Fatigue analysis of brittle materials using indentation flaws

The results of an experimental dynamic fatigue study on glass-ceramic specimens containing indentation flaws are analysed in terms of the theory developed in Part 1. A Vickers indenter is used to introduce the flaws, and a conventional four-point bend apparatus to break the specimens. Base-line data for testing the essential theoretical predictions and for evaluating key material/environment parameters are obtained from polished surfaces, i.e. surfaces prepared to a sufficient finish to ensure removal of any pre-existing spurious stresses. The fatigue tests are carried out in water. Inert strength tests in dry nitrogen are used to calibrate appropriate equilibrium fracture parameters, with dummy indentations on selected control specimens providing a convenient measure of the critical crack dimensions at failure. Regression analysis of the dynamic fatigue data yields values for apparent kinetic parameters, which are converted to true kinetic parameters via the transformation equations of Part I. Regeneration of the fatigue function from the theory using the parameters thus determined gives a curve which passes closely through the experimental data points, thereby providing a self-consistent check of the formalism. The implications of the results in relation to the use of macroscopic fracture parameters in the prediction of strength properties for materials with small-scale flaws is an important adjunct to this work. Finally, a recommended procedure for the general testing of dynamic fatigue properties of ceramics using indentation flaws is described.     

Fatigue analysis of brittle materials using indentation flaws

A two-part study has been made of the fatigue characteristics of brittle solids using controlled indentation flaws. In this part a general theory is developed, with explicit consideration being given to the role played by residual contact stresses in the fracture mechanics to failure. The distinctive feature of the formulation is a stress intensity factor for well-defined indentation cracks, suitably modified to incorporate the residual component. Taken in conjunction with a standard power-law crack velocity function, this leads to a differential equation for the dynamic fatigue response of a given material/ environment system. Reduced variables are then introduced to facilitate generation of universal fatigue curves, determined uniquely by the crack velocity exponent,n. A scheme for using these curves to evaluate basic fracture parameters from strength data is outlined. In this way the foundation is laid for lifetime predictions of prospective brittle components, as well as for reconstruction of the crack velocity function. One of the major advantages of the analysis is the manner in which the residual stress parameters are accommodated in the normalized fracture mechanics equations: whereas it is understood thatall strength data are to be taken from test pieces in their as-indented state, so making it unnecessary to have to resort to inconvenient stress-removal procedures between the contact and failure stages of testing,a priori knowledge of the residual stress level is not required. The method is proposed as an economical route to materials evaluation and offers physical insight into the behaviour of natural flaws.     

Finite element analysis of local damage and post-failure behavior for strain-softening solid

A finite element analysis of the viscoplastic-softening model with the evolution of local damage for strain softening material is presented. An effective damage matrix is introduced to consider the influence of isotropic damage on different types of micro-cracking by different states of stress. The localized strain mode with local damage occurs in the post-failure regime of deformation. The computational techniques for tracing the post-failure path of the softening response are discussed with several examples.     

Finite element analysis of deep indentation by a spherical indenter

Using the finite element analysis, the deep indentation of strain-hardening elastoplastic materials by a rigid, spherical indenter has been studied. The simulation results clearly show that the ratio of the indentation load to the maximum indentation depth increases with the increase of the strain-hardening index and reaches a maximum value at the maximum indentation depth being about 10% of the indenter radius. The power law relation between the indentation load and the indentation depth for shallow indentation becomes invalid for deep indentation. However, the ratio of the plastic energy to the total mechanical work is a linear function of the ratio of the residual indentation depth to the maximum indentation depth, independent of the strain-hardening index and the indentation depth.     

Finite element analysis of reinforcement particle cracking in AlSiCp composites

Abstract

Discontinuously reinforced metal matrix composites are susceptible to reinforcement particle cracking, which reduces tensile elongation. However, many of the particles experience multiple cracking episodes, which would seem unfavourable in a matrix filled with similar particles. Simulations of an aluminium matrix composite reinforced with 9 vol.-SiC particles have been performed using a non-linear axisymmetric finite element model. Reinforcement particles with and without defects were cracked in the simulation in order to study the subsequent behaviour of the composite. Particle defects were found to decrease the impact of reinforcement particle cracking on the stress in the surrounding matrix. Multiple cracking of reinforcement particles was shown to be feasible because of the load bearing ability of fractured particles.     

