Finite Fracture Mechanics Model Research Articles

The effect of fibre orientation on fatigue crack propagation in CFRP: Finite fracture mechanics modelling for open-hole configuration

The demand to capture translaminar crack growth under fatigue loading scenarios led this work contribution to carry out the Finite Fracture Mechanics (FFM) method in fatigue damage growth and the application of the Paris model to generate the translaminar damage propagation prediction. The purpose of this study is to analyse the effect of fibre orientation on translaminar crack propagation rate using the FFM model, which includes cycle damage increment estimation and fractographic analysis. The results confirm the feasibility of FFM in predicting crack growth and estimating life under cyclic loading. However, C-scan analysis and the revised crack propagation direction are critical in determining the realistic crack length, considering adhesive failure along the fibre direction. Additionally, this work contribution is also related to the application of the Paris model (based on dL/dN vs ΔK) to generate the translaminar damage propagation prediction model. The most dominant damage mechanism was the splitting pattern, which changed the aspect of failure for each laminate architecture as a function of fibre orientation. The laminate with multidirectional fibre orientation exhibited higher resistance to translaminar crack propagation due to the growth of splitting and delamination in multiple directions. The fibre orientation changed the propagation path, which influenced the fracture toughness and crack propagation rate behaviour.

Coupled versus energetic nonlocal failure criteria: A case study on the crack onset from circular holes under biaxial loadings

The phenomenon of brittle crack onset stemming from a circular hole in an infinite plate subjected to remote biaxial loading is herein investigated. A thorough analysis on the influence of the loading biaxiality reveals the existence of a wide casuistry in the sign and trend distributions of the stress field and Stress Intensity Factor, thus rendering it an exhaustive case study for assessing different failure criteria. Subsequently, three different approaches are used to determine the biaxial safety domains, two of which rely on the coupling of stress and energy conditions for failure, namely Finite Fracture Mechanics and Cohesive Zone Model, plus the purely energy-driven Phase Field model of fracture. Noteworthy, Finite Fracture Mechanics predicts the existence of a region in the loading space where failure is exclusively governed by the energy condition. Likewise, it is mathematically proven that the system of equations governing Dugdale's Cohesive Zone Model is equivalent to the first-order minimization condition of the energy balance, the resultant predictions being fairly close to those obtained by Finite Fracture Mechanics. Lastly, the Phase Field model of fracture is numerically implemented in the context of Finite Elements while paying special attention to the choice of the energy decomposition, whereof two are implemented: No-Decomposition and No-Tension decomposition. Specifically, the latter showcases satisfactory agreement with both Finite Fracture Mechanics and Dugdale's Cohesive Zone Model, thus posing a solid contender for studying complex fracture scenarios upon combined tension-compression stress states.

Finite Fracture Mechanics and Cohesive Crack Model: Size effects through a unified formulation

Finite Fracture Mechanics and Cohesive Crack Model can effectively predict the strength of plain, cracked or notched structural components, overcoming the classical drawbacks of Linear Elastic Fracture Mechanics. Aim of the present work is to investigate size effects by expressing each model as a unified system of two equations, describing a stress requirement and the energy balance, respectively. Brittle crack onset in two different structural configurations is considered: (i) a circular hole in a tensile slab; (ii) an un-notched beam under pure bending. The study is performed through a semi-analytical parametric approach. Finally, theoretical strength predictions are validated with experimental results available in the literature for both geometries, and with estimations by the point criterion in the framework of Theory of Critical Distances.

An analytical failure model for pressurized blister tests of thermally loaded composite laminates

An analytical finite fracture mechanics model for pressurized blister tests is developed. This paper describes in detail governing equations, solution procedure and stress analysis. The stress solution and incremental energy release rate show good accordance to Finite Element Analysis. The derived failure model is discussed in the context of pressurized blister tests. The blister tests are performed at different temperatures between −40°C and 100°C published by the authors in a previous article. The failure model describes different gap widths with adequately assumed temperature-dependent elastic and strength properties over a wide temperature range.

Failure prediction of irregular arranged multi-bolt composite repair based on finite fracture mechanics model

A numerical method based on the finite fracture mechanics model was proposed in this study to accurately predict the failure of irregular arranged multi-bolt composite repair. The stress distribution and the stress intensity factors required in the model were obtained using a two-stage analysis strategy, which can effectively lower the FE model scale and computational cost while keeping high computational accuracy. In the two-stage analysis strategy, the bolt load distribution was calculated using the global analysis method. After obtaining the fastener load from the first-level model, detailed stress and stress intensity factor analysis were conducted around individual fasteners and cutouts, which were then used to evaluate the failure behaviour of the composite panels. To validate the numerical method, tensile tests were carried out on three kinds of bolted composite repairs with circular, elliptical and oblong cutouts. Failure mode, failure location and failure strength predicted by the proposed numerical method were consistent with the experimental results, illustrating the effectiveness and applicability of the numerical method on predicting the failure behaviour of bolted composite repairs.

