Crack Kinking Research Articles

Weak interface-induced repeated kinking of a central crack in a brittle multilayered plate under remote shear loading

Understanding the repeated kinking pattern of cracks is essential for controlling the complex fracture trajectories in multilayered composites. While previous studies have explored many aspects of fractures in layered materials, the conditions governing the repeated kinking behavior under basic loading modes remain largely unrevealed. This research elucidates the continual kinking condition for a central crack in a brittle, multilayered plate with closely-parallel weak interfaces under remote shear stresses. Using the strain energy release rate (SERR) ratio criterion, we analytically derived a closed-form solution to the condition through the equivalent crack concept. The solution specifies a value domain for the intersection angle and fracture toughness ratio of weak interfaces, where the load-guided direction competes closely with the weak interface-guided direction to shape the crack trajectory into a repeated kinking pattern. Our theoretical results, validated by a series of finite element (FE) simulations, clarify how closely-parallel weak interfaces induce repeated crack kinking in multilayered materials under remote shear loading. This research paves the way for the deeper understanding of intricate crack trajectories under mixed loads in various practical applications.

Verification of strain energy splits of phase field fracture model using Westergaard’s problem under mixed-mode loading

One challenge in verifying strain energy splits in phase field fracture models is the lack of reference problems with exact solutions in mixed-mode loading that could serve as benchmark problems. In this work, different strain energy splits used in the variational phase field model have been applied to the classical Westergaard’s problem. In contrast to other benchmark problems used in the literature, the proposed problem not only includes the singular term as a boundary condition but also implicitly considers all terms. To the authors’ knowledge, this is the first time in the literature that this reference problem has been used to rigorously verify the accuracy of different energy splits of the phase field model. Several critical factors such as the pre-crack definition, mesh size, mixed mode ratio and the length scale parameter have been analysed. A good correlation between the numerical estimations and the analytical predictions was found for some pre-crack definition approaches under mode I. However, we demonstrated that the compatible regularisation length scale and mesh size are significantly lower under mode II loading (i.e., when the crack kinks) than under mode I.

Statistical analysis of microstructurally small fatigue crack growth in three-dimensional polycrystals based on high-fidelity numerical simulations

Microstructurally small cracks (MSCs) are sensitive to their local microstructural neighborhoods, resulting in highly variable 3D crack propagation within individual samples and among a population of samples. Statistically quantifying this complex spatiotemporal variability requires collecting and analyzing a large number of 3D MSC growth observations, which remains challenging due to experimental constraints that limit the availability of 3D observations of MSCs in the existing literature. We address this gap by leveraging virtual observations of MSC growth using a state-of-the-art, high-fidelity simulation framework to provide a statistical perspective on 3D MSC growth behavior. The MSC growth simulations were performed in 40 unique but statistically similar polycrystalline microstructures, and the data extracted from the virtual observations were collectively analyzed to quantify variability in geometric, microstructural, and micromechanical aspects of MSCs. Variability in tortuosity, crack surface crystallography, and MSC growth parameters (local crack extension and kink angle) were quantified statistically. The results show that 3D MSC surfaces do not necessarily propagate along {111} crystallographic planes despite crack traces on radial planes being closely aligned with {111} slip plane traces. Also, the 3D MSC surfaces exhibit increasingly tortuous propagation and spatially varying local crack growth rates (with variability as high as 59% among the population). Moreover, a correlation study revealed some of the highly influential microstructural and micromechanical features controlling MSC growth parameters. The quantified variability holds direct implications for advanced materials prognosis in engineering applications, and the identified features from the correlation study can be leveraged to train machine learning models for rapidly predicting MSC growth behavior in the future.

An experimental and analytical study of mode I fracture and crack kinking in thick adhesive joints

This study investigates the fracture behavior of thick adhesive joints manufactured with composite adherends and bonded with an epoxy-based structural adhesive common to the wind turbine industry. For that purpose, double cantilever beam specimens with an adhesive thickness of approximately 10 mm and different pre-crack lengths are manufactured and tested under mode I loading. Analytical approaches are compared to assess the energy release rate, including the simple beam theory, modified beam theory, compliance calibration method, and beam on an elastic and elastic-plastic foundation. In order to evaluate the applicability of the analytical approaches, an in-situ measurement method based on Digital Image Correlation is also employed to determine the energy release rate of the thick adhesive joints. The crack propagation angle is determined theoretically using the second-order crack kinking theory. A good correlation is observed between the theoretical predictions and experimental results. Furthermore, it is demonstrated that due to the T-stress, the crack tends to deviate from the middle of the joint and propagate towards the interface. By comparing different data reduction methods to evaluate the energy release rate of thick adhesive joints, recommendations for their fracture analysis are made, pinpointing the beam on an elastic and elastic-plastic foundation as the most suitable model.