Finite element analysis of viscoelastic solids responding to periodic disturbances

A finite element analysis for viscoelastic solids responding to periodic disturbances travelling at constant speed is developed. The disturbance is decomposed into harmonic components using the Discrete Fourier Series, and the viscoelastic material response is determined using the Correspondence principle. The procedure is used to solve two and three dimensional contact problems to demonstrate its effectiveness.     

Elastostatic analysis of infinite solids using finite elements

A novel technique is developed to simulate the effects of an infinite elastic solid by using multiple springs having spatially varying stiffnesses. The spring constants are computed by numerical integration of classical solutions for point or line loads in an infinite or semi-infinite elastic mass. Under certain conditions, even the 'exact' values of spring constants may become negative at some nodes. A simple and highly effective algorithm is proposed to remove this computational difficulty. The technique is applied to the computation of displacements and stresses around underground openings. For a circular opening subjected to different stress conditions, spring constants computed by the proposed numerical integration technique are found to be 'identical' to their 'exact' values. Results obtained by the proposed technique for displacements and stresses around circular and non-circular openings are found to be in an excellent agreement with classical and boundary element solutions. The principal advantages of the proposed technique are that an unbounded solid may be simulated by a relatively very small finite model and a standard finite element code requires no modification for its implementation.     

Finite element analysis of bi-material interface notch crack behaviour

The finite element method is extended to the analysis of the behaviour of an interface crack in bi-material specimen with a central hole. First, only the notch effect is considered, the field of stress and variation of the stress concentration factor as a function of the Young’s modulus ratio are determined. Secondly, the notch interface crack behaviour is investigated, the variations of the stress intensity factor versus the Young’s modulus ratio and crack length are shown as well as the distribution of stresses in the plate and along the interface.     

Finite element analysis of interface delamination and buckling in thin film systems by wedge indentation

A finite element method is used to study the interface delamination and buckling of thin film systems subject to microwedge indentation. In the formulation, the interface adjoining the thin film and substrate is assumed to be the only site where cracking may occur. Both the thin film and the substrate are taken to be ductile materials with finite deformation. A traction-separation law, with two major parameters: interface strength and interface energy, is introduced to simulate the adhesive and failure behaviors of the interface between the film and the substrate. The effects of the interface adhesive properties and the thickness of the thin film on the onset and growth of interface delamination and the film buckling are investigated.     

A cohesive finite element formulation for modelling fracture and delamination in solids

In recent years, cohesive zone models have been employed to simulate fracture and delamination in solids. This paper presents in detail the formulation for incorporating cohesive zone models within the framework of a large deformation finite element procedure. A special Ritz-finite element technique is employed to control nodal instabilities that may arise when the cohesive elements experience material softening and lose their stress carrying capacity. A few simple problems are presented to validate the implementation of the cohesive element formulation and to demonstrate the robustness of the Ritz solution method. Finally, quasi-static crack growth along the interface in an adhesively bonded system is simulated employing the cohesive zone model. The crack growth resistance curves obtained from the simulations show trends similar to those observed in experimental studies     

Finite element analysis of deformation behaviour in ductile matrix containing hard particles

Abstract

Three-dimensional finite element analyses were carried out to study the deformation behaviour in ductile matrix-hard particle composite systems. Models with transversely aligned and staggered particle distributions were used. The deformation constraints in the models were investigated and the development of triaxial stress states in the models was studied. It was determined that the strengthening behaviour arises as a result of geometrical hardening in the early stage of composite deformation. Special deformation stages in the overall stress-strain behaviour of the composite microstructures such as initiation of microyielding, expansion of the plastically deformed region, and spread of plastic flow were determined by following the development of plasticity.     

Finite element analysis of anisotropic non-linear incompressible elastic solids by a mixed model

A mixed finite element method is presented for geometrically and materially non-linear analysis of anisotropic incompressible hyperelastic materials. An incremental iteractive total Lagrangian formulation is adopted. The nodal displacements and the hydrostatic pressure are independently interpolated leading to a mixed system of equations, with characteristic zero diagonal terms. Computations are carried out using a three-dimensional linear displacement, constant pressure element. A mixed penalty approximation is then employed to eliminate the pressure variables at the element level. The anisotropic material handling capability of the formulation is tested through a number of transversely isotropic problems and the results compared to analytical solutions. To demonstrate the applicability of this formulation to model complex anisotropic problems, the inflation of a cut toroidal tube with helical fibre orientation is analysed.     

