Crack Surface Displacement Extrapolation Research Articles

A combined interface phase field (CIPF) model for interfacial crack propagation

The phase field method has been very popular in the past decade because it can handle complex crack propagation problems without ad hoc criteria. In this paper, a combined interface phase field (CIPF) model is proposed to better investigate the fracture behaviours of composite systems with a finite-thickness interface. To build the CIPF model, a new numerical method named the modified crack surface displacement extrapolation (MCSDE) method is proposed to determine the real interfacial fracture toughness. Then, an effective interfacial fracture toughness is given based on the coupling relationship between the length scale parameter and the interface thickness. We investigate crack propagation behaviours in bi-material structures with varied initial notch positions and sandwich specimens using the CIPF model. The results show that the MCSDE method can effectively and accurately determine the interface fracture toughness, and the difference between the calculated results and the results obtained by the sing-leg bending (SLB) experiment is 6%. The CIPF model can not only simulate the propagation of cracks in bulk, but also simulate the propagation of cracks between interfaces. For different positions of the initial notch, the propagation patterns of cracks and the mechanical response of the structure are very different.

Mode-III fracture toughness measurements of foam-cored sandwich composites using a constrained Shear-Torsion-Bending specimen

This work presents a constrained version of the Shear-Torsion-Bending (STB) test fixture, specially developed for testing of the mode-III face/core fracture toughness of sandwich specimens. Compared to the traditional STB test fixture, the free end of the specimen is now constrained between two support rollers, restraining the twisting deformation of the specimen resulting from the mode-III shear forces. The constrained STB test fixture was applied for mode-III fracture characterization of sandwich specimens with longitudinal slits and consisting of E-glass/epoxy face sheets and Divinycell PVC foam cores. Three density classes of the foam material were considered and tested, that is, H45, H100, and H160. Furthermore, two core thicknesses were tested for the H160 cored specimens. The experimental results from the constrained STB test method show that stable crack growth is obtained without kinking into the core. However, post-mortem investigations showed that longitudinal 45° tension cracks in the core just below the face/core interface occurred, before interface crack opening. Consequently, an apparent mode-III fracture toughness was computed using a three-dimensional Finite Element (FE) model in conjunction with the Crack Surface Displacement Extrapolation (CSDE) mode-mixity method and an optical Digital Image Correlation (DIC) based crack propagation method. Finally, based on the experimental observations presented in this paper, a general discussion of the existence of pure mode-III face/core interface propagation in foam-cored sandwich composites in relation to core and face/core bond strength is included.

Mixed mode fracture toughness and mode mixity analysis of face/core debonds in a single-leg sandwich bending specimen

Mixed mode fracture, which often occurs during composite materials, can present a safety hazard to the structure. Analytical expressions for the energy release rate (ERR) and mode mixity phase angle are derived for an asymmetric single-leg sandwich bending (SLSB) fracture specimen. Meanwhile, the modified crack surface displacement extrapolation (MCSDE) method is proposed to obtain the numerical solution of ERR and mode mixity. The effects of loading characteristics, core and face sheet geometric parameters and material parameters on ERR and mode mixity are investigated. To solve the problem of excessive deformation of the thin plate specimen during the test, a reinforced single-leg sandwich bending specimen (RSLSB) is proposed, and the detailed derivation process of the RSLSB fracture specimen's analytical solution is given. The results show that loading magnitude greatly affects ERR and mode mixity. The core’s geometric and material parameters have little effect on ERR but have apparent effects on mode mixity. The face sheet's geometric and material parameters have apparent effects on the ERR and mode mixity. The existence of the reinforced layer will increase the mode I fracture component.

Face/core disbond fatigue growth in honeycomb cored aircraft sandwich elements under mixed mode flatwise tension loading

Disbond damage growth in honeycomb cored sandwich structures due to static and fatigue mixed mode loading is investigated numerically and experimentally. A two dimensional finite element model was generated using core homogenization and the Crack Surface Displacement Extrapolation mode separation method, integrated into a fracture mechanics based analysis sub-routine to predict face/core interface fatigue crack propagation. The Cycle Jump technique was furthermore applied to accelerate fatigue analysis. Mixed mode fatigue characterization testing was conducted using Double Cantilever Beam specimens loaded with Uneven Bending Moments, generating a relationship between crack propagation rates and energy release rate amplitudes as a modified Paris Law, measured at three mode-mixity phase angles. The measured Paris laws were subsequently used as input data for the numerical fatigue model. The numerical model was validated against CFRP/Nomex® Sandwich Tearing Test specimen tests with a propagating face/core interface crack yielding varying mode-mixities. The results from the validation showed good agreement between numerical predictions and experimental measurements.

Numerical fracture analysis and model validation for disbonded honeycomb core sandwich composites

Disbond damage propagation in honeycomb core sandwich structures is investigated numerically and experimentally. A fully parametric two-dimensional finite element model of a disbonded honeycomb core sandwich specimen is presented. Energy release rate and mode-mixity were numerically determined using the Crack Surface Displacement Extrapolation (CSDE) method. An advanced method was adopted to obtain the homogenized mechanical properties of the honeycomb core based on the geometry of a single honeycomb cell and the material properties of the cell wall paper. The numerical model was benchmarked against CFRP/Nomex® Single Cantilever Beam (SCB) specimen tests and a closed-form semi-analytical model. The results show a close agreement between analytical, numerical and experimental energy release rate, as well as analytical and numerical mode-mixity. An extensive sensitivity analysis was also carried out and the effects of the geometry and the material properties of the SCB specimen on the energy release rate and mode-mixity have been investigated.