Prediction of the net-tension strength of single bolt joint using the 0° ply strength and fracture toughness

This paper puts forward a new method to predict the net-tension strength of single blot joint based on the Finite Fracture Mechanics (FFM) model. Instead of using the tensile strength and fracture toughness of the laminates, only the properties of the 0° ply are used to obtain the failure stress and critical crack length by considering the relation between mode I fracture toughness of laminates and that of 0° ply. While the tensile strength of the 0° ply can be easily obtained through uniaxial tensile tests, the size effect law of double edge notched specimens is incorporated for the determination of the crack resistance curve of the ply. After validating the proposed method by the experimental results of central-notched IM7/8552 laminates, a 3D finite element model is established and the secondary bending is taken into consideration to find the maximum stress distribution of 0° ply around the bolt hole of the single bolt joint. It is concluded that the predicted strength by the semi-analytical method suits well with the experimental results. The secondary bending and the crack resistance curve, which can be seen as improvements of the Finite Fracture Mechanics model, have an influence on the predicted value.

Finite fracture mechanics and cohesive crack model: Weight functions vs. cohesive laws

The present work represents the prosecution of a previous paper [Short cracks and V-notches: Finite Fracture Mechanics vs. Cohesive Crack Model (2016). P. Cornetti, A. Sapora, A. Carpinteri. Engineering Fracture Mechanics 168:2–12] aiming to corroborate the use of Finite Fracture Mechanics by showing that its failure load estimates are very close to the ones provided by the well-established Cohesive Crack Model. While the above paper focused only on the Dugdale cohesive law and the original Finite Fracture Mechanics approach, here we consider generic cohesive laws of power law type and propose an extension of Finite Fracture Mechanics based on stress weight functions. We argue that excellent agreement between the models is found provided proper correspondence rules between the shape of the cohesive laws and of the weight functions are given. As a test bench for this conjecture, we choose the Griffith crack geometry, where we are able to achieve the solutions in a semi-analytical way for both the models. Finally, we show that similar results can be obtained also by varying the domain of the weight function while keeping fixed its shape.

Towards quasi isotropic laminates with engineered fracture behaviour for industrial applications

Carefully placed patterns of micro-cuts have been inserted in the microstructure of Cross-Ply (CP) and Quasi-Isotropic (QI) thin-ply CFRP laminates to engineer their translaminar fracture behaviour with the purpose of increasing their damage resistance under different loading conditions. A novel Finite Fracture Mechanics model has been developed to predict the translaminar crack propagation behaviour and to guide the microstructure design. This technique led to a 68% increase in the laminate notched strength, and a 460% increase in the laminate translaminar work of fracture during Compact Tension tests for CP laminates. It also allowed to achieve a 27% increase in the laminate notched strength, and a 189% increase in the translaminar work of fracture during Compact Tension tests for QI laminates. Furthermore, an increase of 43% in the total energy dissipated, and of 40% in maximum deflection at complete failure was achieved during quasi-static indentation tests on QI laminates. Given the significant improvements in the mechanical performance under different loading conditions, and the industrial relevance of QI laminates and the increasing industrial interest in thin-ply laminates, these results demonstrate that microstructure design can be used effectively to improve the damage tolerance of CFRP structures in industrially-relevant applications.

Prediction of size effects in open-hole laminates using only the Young’s modulus, the strength, and the [formula omitted]-curve of the 0° ply

Advanced non-linear Finite Element models for the strength prediction of composite laminates normally result in long computing times that are not suitable for preliminary sizing and optimisation of structural details. Macro-mechanical analytical models, in spite of providing quick predictions, are based on properties determined from tests performed at the laminate level, making preliminary design and optimisation of composite structures still too costly in terms of testing requirements. To overcome these disadvantages, an analytical framework is proposed to predict the notched response of balanced carbon fibre-reinforced polymer laminates using only three ply properties as inputs: the longitudinal Young’s modulus, the longitudinal strength, and the R-curve of the 0° plies. This framework is based on invariant-based approaches to predict the stiffness and the strength of general laminates, and an analytical model to estimate the R-curve of balanced laminates. These laminate properties are then used in a Finite Fracture Mechanics model to predict size effects. The predictions for open-hole tension and compression tests are compared with experimental results obtained from the literature for five different material systems. Good agreement is observed considering that only three ply properties are used as inputs for the analytical framework.

