Wavy Crack Research Articles

Interplay of Consolidation Fronts and Cracks in Drying Colloidal Coatings and Its Application in Controlling Crack Pattern Formation

Cracks are frequently observed in drying colloidal coatings. Although a rich collection of crack patterns has been reported, the systematic study on how cracks grow into the final morphology during the drying process remains elusive. In this work, we use directional drying channels with wedge-shaped edges of different angles to study the interplay of advancing consolidation fronts and propagating cracks. We found that although the shape of the advancing consolidation fronts is altered by the drying edge, the growth direction of the following cracks remains perpendicular to the consolidation fronts during the whole drying process, resulting in cracks with a large curvature. We rationalize the evolution of consolidation fronts with the distribution of capillary pressure revealed by a Laplace model. Further, the growth direction of cracks can be explained by the fracture mechanics mechanism that the main orientation of internal tensile stresses developed during the consolidation determines the crack growth direction. Utilizing this understanding, wavy crack patterns are generated in rectangular drying channels with an alternating temperature field, demonstrating a feasible method of designing and controlling drying-induced crack patterns for micro-/nano-fabrication applications.

Impact of ridge cracking on the morphology of buckle-delamination

Ridge-cracked blisters form when ridge cracking occurs in a biaxially compressed film on a relatively rigid substrate during buckle-delamination. The observation of telephone-cord (TC) blister with wavy ridge crack indicates that the ridge-cracked blister is not straight-sided as it used to be. How ridge cracking influences the profile of buckle-delamination remains unclear. Based on Föppl–von Kármán (FvK) nonlinear plate theory, we derive an improved analytical solution for a better description of the cross-sectional profile of the straight-sided blister with straight-sided ridge crack through considering the effect of hinge position caused by the ridge crack. Following a similar procedure in the case of the straight-sided ridge-cracked blister, an approximate solution of FvK plate in curvilinear coordinates is further obtained for the cross-sectional profile of the TC ridge-cracked blister. The results show that the position of the ridge crack significantly modifies the asymmetry, the shape, and the maximum deflection of the cross-sectional profile of the resulting blister.

Numerical analyses of crack path instabilities in quenched plates

Crack path instabilities are observed in rapidly quenched rectangular glass plates whereby wavy crack patterns form as a result of the induced temperature gradients. The peculiar characteristic of these instabilities is that the speed of propagation is several order of magnitudes lower that the Rayleigh wave speed. Experimental studies have shown the dependence of the instabilities on certain geometrical, material, and experimental parameters (e.g. plate width, material toughness, speed of quenching). By perturbing these parameters cracks are observed to propagate along a straight line, oscillate with a periodic sinusoidal or semi-circle like morphology, or propagate in a supercritical manner. Here we formulate the problem of a propagating crack in a brittle thermoelastic material while considering the possibility of the crack undergoing bursts of supercritical crack propagation, by extending the model in Negri and Ortner (2008). We also describe a novel higher order computational framework for its numerical solution centered around Universal Meshes, Mapped Finite Element Methods, and Interaction Integral Functionals. We verify the convergence of the results and compare them against experiments. We reveal crack behaviors not previously observed. Particularly we discuss periods of sudden crack propagation, followed by temporary arrest and crack kinking. We identify various crack morphologies: sinusoidal, asymmetric, semi-circle, kinked and flattened oscillations. We investigate the frequency content of the oscillatory crack paths and study their relation to the dominating problem parameters. Additionally, we identify two new thresholds in phase space corresponding to the transition from oscillatory propagation to rapid propagation and arrest, as well as from permanent crack arrest to temporary crack arrest followed by kinking and branching.

