Analysis of fracture and delamination in laminates using 3D numerical modelling

The static failure behaviour of the fibre-metal laminate GLARE is examined using 3D finite element simulations. The configuration analysed is a centre-cracked tensile specimen composed of two aluminium layers sandwiching a cross-plied, fibre-epoxy layer. The crack and delamination growths are simulated by means of interface elements equipped with a mixed-mode damage model. The mode-mixity is derived from an energy criterion typically used in linear elastic fracture mechanics studies. The damage kinetic law is rate-dependent, in order to simulate rate effects during interfacial delamination and to avoid numerical convergence problems due to crack bifurcations. The numerical implementation of the interface damage model is based on a backward Euler approach. In the boundary value problem studied, the failure responses of GLARE specimens containing elastic aluminium layers and elasto-plastic aluminium layers are compared. The development of plastic deformations in the aluminium layers stabilizes the effective failure response, and increases the residual strength of the laminate. For a ‘quasi-brittle’ GLARE specimen with elastic aluminium layers, the residual strength is governed by the toughness for interfacial delamination, and is in close correspondence with the residual strength obtained from a closed-form expression derived from energy considerations. Conversely, for a ‘ductile’ GLARE specimen with elasto-plastic aluminium layers, the residual strength is also determined by the relation between the fracture strength and the yield strength of the aluminium. The amount of constraint by the horizontal displacements at the vertical specimen edges has a moderate to small influence on the residual strength. Furthermore, the ultimate laminate strength is lower for a larger initial crack length, and shows to be in good correspondence with experimental values.     

Three-dimensional modeling of ductile crack growth: Cohesive zone parameters and crack tip triaxiality

For 10 mm thick smooth-sided compact tension specimens made of a pressure vessel steel 20MnMoNi55, the interrelations between the cohesive zone parameters (the cohesive strength, T_max, and the separation energy, Γ) and the crack tip triaxiality are investigated. The slant shear-lip fracture near the side-surfaces is modeled as a normal fracture along the symmetry plane of the specimen. The cohesive zone parameters are determined by fitting the simulated crack extensions to the experimental data of a multi-specimen test. It is found that for constant cohesive zone parameters, the simulated crack extension curves show a strong tunneling effect. For a good fit between simulated and experimental crack growth, both the cohesive strength and the separation energy near the side-surface should be considerably lower than near the midsection. When the same cohesive zone parameters are applied to the 3D model and a plane strain model, the stress triaxiality in the midsection of the 3D model is much lower, the von-Mises equivalent stress is distinctly higher, and the crack growth rate is significantly lower than in the plane strain model. Therefore, the specimen must be considered as a thin specimen. The stress triaxiality varies dramatically during the initial stages of crack growth, but varies only smoothly during the subsequent stable crack growth. In the midsection region, the decrease of the cohesive strength results in a decrease of the stress triaxiality, while the decrease of the separation energy results in an increase of the triaxiality.     

Analytical stress intensity solution for the stable Poisson loaded specimen

An analytical calibration of the Stable Poisson Loaded (SPL) specimen is presented. The specimen configuration is similar to the ASTM E-561 compact-tension specimen with displacement controlled wedge loading used for R-curve determination. The crack mouth opening displacements (CMOD's) are produced by the diametral expansion of an axially compressed cylindrical pin located in the wake of a machined notch. Due to the unusual loading configuration, a three-dimensional finite element analysis was performed with gap elements simulating the contact between the pin and specimen. In this report, stress intensity factors, CMOD's, and crack displacement profiles, are reported for different crack lengths and different contacting conditions. It was concluded that the computed stress intensity factor decreases sharply with increasing crack length thus making the SPL specimen configuration attractive for fracture testing of brittle, high modulus materials.     

T-stress and its implications for crack growth

Some of the “irregular” crack growth behaviour observed in different specimen geometries may not be unrelated. Discrepancies in fatigue crack growth rate have been observed in different specimen geometries of the same material; crack front “tunnelling” and out-of-plane crack growth have been found in mode I tension at elevated temperature. The results presented in this paper seem to indicate the relevance of a crack tip constraint parameter, the elastic T-stress, to the irregular crack growth behaviour that conventional LEFM fails to explain.     

