Crack Path Selection Research Articles

Crack Path Selection in Microstructurally Tailored Inhomogeneous Polymers

In this work the photodegradation of a polyethylene co-polymer, ECO, is exploited to generate inhomogeneous arrangements of model “granular” media that aids in the experimental study of crack path selection problems. The advantage of our approach is that the well-known sensitivity of ECO’s properties to ultraviolet (UV) light allows knowledge of both grain and grain boundary response a priori to performing the experiments. A model granular arrangement with identical grain structure and of three different levels of grain boundary strength was constructed. Each microstructure was loaded in uniaxial tension, and the resulting strain fields were recorded using digital image correlation (DIC). Depending on the applied load and the local microstructure, crack initiation and growth occurred differently: either one main crack developed and became responsible for failure, or an initial crack formed but arrested, and a host of secondary cracks appeared at different critical locations, including grain boundaries and grain interiors. Thus, the experimental configuration can be used to produce controllable amounts of intergranular vs. transgranular failure. The DIC results were correlated with global load–displacement measurements and were compared to finite element models using ABAQUS that simulated the configurations tested in each case. A von Mises and Tresca yield criterion was used to illustrate areas where failure was possible, and the results were favorably compared with the experimental failure initiation sites in each case.

Crack initiation and path selection in brittle specimens: A novel experimental method and computations

We present a novel experimental method aiming at investigating aspects of dynamic crack propagation in brittle materials under in-plane, quasi-static, mixed mode loading. The method consists in gluing a precracked specimen into a rectangular hole in an aluminum frame using thin layers of epoxy resin. The driving force for crack initiation and propagation lies in the mismatch between the coefficients of thermal expansion (CTE) of the aluminum frame and the specimen, following modest heating of the assembly on an electrical heating stage. The main advantages of this method are in its avoidance of gripping problems and of the need to employ a complicated loading device. An important benefit of this method is the ability to analyze, numerically, the assembly containing the specimen as a boundary value problem by means of finite element analysis without any prior assumptions regarding the boundary conditions.The method enables investigation of various aspects of dynamic crack propagation in brittle materials, including crack initiation, crack path selection criteria, and surface instabilities under a relatively low energy–speed regime. To validate the method’s applicability, we first evaluated the fracture toughness, KIC, of soda lime glass specimens. We then performed fracture experiments of slow and fast crack propagation in these specimens under combined tensile and shear stresses, which revealed the paths selected by the cracks. These paths were calculated using quasi-static finite element analysis (FEA), code Franc2D, and the dynamic eXtended FEA Method, using the criteria for crack path selection. It was found that the crack paths obeyed the law of local symmetry (KII=0) for both the quasi-static and dynamic crack propagation.

Crack path selection in the fracture of fresh and degraded epoxy adhesive joints

The crack paths and fracture surfaces of aluminum–epoxy adhesive joints were characterized as a function of the mode ratio of loading and the amount of degradation that had been generated using the open-faced aging technique. A finite element (FE) model was used to predict the extent of the plastic zone at different crack growth lengths and mode ratios, and a close relationship was found between the evolution of the plastic zone and the previously reported R-curve behavior of these joints. The micro-topography of the fracture surfaces, measured using an optical profilometer, showed that a ductile–brittle transition occurred in the fracture behavior of the joints as degradation progressed. The crack path in the (brittle) degraded specimens was normal to the first principal stress, but could not be predicted in the undegraded joints because of its highly three-dimensional nature. Based on the distribution of the maximum von Mises stress in the adhesive layer ahead of the crack tip, a crack growth mechanism was proposed that is consistent with these experimental observations and explains the highly three-dimensional nature of fracture in these highly constrained joints.

Phase field modeling of crack propagation

Fracture is a fundamental mechanism of materials failure. Propagating cracks can exhibit a rich dynamical behavior controlled by a subtle interplay between microscopic failure processes in the crack tip region and macroscopic elasticity. We review recent approaches to understand crack dynamics using the phase field method. This method, developed originally for phase transformations, has the well-known advantage of avoiding explicit front tracking by making material interfaces spatially diffuse. In a fracture context, this method is able to capture both the short-scale physics of failure and macroscopic linear elasticity within a self-consistent set of equations that can be simulated on experimentally relevant length and time scales. We discuss the relevance of different models, which stem from continuum field descriptions of brittle materials and crystals, to address questions concerning crack path selection and branching instabilities, as well as models that are based on mesoscale concepts for crack tip scale selection. Open questions which may be addressed using phase field models of fracture are summarized.

