Finite element simulations of crack propagation in functionally graded materials under flexural loading

Cracks in stepped and continuously graded material specimens under flexural loading were investigated via finite element analysis. Calculation of mechanical energy release rates and propagation angles with crack-opening displacement correlation and the local symmetry (K_II = 0) criterion, respectively, provided results most efficiently and accurately, as compared with compliance and J-integral approaches and other deflection criteria. A routine was developed for automatic crack extension and remeshing, enabling simulation of incremental crack propagation. Effects of gradient profile and crack geometry on crack-tip stresses and crack propagation path are examined, and implications of these for optimal design of graded components against failure by fast fracture are discussed.     

Analysis of the crack growth propagation process under mixed-mode loading

In the present paper, a computational model for crack growth analysis under Mode I/II conditions is formulated. The focus is on two issues – crack path simulation and fatigue life estimation. The finite element method is used together with the maximum principal stress criterion and the crack growth rate equation based on the equivalent stress intensity factor. To determine the mixed-mode stress intensity factors, quarter-point (Q-P) singular finite elements are employed. For verification purposes, a plate with crack emanating from the edge of a hole is examined. The crack path of the plate made of 2024 T3 Al Alloy is investigated experimentally and simulated by using the finite element method with the maximum tangential stress criterion. Then, the validation of the procedure is illustrated by applying the numerical evaluation of the curvilinear crack propagation in the polymethyl methacrylate (PMMA) beam and the Arcan specimen made of Al Alloy for which experimental results are available in the literature. In order to estimate fatigue life up to failure of the plate with crack emanating from the edge of a hole, the polynomial expression is evaluated for the equivalent stress intensity factor using values of stress intensity factors obtained from the finite element analysis. Additionally, the fatigue life up to failure of the Arcan specimen is analyzed for different loading angles and compared with experimental data. Excellent correlations between the computed and experimental results are obtained.     

Finite element modeling of melting crack tip under thermo-electric Joule heating

The finite element modeling of the melting crack tip under thermo-electric Joule heating is presented in this paper. It is necessary to consider the AC input, temperature-dependent material constants and crack contact conditions. The shape of the melting crack tip zone may be either circular or elliptical. As the crack length relative to the plate width becomes too small, the crack tip may not melt. Finally, this paper demonstrates that the electric current density factor cannot be used to estimate the crack tip temperature and melting condition.     

Finite element simulation of plasticity induced crack closure with different material constitutive models

The study presented in this paper analyses the mechanical effects of material constitutive modelling on the numerical prediction of plasticity induced crack closure. With this aim, an elastoplastic stress analysis of a MT specimen was conducted using an implicit three dimensional finite element program. Two materials were studied: an Aluminium Alloy and a High Strength Steel. Several constitutive models were used to describe their cyclic behaviour, ranging from pure isotropic hardening or pure kinematic hardening models to combined isotropic plus kinematic hardening models. Numerical results showed clear differences in plastic behaviour and crack closure predictions for the different types of mechanical models used to describe the mechanical behaviour of the materials. The mechanisms of opening stress stabilization, usually observed in numerical simulations, are explained in this work by analysing the evolution of plastic deformation along the crack flanks. The same type of plastic deformation stabilization behaviour was observed independently of the hardening model in use.     

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.     

Boundary-only element analysis of crack contact under thermal shock

This paper presents a multi-domain boundary integral equation approach of thermally excited crack surface interference observed under thermal transient conditions. According to this model, crack surface displacements and tractions are not free but subject to constraints simulating contact and prevailing overlapping of crack surfaces. The multi-domain approach allows the two faces of a crack to be modeled in independent sub-regions of the body, avoiding singularity difficulties and making it possible to analyze crack closure problems with contact stresses over part of the cracked faces. Crack-tip singularities are modeled through quarter-point elements. In order to approach the interference configuration, the interfacial traction distribution and solve the resulting equations, an iterative numerical procedure is applied. The numerical solution of this non-linear problem yields crack surface displacements and consequently the crack surface interference. Fracture parameters are evaluated from nodal displacements of singular elements utilizing proper formulas. Various results are illustrated and discussed for edge-cracks subjected to steady-state or thermal shock conditions.     