Effects of surface treatments for the adhesion improvement between Cu and SiCN in BEOL interconnect

This study focuses on the enhancement of interfacial reliability between Cu interconnects and silicon carbon nitride (SiCN) capping layers in semiconductor packaging structures through pre-deposition surface treatments. We compare three distinct treatments combined with H2 plasma, NH3 plasma, and SiH4 gas inflow, evaluating their effectiveness through quantitative measurement of interfacial adhesion energy using a double cantilever beam (DCB) fracture mechanics test. The results exhibit a remarkable adhesion energy improvement of over 1150 % with the addition of SiH4 gas treatment. Thorough investigations reveal that the mechanism of the exceptional adhesion enhancement is attributed to unique chemical bonding and fracture behavior. In other words, Si atoms in the SiH4 gas treatment incorporate onto Cu surfaces with specific crystallographic orientations, resulting in significantly stronger Cu–Si bonding in selective regions compared to other bondings. Moreover, the crystallographic-orientation-dependent bonding characteristic induces crack kinking at grain boundaries, dissipating the crack propagation energy. This work will provide crucial insight into enhancing the interfacial reliability and manufacturing yield of semiconductor devices.

Phase-field modeling of fracture with physics-informed deep learning

We explore the potential of the deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching, and coalescence within the unified variational framework of phase-field modeling of brittle fracture. We elucidate the challenges related to the neural-network-based approximation of the energy landscape, and the ability of an optimization approach to reach the correct energy minimum, and we discuss the choices in the construction and training of the neural network which prove to be critical to accurately and efficiently capture all the relevant fracture phenomena. The developed method is applied to several benchmark problems and the results are shown to be in qualitative and quantitative agreement with the finite element solution. The robustness of the approach is tested by using neural networks with different initializations.

Conglomerate rock interface debonding characteristics and damage evolution based on cohesive phase-field method

Rock failure often occurs due to uneven mechanical strength and discontinuous strain at the interface. However, due to the complex interaction mechanism between different phases of conglomerate, it is necessary to improve the crack growth model at the conglomerates' interface. In view of the physical structure and mechanical properties of conglomerate materials, this paper innovatively adopts the cohesive phase field model to study the material deformation and crack growth of conglomerate materials. Different from the traditional phase field model, this model characterises the real structure of the interface by adding an interface phase field, which is used to simulate the debonding of the interface during crack propagation and damage evolution. The regularization of the phase field is carried out to ensure the smoothness of the interface. The transition state of the interface region is determined by the element and the additional phase field. The energy equation is coupled with the crack propagation process using the crack surface density function. The evolution of the damaged phase field and displacement field is driven by the principle of energy minimization. The innovative assumption is that there is a virtual crack at the crack tip, and the interface related elements show a certain cohesive softening form during the damage evolution, which is the main way to realize the particularity of interface mechanics. By controlling the crack dispersion state and stiffness degradation of the material, several ideal softening models are innovatively assumed according to the cohesive force change law to satisfy the mechanical properties and stress function constraints. When cutting blocks n=2.5×104, the errors of the linear model, exponential model, and compound inverse model are 1.76%, 7.48%, and 5.19%, respectively. The results of the exponential model agree well with the stress strength (the error is 2%) and interface crack kinking angle (68.89°). The simulation results indicate that the deformation process of the conglomerate can be divided into three stages: elastic deformation stage, crack propagation stage, and stable load stage. The tensile strength of conglomerate is positively correlated with interface's fracture toughness and proportion of gravel area, respectively.

Experimental studies on the static sharp notch effects during dynamic crack kinking/nucleation at the material interfaces

Dynamic fracture experiments on four bonded polymers using high-speed photography showed that different static sharp notches formed after the incident dynamic cracks met the material interfaces. In one scenario, an incident dynamic crack induced interfacial crack nucleation, and two convex notches formed after the interfacial crack propagated away. In another scenario, interface-induced crack kinking and a “head-to-tail” crack kinking pattern led to a concave notch with a singular stress field, which merits consideration in fracture mechanics modeling. In contrast, load-induced crack kinking did not cause the above scenarios. In another unique experimental phenomenon, a slightly curved/kinked dynamic crack only had a small local crack kinking angle, but its final crack direction was almost 90° to the initial crack direction over a long crack path.