Microstructural effects on crack path selection in bending and fatigue in a Nb–19Si–5Cr–3.5Hf–24Ti–0.75Sn–1W alloy

Nb–Si alloy containing 19Si, 5Cr, 3.5Hf, 24Ti, 0.75Sn and 1W (in at.%) has been tested by three-point bending and fatigue at both room temperature and 400 °C. The microstructure and fracture surface associated with crack growth were investigated by scanning electron microscopy (SEM) and electron backscattering diffraction (EBSD). The alloy contains Nb solid solution (Nb(ss)) and Nb- or Ti-rich silicides. Some pre-existing microcracks were found in the silicides. EBSD Analyses on the cast and HIPped Nb–Si alloy revealed a preferred orientation in the Nb(ss) similar to that of a unidirectionally solidified alloy. The fatigue crack path preferentially propagated either along the phase boundaries between the silicide and Nb(ss) or through the pre-existing silicide microcracks. Slip steps were observed inside the Nb(ss) during crack propagation, indicating deformation in the alloy occurred in the Nb(ss) while the silicides assisted the crack propagation.

Effects of UV cure on glass structure and fracture properties of nanoporous carbon-doped oxide thin films

The effects of UV radiation curing on the glass structure and fracture properties were examined for a class of nanoporous organosilicate low dielectric constant films. A detailed characterization by nuclear magnetic resonance spectroscopy and Fourier transform infrared spectroscopy showed significant changes in the glass structure with increasing curing time, marked by the removal of terminal organic groups and increased network-forming bonds following the initial removal of porogen material. The higher degree of film connectivity brought about by an increased cure duration is demonstrated to significantly enhance adhesive fracture properties and to moderately improve cohesive fracture resistance. Explanations for the enhanced fracture behavior are considered in terms of the glass structure. The important role of crack path selection during adhesive and cohesive fracture processes is used to rationalize the observed behavior.

Competing failure mechanisms in mixed-mode fracture of an adhesively bonded polymer-matrix composite

In this paper, the use of cohesive-zone models to analyze crack-path selection in adhesive joints made from a polymer-matrix composite is demonstrated. Cohesive-zone parameters for the adhesive and composite obtained in a previous work were used without any modifications to make the predictions presented in this study. The results of numerical simulations of two mixed-mode geometries, single-lap shear and asymmetrical double-cantilever beam specimens, are compared to experimental observations. It is shown that the numerical simulations provided reasonably good predictions for the strength and failure mechanisms of the joints, allowing the nature of the competition between failure of the composite and failure of the interface to be determined.

Macroscopic and microscopic examination of the relationship between crack velocity and path and Rayleigh surface wave speed in single crystal silicon

The speed of Rayleigh surface waves, denoted C R, is the accepted upper limit for Mode I crack velocity in monolithic solids. In the current contribution, we discuss several critical issues associated with the velocity of Rayleigh surface waves and crack velocity in single crystal (SC) brittle solids, and the global and local influence of C R on crack path selection in particular. Recent cleavage experiments in SC silicon showed that crack velocity at certain cleavage planes and crystallographic orientations cannot exceed a small fraction of C R, and thereafter the crack deflects to other cleavage planes. Indeed, C R defined by the continuum mechanics ignores atomistic phenomena occurring during rapid crack propagation, and therefore is limited in predicting the crack velocity. Examination of these anomalies shows that this limitation lies in microstructural lattice arrangement and in anisotropic phonon radiation during rapid crack propagation. Globally, C R has no influence on the crack deflection phenomenon. However, the misfit in C R between the original plane of propagation and the deflected plane generates local instabilities along the deflection zone.

