Crack Configurations Research Articles

Effect of thermal residual stresses on ductile-to-brittle transition of a bi-material specimen by using the CAFE method

The effect of residual stress on fracture of materials or structures has been widely studied. However, its influence on ductile-to-brittle transition (DBT), a crucial phenomenon of structural materials, has rarely been investigated so far. In the present study, employing the eigenstrain method residual stresses are introduced into a bi-material specimen, where two configurations of crack and interface, e.g., one with interface perpendicular and one parallel to the crack extension, are designed to study the influence of residual stress. The DBT of the bi-material specimen in the presence of residual stresses is numerically studied by using the CAFE method where temperature dependent surface energy is implemented to calculate absorbed energy of Charpy impact testing specimen. It is found that residual stress generated in the two configurations affect the DBT in a similar manner. The DBT curves generally shift to higher temperature due to the decrease of absorbed energy with the increase of residual stress. It is found that the decrease of absorbed energy in both configurations is caused by the additional constraint on the notch root, which is induced by the residual stress and can facilitate the fracture.

The Stress Intensity Factors of Multiple Inclined Cracks in a Composite Laminate Subjected to In-Plane Loading

Inclined multiple cracks may appear in composite laminates and sandwich structures. In this paper, we solve the fracture problem of a three-layer sandwich structure which contains multiple inclined cracks in the central layer under tension and antiplane shear. Three types of crack configurations are considered: an isolated crack, a periodic array of inclined cracks with the same length, and two parallel cracks with different lengths. In these cases, we examine the interaction among the cracks under mixed I–II mode and pure mode III based on the stress intensity factors. Then, we apply the solutions to fibre-reinforced composite laminates. The results show that the stress intensity factors of the multiple cracks are significantly affected by the constraining effect of the outer sublaminates and the shielding effect among cracks. For cracks with significantly different sizes, the long crack dominates the stress concentration. This work reveals the influences of the laminate configuration, crack distribution, crack orientation and crack size on the stress concentration at the tips of inclined cracks in the three-layer composite laminate, and the results may be used to analyze the crack propagation in the laminates.

On the BFGS monolithic algorithm for the unified phase field damage theory

Despite the popularity in modeling complex and arbitrary crack configurations in solids, phase-field damage models suffer from burdensome computational cost. This issue arises largely due to the robust but inefficient alternating minimization (AM) or staggered algorithm usually employed to solve the coupled damage–displacement governing equations. Aiming to tackle this difficulty, we propose in this work, for the first time, to use the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to solve in a monolithic manner the system of coupled governing equations, rather than the standard Newton one which is notoriously poor for problems involving non-convex energy functional. It is found that, the BFGS algorithm yields identical results to the AM/staggered solver, and is also robust for both brittle fracture and quasi-brittle failure with a single or multiple cracks. However, much less iterations are needed to achieve convergence. Furthermore, as the system matrix is less reformed per increment, the quasi-Newton monolithic algorithm is much more efficient than the AM/staggered solver. Representative numerical examples show that the saving in CPU time is about factor 3∼7, and the larger the problem is, the more saving it gains. As the BFGS monolithic algorithm has been incorporated in many commercial software packages, it can be easily implemented and is thus attractive in the phase-field damage modeling of localized failure in solids.

Experimental Fatigue Life Investigation on a Standard PMMA Compact Tension Specimen Equipped by the Lock Technique

The lock technique is a method to decrease crack growth by putting a lock on the crack which the focus of this study is to experimentally characterize the influence of the lock technique on crack growth behavior and life assessment. In this study, polymethyl-methacrylate rectangular standard compact tension plates were used as the test samples. Three different edge crack and lock configurations were tested for total six samples in order to assess fatigue life and fracture resistance, and experiments were conducted using a high-frequency fatigue test machine that applies cyclic tension–compression loads to the samples. In this study, effects of varying lock and hole geometry on crack initiation and propagations are investigated. Detecting of the crack initiation life and assessing crack propagation life from crack initiation until fracture moment are investigated. The experimental results show that the crack growth life is reduced in the lockless standard cracked specimen compared to the locked samples, and similarly, fracture strength in specimens equipped with the lock is more in comparison with the lockless specimens.

