Calculation Of Strain Energy Release Rate Research Articles

Strain energy release rate under dynamic loading considering shear and crack tip root rotation effects

A closed form solution for the calculation of the strain energy release rate (SERR), at the initiation of a crack, for a double cantilever beam (DCB) test, under dynamic loading conditions, is presented. The dynamics of a Timoshenko beam are used in the analytical formulation. The equations of motion are obtained using a variational approach and the adhesively bonded region is modelled via a Lagrangian multiplier method. The SERR is calculated based on the contour integral method and is a function of the vibrational mode and the beam's eigenfrequencies. The analytical formulation is applied on two representative joint cases. One consists of isotropic and the other of composite sub-laminates. Finite element analysis was used to validate the analytical formulation. The results demonstrate the advantages of the use of the Timoshenko beam theory and the consideration of crack tip root rotations in dynamic fracture mechanics and emphasize that the localized vibration cannot be neglected in the SERR calculation.

Machine learning predictions on fracture toughness of multiscale bio-nano-composites

Tailorability is an important advantage of composites. Incorporating new bio-reinforcements into composites can contribute to using agricultural wastes and creating tougher and more reliable materials. Nevertheless, the huge number of possible natural material combinations works against finding optimal composite designs. Here, machine learning was employed to effectively predict fracture toughness properties of multiscale bio-nano-composites. Charpy impact tests were conducted on composites with various combinations of two new bio fillers, pistachio shell powders, and fractal date seed particles, as well as nano-clays and short latania fibers, all which reinforce a poly(propylene)/ethylene–propylene–diene-monomer matrix. The measured energy absorptions obtained were used to calculate strain energy release rates as a fracture toughness parameter using linear elastic fracture mechanics and finite element analysis approaches. Despite the limited number of training data obtained from these impact tests and finite element analysis, the machine learning results were accurate for prediction and optimal design. This study applied the decision tree regressor and adaptive boosting regressor machine learning methods in contrast to the K-nearest neighbor regressor machine learning approach used in our previous study for heat deflection temperature predictions. Scanning electron microscopy, optical microscopy, and transmission electron microscopy were used to study the nano-clay dispersion and impact fracture morphology.

Comprehensive dynamic failure mechanism of thermal barrier coatings based on a novel crack propagation and TGO growth coupling model

Comprehensive understanding of failure mechanism of thermal barrier coatings (TBCs) is essential to develop the next generation advanced TBCs with longer lifetime. In this study, a novel numerical model coupling crack propagation and thermally grown oxide (TGO) growth is developed. The residual stresses induced in the top coat (TC) and in the TGO are calculated during thermal cycling. The stresses in the TC are used to calculate strain energy release rates (SERRs) for in-plane cracking above the valley of undulation. The overall dynamic failure process, including successive crack propagation, coalescence and spalling, is examined using extended finite element method (XFEM). The results show that the tensile stress in the TC increases continuously with an increase in an undulation amplitude. The SERRs for TC cracks accumulate with cycling, resulting in the propagation of crack toward the TC/TGO interface. The TGO cracks nucleate at the peak of the TGO/bond coat (BC) interface and propagate toward the flank region of the TC/TGO interface. Both TC cracks and TGO cracks successively propagate and finally linkup leading to coating spallation. The propagation and coalescence behavior of cracks predicted by this model are in accordance with the experiment observations. Therefore, this study proposed coating optimization methods towards advanced TBCs with prolonged thermal cyclic lifetime.

Energy method for the calculation of the energy release rate of delamination in composite beams

An energy method based on beam theory is proposed to determine the strain energy release rate of an existing crack in composite laminates. The developed analytical method was implemented in isotropic materials, and the obtained strain energy release rate of a crack was validated by reference results and finite element solutions. The general behavior of crack growth on the left or right crack tip was evaluated, and basic trends leading to crack propagation to one side of the crack were established. A correction factor was introduced to improve the accuracy of the strain energy release rate for small cracks. The singularity at the crack tip caused by dissimilar materials was investigated and was found that the inclusion of the singularity effect could increase the accuracy for small cracks. The calculated strain energy release rate of a crack in a composite beam has been verified by comparing with a finite element model.