Crack deflection in piezoelectric ceramics

Crack deflection can occur in a specimen subject to a stress gradient of high tensile stresses near the surface which decreases with increasing depth. Such a stress gradient can be induced by strain incompatibilities. These can for example arise under electric fields between the electroded and external regions of a piezoelectric material. Such incompatibilities have been realized in thin rectangular model specimens from PZT-piezoelectric ceramics with top and bottom partial electrodes. Under an electric field, controlled crack propagation has been observed in-situ in an optical microscope. The crack paths are reproducible with very high accuracy. Small electrode widths lead to straight cracks with two transitions between stable and unstable crack growth, while large electrode widths result in curved cracks with four transitions. Poling the specimen prior to the experiment alters the crack path and introduces an anisotropy in the R-curve behavior as well as in the achievable strain mismatch. The crack path selection and crack length can be explained by means of a qualitative fracture mechanics analysis.

Measurement of friction in powder compaction - comparison between laboratories

Fatigue in the polycrystalline Ni-base superalloys is discussed, with particular emphasis on modelling the mechanism at the grain and sub-grain scale. The importance of Ni-base superalloys as aeroengine materials is summarised, and indications are given as to where modelling offers potential for further advancements. In the experimental section, there are three parts. The first identifies how at the microstructural scale, the instantaneous rate of fatigue crack growth is governed by the crack path selection mechanism. The second part describes a statistical analysis of i) crack arrests, ii) instantaneous crack growth rates and iii) and their dependence on linear elastic fracture mechanics parameters. It is shown that all fatigue crack growth events occurring at the microstructural scale can be represented by a few statistical distributions. Thirdly, an initial analysis of the underlying slip band and dislocation mechanism of conventional fatigue in Ni-base superalloys is presented.

Crack path selection in adhesively bonded joints: the roles of external loads and speciment geometry

This paper investigates the roles of external loads and specimen geometry on crack path selection in adhesively bonded joints. First, the effect of mixed mode fracture on crack path selection is studied. Using epoxy as an adhesive and aluminum as the adherends, double cantilever beam (DCB) specimens with various T-stress levels are prepared and tested under mixed mode fracture loading. Post-failure analyses on the failure surfaces using X-ray photoelectron spectroscopy (XPS) suggest that the failure tends to be more interfacial as the mode II fracture component in the loading increases. This fracture mode dependence of the locus of failure demonstrates that the locus of failure is closely related to the direction of crack propagation in adhesive bonds. Through analyzing the crack trajectories in failed specimens, the effect of mixed mode fracture on the directional stability of cracks is also investigated. The results indicate that the direction of the crack propagation is mostly stabilized when more than 3% of mode II fracture component is present at the crack tip regardless of the T-stress levels in the specimens for the material system studied. Second, using a high-speed camera to monitor the fracture sequence in both quasi-static and low-speed impact tests, the effect of debond rate on the locus of failure and directional stability of cracks is investigated. Post-failure analyses including XPS, Auger electron spectroscopic depth profile, and scanning electron microscopy indicate that as the crack propagation rate increases, the failure tends to be more cohesive and the cracks tend to be directionally unstable. Last, as indicated by the finite element analyses results, the T-stresses, and therefore the directional stability of cracks in adhesive bonds, are closely related to the thickness of the adhesive layer and also the thickness of adherend. This specimen geometry dependence of crack path selection is studied analytically and is verified experimentally.

Numerical simulation of cracking processes in dissimilar media

This paper presents a novel numerical technique to simulate the crack propagation process for inhomogeneous solids. The criteria of crack growth and path selection are expressed in terms of some simple functions of fracture energy and loading phase angle. The energy release rate and loading phase angle for mixed mode cracks are evaluated by the finite element method with a mesh-adaptive technique. Examples are considered to show that the method is effective for simulating and predicting crack paths in inhomogeneous solids. They include crack growth or kinking in bi-materials and damage processes of fiber-reinforced composites.

Crack Path Selection in Adhesively-Bonded Joints: The Role of Material Properties