Determination of Surface Crack Configuration by DC Potential Drop Method Assisted by Three-Dimensional Boundary Fitted Coordinates Transformation Technique

Determination of Surface Crack Configuration by DC Potential Drop Method Assisted by Three-Dimensional Boundary Fitted Coordinates Transformation Technique

Transverse ridge cracking in tensile fragmentation tests of thin brittle coatings on polymer substrates

Thin brittle coatings on polymers can be used to improve barrier properties. The interfacial adhesion is known to affect cracking of the coating under deformation. It is therefore desirable to experimentally quantify the adhesive properties. For thin coating systems, this can be done e.g. by tensile fragmentation tests or nanoindentation techniques. For crack opening, an alternative method presents itself in a secondary damage mechanism typically found in tensile fragmentation tests. At large strains, the transverse compressive strains can give rise to ridge cracks, which may be observed in high-resolution scanning electron microscopy. It is shown that such observations can be used to estimate the critical energy release rate in interfacial crack growth. The method is exemplified for 20 nm thick coatings of TiO2 and coatings of mixed oxide TiO2 and Al2O3 on polyethylene terephthalate films. The experiments gave values of 2.5 J/m2 and 1.6 J/m2 for these interfaces, respectively. Energy release rates from a micromechanical model based on beam theory were found to be comparable with non-linear finite element predictions for the present crack configurations. Direct measurement of the transverse strains from digital image correlation resulted in predictions closer to the more exact numerical results as compared with predictions based on an assumed linear elastic Poisson contraction. The effects of the non-linear stress-strain behavior of the polymer film could thus be dealt with by measuring the compressive strains giving rise to the ridge cracks. Overall, this work shows how the ridge cracking can provide insight in interfacial crack growth in predominantly opening mode, and possibly be used to roughly estimate fracture toughness even for ultrathin coatings in this investigation.

Computation of T-stresses for multiple-branched and intersecting cracks with the numerical manifold method

Due to its dual cover systems (i.e., the mathematical cover and the physical cover), the numerical manifold method (NMM) is outstanding in crack modeling, especially in the simulation of complex cracks. In this paper, the NMM is extended to calculate the T-stresses for two-dimensional multiple-branched and intersecting cracks. The displacement jump across crack surface is essentially portrayed by the NMM, and the stress singularity at the crack tip is represented through the incorporation of related asymptotic basis in the NMM local functions. The T-stresses are extracted with the domain-form interaction integral in the NMM postprocessing. To validate the proposed scheme, three numerical examples are tested on uniform mathematical covers nonconforming with all domain boundaries, and the computed results are in nice consistence with the existing solutions. Besides, the effects of crack configurations and boundary conditions on the T-stresses are also revealed.

Boundary element method analysis for mode III linear fracture mechanics in anisotropic and nonhomogeneous media

AbstractWe present here a Boundary Element Method implementation for anti‐plane fracture mechanics in nonhomogeneous and anisotropic media. The results are obtained using two different formulations based on displacement and traction Boundary Integral Equations (BIEs). The crack tips are discretized with special quarter‐point boundary elements. The main crack configurations are studied to determine the stress intensity factors (SIFs). Results for homogeneous and isotropic/anisotropic cases are compared with available solutions in the literature, showing good results. For the case of exponential nonhomogeneity, numerical results are obtained for moderately stiffer media and for softer media.

Multi-parameter fracture mechanics

A mixed-mode geometry has been chosen to investigate a crack propagation using the multi-parameter fracture mechanics concept. The so-called Williams’ series expansion is used for the crack-tip stress field approximation. It has been shown that application of the generalized fracture mechanics concept can be crucial for materials with specific fracture behaviour, such as elastic-plastic or quasi-brittle one, when fracture occurs not only in the very vicinity of the crack tip, but also in a more distant surrounding. Then, considering the higher-order terms of the Williams’ expansion in fracture criteria (describing the crack stability and/or crack propagation direction) can bring more precise results. The coefficients of the Williams’ expansion must be calculated numerically (for instance by means of the over-deterministic method in this work) for each cracked configuration, which is very time-consuming, and the analysis is very extensive even for a few basic cracked specimen configurations. On the other hand, a suitable choice of the geometrical configuration of the cracked disc enables performing experiments only on the specimens that could prove the theory about the importance of using the higher-order terms.