Multiple kinking of a tensile crack in the brittle multilayered media abundant with closely-parallel weak interfaces

Crack kinking is a basic way to form a complex crack trajectory in a multilayered solid abundant with weak interfaces. However, it remains unclear that under which condition a multi-kinked crack emerges with the influence of closely-parallel weak interfaces. According to a basic crack kink criterion, here we consider a brittle multilayered plate with a tensile edge crack to seek the occurrence condition of the multi-kinking behavior. The strain energy release rate ratio of the crack during its propagation is examined based on finite element simulations. We find a value domain of intersection angle and fracture toughness ratio, where the fracture toughness anisotropy competes with the load anisotropy to orient the crack propagation direction. We obtain the continual kinking condition of the tensile edge crack, including the intersection angle range about 0∼38° and the closed form upper and lower bounds of the fracture toughness ratio range. Our multi-kinking results for the tensile crack are helpful to understand the formation of complex crack patterns in the multilayered materials under complicated loads.

The fully coupled thermo-mechanical dual-horizon peridynamic correspondence damage model for homogeneous and heterogeneous materials

To accurately address the thermally induced dynamic and steady-state crack propagation problems for homogeneous and heterogeneous materials involving crack branching, interfacial de-bonding and crack kinking, we propose the fully coupled thermo-mechanical dual-horizon peridynamic correspondence damage model (TM-DHPD). To this end, the integral coupled equations for TM-DHPD are firstly derived within the framework of thermodynamics. And then, the alternative dual-horizon peridynamic correspondence principle is used to derive the constitutive bond force state, heat flow state and their general linearizations. Moreover, the unified criterion for bond damage is proposed to characterize the internal bond damage in a single material and the interface bond damage in dissimilar materials. To ensure convergence and accuracy, the coupled equations are solved using the standard implicit method without the use of artificial damping. In both homogeneous and heterogeneous materials, some representative and challenging numerical cases are examined, such as dynamic crack branching in a centrally heated disk and multiple interface failure of thermal barrier coating. The numerical results are in good agreement with the available experimental results or the previous predictions, which shows the great potential of the proposed TM-DHPD in addressing the physics of numerous thermally induced fractures in the real-world engineering problems.

Engineering the fracture resistance of 2H-transition metal dichalcogenides using vacancies: An in-silico investigation based on HRTEM images

Vacancy engineering of 2H-transition metal dichalcogenides (2H-TMDs) has recently attracted great attention due to its potential to fine-tune the phonon and opto-electric properties of these materials. From a mechanical perspective, this symmetry-breaking process typically reduces the overall crack resistance of the material and adversely affects its reliability. However, vacancies can trigger the formation of heterogeneous phases that synergistically improve fracture properties. In this study, using MoSe2 as an example, we characterize the types and density of vacancies that can emerge under electron irradiation and quantify their effect on fracture. Molecular dynamic (MD) simulations, employing a re-parameterized Tersoff potential capable of accurately capturing bond dissociation and structural phase changes, reveal that isolated transition metal monovacancies or chalcogenide divacancies tend to arrest the crack tip and hence enhance the monolayer toughness. In contrast, isolated chalcogenide monovacancies do not significantly affect toughness. The investigation further reveals that selenium vacancy lines, formed by high electron dose rates, alter the crack propagating direction and lead to multiple crack kinking. Using atomic displacements and virial stresses together with a continuum mapping, displacement, strain, and stress fields are computed to extract mechanistic information, e.g., conditions for crack kinking and size effects in fracture events. The study also reveals the potential of specific defect patterns, “vacancy engineering,” to improve the toughness of 2H-TMDs materials.

Fast atomic crack kinking and branching in WS2

Abstract Dynamic nanocrack propagation in 1T- and 2H-WS2 strips is studied by molecular dynamics, and the T-stress and circumferential stress in linear elastic fracture mechanics are considered. As the crack propagates, the crack-tip speed (v) experiences a rapid acceleration, and then oscillates at ∼55% (1T) and ∼65% (2H) of the Rayleigh-wave speed followed by crack kinking/branching. The critical energy release rates of crack instability are estimated to be ∼1.5 J/m2 (1T) and ∼4.0 J/m2 (2H). The crack path in 1T-WS2 exhibits higher sensitivity of strain rates for atomic asymmetry around the crack tip. Examination of the dynamic crack-tip field shows that the T-stress obtained by the over-deterministic method always fluctuates in negative, and the theoretical circumferential stress curve does not accurately capture the v-dependent atomic stress distribution. Consequently, both T-stress and circumferential stress are limited in predicting the crack kinking/branching directions, which can be attributed to the discrete crystal lattice and local anisotropy of WS2, where a preferred crack path along the zigzag surface is observed. The fracture properties of WS2 might provide useful physics for its applications in nano-devices.