This paper investigates the role of material properties on crack path selection in adhesively bonded joints. First, a parametric study of directionally unstable crack propagation in adhesively-bonded double cantilever beam specimens (DCB) is presented. The results indicate that the characteristic length of directionally unstable cracks varies with the Dundurs' parameters characterizing the material mismatch. Second, the effect of interface properties on crack path selection is investigated. DCB specimens with substrates treated using various surface preparation methods are tested under mixed mode fracture loading to determine the effect of interface properties on the locus of failure. As indicated by the post-failure analyses, debonding tends to be more interfacial as the mode II fracture component in the loading increases. On the other hand, failures in specimens prepared with more advanced surface preparation techniques appear more cohesive for given loading conditions. Using a high-speed camera to monitor the fracture sequence, DCB specimens are tested quasi-statically and the XPS analyses conducted on the failure surfaces indicate that the effect of crack propagation rate on the locus of failure is less significant when more advanced surface preparation techniques are used. The effect of asymmetric interface property on the behavior of directionally unstable crack propagation in adhesive bonds is also investigated. Geometrically-symmetric DCB specimens with asymmetric surface pretreatments are prepared and tested under low-speed impact. As indicated by Auger depth profile results, the centerline of the crack trajectory shifts slightly toward the interface with poor adhesion due to the asymmetric interface properties. Third, through varying the rubber content in the adhesive, DCB specimens with various fracture toughnesses are prepared and tested. An examination of the failure surfaces reveals that directionally unstable crack propagation is more unlikely to occur as the toughness of the adhesive increases, which is consistent with the analytical predictions that were discussed using an energy balance model.

The effect of the T-stress on crack path selection in adhesively bonded joints

This paper investigates the effect of the T-stress on crack path selection in adhesively bonded joints. Fleck et al. (Int. J. Solids Structures 27 (1991) 1683) concluded that, similar to the situation in homogeneous solid media, the directional stability of cracks in adhesive bonds is also significantly influenced by the magnitude of the T-stress. Cracks tend to be directionally stable when the T-stress is negative (compressive) and directionally unstable when the T-stress is positive (tensile). This T-stress dependence of crack path selection in adhesively bonded joints is demonstrated experimentally in this study using double cantilever beam (DCB) specimens with various levels of the T-stress. The technique reported to vary the T-stress involves a mechanical stretching procedure of the specimens and is able to continuously alter the T-stress level over a fairly wide range. Using the finite element analysis (FEA) method, the T-stress for DCB specimens is calculated and comparison is made with the analytical solution obtained by Fleck et al. (Int. J. Solids Structures 27 (1991) 1683) for the bi-material sandwich geometry with semi-infinite adherends. The FEA results show that the T-stress increases as the thickness of the adherends decreases, indicating a mild effect of adherend thickness on the directional stability of cracks. This prediction is verified in this paper using DCB specimens with different thickness adherends.

Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces

The cohesive surface methodology is used in a numerical study of fracture of concrete. The traction vs. separation response is governed by an isotropic damage law in which damage evolves according to a prescribed one-dimensional linear or exponential softening law. Cohesive surfaces are immersed in the continuum to allow for a maximum freedom of crack path selection. The single edge notched four point shear beam and the double edge notched tensile bar are used to study: (i) the influence of the tangential cohesive response on the development of the fracture path and (ii) the mesh alignment sensitivity. It is shown that in the present formulation, the tangential cohesive response has a minor influence on both crack path and global characteristics. Mesh alignment does have a significant influence on the outcome of the numerical analysis.

Microcrack nucleation and growth in elastic lamellar solids

The nucleation and growth of microcracks in elastic lamellar microstructures is studied numerically. The analyses are carried out within a framework where the continuum is characterized by two constitutive relations: one relating the stress and strain in the bulk material and the other relating the traction and separation across a specified set of cohesive surfaces. In such a framework, fracture initiation and crack growth, including micro-crack nucleation ahead of the main crack, arise naturally as a consequence of the imposed loading, without any additional assumptions concerning criteria for crack growth, crack path selection or micro-crack nucleation. Full transient analyses are carried out and plane strain conditions are assumed. The specific problem analyzed is a compact tension specimen with two regions of differing lamellar orientation separated by a fracture resistant layer of finite width d, which is small compared to the physical dimensions of the specimen. An initial crack, normal to the applied loading, is assumed to exist in the first region whose lamellar orientation is fixed. The lamellar orientation of the second region, β, is varied, as is the thickness of the fracture resistant layer. It is found that microcrack nucleation in the second region is highly sensitive to the lamellar orientation in that region for small values of d. However, microcrack nucleation becomes rather insensitive to β with increasing d. It is also shown that a linear elastic fracture mechanics model with one adjustable parameter gives good agreement with the numerical results for fracture initiation.

