Energy Release Rate Of Crack Research Articles

Analytical estimation of fracture toughness for circumferential cracks in thin hard films on ductile substrates

AbstractIn this study, the fracture toughness of circumferential crack caused by indentation effect of a rigid indenter on a thin and elastic coating deposited on the elastic substrate was calculated. In the coating and substrate, the analytical solution of displacement and stress field was used. The complete adhesion was considered for the coating on the substrate. The location of maximum circumferential stress was investigated using the analytical calculation of the stress and it was found that this place was located at a distance away from the center of the indenter. Then, the stress intensity factor and energy release rate for plane strain state was determined, and consequently, the energy release rate for a channel crack was calculated. Finally, the fracture toughness was calculated with energy release rate curves for plane strain crack and crack channeling. This method was used to calculate the fracture toughness of TiN/TiCrN ceramic multilayer coating which was deposited on the GTD450 substrate using the Cathodic Arc PVD method. To validate the results, the analytically calculated crack radius was compared with the experimental crack radius in the fracture load and the difference between the radiuses was in the acceptable range.

Minimizing crack energy release rate by topology optimization

Fatigue cracked primary aircraft structural parts that cannot be replaced need to be repaired by other means. A structurally efficient repair method is to use adhesively bonded patches as reinforcements. This paper considers optimal design of such patches by minimizing the crack extension energy release rate. A new topology optimization method using this objective is developed as an extension of the standard SIMP compliance optimization method. The method is applied to a cracked test specimen that resembles what could be found in a real fuselage and the results show that an optimized adhesively bonded repair patch effectively reduces the crack energy release rate.

Transverse crack formation in unidirectional composites by linking of fibre/matrix debond cracks

Plausible mechanisms of transverse crack formation in unidirectional (UD) composites under applied tension normal to fibres are investigated numerically using a finite element model. Two initial scenarios are considered: Scenario 1 where a pre-existing single fibre/matrix debond crack kinks out into the matrix and induces fibre/matrix debonding at neighbouring fibres, and Scenario 2 where multiple pre-existing debond cracks link up by the debond growth and crack kink-out process. The 2-D finite element model consists of a circular region of matrix with a central fibre surrounded by six fibres in a hexagonal pattern. The region is embedded in a homogenized UD composite of rectangular outer boundary. Energy release rates (ERRs) of interface cracks and kinked-out cracks are calculated under applied tension normal to fibres. Results show that Scenario 2 is more likely to lead to formation of a transverse crack than Scenario 1. These results provide understanding of the roles of fibre clustering and fibre volume fraction on transverse crack formation in composites.

The effect of buffer-layer on the steady-state energy release rate of a tunneling crack in a wind turbine blade joint

The effect of a buffer-layer on the steady-state energy release rate of a tunneling crack in the adhesive layer of a wind turbine blade joint, loaded in tension, is investigated using a parametric 2D tri-material finite element model. The idea of embedding a buffer-layer in-between the adhesive and the basis glass fiber laminate to improve the existing joint design is novel, but the implications hereof need to be addressed.The results show that it is advantageous to embed a buffer-layer near the adhesive with controllable thickness- and stiffness properties in order to improve the joint design against propagation of tunneling cracks. However, for wind turbine blade relevant material combinations it is found more effective to reduce the thickness of the adhesive layer since the stiffness mismatch between the existing laminate and the adhesive is already high. The effect of material orthotropy was found to be relatively small for the blade relevant materials.

Dynamic interfacial fracture of a thin-layered structure

To calculate the dynamic energy release rate of a crack is important for understanding a structure’s fracture behavior under transient or varying loads, such as impact and cyclic loads, when the inertial effect can be significant. In this work, a method is proposed to derive an analytic expression for the dynamic energy release rate of a stationary crack under general applied displacement. An asymmetric double cantilever beam with one very thin layer is considered as a special case, with vibration superimposed onto a constant displacement rate applied to the free end. The resulting expression for dynamic energy release rate is verified using the finite-element method (FEM) in conjunction with the virtual crack closure technique. The mode-mixity of the dynamic energy release rate is also calculated. The predicted total dynamic energy release rate and its components, GI and GII, are both in close agreement with results from FEM simulations.

