Energy Release Rate For Delamination Research Articles

Thickness effects on the delamination energy release rate of thermal barrier coating subjected to thermo-mechanical loads

The delamination energy release rate of the thermal barrier coating (TBC) under steady thermal gradient coupled with mechanical loads is theoretically investigated. We first derive a set of integral equations to calculate the energy release rate and mode mixity phase angle of the bilayer TBC with thermo-mechanical loads. Then from the cut and paste procedure, a closed form energy release rate solution is obtained for the thermal gradient case, which is demonstrated to be identical to the numerical results for the coat/substrate thickness ratio less than 0.4. As the coat/substrate thickness ratio increases, when the substrate thickness is fixed, the energy release rate increases from zero except for a drop corresponding to the transition from crack model I to model II. When the film thickness is fixed, the energy release rate decreases from the isothermal result to a minimum point and then increases to a maximum point and then decreases. The mechanical loads are shown to reduce the energy release rate. A new model transition point emerges for larger thickness ratio due to the fact that the compression of the coating is relieved by the mechanical loads. The effects of the stress free reference temperature, Young's modulus, Poisson’s ratio, thermal conductivity and thermal expansion coefficient on the energy release rate are also disclosed. The obtained results can shed considerable insights for the assessment and design of TBCs and other layered structures subjected to thermo-mechanical loads.

Enabling lightweight polycarbonate-polycarbonate (PC-PC) photovoltaics module technology – Enhancing integration of silicon solar cells into aesthetic design for greener building and urban structures

Light weight photovoltaic (PV) modules have advantages both to reduce costs of PV installations as well as to enhance their further integration with building and other urban structures such as roofs of public parking areas and bus stations. Polycarbonate (PC) materials have been studied before as glass or front sheet replacement, but recently the PC-PC module design (where both front and back sheets are made of PC) has gained attractions both in industry as well as in research. It offers further additional benefits, such as improved reliability (in terms of silicon cell cracks) and enhanced ease of integration into not only flat surfaces, but also curved ones such as integrated PV in cars, trucks, and boats. These benefits may enable more aesthetic design that can increase the appeal of the PV technology. However, a few technological issues stand between the current forms of PC-PC PV module design and the increasing market demands for more aesthetically pleasing and contour-confirming PV integrations. Two of the most important ones are the silicon sensitivity against fracture (especially in bending mode) and interface delamination (especially between PC and the encapsulants). Both are driven by mechanical stresses in the silicon cells as well as in other materials in the PV module/package design. Having published widely our studies in stresses in silicon solar cells in PV module design, both experimentally as well as computationally as shown in the literature review of this manuscript, our research group has obtained unique insights in the primary driving forces of failures in the typical PV module design (glass-back sheet). In the present manuscript, we use the Width Tapered Cantilever Beam (WTCB) method to investigate the interfacial delamination issues systematically. We found that the energy release rate for delamination or fracture at the interfaces between PC and EVA (Ethylene Vinyl Acetate) was fairly low (i.e. low adhesion strength), but could be enhanced with process parameters during the PV lamination step or separate thermal treatment. Hence, this could be taken advantage for enabling unique and highly innovative PV modules based on PC, and for aesthetic purposes for the wider applications of PV technology.

Propose a generic framework for probabilistic prediction of the onset and growth of matrix cracking induced delamination in composite laminates

Matrix cracking induced delamination (MCID) is one of the catastrophic modes that can occur in composite laminates. In this paper, an efficient algorithm based on the concept of energy release rate for delamination due to matrix cracking and mode II interlaminar fracture toughness is developed and by applying this proposed framework, the reliability analysis of MCID damage is performed. The limit state function is formulated using a general and effectual failure criterion which is developed by the authors of this article, previously. To represent the performance of the proposed algorithm, the probability of the occurrence and growth of MCID in a quasi-isotropic laminate including 45°, 90°, −45° and 0° plies under different loading conditions and various stacking sequences is extracted by using first and second order reliability methods. The obtained results are verified using Monte Carlo simulation. In addition, some significant probability results are compared with several experimental data for validation of the proposed method, qualitatively. For the first time, stochastic failure envelopes called reliability based failure envelops are generated to attain deeper and clear insight about laminate random behavior under MCID mode. The effect of some variables such as the ply thickness, different stress level and stress states and matrix cracking density on the probability of occurrence and growth of MCID is investigated.

