Uneven Bending Moments Research Articles

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.

Strain energy release rate and mode partitioning of moment-loaded elastically coupled laminated beams with hygrothermal stresses

New closed-form, analytical solutions are derived for the strain energy release rate (SERR) and mode partitioning of uneven bending moments-loaded tests on layered beams with bending-extension coupling and residual hygrothermal stresses. The analytical modeling utilizes Timoshenko beam kinematics, a semi-rigid interface model, and the global method to perform mode partitioning. The proposed solutions are validated via the finite element method in two typical examples of metal-composite joints. In addition, experiments using the double cantilever beam with uneven bending moments test setup are performed in a titanium-carbon fiber reinforced plastic adhesive joint, and data reduction is performed utilizing the new analytical solutions. We demonstrate that the residual thermal stresses effect on the SERR and mode mixity of the metal/composite interfaces can be non-negligible and, thus, should be considered in the design and analysis of such structures. The proposed formulas serve as a data reduction scheme for the fracture toughness and mode mixity determination in the general case of layered beams with bending-extension coupling and hygrothermal stresses, when utilizing uneven bending moments for the characterization tests.

Influence of Dynamic Loading on Fracture Behaviour of DCB Sandwich Specimen

Numerical simulations of dynamic fracture behaviour of a double cantilever sandwich beam subjected to uneven bending moments in plane conditions are carried out using the dynamic finite element analyses with the ABAQUSTM code. The strain energy release rate was evaluated by means of the finite element model developed within the two-dimensional (2-D) linear elastodynamic theory. This demonstrates the capability and the reliability of the finite element modelling as an extremely useful numerical tool for solving dynamic fracture mechanics problems. Also, the dynamic behaviour of fracture parameters and interface crack progression is discussed.

A modified DCB-UBM test method for interfacial fracture toughness characterization of sandwich composites

A novel double cantilever beam test method for interface fracture toughness characterization of debonded sandwich composites is introduced. The method is called DCB-UBM (Double Cantilever Beam loaded with Uneven Bending Moments), where pure moments are applied to the beams at the crack end using torsional actuators, to generate crack propagation along the face sheet/core interface. A data reduction method is proposed to determine the fracture toughness. Fracture testing is performed on a typical marine grade sandwich configuration consisting of PVC H45 foam core and glass fiber face sheets to demonstrate the applicability of the test method. The obtained fracture toughness agrees with interface toughness values in the literature measured using other test methods with the same material system. The effective kinematics of the test rig is measured using Digital Image Correlation (DIC) by studying the rotations and moments of a specially designed calibration specimen and comparing the results against finite element results. The DCB-UBM specimen and test method is a promising candidate for obtaining face sheet/core interface fracture toughnesses in sandwich composites.

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.

A thermodynamically consistent derivation of a frictional-damage cohesive-zone model with different mode I and mode II fracture energies

Abstract The present paper deals with the derivation of an interface model characterized by macroscopic fracture energies which are different in modes I and II, the macroscopic fracture energy being the total energy dissipated per unit of fracture area. It is first shown that thermo-dynamical consistency for a model governed by a single damage variable, combined with the choice of employing an equivalent relative displacement and of a linear softening in the stress-relative displacement law, leads to the coincidence of fracture energies in modes I and II. To retrieve the experimental evidence of a greater fracture energy in mode II, a micro-structured geometry is considered at the typical point of the interface where a Representative Interface Element (RIE) characterized by a periodic arrangement of distinct inclined planes is introduced. The interaction within each of these surfaces is governed by a coupled damage-friction law. A sensitivity analysis of the correlation between micromechanical parameters and the numerically computed single-point microstructural response in mode II is reported. An assessment of the capability of the model in predicting different mixed mode fracture energies is carried out both at the single microstructural interface point level and with a structural example. For the latter a double cantilever beam with uneven bending moments has been analyzed and numerical results are compared with experimental data reported in the literature for different values of mode mixity.