Crack path selection in piezoelectric bimaterials

The problem of crack path selection in piezoelectric bimaterials is considered in this paper. Based on the Stroh formulation for anisotropic material and Green’s functions for piezoelectric bimaterials, the crack problem is expressed in terms of coupled singular integral equations at first, and then the equations are used to solve for stress and electric displacement fields numerically. A crack impinging an interface joining two dissimilar materials may arrest or may advance by either penetrating the interface or deflecting into it. The competition between deflection and penetration is investigated using the maximum energy release rate criterion. Numerical results are presented to study the role of remote electroelastic loads on the path selection of crack extension.

Fatigue crack growth resistant microstructures in polycrystalline Ni-base superalloys for aeroengines

Fatigue in the polycrystalline Ni-base superalloys is discussed, with particular emphasis on modelling the mechanism at the grain and sub-grain scale. The importance of Ni-base superalloys as aeroengine materials is summarised, and indications are given as to where modelling offers potential for further advancements. In the experimental section, there are three parts. The first identifies how at the microstructural scale, the instantaneous rate of fatigue crack growth is governed by the crack path selection mechanism. The second part describes a statistical analysis of i) crack arrests, ii) instantaneous crack growth rates and iii) and their dependence on linear elastic fracture mechanics parameters. It is shown that all fatigue crack growth events occurring at the microstructural scale can be represented by a few statistical distributions. Thirdly, an initial analysis of the underlying slip band and dislocation mechanism of conventional fatigue in Ni-base superalloys is presented.

Effect of Mode-mixity on the Fracture Toughness of Ti-6al-4v/fm-5 Adhesive Joints

Using several different fracture tests, the fracture toughness of a chromic acid anodized titanium (Ti-6A-4V)/polyimide (FM-5) adhesive system was evaluated. Mode I, mode II, and mixed mode (I and II) tests were conducted using double cantilever beam (DCB), end notch flexure (ENF), and mixed mode flexure (MMF) geometries. Interfacial type failures were observed in the ENF and MMF specimens as a result of the mode II loading inherent in these tests. Pure mode I loading, as is the case with symmetric DCB specimens, resulted in cohesive failures with a fracture energy around 2500 J/m2 on as-received specimens. The asymmetric DCB specimens had fracture energy values around 2000 J/m2, the MMF specimens close to 1970 J/m2, and ENF specimens around 1300 J/m2. All the above measurements were made on as-bonded (unaged) specimens. Titanium/FM-5 bonds supplied by the Boeing Company were then aged in one of three different environments for 2 and 6 months respectively. The environments included: 177degC in air and 2 psia, and 204degC in air. Following the aging, DCB, ENF, and MMF tests were conducted on the specimens. The results showed that aging in all three environments resulted in decreases in fracture energy for the above specimen testing configurations. The largest drop (20 percent) in fracture toughness was noted in specimens aged for 6 months in air at 204degC. An unusual finding from this study, in contrast to what other researchers have seen on other systems, was that increasing mode II loading resulted in significant reductions in toughness. Crack path selection and interaction with the woven glass scrim within the bonded specimens may be responsible for the lower mode II fracture energies. From the tests conducted, failure envelopes were developed to predict failure energy and type for use in designing structural joints.

Details of the integral equation method applied to the analysis of an adhesive layer crack

The mathematical model for a crack in an elastic adhesive layer sandwiched between two adherends proposed by Fleck, Hutchinson and Suo ((1991) Crack path selection in a brittle adhesive layer. International Journal of Solids and Structures27(13), 1683–1703) was considered. The elastic mismatch between the adhesive and adherend materials modifies the far-field values of the stress intensity factors and of the T-stress in a manner that depends on the position of the crack inside the layer and on the Dundurs parameters. A complex-potential stress-function formulation, using dislocation distributions represented by truncated Chebyshev series, yielded an integral equation that was solved numerically by the method of collocations. The symbolic derivation of the integral equations was checked, and a few differences from Fleck, Hutchinson and Suo's expressions were identified and reconciled. The computational aspects of the solution were studied in detail using two programming languages, MATHCAD and C++, run on standard PC hardware. A palette of numerical techniques were utilized to study and control the consistency and accuracy of the solution. Symmetry and anti-symmetry arguments were used to identify numerically sensitive regions. Fast Fourier Transform calculation of sine and cosine Fourier integrals was used to increase speed. Convergence of intermediate and final results was examined. It was found that the method is very sensitive to the details of numerical computation, especially for combinations of parameters that lead to nearly singular matrices.