Block structured adaptive mesh refinement and strong form elasticity approach to phase field fracture with applications to delamination, crack branching and crack deflection

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure. The phase field method for fracture uses a surrogate damage field to model crack propagation, eliminating the arduous need for explicit crack meshing. In this work a novel numerical framework is proposed for implementing hybrid phase field fracture in heterogeneous materials. The proposed method is based on the “reflux-free” method for solving, in strong form, the equations of linear elasticity on a block-structured adaptive mesh refinement (BSAMR) mesh. The use of BSAMR enables highly efficient and scalable regridding, facilitates the use of temporal subcycling for explicit time integration, and allows for ultra-high refinement at crack boundaries with minimal computational cost. The method is applied to a variety of simple heterogeneous structures: laminates, wavy interfaces, and circular inclusions. In each case a non-dimensionalized parameter study is performed to identify regions of behavior, varying both the geometry of the problem and the relative fracture energy release rate. In the laminate and wavy interface cases, regions of delamination and fracture correspond to simple analytical predictions. For the circular inclusions, the modulus ratio of the inclusion is varied as well as the delamination energy release rate and the problem geometry. In this case, a wide variety of behaviors was observed, including deflection, splitting, delamination, and pure fracture.

On the interaction of delamination buckling and damage growth in cross-ply laminates

The compressive behaviour of cross-ply laminates with delaminations and matrix cracked layers is investigated by means of an analytical modelling approach. Insight into the post-buckling and damage growth behaviour is obtained owing to comprehensive parametric studies varying delamination length and depth as well as matrix crack density for cross-ply laminates with different layups. The efficient modelling approach comprises the well-known total potential energy principle and the Equivalent Constrained Model for determining reduced stiffness properties depending on the matrix crack density. Thus, unlike previous studies on delamination buckling, the effect of matrix cracked layers is taken into consideration. The analysis of the energy release rates for delamination and matrix crack growth enables the identification of configurations (e.g. delamination depth and length, total thickness of the laminates) which are prone to delamination growth and matrix crack growth, respectively. Beyond that, relationships between post-buckling and damage growth behaviour are identified and discussed.

An approximate solution for the inverted four-point bending test in symmetric specimens

An approximate solution is derived for the interfacial energy release rate of the inverted four-point bending test. The analysis builds on a previous model developed by one of the authors for an orthotropic edge-cracked layer subject to arbitrary generalized end forces. Contact forces exerted from the upper on the lower layer of the edge-cracked portion behind the delamination tip are introduced. Their value is chosen such that the two layers undergo the same deflection. The effects of both shear deformations along the layers and friction at the point of contact are taken into account within beam theories and approximate Coulomb model with a prescribed friction coefficient. The delamination energy release rate is derived for homogeneous and symmetric specimens. A parametric analysis is performed on varying the mechanical parameters of the model to analize the influence of shear deformations and friction. The results show that both shear deformations and friction affect the value of the energy release rate for short/intermediate interfacial cracks. For very long interfacial cracks the delamination energy release rate tends to a constant limit value which corresponds to that obtained within classical Euler-Bernoulli beam theory in absence of friction.

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.

Analysis of thermally induced delamination and buckling of thin-film thermoelectric generators made up of pn-junctions

This paper investigates the problem of delamination and buckling of thermoelectric pn-junctions, which have many potential civil and military applications including thermal protection systems in space industry. Based on the compatibility equations of deformation, equilibrium equations of axial force and the strain compatibility equation at the interface of the bonding part are derived. Analytical solution of the delamination energy release rate is obtained. It is noted that there is no energy release rate when the magnitude of the temperature difference between the right end and the left end of the pn-junction is zero. The energy release rate can decrease or increase with the coefficient of thermal expansion. Distributions of the critical temperature differences for the delamination propagation and buckling are presented graphically. The critical temperature differences decrease continually with delamination and buckling lengths. Either a higher temperature difference or a higher electric current density can result in a bigger delamination energy release rate, a larger buckling deflection and a strong axial force. The buckling deflection increases but the axial force decreases with the increase of buckling length.

Demonstration of pseudo-ductility in high performance glass/epoxy composites by hybridisation with thin-ply carbon prepreg

A new approach and material architecture is presented in order to overcome the inherent brittleness and unstable failure characteristic of conventional high performance composites. The concept is the use of thin-ply hybrid laminates. Fracture mechanics calculations were carried out to determine the critical carbon layer thickness for stable pull-out in a three layer unidirectional hybrid laminate, which can provide a pseudo-ductile failure. Unidirectional hybrid composites were fabricated by sandwiching various numbers of thin carbon prepreg plies between standard thickness glass prepreg plies and tested in tension. Specimens with one and two plies of thin carbon prepreg produced pseudo-ductile failure, whereas ones with three and four plies failed with unstable delamination. An explanation of the different failure modes is given in terms of the different energy release rates for delamination in various specimens. The observed damage characteristics agreed well with the expectations according to the estimated critical carbon layer thickness.