Experimental approach for mixed-mode fatigue delamination crack growth with large-scale bridging in polymer composites

An experimental apparatus utilizing double cantilever beam specimens loaded with uneven bending moments was developed to study the mixed-mode fatigue crack growth in composites. The approach is suitable when large-scale bridging of cracks is present. To illustrate the testing method, cyclic growth of delaminations in a typical fibre-reinforced polymer composite was investigated under a constant cyclic loading amplitude. Pure mode I, mode II and mixed-mode crack growth conditions were examined. The results, analysed using a J-integral approach, show that the double cantilever beam loaded with uneven bending moments configuration provides a robust approach to investigate the fatigue crack growth of composites for pure mode and mixed-mode cracking. A steady-state crack growth regime was observed for mode I and mixed-mode loading. For mode II loading, steady-state was absent, and a progressively decreasing crack growth rate observed. In addition to details concerning the equipment, a general discussion of the development of cyclic bridging laws for delamination growth in the presence of large-scale bridging is provided.

Determination of the J integral for laminated double cantilever beam specimens: The curvature approach

A new approach is proposed for measuring the J integral (and thus the fracture resistance) of interface cracks in multiply laminates. With this approach the J integral is found from beam curvatures and applied moments. Knowledge of ply layup and stiffness is not required. In order to test the accuracy of the proposed approach, double cantilever beam specimen loaded with uneven bending moments (DCB-UBM) specimens were tested and analysed using the curvature approach and a method based on laminate beam theory. Beam curvatures were determined using a configuration of strain gauges. Good agreement was obtained between the two approaches.

Tailoring Sandwich Face/Core Interfaces for Improved Damage Tolerance—Part I: Finite Element Analysis

Various modifications of the face/core interface in foam core sandwich specimens are examined in a series of two papers. This paper constitutes part I and describes the finite element analysis of a sandwich test specimen, i.e. a DCB specimen loaded by uneven bending moments (DCB-UBM). Using this test almost any mode-mixity between pure mode I and mode II can be obtained. A cohesive zone model of the mixed mode fracture process involving large-scale bridging is developed. Results from the analysis are used in Part II, which describes methods and results of a series of experiments.

Tailoring Sandwich Face/Core Interfaces for Improved Damage Tolerance—Part II: Experiments

A face/core debond in a sandwich structure may propagate in the interface or kink into either the face or core. It is found that certain modifications of the face/core interface region influence the kinking behavior, which is studied experimentally in the present paper. A sandwich double cantilever beam specimen loaded by uneven bending moments (DCB-UBM) allows for accurate measurements of the J integral as the crack propagates under large scale fibre bridging. By altering the mode-mixity of the loading, the crack path changes and deflects from the interface into the adjacent face or core. The transition points where the crack kinks are identified and the influence of four various interface design modifications on the propagation path and fracture resistance are investigated.

Delamination of thin coatings at scratching: experiments and numerics

Scratching of thin coatings on hard substrates is studied experimentally and numerically, in the latter case by use of the finite element method. In particular the delamination behaviour at scratching, by increasing the normal load up to failure, is of interest. The adhesion of the coating to the substrate is modelled as a cohesive zone where relevant model parameters are determined experimentally using the double cantilever beam test with uneven bending moments (DCB-UBM). Good correlation between experimental and numerical results were achieved and the most important finding confirms the fact that the delamination behaviour was very much dependent on the critical energy release rate of the film/substrate interface. The results achieved are directly relevant for thin film polymer coatings but can also be applied in more general situations as a comprehensive parameter study is performed using the finite element method.

On scratch testing of pressure-sensitive polymeric coatings

Scratching of polymeric coatings on hard substrates is studied experimentally and numerically from a mechanical point of view. In particular, the behavior of local and global mechanical properties, as well as the delamination behavior, at scratching due to pressure-sensitive effects is of interest. The numerical investigation is performed using the finite element method (FEM) where pressure sensitivity is modeled using the classical Drucker–Prager plasticity model (Drucker, Prager, Q. Appl. Math., 10 157–165 (1952)) while the adhesion of the coating to the substrate is modeled as a cohesive zone where relevant model parameters are determined experimentally using the double cantilever beam test with uneven bending moments (DCB-UBM). Good correlation between experimental and numerical results were achieved and the most important finding concerns the fact that the dependence of pressure sensitivity proved to be different for different mechanical quantities.