Fracture of bio-cemented sands

Bio-chemical reactions enable the production of biomimetic materials such as sandstones. In the present study, microbiologically-induced calcium carbonate precipitation (MICP) is used to manufacture laboratory-scale specimens for fracture toughness measurement. The mode I and mixed-mode fracture toughnesses are measured as a function of cementation, and are correlated with strength, permeability and porosity. A micromechanical model is developed to predict the dependence of mode I fracture toughness upon the degree of cementation. In addition, the role of the crack tip T-stress in dictating kink angle and toughness is determined for mixed mode loading. At a sufficiently low degree of cementation, the zone of microcracking in the vicinity of the crack tip is sufficiently large for a crack tip K-field to cease to exist and for crack kinking theory to not apply. The interplay between cementation and fracture properties of sedimentary rocks is explained; this understanding underpins a wide range of rock fracture phenomena including hydraulic fracture.

Kinking prohibition enhancement of interface crack in artificial periodic structures with local resonators

In this study, the propagation and kinking of an interface crack between two dissimilar artificial periodic structures with local resonators is investigated. By Fourier transform, the dynamic fracture problem is derived as an equation with Wiener–Hopf type. An additional band gap can be created by local resonators. During the dynamic failure, elastic waves will be excited continuously from the crack tip and result in the energy dissipation. Moreover, the energy release ratio which characterizes the fracture resistance is obtained. The meta-arrest property of the artificial periodic structure with local resonators is illustrated. Based on inverse Fourier transform, the displacement field is given to further understand the deformation and oscillation of crack faces. Based on the crack-tip field, the maximum energy release rate criterion is presented to discuss about whether the crack can propagate through kinking out of the interface. Comparing with the model without local resonators, we find that crack kinking can be prohibited in the proposed artificial periodic structures. Finally, finite element simulation and experiment are performed to show the good agreement with the theoretical predictions.

Influence of hard phase size and spacing on the fatigue crack propagation in tool steels—Numerical simulation and experimental validation

AbstractIn this study, the fatigue crack growth rate in four different tool steel microstructures (hot rolled, powdermetallurgically processed, as‐cast, and carbide‐free) is experimentally measured and correlated with hard phase size and spacing, as well as with the roughness of the fracture surface that is created by crack kinking. Numerical simulations of crack growth in carbide‐containing microstructures are conducted and investigated. The results indicate a favorable influence of carbides with a larger size and higher degree of roundness, as they create the largest mean free path between the individual carbides at the same hard phase volume content. This facilitates the formation of a plastic zone in the matrix, which dissipates crack energy and reduces the effective stress intensity. In addition, the effect of crack kinking is increased at larger carbide sizes. Concerning practical application, the results suggest that a high degree of deformation is favorable regarding the fatigue growth resistance of tool steels, and that the use of powder metallurgically (PM) grades with small carbides is discouraged, if the lifetime of a tool is mainly controlled by the crack growth rate and not crack initiation.

Cracking direction in graphene under mixed mode loading

Crack branching in graphene under complex stresses is investigated by molecular dynamics simulations and boundary-layer models. Using the maximum energy release rate (MERR) criterion, an analogy of Wulff curve is plotted considering the anisotropic fracture toughness of hexagonal graphene, which shows the direction of crack kinking (local bump on the curve) is consistent with that of the weak fracture toughness (along zigzag edge). The angle of crack kinking prefers 0°/30°/60°, rather than the angle predicted by maximum circumferential stress criterion. The T-stress along crack front, obtained by the over-deterministic method, can indicate the possibility of kink by its transformation between positive and negative, especially for zigzag cracks. This study incorporates Wulff-like curve and MERR criterion to provide an accurate prediction of nanocrack paths in graphene.