The Influence of Transient Thermal Gradients and Substrate Constraint on Delamination of Thermal Barrier Coatings

A systematic study of factors affecting the delamination energy release rate and mode mix of a thermal barrier coating attached to a substrate is presented accounting for the influence of thermal gradients combined with rapid hot surface cooling. Transient thermal gradients induce stress gradients through the coating and substrate, which produce overall bending if the substrate is not very thick and if it is not constrained. Due to their influences on the coating stresses, substrate thickness and constraint are important aspects of the mechanics of delamination of coating-substrate systems, which must be considered when laboratory tests are designed and for lifetime assessment under in-service conditions. Temperature gradients in the hot state combined with rapid cooling give rise to a maximum energy release rate for delamination that occurs in the early stage of cooling and that can be considerably larger than the driving force for delamination in the cold state. The rates of cooling that give rise to a large early stage energy release rate are identified.

Analytic formulas of energy release rates for delamination using a global–local method

This article presents analytic solutions of energy release rates of a cracked laminate by using a global–local method. Deformations of a cracked laminate subjected to pure bending moments are analyzed and then a new mode partition equation is proposed. By using this partition equation, closed-form solutions of energy release rates GI and GII are derived by using a global method. For a cracked laminate subjected to axial forces and bending moments, a local method based on the crack-tip force model is used and the unknown coefficient is solved by combining the present analytic solutions for the bending moment loading case. Numerical results of the mode mixity predicted by the present closed-form formulations correlate well with those numerically calibrated on the basis of the singular field and crack-tip force models.

Axisymmetric thermo-mechanical analysis of laser-driven non-contact transfer printing

An axisymmetric thermo-mechanical model is developed for laser-driven non-contact transfer printing, which involves laser-induced impulsive heating to initiate separation at the interface between a soft, elastomeric stamp and hard micro/nanomaterials (i.e., inks) on its surface, due to a large mismatch in coefficients of thermal expansion. The result is the active ejection of the inks from the stamp, to a spatially separated receiving substrate, thereby representing the printing step. The model gives analytically the temperature field, and also a scaling law for the energy release rate for delamination at the interface between the stamp and an ink in the form of a rigid plate. The normalized critical laser pulse time for interfacial delamination depends only on the normalized absorbed laser power and width of the ink structure, and has been verified by experiments.

Toward efficient and robust computation of energy release rate and mode mix for delamination

Different methods for computing energy release rates for delamination are assessed with emphasis on their performance with large elements and irregular meshes. The jump in stress and strain that appears at the crack front with shell kinematics is used to compute the energy release rate in a simple manner via the jump in Eshelby tensor, without the mesh requirements that are associated with the virtual crack closure technique. The robustness of the results is examined for different kinematic formulations. For mode partitioning, another method that also makes use of the jump in stress [15], is modified for better performance with large elements. In this manner, the proposed method connects to existing concepts for characterization of fracture toughness based on linear elastic fracture mechanics. However, by presenting a size effect in the mode mix predicted with a cohesive method, it is emphasized that the validity of these concepts is questionable.

Thermo-mechanical modeling of laser-driven non-contact transfer printing: two-dimensional analysis

Transfer printing is an emerging technique for materials assembly and micro-/nano-fabrication. An important emerging variant of this process involves laser-induced impulsive heating to initiate separation at the interface between a soft, elastomeric stamp and hard micro-/nano-materials (i.e. inks) on its surface, due to a large mismatch in coefficients of thermal expansion. The result is the active ejection of the inks from the stamp to a spatially separated receiving substrate, thereby representing the printing step. In the following, a thermo-mechanical model is established to analytically obtain the temperature field, and the energy release rate for delamination at the interface between the stamp and ink in the form of a rigid plate. The normalized critical laser pulse time for interfacial delamination depends only on the normalized total heat flux at the interface and the normalized width of the ink structure. This scaling law has been verified by experiments and the finite element method.

