Cohesive Fracture Model Research Articles

Homogenization of fiber reinforced brittle materials: the intermediate case

We derive a cohesive fracture model by homogenizing a periodic composite material whose microstructure is characterized by the presence of brittle inclusions in a reticulated unbreakable elastic structure.

An adaptive spacetime discontinuous Galerkin method for cohesive models of elastodynamic fracture

AbstractThis paper describes an adaptive numerical framework for cohesive fracture models based on a spacetime discontinuous Galerkin (SDG) method for elastodynamics with elementwise momentum balance. Discontinuous basis functions and jump conditions written with respect to target traction values simplify the implementation of cohesive traction–separation laws in the SDG framework; no special cohesive elements or other algorithmic devices are required. We use unstructured spacetime grids in a h‐adaptive implementation to adjust simultaneously the spatial and temporal resolutions. Two independent error indicators drive the adaptive refinement. One is a dissipation‐based indicator that controls the accuracy of the solution in the bulk material; the second ensures the accuracy of the discrete rendering of the cohesive law. Applications of the SDG cohesive model to elastodynamic fracture demonstrate the effectiveness of the proposed method and reveal a new solution feature: an unexpected quasi‐singular structure in the velocity response. Numerical examples demonstrate the use of adaptive analysis methods in resolving this structure, as well as its importance in reliable predictions of fracture kinetics. Copyright © 2009 John Wiley & Sons, Ltd.

Simulation of Fracture Behavior in Asphalt Concrete Using a Heterogeneous Cohesive Zone Discrete Element Model

With increasing traffic loads and changes in crude petroleum refining techniques, cracking in asphalt pavements continues to be a major cause of structural and functional deterioration of these systems, particularly in cold climates. Although modern design tools such as the AASHTO Mechanistic Empirical Pavement Design Guide have recognized the need to predict pavement cracking in pavement life cycle cost analyses, the development of true fracture tests and associated models is hampered by a lack of fundamental knowledge of the physical nature of cracking in asphalt concrete materials. A clustered discrete element method (DEM) was employed as a means to investigate fracture mechanisms in asphalt concrete at low temperatures. The DEM approach was first verified by comparing elastic continuum theory and the discontinuum approach using uniform axial compression and cantilever beam models. A bilinear cohesive zone model was implemented into the DEM framework to enable simulation of crack initiation and propagation in asphalt concrete. Verification of the cohesive zone fracture model was carried out using a double cantilever beam. The main advantage of the DEM approach was that a mesoscale representation of the morphology of the material could be easily incorporated into the model using high-resolution imaging, image analysis software, and by developing a relatively simple mesh generation code. The simulation results were shown to compare favorably with experimental results, and moreover, the simulations provide new insight into the mechanisms of fracture in asphalt concrete. The modeling technique can provide more details of the fracture process in laboratory fracture tests, the influence of heterogeneity on crack path, and the effects of local material strength and fracture energy on global fracture test response.

Cohesive crack model for mixed mode fracture of brick masonry

This paper presents a numerical procedure for mixed mode fracture of brickwork masonry. The model is an extension of the cohesive model prepared by the authors for concrete, and takes into account the anisotropy of the material. After the crack path is obtained, an interface finite element (using the cohesive fracture model) is incorporated into the trajectory. Such a model is then implemented into a commercial code by means of a user subroutine, consequently being contrasted with experimental results. Fracture properties of masonry are independently measured for two directions on the composed masonry, and then input in the numerical model. This numerical procedure accurately predicts the experimental mixed mode fracture records for different orientations of the brick layers and two homothetic sizes on masonry panels.