A crystal plasticity study of cyclic constitutive behaviour, crack-tip deformation and crack-growth path for a polycrystalline nickel-based superalloy

Crystal plasticity has been applied to model the cyclic constitutive behaviour of a polycrystalline nickel-based superalloy at elevated temperature using finite element analyses. A representative volume element, consisting of randomly oriented grains, was considered for the finite element analyses under periodic boundary constraints. Strain-controlled cyclic test data at 650 °C were used to determine the model parameters from a fitting process, where three loading rates were considered. Model simulations are in good agreement with the experimental results for stress–strain loops, cyclic hardening behaviour and stress relaxation behaviour. Stress and strain distributions within the representative volume element are of heterogeneous nature due to the orientation mismatch between neighbouring grains. Stress concentrations tend to occur within “hard” grains while strain concentrations tend to locate within “soft” grains, depending on the orientation of grains with respect to the loading direction. The model was further applied to study the near-tip deformation of a transgranular crack in a compact tension specimen using a submodelling technique. Grain microstructure is shown to have an influence on the von Mises stress distribution near the crack tip, and the gain texture heterogeneity disturbs the well-known butterfly shape obtained from the viscoplasticity analysis at continuum level. The stress–strain response near the crack tip, as well as the accumulated shear deformation along slip system, is influenced by the orientation of the grain at the crack tip, which might dictate the subsequent crack growth through grains. Individual slip systems near the crack tip tend to have different amounts of accumulated shear deformation, which was utilised as a criterion to predict the crack growth path.     

The fracture toughness of Ni/Al2O3 laminates by digital image correlation I: Experimental crack opening displacement and R-curves

The crack opening displacement of laminates made of alumina/nickel was measured using digital image correlation (DIC). The crack opening displacements were validated with a finite-element model that uses the characteristic bridging-stress bridging-displacement relationship obtained experimentally by testing a constrained nickel sandwich in tension. The method is a simple, accurate way of measuring the crack opening displacement (COD) in ceramic/metal laminates.     

CTOD-R curve construction from surface displacement measurements

The construction of a fracture resistance δ–R (or J–R) curve requires the appropriate measurement of crack-tip opening displacement (CTOD) as a function of crack extension. This can be made by different procedures following ASTM E1820, BS7448 or other standards and procedures (e.g., GTP-02, ESIS-P2, etc.) for the measurement of fracture toughness. However, all of these procedures require standard specimens, displacement gauges, and calibration curves to get intrinsic material properties. This paper deals with some analysis and aspects related to the measurement of fracture toughness by observing the surface of the specimen. Tests were performed using three-dimensional surface displacement measurements to determine the fracture parameters and the crack extension values. These tests can be conducted without using a crack mouth opening displacement-CMOD or load-line displacement gauge, because CMOD can be calculated by using the displacement of the surface points. The presented method offers a significant advantage for fracture toughness testing in cases where a clip gauge is not easy to use, for example, on structural components. Simple analysis of stereo-metrical surface displacements gives a load vs. crack opening displacement curve. Results show that the initiation of stable crack propagation can be easy estimated as the point of the curve’s deviation. It is possible to determine the deviation point if the crack opening displacement measurements are close to crack tip in the plastic zone area. The resistance curve, CTOD-R, is developed by the local measurement of crack opening displacement (COD) in rigid body area of specimen. COD values are used for the recalculation with the CMOD parameter as a remote crack opening displacement, according to the ASTM standard.     

Neural Network-Based Inverse Analysis for Defect Identification with Laser Ultrasonics

Abstract

This paper describes an application of the neural network-based inverse analysis method to the identification of a surface defect hidden in a solid, using laser ultrasonics. The inverse analysis method consists of three subprocesses. First, sample data of identification parameters versus dynamic responses of displacements at several monitoring points on the surface are calculated using the dynamic finite-element method. Second, the back-propagation neural network is trained using the sample data. Finally, the well-trained network is utilized for defect identification. Fundamental performance of the method is examined quantitatively and in detail, through both numerical simulations and laser ultrasonics experiments. Locations and depths of vertical defects are successfully estimated within 12.5% and 4.1% errors relative to the specimen thickness, respectively.     