The Proposal of The Method to Predict Delamination Growth Rate between Resin and Metal

The method to predict delamination growth rate between resin and metal was proposed. This method was used static mechanical properties and energy release rate of the interface crack between Resin and metal.

Semi-permeable Yoffe-type interfacial crack analysis in MEE composites based on the strip electro-magnetic polarization saturation model

Fracture analysis of a semi-permeable Yoffe-type interfacial crack propagating subsonically in magneto-electro-elastic (MEE) composites is presented based on the strip electro-magnetic polarization saturation (SEMPS) model. The electro-magnetic fields inside the crack are considered under the semi-permeable boundary condition. Nonlinear effects near the interfacial crack tip are represented by different electro-magnetic saturation zones. Utilizing the extended Stroh's method, we derive the moving dislocation densities as well as intensity factor and energy release rate for Yoffe-type MEE interfacial crack. Numerical results through an iterative approach are presented to show the characteristics of fracture-dominant parameters with respect to propagation velocity and boundary condition category. The fracture-dominant parameters under the semi-permeable boundary condition are lower than those under the impermeable one, which implies that the electro-magnetic fields in the crack gap can retard the propagation of MEE interfacial crack.

Interfacial Fracture of Nanowire Electrodes of Lithium-Ion Batteries

Nanowires (NW) have emerged as a promising design for high power-density lithium-ion battery (LIB) electrodes. However, volume changes during cycling can lead to fracture of the NWs. In this paper, we investigate a particularly detrimental form of fracture: interfacial detachment of the NW from the current collector (CC). We perform finite element simulations to calculate the energy release rates of NWs during lithiation as a function of geometric parameters and mechanical properties. The simulations show that the energy release rate of a surface crack decreases as it propagates along the NW/CC interface toward the center of the NW. Moreover, this paper demonstrates that plastic deformation in the NWs drastically reduces stresses and thus crack-driving forces, thereby mitigating interfacial fracture. Overall, the results in this paper provide design guidelines for averting NW/CC interfacial fractures during operation of LIBs.

Fatigue fracture of a highly stretchable acrylic elastomer

Dielectric elastomer has been extensively explored in various applications as soft active material. In most applications, dielectric elastomer is subjected to cyclic loading-unloading condition. As a result, a small initial defect in a dielectric elastomer may finally grow to a critical size to induce catastrophic rupture. In this article, we carried out an experimental study of the crack growth in an acrylic dielectric elastomer under cyclic loading-unloading. Pure-shear test specimens were used to measure the relationship between crack growth rate and energy release rate. Such relationship can be simply fit to a power-law. We further used the measured power-law to successfully predict the fatigue lifetime of the acrylic elastomer with an edge crack and subject to simple extension cyclic loading-unloading test.

J-Integral Calculation by Finite Element Processing of Measured Full-Field Surface Displacements

A novel method has been developed based on the conjoint use of digital image correlation to measure full field displacements and finite element simulations to extract the strain energy release rate of surface cracks. In this approach, a finite element model with imported full-field displacements measured by DIC is solved and the J-integral is calculated, without knowledge of the specimen geometry and applied loads. This can be done even in a specimen that develops crack tip plasticity, if the elastic and yield behaviour of the material are known. The application of the method is demonstrated in an analysis of a fatigue crack, introduced to an aluminium alloy compact tension specimen (Al 2024, T351 heat condition).

Influence of the laser pre-quenched substrate on an electroplated chromium coating/steel substrate

The chromium coatings were electroplated onto a laser pre-quenched steel substrate to improve the interfacial adhesion properties of chromium coating/steel substrate system. The influence of laser pre-treatment on the substrate, coating as well as interface was investigated by using microstructure characterization, hardness testing, tensile testing and finite element analysis. An apparent boundary line instead of an interlayer was identified between chromium coating/pre-quenched steel substrate. The Vickers hardness and yield strength of steel substrate were significantly improved after laser pre-quenching. The fracture toughness of chromium coating was increased by about 28.6% compared to the un-treated counterpart. The energy release rate for an interfacial crack in the chromium coating/laser-quenched substrate was smaller than that in the untreated specimen. These results may help understand the life prolongation mechanism for the laser pre-quenched chromium/coated steel parts.