Measuring the notched compressive strength of composite laminates: Specimen size effects

Large fibre reinforced composite structures can give much lower strengths than small test specimens, so a proper understanding of scaling is vital for their safe and efficient use. Small size (scale) specimens are commonly tested to justify allowable stresses, but could be dangerous if results are extrapolated without accounting for scaling effects. On the other hand large factors are sometimes applied to compensate for uncertainties, resulting in overweight designs. The most important variables of scaling effects on the strength of composites with open holes have been identified from experimental tests as notch size, ply and laminate thickness. In this study, these have been scaled both independently and simultaneously over a large range of combinations. The specimens are fabricated from commercially available (Hexcel Composites Ltd.) carbon/epoxy pre-impregnated tapes 0.125 mm thick (IM7/8552). The material is laid up by hand in unidirectional [0 4] ns with n = 2, 3, 4, and 8 (i.e., 2, 3, 4 and 8 mm thick) and multidirectional laminates; two generic quasi-isotropic lay-ups, one fabricated with blocked plies [45 n /90 n /−45 n /0 n ] s and the other with distributed layers [45/90/−45/0] ns with n = 2, 4 and 8 are examined. It is shown that the critical failure mechanism in these laminates is in the form of fibre microbuckling or kinking. The unnotched compressive strength in unidirectional specimens thicker than 2 mm is found to be limited by the stress concentration developed at the end tabs and manufacturing induced defects in the form of ply waviness, fibre misalignment and voids rather than specimen size (scaling). In the open hole specimens, for both lay-ups, the strength reduction observed is due to hole size effect rather than specimen thickness or volume increase. The open hole (notched) compressive strength results obtained compare favourably to predictions by a linear softening cohesive zone fracture model developed in earlier work by the second author.

Cohesive fracture modeling of crack growth in thick-section composites

This paper presents a combined method for modeling the mode-I and II crack growth behavior in thick-section fiber reinforced polymeric composites having a nonlinear material response. The experimental part of this study includes crack growth tests of a thick composite material system manufactured using the pultrusion process. It consists of alternating layers of E-glass unidirectional roving and continuous filament mats in a polymeric matrix. Integrated micromechanical and cohesive finite element (FE) models are used to simulate the crack growth response in eccentrically loaded single-edge-notch, (tension), ESE(T) and notched butterfly specimens. Micromechanical constitutive models for the mat and the roving layers are used to generate the effective nonlinear material behavior from the in situ fiber and matrix responses. The validity of the numerical modeling approach before the onset of crack growth is investigated using an infrared thermal method. Cohesive FE models are calibrated and used to simulate the complete crack growth behavior for different crack configurations. The proposed integrated framework of multi-scale material models with cohesive fracture models is shown to be an effective method for predicting the structural and material responses including failure load and crack growth in thick-section fiber reinforced polymeric composites.

Inverse Analyses in Fracture Mechanics

The present purpose is a survey of some engineering-oriented research results which may be representative of the main issues in the title subject. Some recent or current developments are pointed out in the growing area of fracture mechanics centered on the calibration of cohesive fracture models for quasi-brittle materials, by approaches which combine experimentation, experiment simulation and minimisation of the discrepancy between measured and computed quantities. Specifically, reference is made herein to the following topics in calibration of fracture constitutive models: (a) deterministic characterisation of concrete-like materials by traditional three-point-bending tests (TPBTs), supplemented by optical measurements; (b) wedge-splitting tests (WST) and extended Kalman filter (EKF) for the stochastic estimation of fracture parameters; (c) in situ parameter identification for the local diagnosis of possibly deteriorated concrete dams on the basis of flat-jack tests; (d) fracture properties of ceramic materials and coating-substrate interfaces identified through indentation tests, imprint mapping and inverse analysis in micro-technologies.

Computational Model to Predict Fatigue Damage Behavior of Asphalt Mixtures Under Cyclic Loading

Fatigue cracking and failure of inelastic heterogeneous asphalt concrete mixtures were modeled computationally with the finite element method. The model incorporates elastic behavior of the aggregate particles, visco-elastic behavior of the asphalt matrix, and time-dependent fracture both within the asphalt matrix and along boundaries between matrix and aggregate particles. Rate-dependent progressive cracking up to failure was implemented by incorporation of a cohesive zone fracture model. The resulting model was used to simulate comprehensive fatigue damage-associated mechanical behavior including microcracking, macrocracking, and eventual sample failure of several asphalt mixtures composed of different mixture constituents, which results in different damage evolution characteristics. Simulation results were compared with real fatigue testing data in both load-controlled and displacement-controlled modes and demonstrated good correlations to laboratory data with model calibrations. The approach proposed ...