Calculation of stress intensity factors for an interfacial crack between dissimilar anisotropic media,using a hybrid element method and the mutual integral

Using Beom and Atluri's complete eigen-function solutions for stresses and displacements near the tip of an interfacial crack between dissimilar anisotropic media, a hybrid crack tip finite-element is developed. This element, as well as a mutual integral method are used to determine the stress intensity factors for an interfacial crack between dissimilar anisotropic media. The hybrid element has, for its Galerkin basis functions, the eigen-function solutions for stresses and displacements embedded within it. The mutual integral approach is based on the application of the path-independent J integral to a linear combination of two solutions: one, the problem to be solved, and the second, an auxiliary solution with a known singular solution. A comparison with exact solutions is made to determine the accuracy and efficiency of both the methods in various mixed mode interfacial crack problems. The size of the hybrid element was found to have very little effect on the accuracy of the solution: an acceptable numerical solution can be obtained with a very coarse mesh by using a larger hybrid element. An equivalent domain integral method is used in the application of the mutual integral instead of the line integral method. It is shown that the calculated mutual integral is domain independent. Therefore, the mutual integral can be evaluated far away from the crack-tip where the finite element solution is more accurate. In addition, numerical examples are given to determine the stress intensity factors for a delamination crack in composite lap joints and at plate-stiffener interfaces.This work was supported by a grant from the NASA Langley Research Center.     

Towards the computation of electrically permeable cracks in piezoelectrics

The focus of this paper is not the well-known and examined behavior of electrically impermeable and fully permeable cracks but the analysis of limited permeable cracks, i.e. the influence of a dielectric medium inside the crack. The boundary conditions of the impermeable or the fully permeable crack can be considered as simple approximations representing upper and lower bounds for the electrical energy penetrating the crack. In this paper, the accuracy of a known theoretical approach “capacitor analogy” for analyzing limited permeable cracks in piezoelectric ceramics is verified by means of numerical methods and analytical estimations. Different crack configurations in 2D and 3D are analyzed. The cracks are subjected to combined electrical and mechanical loads, which lead to a mixed Mode loading in Mode-I and Mode-IV. The influence of errors committed by the capacitor analogy approaching the crack tip is investigated using piezoelectric crack weight functions and special finite element techniques meshing the medium inside the crack. The numerical results of stress intensity factors, obtained by the crack tip element method which is valid for loaded crack faces, are presented. Finally, the theory is applied to the evaluation of a fracture experiment with a DCB specimen.     

Simulation of fatigue crack growth in components with random defects

The paper presents a probabilistic method for the simulation of fatigue crack growth from crack-like defects in the combined operating and residual stress fields of an arbitrary component. The component geometry and stress distribution are taken from a standard finite element stress analysis. Number, size and location of crack-like defects are ‘drawn’ from probability distributions. The presented fatigue assessment methodology has been implemented in a newly developed finite-element post-processor, P • FAT, and is useful for the reliability assessment of fatigue critical components. General features of the finite element post-processor have been presented. Important features, such as (i) the determination of the life-controlling defect, (ii) growth of short and long cracks, (iii) fatigue strength and fatigue life distribution and (iv) probability of component fatigue failure, have been treated and discussed. Short and long crack growth measurements have been presented and used for verification of the crack growth model presented.     

Stress intensity factors for large aspect ratio surface and corner cracks at a semi-circular notch in a tension specimen

Stress intensity factor solutions for semi-elliptic surface and quarter-elliptic corner cracks emanating from a semi-circular notch in a tension specimen are presented. A threedimensional finite-element analysis in conjunction with the equivalent domain integral was used to calculate stress intensity factors (SIF). SIF solutions for surface or corner crack (crack length to depth ratio of 2) at a notch are presented for a wide range of crack sizes and notch radii. Results showed that the SIF are larger for larger crack lengths and for larger notch radii. The SIF are nearly constant all along the crack front for deep surface cracks and for all corner cracks analysed.     

Finite-element modelling of crack propagation in elastic–plastic media: Part II Horizontal subsurface cracks

Horizontal subsurface cracks in an elastic–plastic material are analysed using finite-element techniques. The sliding surface is modelled as a rigid cylinder. The effect of such parameters as the friction between the cylinder and the material being indented, the elastic and plastic modulus of the material and the depth of crack location on the J-integral values at the left and right tips of a horizontal subsurface crack is considered. The prospective crack propagation direction is taken as the direction along which the J integral assumes a maximum as the indenter slides along the material surface. The left and right tip cracks were found likely to propagate at about 10° to the horizontal. This propagation direction was found to depend strongly on the location of the crack. Both crack tips are expected to propagate closer to the vertical direction as the depth of crack location is reduced. Also, horizontal cracks closer to the surface are found to have higher J integral values. While friction between the slider and the specimen did not affect the crack propagation direction, the crack-tip plasticity reduced the propagation direction, with respect to the horizontal.     