Energy release rates for interfacial cracks in elastic bodies with thin semirigid inclusions

In this paper, we present some rigorous results for an equilibrium problem arising from the study of fiber-reinforced composites. We consider a two-dimensional homogeneous anisotropic linear elastic body containing a thin semirigid inclusion. The semirigid inclusion is an anisotropic thin structure that stretches along one direction and moves like a rigid body possessing both rotational and translatory motion along the perpendicular direction. A pre-existing interfacial crack is subject to nonlinear conditions that do not allow the opposite crack faces to penetrate each other. We focus on a variational approach to modelling the physical phenomenon of equilibrium and to demonstrate that the energy release rate associated with perturbation of the crack along the interface is well defined. A higher regularity result for the displacement field is formulated and proved. Then, taking into account this result, we deduce representations for the energy release rates associated with local translation and self-similar expansion of the crack by means of path-independent energy integrals along smooth contour surrounding one or both crack tips. Finally, some relations between the integrals obtained are discussed briefly.

Crack deflection in brittle media with heterogeneous interfaces and its application in shale fracking

Driven by the rapid progress in exploiting unconventional energy resources such as shale gas, there is growing interest in hydraulic fracture of brittle yet heterogeneous shales. In particular, how hydraulic cracks interact with natural weak zones in sedimentary rocks to form permeable cracking networks is of significance in engineering practice. Such a process is typically influenced by crack deflection, material anisotropy, crack-surface friction, crustal stresses, and so on. In this work, we extend the He-Hutchinson theory (He and Hutchinson, 1989) to give the closed-form formulae of the strain energy release rate of a hydraulic crack with arbitrary angles with respect to the crustal stress. The critical conditions in which the hydraulic crack deflects into weak interfaces and exhibits a dependence on crack-surface friction and crustal stress anisotropy are given in explicit formulae. We reveal analytically that, with increasing pressure, hydraulic fracture in shales may sequentially undergo friction locking, mode II fracture, and mixed mode fracture. Mode II fracture dominates the hydraulic fracturing process and the impinging angle between the hydraulic crack and the weak interface is the determining factor that accounts for crack deflection; the lower friction coefficient between cracked planes and the greater crustal stress difference favor hydraulic fracturing. In addition to shale fracking, the analytical solution of crack deflection could be used in failure analysis of other brittle media.

Nonlocal modeling and buckling features of cracked nanobeams with von Karman nonlinearity

Buckling and postbuckling behaviors of cracked nanobeams made of single-crystalline nanomaterials are investigated. The nonlocal elasticity theory is used to model the nonlocal interatomic effects on the beam’s performance accounting for the beam’s axial stretching via von Karman nonlinear theory. The crack is then represented as torsional spring where the crack severity factor is derived accounting for the nonlocal features of the beam. By converting the beam into an equivalent infinite long plate with an edge crack subjected to a tensile stress at the far field, the crack energy release rate, intensity factor, and severity factor are derived according to the nonlocal elasticity theory. An analytical solution for the buckling and the postbuckling responses of cracked nonlocal nanobeams accounting for the beam axial stretching according to von Karman nonlinear theory of kinematics is derived. The impacts of the nonlocal parameter on the critical buckling loads and the static nonlinear postbuckling responses of cracked nonlocal nanobeams are studied. The results indicate that the buckling and postbuckling behaviors of cracked nanobeams are strongly affected by the crack location, crack depth, nonlocal parameter, and length-to-thickness ratio.

Toughening effect of the nanoscale twinning induced by particle/matrix interfacial fracture on fine-grained Mg alloys