Formation of wavy crack morphology in silicon oxide films due to collaborative interface debonding

When a thin film moderately adherent to a substrate is subjected to residual tensile stress, the cooperation between film crack and interface debonding leads to unusual crack patterns, such as spirals, alleys of crescents and variously oriented strips. We use sol-gel method to fabricate silica sol, and then get a film-glass-substrate system via spin coating technique. Many unique crack morphologies are observed after high temperature drying, such as straight-sided crack network, wavy crack network and their coexistence. The optical microscope and scanning electron microscope reveal that the coexistence and transition of these two kinds of crack networks are closely related to whether the interface debonding occurs simultaneously or not. There is a linear relationship between wavelength and thickness of the crescent crack. Some other unique crack patterns and their growth processes are observed as well. Finally, we propose a phase field simulation tool to study the evolution of film cracking with the concurrent interface debonding. It is worthwhile to further elucidate how the interface debonding facilitates formation of the wavy crack network by using such phase field modeling in future.

A31 熱応力解析と観察に基づくき裂蛇行現象の研究(A3材料力学III)

A31 熱応力解析と観察に基づくき裂蛇行現象の研究(A3材料力学III)

Microscale oscillating crack propagation in silicon nitride thin films

Controlled microscale (<50 μm) wavy cracks in silicon nitride thin films have been produced through a simple heating process. The crack paths were controlled by metal patterns under the silicon nitride thin films. Wavy crack characteristics were investigated by changing the metal, metal linewidths, metal thickness, and silicon nitride thickness. We discuss the differences in the characteristics and mechanisms of propagation of wavy cracks formed due to differential thermal expansion and those that result from thermal gradients.

Observation and model of highly ordered wavy cracks due to coupling of in-plane stress and interface debonding in silica thin films

Highly ordered wavy cracks are observed in silica films deposited on crystalline Si wafer. The wavy crack path is interpreted in terms of the coupling of the in-plane film crack and the interface debonding. A model based on the analyzing of the crack path and the stress evolution is proposed to describe the propagation of the wavy cracks. A scaling relationship between the wavelength $(\ensuremath{\lambda})$ and amplitude $(A)$ is found $(\ensuremath{\lambda}\ensuremath{\sim}{A}^{\ensuremath{\xi}})$ and the scaling factor is determined to be $\ensuremath{\xi}=0.47\ifmmode\pm\else\textpm\fi{}0.01$.

Thermal fracture as a framework for quasi-static crack propagation

We address analytically and numerically the problem of crack path prediction in the model system of a crack propagating under thermal loading. We show that one can explain the instability from a straight to a wavy crack propagation by using only the principle of local symmetry and the Griffith criterion. We then argue that the calculations of the stress intensity factors can be combined with the standard crack propagation criteria to obtain the evolution equation for the crack tip within any loading configuration. The theoretical results of the thermal crack problem agree with the numerical simulations we performed using a phase field model. Moreover, it turns out that the phase-field model allows to clarify the nature of the transition between straight and oscillatory cracks which is shown to be supercritical.

Fatigue and Fracture of a Bulk Nanocrystalline NiFe Alloy

This article presents the results of an experimental study of fracture and fatigue in a nanostructured (an average grain size of ∼23 nm) bulk Ni-18 wt pct Fe alloy that was produced using a pulsed electrodeposition technique. The fracture behavior of the alloy is investigated using fracture resistance experiments, while the fatigue behavior is studied in fatigue crack growth experiments. The alloy exhibits limited toughening as the crack initiates at a fracture toughness of about \( 25\,{\text{MPa}}{\sqrt {\text{m}} } \) and propagates with a slight increase to a plateau value of about \( 30\,{\text{MPa}}{\sqrt {\text{m}} } \). The limited toughening arises from the slight increase in the crack-tip plastic-deformation zone at the early crack growth and ligament bridging due to the microcrack formation ahead of the tip of the main crack. In contrast with a flat fatigue-crack wake, a wavy crack wake was observed under monotonic loading. This trend is attributed to the following: (a) nanovoid coalescence at grain boundaries, (b) microcrack formation by joining nanovoids, and (c) the linking of microcracks with the main crack through the fracture of inclined bridging ligaments. The fractured surface is shown to contain ductile dimple structures with average diameters of ∼100 nm. Focused-ion-beam (FIB) methods are also used to study fatigue-crack growth. These results show that fatigue crack growth occurs by the coalescence of nanovoids that form ahead of the crack tip. The observed mechanisms of fatigue crack growth are shown to be consistent with the results of prior atomistic simulations.