Mixed-mode fracture evaluation of aerospace grade honeycomb core sandwich specimens using the Double Cantilever Beam–Uneven Bending Moment test method

Fracture testing of aerospace grade honeycomb core sandwich composites is carried out using the Double Cantilever Beam specimen loaded with Uneven Bending Moments, and a Double Cantilever Beam–Uneven Bending Moment test rig capable of applying pure moments is utilized. Specimens with carbon fiber-reinforced plastic face sheets are employed with a range of honeycomb core grades comprising of Nomex® and Kevlar paper. The sandwich specimens are reinforced with steel doublers to reduce excessive rotation of the face sheets. The mode mixity phase angle pertaining to a particular ratio of moments between the two arms of the Double Cantilever Beam specimen is determined using the numerical mode mixity method—Crack Surface Displacement Extrapolation method. For Nomex® honeycomb core sandwich specimens, it is observed that the mode I interface fracture toughness increases with increase in core density. The interface fracture toughnesses for Nomex®-based honeycomb cores are also compared against specimens with Kevlar paper-based honeycomb cores. Crack propagation is observed at the interface just beneath the meniscus layer for the majority of the tested specimen configurations. The Double Cantilever Beam–Uneven Bending Moment test methodology with the concept of direct application of moments on both crack flanks has proven to have a significant potential for mixed mode face/core fracture characterization of aerospace grade sandwich composites.

On the analysis of a mixed mode bending sandwich specimen for debond fracture characterization

The mixed mode bending specimen originally developed for mixed mode delamination fracture characterization of unidirectional composites has been extended to the study of debond propagation in foam cored sandwich specimens. The compliance and strain energy release rate expressions for the mixed mode bending sandwich specimen are derived based on a superposition analysis of solutions for the double cantilever beam and cracked sandwich beam specimens by applying a proper kinematic relationship for the specimen deformation combined with the loading provided by the test rig. This analysis provides also expressions for the global mode mixities. An extensive parametric analysis to improve the understanding of the influence of loading conditions, specimen geometry and mechanical properties of the face and core materials has been performed using the derived expressions and finite element analysis. The mixed mode bending compliance and energy release rate predictions were in good agreement with finite element results. Furthermore, the numerical crack surface displacement extrapolation method implemented in finite element analysis was applied to determine the local mode mixity at the tip of the debond.

Stress intensity solutions for cracked plates by the dual boundary method

We describe the application of the dual boundary element method for the determination of stress intensity factors in plate bending problems. The loadings considered include internal pressure, and also combined bending and tension. Mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. The boundary element results for the case studies considered in the paper have been compared with either analytical or finite element results and in all cases good agreement has been achieved.

Interface crack in sandwich specimen

Fracture of a sandwich specimen loaded with axial forces and bending moments is analyzed in the context of linear elastic fracture mechanics. A closed form expression for the energy release rate for interface cracking of a sandwich specimen with isotropic face sheets is found from analytical evaluation of the J-integral. An approach is applied, whereby the mode mixity for any combination of the loads can be calculated analytically when a load-independent phase angle has been determined. This load-independent phase angle is determined for a broad range of sandwich configurations of practical interest. The load-independent phase angle is determined using a novel finite element based method called the crack surface displacement extrapolation method.

Experimental and Numerical Study of Interface Crack Propagation in Foam-cored Sandwich Beams

This article deals with the prediction of debonding between core and face sheet in foam-cored sandwich structures. It describes the development, validation, and application of a FEM-based numerical model for the prediction of the propagation of debond damage. The structural mechanics is considered to be geometrically nonlinear while the local fracture mechanics problem is assumed to be linear. The presented numerical procedure for the local fracture mechanics is a further development of the crack surface displacement method, here denoted as the crack surface displacement extrapolation method. The considered application example is to tear off one of the face laminates from the sandwich. This configuration can be found in many applications but is considered here to be occurring in a ship structure, particularly at the hard spot where the superstructure meets the deck. Face tearing experiments are carried out for structures with three different core densities, material tests are carried out and finally the face tearing tests are simulated with the developed procedure. It is shown that for low core densities, where the crack propagates in the interface immediately below the face sheet, there is fair agreement between experiments and theory. For cores with higher density, the crack tends to propagate in the laminate itself with extensive fiber bridging leading to rather conservative numerical predictions. However, for structural configurations where LEFM can be applied, the presented procedure is sufficiently robust and accurate to be used in a number of important engineering applications, for example risk-based inspection and repair schemes.

Non-uniform Compressive Strength of Debonded Sandwich Panels – II. Fracture Mechanics Investigation

This article describes the development, validation and application of a FEM based numerical model for prediction of residual strength of damaged sandwich panels. The core of the theoretical method is a newly developed procedure for prediction of the propagation of a face-core debond. As demonstrated, the method can predict the maximum load carrying capacity of real-life panels with debond damages, where the failure is governed by face-sheet buckling followed by debond growth. The developed theoretical procedure is an extension of the as Crack Surface Displacement method, here denoted as the Crack Surface Displacement Extrapolation method. The method is first developed in 2D and then extended to 3D by use of a number of realistic assumptions for the considered configurations. Comparison of the theoretical predictions to a series of large-scale experiments, described in [17], shows that the model is indeed able to predict the failure modes and the residual strength of damaged panels with accuracy sufficient for practical applications. This opens up for a number of important engineering applications, for example risk-based inspection and repair schemes.

Stress intensity factors for cracks in thin plates

This paper presents stress intensity factor solutions for several crack configurations in plates. The loadings considered include internal pressure, and also combined bending and tension. The dual boundary element method is used to model the plate and mixed mode stress intensity factors are evaluated by a crack surface displacement extrapolation technique and the J-integral technique. Several cases including centre crack, edge crack and cracks emanating from a hole in finite width plates are presented.