This study theoretically analyzes the toughening effect of the nanoscale twinning induced by the high stress concentration at the particle/matrix interfacial crack tip on fine-grained magnesium (Mg) alloys. The nanoscale twinning within the interfacial crack-tip plastic zone is modeled by a wedge disclination quadrupole. The closed form expressions of the stress intensity factors (SIFs) and the energy release rate (ERR) for the arc-shaped interfacial crack are achieved applying the complex potential method for plane elasticity and conformal mapping. The impacts of twin dimensions, the shear modulus ratio of the particle to Mg matrix, the particle radius and spacing, twinning orientations, as well as the relative orientation between the twin and the crack on the toughening effect are discussed and presented as follows: (1) the nanoscale twin lath with a larger thickness-length ratio is an energetic energy dissipating mechanism for ductile fracture in fine-grained Mg alloys, which favors the fracture toughness enhancement; (2) the interface can be gradually weakened with increasing shear modulus of the particle; (3) under the toughening effect of nanoscale twinning, the interfacial fracture toughness is strongly dictated by the particle size and spacing. Specifically, the optimum particle radius and spacing that can strengthen the interface exist; and (4) the toughening effect is also dependent on the relative orientation and the twinning orientation. Based on the interaction among microstructures, this study essentially and quantitatively mends the classical fracture toughness models for particle reinforced metal matrix materials.

Interfacial Delamination of Inorganic Films on Viscoelastic Substrates

The performance of flexible/stretchable electronics may be significantly reduced by the interfacial delamination due to the large mismatch at the interface between stiff films and soft substrates. Based on the theory of viscoelasticity, a cracked composite beam model is proposed in this paper to analyze the delamination of an elastic thin film from a viscoelastic substrate. The time-varying neutral plane of the composite beam is derived analytically, and then the energy release rate of the interfacial crack is obtained from the Griffith's theory. Further, three different states of the crack propagation under constant external loadings are predicted, which has potential applications on the structural design of inorganic flexible/stretchable electronics.

Closed-Path J-Integral Analysis of Bridged and Phase-Field Cracks

We extend the classical J-integral approach to calculate the energy release rate of cracks by prolonging the contour path of integration across a traction-transmitting interphase that accounts for various phenomena occurring within the gap region defined by the nominal crack surfaces. Illustrative examples show how the closed contours, together with a proper definition of the energy momentum tensor, account for the energy dissipation associated with material separation. For cracks surfaces subjected to cohesive forces, the procedure directly establishes an energetic balance à la Griffith. For cracks modeled as phase-fields, for which no neat material separation occurs, integration of a generalized energy momentum (GEM) tensor along the closed contour path that traverses the damaged material permits the calculation of the energy release rate and the residual elasticity of the completely damaged material.

A numerical study of failure of an adhesive joint influenced by a void in the adhesive

This study examines the effect of manufacturing induced voids on failure of adhesive joints. A single lap joint with preexisting crack between the adherend and the adhesive is considered and the crack growth behavior is studied in the presence of a void in the adhesive. The analysis conducted is numerical using finite elements and a revised virtual crack closure technique for calculating the energy release rate of the interface crack. After verifying the numerical model for a case where analytical solution exists, it is used to gain insight into the failure of the adhesive joint by conducting a parametric study where the size, shape and location of the void with respect to the crack tip are varied. The case of two preexisting cracks on opposite interfaces in the presence of a void is also examined.

Effects of electrostatic tractions on the interfacial fracture behavior of two-phase piezoelectric materials

A bilayer beam model constructed using two-phase piezoelectric materials is developed to study the fracture behavior of interfacial cracks under mechanical/electrical loading, in which the effects of electrostatic traction on the interfacial crack faces and the piezoelectricity of the materials are taken into account. An analytical solution is derived, and the energy release rate of the interfacial cracks is obtained. The electrostatic traction on the crack faces and the interfacial crack behavior are successfully simulated using the finite element method integrated with an iterative approach. The numerical and analytical solutions are compared and are found to agree with each other.

How does surface tension affect energy release rate of cracks loaded in Mode I?

The role of surface stress on fracture of elastic solids has been studied by two group of researchers with different conclusions. One group concludes that surface stress has no effect on energy release rate except that the singularity of the crack tip field is stronger than the usual inverse square root singularity dictated by linear elastic fracture mechanics. The other group concludes that the singularity of the stress field reduces to a logarithmic singularity, thus implying that the local energy release rate is zero. In this letter we resolve this paradox by examining the solution of a special case where surface stress is isotropic and independent of surface strain. We show that surface tension resists crack growth by lowering the applied energy release rate while retaining the inversely square root singularity of the elastic crack tip field. We demonstrate this idea by solving a perturbation problem where the capillary length is much smaller than the crack length. A closed form expression for the local energy release rate is obtained in the limit of small surface tension.