Short cracks and V-notches: Finite Fracture Mechanics vs. Cohesive Crack Model

In recent years, Finite Fracture Mechanics has proven to be an effective tool to estimate the strength of mechanical components, allowing fast strength predictions suitable for preliminary sizing and optimization of structures. In the present paper, we intend to corroborate the Finite Fracture Mechanics approach by showing that failure load estimates are very close to the ones provided by the well-established Cohesive Crack Model. To this aim, we consider two classical fracture mechanics problems, i.e. short cracks and V-notches. In the latter case, we believe to be of relevance also the Cohesive Crack Model semi-analytical solution herein provided.

A model for brittle failure in adhesive lap joints of arbitrary joint configuration

In this work an efficient general Finite Fracture Mechanics model for crack initiation in adhesively bonded joints is presented which is applicable to various joint configurations with shear flexible laminate and metallic adherends. The mechanical behaviour of the adhesive joints is modeled by a general sandwich-type model for the analysis of bonded joints with composite adherends which gives solutions for the peel and shear stresses in the adhesive. The failure behaviour is described by a physically sound combined stress and energy criterion which requires only two basic failure parameters: the strength and the fracture toughness of the adhesive. The implicit equations are solved with a highly efficient iterative solution scheme. In a comprehensive study, experimental and numerical results of an elaborated Cohesive Zone Model (CZM) are used for comparison. It is shown that the predicted failure loads are in good to very good agreement with the experimentally determined results and the effects of the geometric parameters on the failure load are rendered correctly.

Fracture mechanics of planetary gear set by using extended finite element method-linear elastic fracture mechanics approach

Contour integral method is the conventional approach in order to characterise main crack parameters in fracture studies. This method is used in verity fields in fractures mechanics because of its capability in linear and non-linear fracture mechanics. Whereas, requirements such as mesh singularity in crack tip and refined layers of elements in surrounding contours, which increase computing time and make it prolix for large components. The main aim of this paper is to develop an extended finite element method-linear elastic fracture mechanics (XFEM-LEFM) model to impart XFEM advantages in survey of fracture mechanics of planetary gear sets. At first main crack parameters of root crack of the planet gear have been obtained and compared with conventional method, and after that crack growth path is predicted, and finally effect of rim thickness is investigated and compared with other researches to illustrate the efficiency of the developed model. For this purpose, Python script code is generated to automatically calculate the stress intensity factors of root crack and after that simulate the crack growth path until final fracture.

A Finite Fracture Mechanics Model for the Prediction of the Notched Response and Large Damage Capability of Composite Laminates

A new model based on Finite Fracture Mechanics (FFMs) has been proposed to predict the open-hole tensile strength of composite laminates [1]. Failure is predicted when bothstress-based and energy-based criteria are satisfied. This model is based on an analytical solution, and no empirical adjusting parameters are required, but only two material properties: the unnotched strength and the fracture toughness. In the present work, an extension of the proposed FFMs model to predict the notched response of composite laminates with notch geometries other than a circular opening [2] is presented and applied to the prediction of size effects on the tensile and compressive notched strength of composite laminates. The present model is also used to assess the notch sensitivity and brittleness of composite laminates by means of versatile design charts and by the identification of a dimensionless parameter designated as notch sensitivity factor. A further extension of the FFMs model is proposed, which takes into account the crack resistance curve of the laminate in the model's formulation, and it is used to predict the large damage capability of a non-crimp fabric thin-ply laminate [3].

Large damage capability of non-crimp fabric thin-ply laminates

The residual strength of thin-ply non-crimp fabric laminates with large through-the-thickness cracks is investigated in this paper. Analysis methods such as the linear elastic fracture mechanics, inherent flaw, point-stress, average-stress and Finite Fracture Mechanics are used to predict large damage capability. Experiments show that thin-ply non-crimp fabric laminates exhibit high resistance to propagation of large cracks and a remarked crack-bridging effect. Due to the unsuitability of existing models to capture such bridging processes, large damage capability is systematically underestimated by the traditional analysis methods. By taking into account the R-curve of the material in the Finite Fracture Mechanics analysis good predictions of the notched response of laminated plates with large through-penetration damage are obtained using only independently measured material properties; in addition, the Finite Fracture Mechanics model does not require fitting parameters or complex finite element analyses.