Computational Model to Predict Fatigue Damage Behavior of Asphalt Mixtures under Cyclic Loading

Fatigue cracking and failure of inelastic heterogeneous asphalt concrete mixtures were modeled computationally with the finite element method. The model incorporates elastic behavior of the aggregate particles, viscoelastic behavior of the asphalt matrix, and time-dependent fracture both within the asphalt matrix and along boundaries between matrix and aggregate particles. Rate-dependent progressive cracking up to failure was implemented by incorporation of a cohesive zone fracture model. The resulting model was used to simulate comprehensive fatigue damage–associated mechanical behavior including microcracking, macrocracking, and eventual sample failure of several asphalt mixtures composed of different mixture constituents, which results in different damage evolution characteristics. Simulation results were compared with real fatigue testing data in both load-controlled and displacement-controlled modes and demonstrated good correlations to laboratory data with model calibrations. The approach proposed can be employed to predict complex fatigue behavior of asphalt mixtures by measurement of only fundamental material properties and fracture or damage properties of mixture constituents without recourse to expensive laboratory fatigue tests.

Review of delamination predictive methods for low speed impact of composite laminates

Predicting the damage tolerance of laminated composite aircraft components subjected to low velocity impact events, such as runway debris or hail, is providing a significant challenge to the current methods. This paper reviews the current damage mechanics and fracture methods for predicting delamination under impact available in the literature. Many damage mechanics models are available, some providing good delamination predictions. The linear elastic fracture mechanics method has been used extensively where the shape of the delamination front can be predicted and a suitably shaped mesh can be provided. However, as impact events produce irregular shaped delamination fronts, this method requires an adaptive mesh approach that is not yet available in any of the major analysis codes. The cohesive fracture model solves some of the limitation of the linear elastic fracture mechanics method, however a definitive study of its abilities has yet to be found in the literature. The delamination threshold load method is an extremely simple method and provides surprisingly good results. The review concludes that additional development of current techniques is required before a definitive predictive delamination method will be available.

Finite Element Investigation of Quasi-Static Crack Growth in Functionally Graded Materials Using a Novel Cohesive Zone Fracture Model

This work studies mode I crack growth in ceramic/metal functionally graded materials (FGMs) using three-dimensional interface-cohesive elements based upon a new phenomenological cohesive fracture model. The local separation energies and peak tractions for the metal and ceramic constituents govern the cohesive fracture process. The model formulation introduces two cohesive gradation parameters to control the transition of fracture behavior between the constituents. Numerical values of volume fractions for the constituents specified at nodes of the finite element model set the spatial gradation of material properties with standard isoparametric interpolations inside interface elements and background solid elements to define pointwise material property values. The paper describes applications of the cohesive fracture model and computational scheme to analyze crack growth in compact tension, C(T), and single-edge notch bend, SE(B), specimens with material properties characteristic of a TiB/Ti FGM. Young’s modulus and Poisson’s ratio of the background solid material are determined using a self-consistent method (the background material remains linear elastic). The numerical studies demonstrate that the load to cause crack extension in the FGM compares to that for the metal and that crack growth response varies strongly with values of the cohesive gradation parameter for the metal. These results suggest the potential to calibrate the value of this parameter by matching the predicted and measured crack growth response in standard fracture mechanics specimens.

Ductile tearing in thin aluminum panels: experiments and analyses using large-displacement, 3-D surface cohesive elements

This paper describes a large-displacement formulation for a 3-D, interface-cohesive finite element model and its application to predict ductile tearing in thin aluminum panels. A nonlinear traction–separation relationship defines the constitutive response of the initially zero thickness interface elements. Applications of the model simulate crack extension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Tests of the M(T) specimens without guide plates exhibit significant out-of-plane (buckling) displacements during crack growth which necessitates the large-displacement, cohesive formulation. The measured load vs. outside surface crack extension behavior of high constraint ( T-stress>0) C(T) specimen drives the calibration process of the cohesive fracture model. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a/ W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and measured outside surface crack extensions. The models capture accurately the strong 3-D effects leading to out-of-plane buckling and various degrees of crack front tunneling in the C(T) and M(T) specimens. Previous analyses of these specimens using a crack tip opening angle (CTOA) criterion for growth show good agreement with measured peak loads. However, without the ability of the interface-cohesive model to predict tunneling behavior, the CTOA approach overestimates crack extensions early in the loading when tunneling behavior dominates the response.