Neural Network-Based Inverse Analysis for Defect Identification with Laser Ultrasonics

This paper describes an application of the neural network-based inverse analysis method to the identification of a surface defect hidden in a solid, using laser ultrasonics. The inverse analysis method consists of three subprocesses. First, sample data of identification parameters versus dynamic responses of displacements at several monitoring points on the surface are calculated using the dynamic finite-element method. Second, the back-propagation neural network is trained using the sample data. Finally, the well-trained network is utilized for defect identification. Fundamental performance of the method is examined quantitatively and in detail, through both numerical simulations and laser ultrasonics experiments. Locations and depths of vertical defects are successfully estimated within 12.5% and 4.1% errors relative to the specimen thickness, respectively.     

Derivation of effective stress intensity factors from measured crack face displacements

When a crack is subjected to cyclic shear-mode loading, crack faces interference wedge the crack open and reduce the effective ΔK_II. The methods proposed in the literature to prevent it or to derive the effective ΔK_I and ΔK_II are discussed. It is shown that when crack tip plasticity becomes important it tends to make displacements larger than those predicted by LEFM and to “hide” friction effects. Finite element simulations combining friction and plasticity can separate these two effects, but the analysis of force-sliding displacement loops derived from displacement field measurements based on image correlation is a more straightforward and efficient method.     

The use of interlayers in modeling interface crack propagation

Delaminations are a common mode of failure at interfaces between two material layers which have dissimilar elastic constants. There is a well-known oscillatory nature to the singularity in the stress fields at the crack tips in these bimaterial delaminations, which creates a lack of convergence in the modewise energy release rates. This makes constructing fracture criteria somewhat difficult. An approach used to overcome this is to artificially insert a thin, homogeneous, isotropic layer (the interlayer) at the interface. The crack is positioned in the middle of this homogeneous interlayer, thus modifying the original ‘bare’ interface crack problem into a companion ‘interlayer’ crack problem. Individual modes I and II energy release rates are convergent and calculable for the companion problem and can be used in the construction of a fracture criterion or locus. However, the choices of interlayer elastic and geometric properties are not obvious. Moreover, a sound, consistent, and comprehensive methodology does not exist for utilizing interlayers in the construction and application of mixed-mode fracture criteria in interface fracture mechanics. These issues are addressed here. The role of interlayer elastic modulus and thickness is examined in the context of a standard interface fracture test specimen. With the help of a previously published analytical relation that relates the bare interface crack stress intensity factor to the corresponding interlayer crack stress intensity factor, a suitable thickness and elastic modulus are identified for the interlayer in a bimaterial four-point bend test specimen geometry. Interlayer properties are chosen to make the interlayer fracture problem equivalent to the bare interface fracture problem. A suitable mixed-mode phase angle and a form for the fracture criterion for interlayer-based interface fracture are defined. A scheme is outlined for the use of interlayers for predicting interface fracture in bimaterial systems such as laminated composites. Finally, a simple procedure is presented for converting existing bare interface crack fracture loci/criteria into corresponding interlayer crack fracture loci.     

Crack arrest testing of high strength structural steels for naval applications

The crack arrest fracture toughness of two high strength steel alloys used in naval construction, HSLA-100, Composition 3 and HY-100, was characterized in this investigation. A greatly scaled-down version of the wide-plate crack arrest test was developed to characterize the crack arrest performance of these tough steel alloys in the upper region of the ductile-brittle transition. The specimen is a single edge-notched, 152 mm wide by 19 mm thick by 910 mm long plate subjected to a strong thermal gradient and a tensile loading. The thermal gradient is required to arrest the crack at temperatures high in the transition region, close to the expected service temperature for crack arrest applications in surface ships. Strain gages were placed along the crack path to obtain crack position and crack velocity data, and this data, along with the applied loading is combined in a “generation mode” analysis using finite element analysis to obtain a dynamic analysis of the crack arrest event. Detailed finite element analyses were conducted to understand the effect of various modeling assumptions on the results and to validate the methodology compared with more conventional crack arrest tests.Brittle cracks initiation, significant cleavage crack propagation and subsequent crack arrest was achieved in all 15 of the tests conducted in this investigation. A crack arrest master curve approach was used to characterize and compare the crack arrest fracture toughness. The HSLA-100, Comp. 3 steel alloy had superior performance to the HY-100 steel alloy. The crack arrest reference temperature was T_KIA = −136 °C for the HSLA-100 plate and T_KIA = −64 °C for the HY-100 plate.