Fiber-size effects on the onset of fiber–matrix debonding under transverse tension: A comparison between cohesive zone and finite fracture mechanics models

The problem of fiber–matrix debonding due to transverse loading is revisited. Predictions of the critical load for the debond onset obtained by a Cohesive Zone Model combined with contact mechanics and by a Finite Fracture Mechanics model based on a coupled stress and energy criterion are compared. Both models predict a strong nonlinear dependence of the critical load on the fiber size. A good agreement between the predictions provided by these models is found for large and medium fiber radii. However, different scaling laws for small fiber radii are noticed. A discussion of the asymptotic trends for very small and very large fiber radii is presented. Limitations of both models are also discussed. For very small fibers, it is shown that matrix plasticity can prevail over fiber–matrix debonding, leading to an upper bound for the critical load. When fiber–matrix debonding prevails over plasticity for large enough fibers, the predictions provided by the two models are still in fair good agreement.

Notched response of non-crimp fabric thin-ply laminates: Analysis methods

Analysis methods to predict the open-hole tensile and compressive response of thin-ply non-crimp fabric laminates are investigated in this paper. The point- and average-stress models and the Finite Fracture Mechanics model are used. It is shown that all models predict with reasonable accuracy the observed size effects in both tension and compression. The Finite Fracture Mechanics model, which requires two material properties (the unnotched strength and the fracture toughness) and does not need calibration from a baseline specimen, is used to predict the notched response of thin-ply non-crimp fabric laminates and of typical aerospace grade laminates based on unidirectional pre-impregnated plies. No substantial differences in notch sensitivity and inherent material/geometry brittleness is predicted.

Finite Fracture Mechanics model for mixed mode fracture in adhesive joints

Up to now the failure load assessment of bonded joints is still not fully understood. This work provides a new approach for assessing the crack initiation load of bonded joints. A failure model for single lap joints is proposed that is based on Finite Fracture Mechanics. Only two basic fracture parameters are required: the tensile strength and the fracture toughness of the adhesive. A coupled stress and energy criterion proposed in 2002 by Leguillon is used to model crack initiation in the adhesive layer. The theory of this criterion is outlined in detail, its relationship to other failure criteria is discussed and an overview of applications found in literature is given. An enhanced weak interface model that predicts a linear variation of the shear stresses in the adhesive layer is utilized to model the single lap joint. To compare joint designs and to reveal the limitations of the given approach a dimensionless brittleness number for mixed-mode loading is proposed. Along with a detailed discussion of the results for exemplary joint designs a comparison to experimental results from literature is performed. The two necessary fracture parameters are each taken from standard test results published in literature. A good agreement of the failure load predictions with the experimental results is observed. A remarkable outcome is that the presented failure model renders the adhesive thickness effect correctly. The paper concludes with a discussion of the limitations of the approach and the effect of material parameters.

A semi-analytical method to predict net-tension failure of mechanically fastened joints in composite laminates

A Finite Fracture Mechanics model is proposed to predict the net-tension strength of composite mechanically fastened joints. A modification of coupled stress–energy criteria is suggested to take properly into account the effect of the R-curve in determining the crack length corresponding to the unstable crack propagation. The proposed model works for quasi-isotropic laminates and it requires as input the longitudinal strength and the fracture toughness of the laminate. The predictions obtained show good agreement when compared with the experimental results.

Size effects on the tensile and compressive failure of notched composite laminates

An experimental and analytical investigation of the effect of size on the strength of composite laminates with central holes loaded in tension and compression is presented. Specimens with different hole sizes and with constant width-to-diameter ratios were tested in tension and compression under quasi-static loading and the strength reduction for increasing sizes was quantified for two lay-ups and for the two loading conditions. The first-ply failure load of the outer ply was identified using a new method that post-processes the displacement field obtained using the digital image correlation technique. The accuracy of the available strength prediction methods (point and average stress methods, inherent flaw model, semi-analytical cohesive zone model and finite fracture mechanics) to simulate the effect of size on the strength of notched composites is discussed. It is shown that the finite fracture mechanics model is the most accurate method.

A finite fracture mechanics model for the prediction of the open-hole strength of composite laminates

A new model based on finite fracture mechanics is proposed to predict the open-hole tensile strength of composite laminates. Failure is predicted when both stress-based and energy-based criteria are satisfied. The material properties required by the model are the ply elastic properties, and the laminate unnotched strength and fracture toughness. No empirical adjusting parameters are required. Using experimental data obtained in quasi-isotropic carbon–epoxy laminates it is concluded that the model predictions are very accurate, resulting in improvements over the traditional strength prediction methods. It also is shown that the proposed finite fracture mechanics model can be used to predict the brittleness of different combinations of materials and geometries.