Modeling progressive failure and crack evolution in a randomly distributed fiber system via a coupled phase-field cohesive model

Despite the high microstructural heterogeneity of fiber-reinforced composites, few modeling framework provides a comprehensive and detailed understanding of the failure mechanisms of these materials. The aim of this work is to present a coupled phase-field cohesive-modeling framework that can precisely capture the progressive failure and damage behaviors of multiphasic microstructures and multifiber systems. Here, the phase-field method captures crack evolution in the matrix, and a coupled cohesive-zone model is introduced to characterize interfacial debonding. The novel model framework comprises the following novel aspects. (1) A newly developed scalar indicator that directly extracts inelastic strain from the total strain field and couples the cohesive traction-separation law with the phase-field model to determine the regularized interfacial displacement jump. (2) The periodic boundary conditions in the coupled phase-field cohesive framework are incorporated to characterize crack evolution in random fiber systems. (3) A complete set of failure modes, namely crack initiation, propagation, kinking, and coalescence are characterized in highly heterogeneous solids. Parametric studies of the novel framework yield numerical results that are highly consistent with experimental findings and reveal the effects of fiber distributions, fiber volume fractions, and boundary conditions on the nonlinear mechanical behaviors of fiber-reinforced composites. The results demonstrate the excellent potential of the novel numerical framework to evaluate the mechanical performances of composite materials in engineering applications.

A comparative study between phase‐field and micromorphic gradient‐extended damage models for brittle fracture

AbstractTo circumvent a mesh dependency of damage models, non‐local approaches such as phase‐field and gradient‐extended damage models have shown a good capability and attracted a lot of attention for modeling fracture. These models can predict crack nucleation, kinking, and branching. The gradient‐extended formulation proposed by [1, 2], which includes a micromorphic degree of freedom for damage, is connected to a phase‐field damage model presented in [3]; by connecting fracture parameters in brittle fracture. The latter is followed by comparing the thermodynamic consistency of these models. Despite having similarities in the formulation, gradient‐extended models differ from the standard phase‐field ones by having a damage threshold. Besides that, the local iteration exists in the gradient‐extended damage models. By employing the cohesive phase‐field model or the Angiotensin type 1 (AT1), a damage threshold appears in the formulation; by having a linear term for damage in the crack density function, see [4,5,12]. A comparison between these models is made, by taking several numerical examples and comparing their responses in a quasi‐static case. Moreover, the feasibility of different responses is addressed when one uses a standard Newton‐Raphson solver or the arc‐length one for solving a boundary value problem.

Interfacial fracture analysis for heterogeneous materials based on phase field model

Simulating crack initiation/propagation in heterogeneous materials has long been a challenge due to their complex topology and the complicated interactions between each phase. In order to address this task, an interfacial debonding phase field model is established for interfacial fracture behavior of highly heterogeneous solids in this work. Inspired by the phase field framework, a discrete interface is transformed into a smeared interface using interface phase field. The developed model has the following novelties: (1) interface properties are smeared such that singularity of material property can be eliminated; (2) due to the interaction between characteristic length scale parameters of the interface and the crack, critical energy release rate of interface is regularized; and (3) it can predict complex cracking phenomena such as multiple crack initiation, merging and branching. Particularly, the proposed model is validated experimentally and numerically. With the proposed model, influence of interface properties such as Young’s modulus and critical energy release rate on fracture behavior is studied in detail. The proposed model is potential in predicting interfacial debonding and the crack kinking path in complicated quasi-brittle heterogeneous materials.

Mode mixity and fracture in pull-off adhesion tests

Following pull-off coating adhesion tests such as ASTM D4541, visual examination of the fracture surfaces often reveals intriguing fracture patterns where similar (and seemingly predictable) features are observed across like coating systems. Nonetheless, adhesion test stubs are typically discarded after a brief visual inspection or no inspection at all—suggesting a missed opportunity to gain further insight into fracture processes. This paper examines the pull-off adhesion test from a fracture mechanics perspective. We present two microscopy-based methods for extracting analytically useful fracture data from pull-off adhesion tests. First, we develop an energy-based method for obtaining mode mixity from observed crack kink angles, providing the powerful capability to disambiguate mode I and mode II fracture. We demonstrate agreement between experimental results and theoretical predictions in a set of 1,305 crack path measurements for 111 pull-off adhesion test stubs, representing both single- and multi-layered coating systems. Second, we deploy a machine-learning based image segmentation technique (Trainable WEKA) to rapidly quantify the fractional area coverage of materials removed with the pull stub, enabling further insight into the surfaces most vulnerable to delamination in a layered coating stack. Beyond the immediate utility of these techniques for data enhancement in pull-off adhesion tests, these techniques also have long-term potential as tools for failure analysis in coated systems.