Effects of Seawater and Low Temperatures on Polymeric Foam Core Material

Polymeric composite sandwich structures, often manufactured using a thick foam core material and thin composite facings, are of significant interest in naval applications. This paper summarizes the coupled effect of sea water and low temperature on the mechanical properties of closed cell polymeric H100 foam core material. The study considers the effects of harsh sea environmental conditions on the fracture and deformation behavior of such a foam material under complex loading conditions that include tension, torsion, compression, and true-triaxial stress paths. Mechanical testing techniques are developed using coupon samples of suitable geometry that minimize grip effects on these low density complex foam materials, along with information associated with the observed cross-anisotropic behavior. Interfacial delamination fracture response for the sandwich structures due to the combined effects of sea water and low temperature are evaluated and the associated degradation in critical energy release rate for delamination is found to be substantial. Experimental data for H100 foam cores associated with moisture induced expansional strains are also included.

Characterization of the interlaminar fracture toughness of a laminated carbon/epoxy composite

Delamination between layers is an important problem in applications of fiber reinforced composite laminates. Tests were carried out to determine the interlaminar fracture toughness of AS4/3501-6 (carbon/epoxy) composite laminates using mixed-mode bending tests. Analysis of the test specimens in terms of mode I and mode II energy release rates showed good agreement between methods based on beam equations, compliance measurements, and detailed finite element analyses. The results showed that the critical mode I energy release rate for delamination decreased monotonically with increasing mode II loading. This is in contrast to some results in the literature. Various analytic representations of the mode interaction from the literature were compared, and shown to fit the data with reasonable accuracy.

A unified approach to quantify the role of friction in beam-type specimens for the measurement of mode II delamination resistance of fibre-reinforced polymers

This paper presents an approach that captures the effect of frictional force in beam-type specimens that are used for delamination tests in shear mode (mode II), including end-notched flexure (ENF), end-loaded-split (ELS), 4-point bend ENF (4ENF) and over-notched-flexure (ONF) tests. The approach is based on crack tip element analysis, and produces a single parameter that quantifies the role of the frictional force on the energy release rate for delamination. The parameter is a combination of the coefficient of friction of the contact surfaces and dimensions of specimens used in the tests. Accuracy of the parameter for quantifying the frictional force effect is evaluated by comparing the prediction with that based on finite element modeling. The comparison shows excellent agreement. Therefore, the study concludes that the parameter provides an accurate measure of the frictional force effect on the energy release rate for delamination in the beam-type specimens.

Testing and life prediction for composite rotor hub flexbeams

A summary of several studies of delamination in tapered composite laminates with internal ply-drops is presented. Initial studies used 2D FE models to calculate interlaminar stresses at the ply-ending locations in linear tapered laminates under tension loading. Strain energy release rates for delamination in these laminates indicated that delamination would likely start at the juncture of the tapered and thin regions and grow unstably in both directions. Tests of glass/epoxy and graphite/epoxy linear tapered laminates under axial tension delaminated as predicted. Nonlinear tapered specimens were cut from a full-size helicopter rotor hub and were tested under combined constant axial tension and cyclic transverse bending loading to simulate the loading experienced by a rotor hub flexbeam in flight. For all the tested specimens, delamination began at the tip of the outermost dropped-ply group and grew first toward the tapered region. A 2D FE model was created that duplicated the test flexbeam layup, geometry, and loading. Surface strains calculated by the model agreed very closely with the measured surface strains in the specimens. The delamination patterns observed in the tests were simulated in the model by releasing pairs of multi-point constraints (MPCs) along those interfaces. Strain energy release rates associated with the delamination growth were calculated for several configurations and using two different FE analysis codes. Calculations from the codes agreed very closely. The strain energy release rate results were used with material characterization data to predict fatigue delamination onset lives for nonlinear tapered flexbeams with two different ply-dropping schemes. The predicted curves agreed well with the test data for each case studied.

Revisit the analysis of end-notched-flexure (ENF) specimen

Inconsistency of expressions for energy release rate for delamination (G) of end-notched-flexure (ENF) specimen is presented. The paper identifies the source of the inconsistency, and shows that based on Timoshenko beam theory, value of G should not depend on the shear modulus of the fibre composite materials.

Energy-based analyses of delamination development in fibre-reinforced polymers under 3-point bending

A study was conducted to investigate possibility of predicting delamination development in fibre-reinforced polymer specimens that have single off-axis insert layer and are subjected to 3-point bending. Experimental results showed that the delamination development was at a very fast rate, which occurred at nearly constant deflection. Using high-speed photography, energy consumed for specimen vibration that was caused by the rapid delamination growth, was quantified and found to be a small fraction of the total energy loss incurred for the delamination development. Critical strain energy release rate for delamination ( G c) was determined after removing this part of energy loss from the total energy loss, and was used in two analytical approaches to predict the delamination size development, based on energy release rate ( G) and change of total energy, respectively. Results show that the two approaches provide upper and lower bounds of delamination size observed in the 3-point bending tests.