Extended digital image correlation with crack shape optimization

AbstractThe methodology of eXtended finite element method is applied to the measurement of displacements through digital image correlation. An algorithm, initially based on a finite element decomposition of displacement fields, is extended to benefit from discontinuity and singular enrichments over a suited subset of elements. This allows one to measure irregular displacements encountered, say, in cracked solids, as demonstrated both in artificial examples and experimental case studies. Moreover, an optimization strategy for the support of the discontinuity enables one to adjust the crack path configuration to reduce the residual mismatch, and hence to be tailored automatically to a wavy or irregular crack path. Copyright © 2007 John Wiley & Sons, Ltd.

Evaluation of the Lazarus–Leblond constants in the asymptotic model of the interfacial wavy crack

The paper addresses the problem of a semi-infinite plane crack along the interface between two isotropic half-spaces. Two methods of solution have been considered in the past: Lazarus and Leblond [1998a. Three-dimensional crack-face weight functions for the semi-infinite interface crack-I: variation of the stress intensity factors due to some small perturbation of the crack front. J. Mech. Phys. Solids 46, 489–511, 1998b. Three-dimensional crack-face weight functions for the semi-infinite interface crack-II: integrodifferential equations on the weight functions and resolution J. Mech. Phys. Solids 46, 513–536] applied the “special” method by Bueckner [1987. Weight functions and fundamental fields for the penny-shaped and the half-plane crack in three space. Int. J. Solids Struct. 23, 57–93] and found the expression of the variation of the stress intensity factors for a wavy crack without solving the complete elasticity problem; their solution is expressed in terms of the physical variables, and it involves five constants whose analytical representation was unknown; on the other hand, the “general” solution to the problem has been recently addressed by Bercial-Velez et al. [2005. High-order asymptotics and perturbation problems for 3D interfacial cracks. J. Mech. Phys. Solids 53, 1128–1162], using a Wiener-Hopf analysis and singular asymptotics near the crack front. The main goal of the present paper is to complete the solution to the problem by providing the connection between the two methods. This is done by constructing an integral representation for Lazarus–Leblond's weight functions and by deriving the closed form representations of Lazarus–Leblond's constants.

Fatigue damage in bulk metallic glass II: Experiments

Cyclic fatigue was investigated in metallic glasses using fracture mechanics-based crack-growth and stress-life experiments. Steady-state crack growth in a Zr-based bulk metallic glass occurred with a Paris law exponent of ∼1.5. Growing planar fatigue cracks were often noted to destabilize into a wavy crack front geometry, and the conditions determining the stability of these cracks are analyzed. Transient crack-growth rates were measured during variable-amplitude fatigue. Stress-life experiments showed low endurance limits. Fatigue damage initiated at an angle to the applied load, but changed direction at a critical length and grew as mode I cracks. However, the initiation stage of fatigue damage was very short, and almost the entire fatigue life was spent in the crack-growth stage.

High-order asymptotics and perturbation problems for 3D interfacial cracks

We present an asymptotic algorithm for analysis of a singularly perturbed problem in a domain containing an interfacial crack. The crack is assumed to be flat and its front, initially straight, is perturbed in the plane containing the crack. The aim of the work is to determine the asymptotic representation of the stress-intensity factors near the edge of the crack. Mathematically, the limit problem is reduced to the analysis of a matrix, 3 × 3 , Wiener-Hopf problem, and its solution generates the “weight matrix-function” characterised by a special singular solution near the crack edge. The two-term asymptotic representation for the weight function components is required by the asymptotic algorithm, together with two-term asymptotics for stress components associated with the physical fields near the edge of the crack. The particular feature of the solution is the coupling between the normal opening mode (Mode-I), and the shear modes (Mode-II and Mode-III), and the oscillatory behaviour of certain stress components near the crack edge. Explicit asymptotic formulae for the stress-intensity factors are obtained at the edge of a “wavy crack” at an interface.

