plastic objects that exhibit brittle and/or ductile fracture.     

橡胶材料疲劳断裂特性研究进展

由于橡胶材料的动态疲劳特性对保证橡胶制品使用时的安全性和可靠性具有重要意义,综述机械载荷、环境和橡胶配方等因素对橡胶材料疲劳寿命的影响,总结用疲劳裂纹萌生寿命法和基于断裂力学的疲劳裂纹扩展法预测橡胶材料动态疲劳寿命方法的优缺点,并展望这2种方法的发展趋势.     

Evaluation of thermo-mechanical damage and fatigue life of solar cell solder interconnections

The soldering process of interconnecting crystalline silicon solar cells to form photovoltaic (PV) module is a key manufacturing process. However, during the soldering process, stress is induced in the solar cell solder joints and remains in the joint as residual stress after soldering. Furthermore, during the module service life time, thermo-mechanical degradation of the solder joints occurs due to thermal cycling of the joints which induce stress, creep strain and strain energy. The resultant effect of damage on the solder joint is premature failure, hence shortened fatigue life. This study seeks to determine accumulated thermo-mechanical damage and fatigue life of solder interconnection in solar cell assembly under thermo-mechanical cycling conditions. In this investigation, finite element modelling (FEM) and simulations are carried out in order to determine nonlinear degradation of SnAgCu solder joints. The degradation of the solder material is simulated using Garofalo-Arrhenius creep model. A three dimensional (3D) geometric model is subjected to six accelerated thermal cycles (ATCs) utilising IEC 61215 standard for photovoltaic panels. The results demonstrate that induced stress, strain and strain energy impacts the solder joints during operations. Furthermore, the larger the accumulated creep strain and creep strain energy in the joints, the shorter the fatigue life. This indicates that creep strain and creep strain energy in the solder joints significantly impacts the thermo-mechanical reliability of the assembly joints. Regions of solder joint with critical stress, strain and strain energy values including their distribution are determined. Analysis of results demonstrates that creep energy density is a better parameter than creep strain in predicting interconnection fatigue life. The use of six ATCs yields significant data which enable better understanding of the response of the solder joints to the induced loads. Moreover, information obtained from this study can be used for improved design and better-quality fabrication of solder interconnections in solar cell assembly for enhanced thermo-mechanical reliability.