Fatigue Crack Propagation Life Prediction of 2A12 Aluminum Alloy Based on VCCT

The fatigue crack propagation behavior of the prior corrosion 2A12 aluminum alloy fastener involving a central hole was investigated. The virtual crack closure technique (VCCT), is straightforward and not sensitive to the FEA mesh size, was carried out to calculate strain energy release rate and SIFs of AA 2A12 under different stress levels and corrosion years. Based on the VCCT, the simulation carried out to analyze the corrosion fatigue crack growth behavior. It was proved to be convenient to simulate the crack propagation life and the predicted crack growth curve was in good agreement with the experimental results.

The LS1 model for delamination propagation in multilayered materials at [formula omitted] interfaces: A comparison between experimental and finite elements strain energy release rates

The aim of this paper is to analyze delaminated multilayered plates under classical loads using an alternative model to the existing three-dimensional finite element methods (3D-FEM). The proposed alternative model, named LS1, is a layerwise stress model proving significantly less computationally expensive while accurate and efficient. In particular this paper uses experimental data from different simple test specimens in a finite element code, which is based on LS1, in order to calculate strain energy release rates (SERR) in different modes of delamination. The focus is on two types of delaminated interfaces 0°/0° and 0°/45°. The obtained SERR results are in very good agreement with the experimental values and, in the case of mixed-mode delamination, they are as accurate as the SERR obtained by 3D-FE models. The other interesting property of the LS1 model is the very fast calculation speed as the SERR can be analytically deduced from interfacial stresses. This relation which only depends on the stacking sequence and the position of delamination is presented.

Corrosion Fatigue Crack Propagation of 6151-T6 Aluminum Alloy Based on Virtual Crack Closure Technique

Using the virtual crack closure technique (VCCT), an interface element that can calculate stress intensity factors (SIFs) directly and simulate the crack propagation conveniently has been developed. Based on an accelerated corrosion experiment, the fatigue crack propagation behavior of the 6151-T6 aluminum alloys under different corrosion years and stress levels were simulated, and it was proved to be convenient to calculate strain energy release rate and SIFs of AA 6151-T6 under different stress levels and corrosion years. The proposed method is characterized by higher accuracy and less calculation elements, provides a new way for engineering fracture analysis of the structure.

Fracture analysis in adhesive composite material/aluminum joints under mode-I loading; experimental and numerical approaches

Assessment and evaluation of fracture characteristics are very important in adhesive joint for achieving a safety mode. In this paper, fracture was investigated in mode-I in adhesive composite material/aluminum alloy joints. To achieve this aim, Double Cantilever Beam (DCB) was used to evaluate fracture in mode-I loading (opening). Bonding was realized by epoxy adhesive as one of the most important and widely used adhesives in aerospace and automotive industries. Modified Beam Theory (MBT) and Compliance Calibration Method (CCM) were formulated to calculate Strain Energy Release Rate (SERR). The obtained experimental results were verified by comparison with Finite Element (FE) analysis. FE results were derived from using Virtual Crack Closure Technique (VCCT) and J-integral approaches in two and three dimension (2-D & 3-D) simulation. Experiment tests and numerical analyses showed good agreement and demonstrated the effectiveness of the proposed experiment and numerical methods.

Delamination growth behavior in carbon fiber reinforced plastic angle ply laminates under compressive fatigue loads

Delamination fatigue growth experiments are carried out on angle ply T700/TDE85 Graphite/Epoxy laminates under compressive fatigue loads. Delamination growth is monitored in real time during fatigue test. Three-dimensional finite element methods are used to calculate strain energy release rate G by standard ABAQUS procedures. Components of strain energy release rate as the delamination grows are discussed. In particular, the delamination growth rate da/dN and the stabilized delamination length are systematically investigated in order to define the effect of loading level, delamination size, and delamination position on delamination growth behavior under compressive fatigue loads. Furthermore, scanning electron microscopy techniques are used to identify the fatigue delamination growth mechanisms and to assess the delamination growth behavior.

Fracture mechanics based predictions of initiation and growth of multi-level delaminations in a composite specimen

Design and manufacture of composite test specimens with two embedded delaminations subjected to transverse tension is described in this paper. The behaviour of the specimens has been investigated through experimental testing and finite element analyses. Fracture mechanics approaches were applied to predict the initiation and growth of delaminations and the degradation of the load carrying capacity of the specimens. Models were generated in the FE software programs MSC.Nastran and Abaqus. The MSC.Nastran model was used to calculate strain energy release rates employing a crack tip element methodology. The Abaqus model was evaluated using the virtual crack closure technique. The accuracy of numerical solutions was established by qualitative and quantitative comparisons with the experimental measurements, the results obtained from the ultrasonic non-destructive inspections and microscopic examination. It was shown that fracture mechanics can be used to accurately predict the failure initiation locations and failure loads of composite specimens containing multi-level delaminations.