On the Wavy Crack Propagation Behavior in Internally Pressurized Brittle Tube

Fracture experiments were conducted using glass tubes by pressurizing internally with high pressure water and the paths of the crack propagations were observed. As the results, it has been clarified that regular wavy cracks often appear in glass tubes and that the shapes of the wavy cracks are approximately similar to one another. Monitoring crack propagations by a high-speed video camera system revealed that a crack snakes sinusoidally only when the crack propagation velocity is sufficiently small comparing with the elastic wave velocity of glass and that the wavy crack never appears when the crack tip velocity is large. Therefore, it can be concluded that the mechanism of the wavy crack propagation is not due to the dynamic effect resulting from the rapid crack propagation. Furthermore, by observing the fracture surface, it was found that the anti-plane shear stress plays an important role in the formation of wavy cracks.

Influence of intralaminar cracking on the apparent interlaminar mode I fracture toughness of cross‐ply laminates

ABSTRACTOne of the major difficulties in interlaminar fracture tests of multidirectional laminates is the high tendency for intralaminar cracking and the resulting wavy crack propagation. Experimental work showed that this occurred in double cantilever beam (DCB) tests of cross‐ply laminates having a starter crack on a 0°/90° interface. Moreover, under steady‐state propagation conditions, the apparent values of the critical strain energy release rate GIc were two times higher than those of 0°/0° specimens. In this paper, a finite‐element‐based progressive damage model was used to simulate crack propagation in cross‐ply specimens. The results showed that transverse cracking alone cannot be responsible for the above difference of GIc values. Therefore, the higher propagation GIc values for cross‐plies must be attributed to the more extensive fibre bridging observed and to plastic deformations of the 90° interfacial ply.

Use of Plasma Spraying in the Manufacture of Continuously Graded and Layered/Graded Molybdenum Disilicide/Alumina Composites

Plasma spraying was used to produce continuously graded and graded/layered structures of molybdenum disilicide (MoSi2) and alumina (Al2O3). These functionally graded materials (FGMs) were achieved by manipulating the powder hoppers and plasma torch translation via in-house created computer software. The resultant microstructures sprayed uniformly and were crack free. The interface between MoSi2 and Al2O3 was continuous and no evidence of debonding or cracking at the interface was found. The mechanical strength of these sprayed materials was evaluated using C-ring samples (in diametrical compression). Weibull analysis conducted on the C-ring data indicated that the continuously graded samples were slightly stronger and had a significantly narrower strength distribution than the graded/layered samples. Although the average strength values of both types of functionally graded samples were closer to those of monolithic MoSi2, the fracture energy of the graded samples was significantly larger (∼2–3 times) compared with the monolithic materials. Scanning electron microscopy (SEM) conducted on the fracture surfaces of the FGMs illustrated a wavy and tortuous crack path through the composite cross section of the sample, with extensive crack kinking. This study has two important results. First, we demonstrated the ability to produce such functionally graded composite ceramic microstructures using a conventional plasma spraying process. Second, we quantified the improvements in mechanical performance provided by these FGMs over conventional monolithic materials.

Grinfeld instability on crack surfaces.

The surface of a propagating crack is shown to be morphologically unstable because of the nonhydrostatic stresses near the surface (Asaro-Tiller-Grinfeld instability). We find numerically that the energy of a wavy crack becomes smaller than the energy of a straight crack if the crack length exceeds a critical length L(c)=5.18 L(G) (L(G) is the Griffith length). We analyze the dynamic evolution of this instability, governed by surface diffusion or condensation and evaporation. It turns out that the curvature of the crack surface becomes divergent near the crack tips. This implies that the widely used condition of the disappearance of K(II), the stress intensity factor of the sliding mode, is replaced by the more general requirement of matching chemical potentials of the crack surfaces at the tips. The results are generalized to situations of different external loading.