Simulation of ductile crack growth in thin aluminum panels using 3-D surface cohesive elements

This work describes the formulation and application of a 3-D, interface-cohesive finite element model to predict quasi-static, ductile crack extension in thin aluminum panels for mode I loading and growth. The fracture model comprises an initially zero thickness, interface element with constitutive response described by a nonlinear traction-separation relationship. Conventional volumetric finite elements model the nonlinear (elastic-plastic) response of background (bulk) material. The interface-cohesive elements undergo gradual decohesion between faces of the volumetric elements to create new traction free crack faces. The paper describes applications of the computational model to simulate crack extension in C(T) and M(T) panels made of a 2.3 mm thick, Al 2024-T3 alloy tested as part of the NASA-Langley Aging Aircraft program. Parameters of the cohesive fracture model (peak opening traction and local work of separation) are calibrated using measured load vs. outside surface crack extensions of high constraint (T-stress > 0) C(T) specimens. Analyses of low constraint M(T) specimens, having widths of 300 and 600 mm and various a/W ratios, demonstrate the capabilities of the calibrated model to predict measured loads and outside surface crack extensions. The models capture accurately the strong 3-D effects leading to various degrees of crack front tunneling in the C(T) and M(T) specimens. The predicted crack growth response shows rapid convergence with through-thickness mesh refinement. Adaptive load increment procedures to control the rate of decohesion in the interface elements leads to stable, rapidly converging iterations in the globally implicit solution procedures.

Perturbative simulations of crack front waves

Willis and Movchan [Willis, J.R., Movchan, A.B., 1995. Dynamic weight functions for a moving crack I. Mode I loading. J. Mech. Phys. Solids 43, 319.] devised weight functions for a dynamic mode I fracture, within the singular crack model, using a first order perturbation of in-plane crack motion from the 2D results. Ramanathan and Fisher [Ramanathan, S., Fisher, D.S., 1997. Dynamics and instabilities of planar tensile cracks in heterogeneous media. Phys. Rev. Lettr. 79, 877.] reformulated the Willis-Movchan’s result in terms of crack growth at constant fracture energy, thereby confirming the existence of a crack front wave. Such a wave, as a propagating mode local to the moving crack front, was seen in the non-perturbative numerical simulations based on a cohesive zone fracture model, equivalent to growth at constant fracture energy. In this paper, the result of Ramanathan and Fisher, given in the wavenumber–frequency domain, is recast in the wavenumber–time domain to analyze fracture propagation within first-order perturbations for the singular crack model. This allows application of a spectral numerical methodology and is shown to be consistent with the known 2D results. Through analysis of a single spatial mode of crack shape, the propagating crack front wave and its resonance are demonstrated. Crack propagation through a randomly heterogeneous zone, and growth of disorder with propagation distance, are also examined.

Crack growth prediction in scaled down model of concrete gravity dam

Mixed-mode crack growth in a scaled-down model of a concrete gravity dam is investigated. An initial crack is assumed under equivalent hydraulic and self-weight loadings. The two-domain boundary element method (BEM) is applied in conjunction with the theory of linear elastic fracture mechanics (LEFM). The body force is included to simulate the weight effect of the dam on crack growth. The criteria of maximum tangential stress, minimum strain energy density function, maximum tangential strain and maximum energy release rate are used to predict the mixed-mode crack path. The numerical simulations are compared with the experimental results for the scaled down 1:40 model of a concrete gravity dam. Analytical results obtained from a cohesive fracture model using a finite element code are also discussed. It is found that the four foregoing LEFM criteria perform equally well for predicting crack trajectories, load versus crack tip opening displacement (CTOD), and load versus crack tip sliding displacement (CTSD) relations. This may be due to the dominance of the Mode I effect in crack growth as the contribution of Mode II is found to be negligibly small.