A mechanistic model for transverse damage initiation, evolution, and stiffness reduction in laminated composites

A constitutive model to predict stiffness reduction due to transverse matrix cracking is derived for laminae with arbitrary orientation, subject to in-plane stress, embedded in laminates with symmetric but otherwise arbitrary laminate stacking sequence. The moduli of the damaged laminate are a function of the crack densities in the damaging laminae, which are analyzed one by one. The evolution of crack density in each lamina is derived in terms of the calculated strain energy release rate and predicted as function of the applied load using a fracture mechanics approach. Unlike plasticity-inspired formulations, the proposed model does not postulate damage evolution functions and thus there is no need for additional experimental data to adjust material parameters. All that it is needed are the elastic moduli and critical energy release rates for the laminae. The reduction of lamina stiffness is an integral part of the model, allowing for stress redistribution among laminae. Comparisons with experimental data and some results from the literature are presented.

Fundamentals of adhesion of thermal spray coatings: Adhesion of single splats

Indentation experiments were performed inside a scanning electron microscope to measure adhesive strength of individual alumina splats on a steel substrate. The in situ nature of experimental evaluations made characterization of interfacial crack propagation possible by direct observation. The increase in the strain energy of brittle alumina splats originating from indentation deformation was correlated to the strain energy release rate through the characterization of interfacial crack propagation. An analytical model previously reported and evaluated in studies of the adhesive strength of thin films was employed. An average calculated strain energy release rate of 80 J m −2 was found for single splats. This high value suggests that splat adhesion can make a significant contribution to the adhesion of thermal sprayed coatings.

Prediction of initiation and growth of single level delaminations in a transversely loaded composite specimen using fracture mechanics

The behaviour of a composite test specimen with an embedded delamination subjected to transverse tension has been investigated through experimental testing and finite element (FE) analyses. The testing program consisted of specimens in two geometrical configurations; square and rectangular delamination. The initiation and growth of the delamination was numerically predicted by fracture mechanics. FE models were analysed with both MSC.Nastran and Abaqus FE codes. The MSC.Nastran model was used to calculate strain energy release rates employing a crack tip element methodology. The Abaqus model was evaluated using the virtual crack closure technique. Both approaches accurately predicted failure initiation locations as observed in the test specimens. Failure loads were also well predicted. The mode mix at the crack tip in the proposed specimen was found to be similar to the mode mix expected in a conventional in-plane compression specimen.

Strain energy release rate determination of prescribed cracks in adhesively-bonded single-lap composite joints with thick bondlines

An analytical model for determining the strain energy release rate due to a prescribed crack in an adhesively-bonded, single-lap composite joint with thick bondlines and subjected to axial tension is presented. An existing analytical model for determining the adhesive stresses within the joint is used as the foundation for the strain energy release rate calculation. In the stress model, the governing equations of displacements within the adherends are formulated using the first-order laminated plate theory. In order to simulate the thick bondlines, the field equations of the adhesive are formulated using the linear elastic theory to allow non-uniform stress distributions through the thickness. Based on the adhesive stress distributions, the equivalent crack tip forces are obtained and the strain energy release rate due to the crack extension is determined by using the virtual crack closure technique (VCCT). The specimen geometry of ASTM D3165 standard test is followed in the derivation. The system of second-order differential equations is solved to provide the adherend and adhesive stresses using the symbolic computational tool, Maple 7. Finite element analyses using J-integral as well as VCCT are performed to verify the developed analytical model. Finite element analyses are conducted using the commercial finite element analysis software ABAQUS™. The strain energy release rates determined using the analytical method correlate well with the results from the finite element analyses. It can be seen that the same prescribed crack has a higher strain energy release rate for the joints with thicker bondlines. This explains the reason that joints with thick bondlines tend to have a lower load carrying capacity.

Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part II: Sensitivity study on modeling details

The interface element and VCCT process described in Part I of this two-part paper, developed to compute strain energy release rates of an arbitrary delamination front using non-orthogonal finite element meshes, are further investigated in this paper for robustness and ease of use in tracking delamination growth. Standard 3-D elements are used in conjunction with the interface elements. No special singularity elements are required. Stationary meshes that are independent of the shape of the delamination front can be used. Three cases having different initial delamination shapes are examined. The process is shown to be insensitive to the values used for the interfacial spring stiffness, the orientation of the interface element, or even the mesh pattern if the mesh has a reasonable degree of refinement. Therefore, the method can be used with ease and confidence in general-purpose delamination growth analysis for engineering applications.

Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the virtual crack closure technique. Part I: Formulation and validation

This paper proposes a simple, efficient algorithm to trace a moving delamination front with an arbitrary and changing shape so that delamination growth can be analyzed by using stationary meshes. Based on the algorithm, a delamination front can be defined by two vectors that pass through any point on the front. The normal vector and the tangent vector for the local coordinate system can then be obtained based on the two delamination front vectors. An important feature of this approach is that it does not require the use of meshes that are orthogonal to the delaminations front. Therefore, the approach avoids adaptive re-meshing techniques that may create a large computational burden in delamination growth analysis. An interface element that can trace the instantaneous delamination front, determine the local coordinate system, approximate strain energy release rate components and apply fracture mechanics criteria has been developed and implemented into ABAQUS ® with its user-defined element (UEL) feature. In this Part I of a two-part paper, the approach and its implementation are described and validated by comparison to results from existing cases having analytical solutions or other established FEA predictions.

Prediction of fatigue crack growth using finite element analysis techniques applied to three-dimensional elastomeric components

Elastomer components fail at cyclic strain amplitudes much lower than their catastrophic tear strength as a result of cumulative cyclic fatigue crack growth. Cracks typically develop in regions of high stress concentrations. In general, the rate of growth is determined by the shape of the component, and the nature and magnitude of the deformation imposed. Extensive earlier work has been done on the prediction of fatigue life of components. However, the reproducibility of the results was poor and, in addition, there was a low degree of accuracy. A fracture mechanics approach, which uses finite element analysis techniques to calculate strain energy release rates for cracks located in three-dimensional components, was used in combination with experimental measurements of cyclic crack growth rates of specific strain energy release rate to predict the cyclic crack growth propagation rate and the eventual fatigue failure of an elastomeric engineering component in three modes of deformation, namely: tension, simple shear and combined shear and tensile (45° angle) deformations. The fatigue crack growth for the gearbox mount under investigation was predicted within a factor of 2 at different displacements for all three modes of deformation.

Cryogenic Damage and Fracture Behaviors of G-11 Woven Glass-Epoxy Laminates

We discuss the cryogenic damage and fracture behaviors of G-11 woven glass-epoxy laminates. In conjunction with the cryogenic fracture toughness test, a finite element analysis was conducted to predict the fracture and deformation for models of the compact tension (CT) specimens. Effective elastic moduli were determined under the assumption of uniform strain inside the representative volume element. Hoffman’s criterion was selected as the criterion for fiber-dominated failure, and matrix cracking was detected by the maximum strain criterion. The virtual crack extension method was adopted to calculate strain energy release rate which leads to determination of stress intensity factor. In order to verify the model, correlations between experimental and analytical results were made, in terms of the load-displacement response and the extent of damage growth. Reasonable agreements between the calculations and the experimental data were achieved.

On the analytical determination of strain energy release rate in bonded DCB joints

A comparison of the different methods used to calculate strain energy release rate in bonded DCB joints has been made. The standard beam theory method has been shown to be in error and models with a compliant crack front have been evaluated in search of a more reliable analytical method. It is found that in fatigue testing, a beam on elastic foundation (BEF) model gives excellent results and a simple form of the BEF equation is proposed.

極低温における織物ガラス-エポキシ積層材料G-11の損傷・破壊力学解析

We discuss the cryogenic damage and fracture behaviors of G-11 woven glass-epoxy laminates. In conjunction with the cryogenic fracture toughness test, a two-dimensional finite element analysis was conducted to predict the fracture and deformation for models of the compact tension specimens. Effective elastic moduli were determined under the assumption of uniform strain inside the representative volume element. Hoffman’s criterion was selected as the criterion for damage accumulation induced by fiber breakage and matrix cracking was detected by the maximum strain criterion. The strain energy method was adopted to calculate strain energy release rate which leads to determination of stress intensity factor. In order to verify the model, correlations between experimental and analytical results were made, in terms of the load-displacement response and the extent of damage growth. At room temperature and 77 K, good agreements were found between the calculations and the experimental data. The predictions showed that the fracture behavior was influenced by temperature rises associated with individual damage events at 4 K. An apparent fracture toughness, Ki, was calculated for each specimen using the load, Pi, at which a significant change of slope in the damage zone size versus load curve was observed. The Ki value was independent of notch length but increased with specimen size.