Finite element analysis of free-edge stresses in composite laminates under mechanical an thermal loading

In this paper, a multi-particle finite element [Nguyen VT, Caron JF. A new finite element for free edge effect analysis in laminated composites. Comput Struct, accepted for publication] is applied for general laminated and is shown to be capable of simultaneously predicting global and local responses. The analysis of free-edge stresses of composite laminates subjected to mechanical and thermal loads is performed using this C^o${\mathbb{C}}^o$ eight-node layer-wise finite element after a classical bending validation. Laminates with finite dimensions are considered and three-dimensional out-of-plane stresses in the interior and near the free edges are evaluated. The results obtained with this finite element modelling are compared with those available in the literature. The present calculation provides accurate stresses and can be utilised as and operational tool to predict interlaminar stresses under the loads of mechanical and thermal combined.     

Finite element analysis of stiffened laminated plates under transverse loading

A finite element model is developed to study the behavior of stiffened laminated plates under transverse loadings. Transverse shear flexibility is incorporated in both beam and plate displacement fields. A laminated plate element with 45 degrees of freedom is used in conjunction with a laminated beam element having 12 degrees of freedom for the bending analysis of eccentrically-stiffened laminated plates. The validity of the formulation is demonstrated by comparing with the available solutions in the literature. The numerical results are presented for eccentrically-stiffened layered plates having various boundary conditions and with stiffeners varying in number.     

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.     

A finite element analysis of quasistatic crack growth in a pressure sensitive constrained ductile layer

Polymeric adhesive layers are employed for bonding two components in a wide variety of technological applications. It has been observed that, unlike in metals, the yield behavior of polymers is affected by the state of hydrostatic stress. In this work, the effect of pressure sensitivity of yielding and layer thickness on quasistatic interfacial crack growth in a ductile adhesive layer is investigated. To this end, finite deformation, finite element analyses of a cracked sandwiched layer are carried out under plane strain, small-scale yielding conditions for a wide range of mode mixities. The Drucker–Prager constitutive equations are employed to represent the behavior of the layer. Crack propagation is simulated through a cohesive zone model, in which the interface is assumed to follow a prescribed traction–separation law. The results show that for a given mode mixity, the steady state fracture toughness |K|_ss is enhanced as the degree of pressure sensitivity increases. Further, for a given level of pressure sensitivity, |K|_ss increases steeply as mode II loading is approached.     

Finite element analysis of sandwich panels with stepwise graded aluminum honeycomb cores under blast loading

This paper presents details and brief results of an experimental investigation on the response of metallic sandwich panels with stepwise graded aluminum honeycomb cores under blast loading. Based on the experiments, corresponding finite element simulations have been undertaken using the LS-DYNA software. It is observed that the core compression stage was coupled with the fluid–structure interaction stage, and the compression of the core layer decreased from the central to the peripheral zone. The blast resistance capability of sandwich panels was moderately sensitive to the core relative density and graded distribution. For the graded panels with relative density descending core arrangement, the core plastic energy dissipation and the transmitted force attenuation were larger than that of the ungraded ones under the same loading condition. The graded sandwich panels, especially for relative density descending core arrangement, would display a better blast resistance than the ungraded ones at a specific loading region.     

Approximation of curved cracks under mixed-mode loading

The calculation of stress intensity factors or mechanical energy release rate for non-straight cracks can be complicated. Approximation to equivalent crack shapes can simplify calculations considerably, but this requires an understanding of the influence of key shape parameters on crack-tip stresses. A simple analytical model has been developed, based on the concept of a relaxed volume, to predict mechanical energy release rate and deflection angle for a range of crack shapes under mixed-mode loading. Results from this model compared well with those obtained from finite element (FE) simulations, and with predictions from previous analytical models. It was found that the crack length and orientation of the crack-tip with respect to loading direction are the key influences on fracture parameters, whilst curvature near the crack-tip can also affect results.     

Finite element prediction of crack formation induced by quenching in a forged valve

Quenching treatment is commonly used to improve the mechanical properties of steel components. However, in these components, quench cracks are often observed as a result of improper material choice and thermal treatment process. Prediction of quench cracks is important to reduce production cost and to prevent in-service component failure; however, a generally accepted criterion for their formation has to be still established. In this study, finite element prediction of crack formation induced by quenching in a forged valve used in the offshore oil drilling field, is performed by means of the commercial finite element software Abaqus®. Microstructures (austenite, martensite, bainite, pearlite and ferrite) which can be formed during the thermal treatment are taken into account. The simulation results, compared with the effects of the quenching on the actual component, indicate that this type of simulation can effectively predict the quench cracks formation in 3D components.     