Thermally induced quasi-static wavy crack propagation in a brittle solid

Morphological aspects of thermally induced brittle cracks are revisited. The formation of a growth pattern of cracks, which are subjected to the thermal loading due to the penetration of surface cooling, has formerly been studied for a system of parallel interacting straight cracks. In the present paper, attention is focused on the transition from straight to wavy crack propagation. The incremental extension of a curved crack is predicted by using the local symmetry criterion, where the step-by-step stress analyses are carried out by the finite-element method with the aid of an automatic mesh generation which is based on the paving method. Varieties of numerical results are obtained so that the influencing factor which may control the wavy crack paths is identified. Discussions are also made by comparing the numerical results with experimental observation.

Morphological Aspects of Thermally Induced Wavy Cracks in a Brittle Solid.

Morphological aspects of thermally induced brittle cracks are revisited. The formation of a growth pattern of cracks, which are subjected to the thermal loading due to the penetration of surface cooling, had been extensively discussed for the system of parallel interacting straight cracks. In the present paper, attentions are focused on the transition from straight to wavy crack propagation of edge cracks due to the penetration of surface cooling in a brittle solid. Curved crack extension is predicted based on the local symmetry criterion, where step-by-step finite element calculations are carried out by the automatic mesh generation using the paving method. Based on the variety of numerical results, the influencing factors which control the wavy crack paths are identified. Qualitative discussions are also made by comparing the numerical results with some experimental observation.

Surface Instabilities in Cracks

The surface of a propagating crack is shown to be morphologically unstable because of the nonhydrostatic stresses near the surface (Asaro-Tiller-Grinfeld instability). We find that the energy of a wavy crack becomes smaller than the energy of a straight crack if the crack length is a few times larger than the Griffith length. The local dispersion relation is derived assuming that the instability develops via mass transport by surface diffusion. We also argue that the widely used condition of the vanishing of KII, the stress-intensity factor of the sliding mode, appears in a natural way in our description as an effective boundary condition at the tip of the crack. [S0031-9007(98)07834-X] The uniform motion of a straight crack is well understood [1]. Experiments on the fracture of bulk specimens, however, show that the crack surfaces are often rough [2]. Some of these results are interpreted in the framework of models of cracks propagating in heterogeneous media. The other possibility for the roughening of the crack surfaces is the instability of the straight motion of the crack tip. Recent experiments on the fracture of thin plates [3] clearly established that many puzzling phenomena in brittle fracture dynamics are related to an oscillatory instability at velocities appreciably below the Rayleigh speed VR. Beyond a critical velocity the crack dynamics change dramatically. At that point, the mean acceleration of the crack drops, the crack velocity starts to oscillate, and a pattern correlated with the velocity oscillation is created on the fracture surface. These results stimulated many recent investigations (see, for example, Ref. [4]) but the instability is not well understood yet. There were several attempts in literature to investigate the stability of the propagating cracks. The linear stability analysis of the quasistatic crack subject to mode I (opening-mode) loading has been performed by Cotterell and Rice [5] with subsequent refinement by Adda-Bedia and Ben Amar [6]. They employ the Griffith theory and the so-called principle of local symmetry, i.e., the condition that the mode II (sliding-mode) stress-intensity factor KII vanishes on the tip of the crack. They found that the straight motion of the crack becomes unstable if the tangential loading exceeds a critical value. A fully dynamical model, including the microscopic description of the cohesive zone of the crack tip, has been discussed by Ching, Langer, and Nakanishi [7]. The cohesive force in the neighborhood of the tip provides a fracture energy and a mechanism for regularizing the stress singularity. The use of such a model removes the need to speculate about a principle of local symmetry. In addition to the results of Refs. [5,6], they found a strong microscopic instability even for very low crack velocities. The main reason for such a strong instability is that the tangential stress, which deflects the crack away from a straight motion, exceeds the normal stress on the fracture surface throughout the tip region at all nonzero velocities. This instability is very sensitive to tiny details of the cohesive-zone model. In all of these descriptions, a crack surface is viewed as the trace left behind by the crack tip as it traverses the sample. All modes related to the further surface deformations due to a transfer of matter are assumed to be frozen. The main purpose of this Letter is to describe the instabilities of the crack surface related to these so far missing degrees of freedom. We will find that the surfaces of a propagating crack undergo an Asaro-TillerGrinfeld (ATG) instability [8,9] of purely macroscopic origin.