Strength scaling of adhesive joints in polymer–matrix composites

The fracture of adhesive joints between two glass-fibre laminates was studied by testing double cantilever beam test specimens loaded by uneven bending moments. A large-scale fracture process zone, consisting of a crack tip and a fibre bridging zone, developed. The mixed mode fracture resistance increased with increasing crack length, eventually reaching a steady-state level ( R-curve behaviour). The steady-state fracture resistance level increased with increasing amount of tangential crack opening displacement. Cohesive laws, obtained from fracture resistance data, were used for prediction the load carrying capacity of 2-m long “medium size” adhesive joint specimens subjected to four point flexure. Medium size specimens were manufactured and tested. A good agreement was found between the predicted and measured strength values of the medium-size specimens. Thus, the scaling from small specimens to medium-size specimens was successfully achieved.

Measurement of Interface Fracture Toughness of Sandwich Structures under Mixed Mode Loadings

Fracture of sandwich structures 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 of interface cracking of a sandwich specimen is found by analytical evaluation of the J-integral. A method for determining the mode mixity is described and applied. Expressions are presented whereby the mode mixity can be calculated analytically for any load combination when the mode mixity is known for just one load case. The theory presented is applied to a new test method based on double cantilever beam sandwich specimens loaded with uneven bending moments. The interface fracture toughness of two sandwich types are measured as function of the mode mixity. The sandwich structures that are tested consist of glass fiber reinforced polyester skins and PCV core. The tests show that the interface fracture toughness depends strongly on the mode mixity. Under dominated normal crack opening, the crack grows just below the interface in the core at a constant fracture toughness. Under dominated tangential crack deformation, the crack grows into the laminate resulting in extensive fiber bridging and an increase in fracture toughness. As a result of the development of a large process zone due to fiber bridging, the analysis by linear elastic fracture mechanics becomes invalid and modeling with cohesive zones is proposed.

A modified DCB sandwich specimen for measuring mixed-mode cohesive laws

A test method is described for measuring cohesive laws for interfaces in sandwich structures. It is proposed to increase the bending stiffness of the sandwich faces by adhering steel bars onto the sandwich faces. This stiffening reduces rotations and ensures that the method is applicable for thin face sandwich specimens. Crack growth along the face/core interface is obtained by a stiffened double cantilever beam specimen loaded with uneven bending moments (DCB-UBM). The J integral is employed and the opening of the pre-crack tip is measured using a commercial optical measurement system, from which mixed-mode cohesive laws are extracted.

DCB-specimen loaded with uneven bending moments

A double cantilever beam specimen loaded with uneven bending moments (DCB-UBM) is proposed for mixed mode fracture mechanics characterisation of adhesive joints, laminates and multilayers. A linear elastic fracture mechanics analysis gives the energy release rate and mode mixity analytically for both isotropic and orthotropic materials. By varying the ratio between the two applied moments, the crack tip stress state can be varied from pure mode I to pure mode II for the same specimen geometry. The specimen allows stable crack growth. A special test fixture is developed to create uneven bending moments. As a preliminary example, the DCB-UBM specimen was used for characterising fracture of adhesive joints between two laminates of thermoset glass fibre reinforced plastic.

Determination of mixed mode cohesive laws

A novel approach is proposed for the determination of mixed mode cohesive laws for large scale crack bridging problems. The approach is based on a plane, two-dimensional analysis utilizing the J integral applied a double cantilever beam specimens loaded with uneven bending moments. The normal and shear stresses of the cohesive laws are obtained from consecutive values of the fracture resistance, the normal and tangential displacements of the end of the cohesive zone. The data analysis involves fitting and determination of partial differentials. This is done by a numerical method using Chebyshev polynomials. The accuracy of the numerical procedure is investigated by the use of synthetic data. It is found that both the shape and peak stress of the cohesive law can be determined with high accuracy, providing that the data possess low noise and a sufficiently high number of datasets are used. The investigation leads to some practical guidelines for experimental use of the proposed approach.