Finite element analysis of lateral sloshing response in axisymmetric tanks with triangular elements

A finite element analysis is presented for the sloshing motion of liquid-filled axisymmetric tanks during lateral excitation, for a circumferential mode number, m=1, antisymmetric. The system of finite element equations concerned is derived by means of variational principle. Linear basis functions associated with the regular triangulation of Friedrichs-Keller type was used. The analytical expressions of the mass and stiffness matrices for a finite element were obtained. Numerical results of the free vibration for cases of annular and cylindrical tanks were obtained, and compared with existing experiments and other predicted results, showing a good agreement between the experiment and numerical results.     

Dynamic analysis of cracked linear viscoelastic solids by finite element method using singular element

The finite element method for the dynamic problem of cracked linear viscoelastic solids is developed using the singular element where the displacement function is taken from the analytical solution near the crack-tip. The time variation of the dynamic stress intensity factors is determined for a center crack and an oblique crack in standard linear viscoelastic rectangular plates subjected to dynamic loading.

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Résumé La méthode par éléments finis permettant d'aborder le problème dynamique des solides linéaires viscoélastiques fissurés est développée en recourant à un élément singulier pour lequel la fonction de déplacement est prise dans une solution analytique au voisinage del'extrémité de la fissure. La variation dans le temps des facteurs d'intensité de contrainte dynamique est déterminée pour une fissure centrale et pour une fissure oblique dans des plaques rectangulaires standard en matériau linéaire viscoélastique soumises à une sollicitation dynamique.

     

Finite element analysis of viscoelastic structures using Rosenbrock-type methods

The consistent application of the space-time discretisation in the case of quasi-static structural problems based on constitutive equations of evolutionary type yields after the spatial discretisation by means of the finite element method a system of differential-algebraic equations. In this case the resulting system of differential-algebraic equations with the unknown nodal displacements and the evolution equations at all spatial quadrature points of the finite element discretisation are solved by means of a time-adaptive Rosenbrock-type methods leading to an iteration-less solution scheme in non-linear finite element analysis. The applicability of the method will be studied by means of a simple example of a viscoelastic structure.     

Finite element analysis of quasi-prismatic bodies using Chebyshev polynomials

A new kind of finite element is presented in this paper which is designed to work efficiently for bodies that are either prismatic or ‘quasi-prismatic’ in shape. Quasi-prismatic shapes are those which can be obtained from prismatic shapes by mere distortion. The element which is formulated in this paper may be coupled with other types of three-dimensional elements to allow the modelling of structures which are only partially prismatic or which have prismatic shapes within them. The element allows for a variety of boundary conditions, yet yields meshes which are easy to generate. The performance of this element is evaluated by numerical experiments that compare its results with analytical solutions for a thick cylinder problem and a curved beam problem. The element has also been demonstrated on a turbine blade model.     

Delamination buckling and propagation analysis of honeycomb panels using a cohesive element approach

The cohesive element approach is proposed as a tool for simulating delamination propagation between a facesheet and a core in a honeycomb core composite panel. To determine the critical energy release rate (G _c) of the cohesive model, Double Cantilever Beam (DCB) fracture tests were performed. The peak strength (_c) of the cohesive model was determined from Flatwise Tension (FWT) tests. The DCB coupon test was simulated using the measured fracture parameters, and sensitivity studies on the parameters for the cohesive model of the interface element were performed. The cohesive model determined from DCB tests was then applied to a full-scale, 914×914 mm (36×36 in.) debond panel under edge compression loading, and results were compared with an experiment. It is concluded that the cohesive element approach can predict delamination propagation of a honeycomb panel with reasonable accuracy.     

Simulation of multiple delaminations in impacted cross-ply laminates using a finite element model based on cohesive interface elements

The paper investigates the capability of a finite element model based on cohesive interface elements to simulate complex three-dimensional damage patterns in composite laminates subjected to low-velocity impact. The impact response and the damage process of cross-ply laminated plates with grouped ([0₃/90₃]s and [90₃/0₃]s) and interspersed ([0/90]₃s) ply stacking was simulated using a FE model developed by the authors in a previous study and the numerical results were compared to experimental observations. The model provided a correct simulation of size, shape and location of the principal fracture modes occurring in impacted [0₃/90₃]s and [90₃/0₃]s laminates. In [0/90]₃s laminates, characterized by a complex spatial damage distribution, the model was able to predict the approximately circular shape of the overall projected damage area and to capture the typical shape features of individual delaminations; significant discrepancies between experiments and predictions were however observed in terms of delamination sizes at single interfaces. Further investigations are needed to clarify the main reasons of these discrepancies.