Finite element analysis of plasticity-induced fatigue crack closure: an overview

Finite element analysis is perhaps the most commonly used numerical method to model plasticity-induced fatigue crack closure. The state-of-the-art is reviewed and a comprehensive overview is presented, summarizing issues which must be considered and emphasizing potential difficulties. These include mesh refinement level, crack advancement schemes, crack shape evolution, geometry effects, and crack opening value assessment techniques.     

Elastic–plastic finite element analysis of the effect of compressive loading on crack tip parameters and its impact on fatigue crack propagation rate

The effects of applied compressive stress on the crack tip parameters and their implications on fatigue crack growth have been studied. Four center-cracked panel specimens with different crack lengths are analysed using finite element method. The results show that under tension–compression loading the local crack tip parameters are determined by two loading parameters. The two loading parameters are the maximum stress intensity and the maximum compressive stress in the applied stress cycle. Predictions of fatigue crack propagation behaviour based on the maximum stress intensity and maximum compressive stress agree well with experimental observations.     

Micro-mechanical finite element analysis of Z-pins under mixed-mode loading

This paper presents a three-dimensional micro-mechanical finite element (FE) modelling strategy for predicting the mixed-mode response of single Z-pins inserted in a composite laminate. The modelling approach is based upon a versatile ply-level mesh, which takes into account the significant micro-mechanical features of Z-pinned laminates. The effect of post-cure cool down is also considered in the approach. The Z-pin/laminate interface is modelled by cohesive elements and frictional contact. The progressive failure of the Z-pin is simulated considering shear-driven internal splitting, accounted for using cohesive elements, and tensile fibre failure, modelled using the Weibull’s criterion. The simulation strategy is calibrated and validated via experimental tests performed on single carbon/BMI Z-pins inserted in quasi-isotropic laminate. The effects of the bonding and friction at the Z-pin/laminate interface and the internal Z-pin splitting are discussed. The primary aim is to develop a robust numerical tool and guidelines for designing Z-pins with optimal bridging behaviour.     

A numerical study of crack shielding and deflection under extensive plasticity

Experimentally observed crack deflection events in multi-layered material systems, occurring even under pure mode-I loading, are here simulated and explained through elasto-plastic finite element modelling. The crack tip opening displacement is adopted as the crack driving force and estimated along crack paths whose deflection is predicted using the maximum tangential strain criterion. Shielding conditions that promote deflection and bifurcation are evaluated. It is shown that, under conditions of extended plasticity, CTOD evolution as a crack approaches an interface can reveal crack shielding and amplification, and that crack deflection and growth can be assessed from the variation of tangential strains around the crack tip.     

Estimation of the plastic zone by finite element method under mixed mode (I and II) loading

Material fracture by opening (mode I) is not lonely responsible for fracture propagation. Many industrial examples show the presence of mode II and mixed mode I + II. The present work consists in the elaboration of a code to estimate the size of the plastic zone at the crack tip under mode I, mode II and mixed mode I + II loading. The computations are made according to Von Mises and Tresca criteria. The results obtained are compared to those measured by experiments.     

Finite element analyses of three-dimensional crack problems in piezoelectric structures

In this paper, electromechanical fracture mechanics and finite element techniques for crack analyses are extended to three-dimensional crack configurations. Penny-shaped cracks and elliptical cracks are analyzed, subjected to combined mechanical tension and electric fields. For the penny-shaped crack, exact solutions originating from different resources are compared with numerical results. Some errors in the literature concerning the analytical solution for the elliptical crack are corrected. Numerical results of the stress-intensity factors and energy release rates for these crack configurations are presented.     

Finite element analysis of fretting crack propagation

In this work, the finite elements method (FEM) is used to analyse the growth of fretting cracks. FEM can be favourably used to extract the stress intensity factors in mixed mode, a typical situation for cracks growing in the vicinity of a fretting contact. The present study is limited to straight cracks which is a simple system chosen to develop and validate the FEM analysis. The FEM model is tested and validated against popular weight functions for straight cracks perpendicular to the surface. The model is then used to study fretting crack growth and understand the effect of key parameters such as the crack angle and the friction between crack faces. Predictions achieved by this analysis match the essential features of former experimental fretting results, in particular the average crack arrest length can be predicted accurately.