Assessing multiple cracks in beams by a method based on the damage location coefficients

In this paper, we analyze the case of structural integrity assessment when the beams have several cracks. The relationship between the location and the severity of one crack and the resulting frequency shift is known. That is why we can design databases containing many defects for which we can calculate precisely the frequency changes and the subsequent damage location coefficients. When the natural frequency evolution of several vibration modes is monitored, we can find alteration due to the crack. Comparing the results of the measurements with the values contained in the database, for instance by involving a bin-by-bin dissimilarity estimator, we can find the location and severity of the crack. For multiple cracks, this approach was not investigated. In this study, we design a database for two cracks affecting at the same time the beam. For these cracks, which have various severities and locations, we calculated the frequency changes by applying the superposition principle. Afterward, we find the frequency shifts for a test structure by means of the finite element method. The comparison between the damage location coefficients in the database and the signature of the damages achieved by simulation is made by the software we have developed in Visual Basic for Application in Excel. We succeed to find the severity and the location of the two cracks for all considered crack configurations.

Evaluation of the two‐parameter fracture criterion for various crack configurations made of 7075‐T6 aluminium alloy using finite‐element fracture simulations

AbstractFor many years, a two‐parameter fracture criterion (TPFC) has been used to correlate and predict failure loads on cracked metallic fracture specimens. The current study was conducted to evaluate the use of the TPFC on a high‐strength aluminium alloy, using elastic‐plastic finite‐element (FE) analyses with the critical crack‐tip‐opening angle (CTOA) fracture criterion. In 1966, Forman generated fracture data on middle‐crack tension, M(T), specimens made of thin‐sheet 7075‐T6 aluminium alloy, which is a quasi‐brittle material. The fracture data included a wide range of specimen half‐widths (w) ranging from 38 to 305 mm. A two‐dimensional FE analysis code (ZIP2D) with a “plane‐strain core” option was used to model the fracture process with a critical CTOA chosen to fit the M(T) test data. Fracture simulations were then conducted on other M(T), single‐edge‐crack tension, SE(T), and bend, SE(B), specimens over a wide range in widths (w = 19‐610 mm). No test data were available on the SE‐type specimens. The results supported the TPFC equation for net‐section stresses less than the material proportional limit. However, some discrepancies in the FE fracture simulations results were observed among the numerical analyses made on the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens for quasi‐brittle materials.

An analytical model for the fracture behavior in hollow cylindrical anodes

Silicon cylindrical anodes suffer from chemo-mechanical degradation and unpredictable fracture problems in high performance lithium-ion batteries, which resulting in capacity fade. A new fracture model based on core-shell structure is derived in this work, which combines diffusion-induced stress and surface stress, to demonstrate the mechanical behavior including the evolution of diffusion-induced stress and stress intensity factor in the hollow cylindrical anode during lithiation and delithiation. By evaluating the evolution of the radial and circumferential cracks, we find that maximum stress intensity factor for the radial crack is larger than the circumferential crack, both for internal and external cracks, which indicates that the radial crack is more dangerous than the circumferential crack for a cylindrical anode. Furthermore, the critical sizes of the hollow cylindrical anode among various crack configurations are obtained. The radial cracks caused by the hoop stress are found to be more essential in determining critical size of the electrode. The present work provides the fracture behavior in Si cylindrical anode during lithiation, which is helpful to the understanding the chemo-mechanical degradation.

Detection of sub-500-μm cracks in multicrystalline silicon wafer using edge-illuminated dark-field imaging to enable thin solar cell manufacturing

High capital expenditures associated with manufacturing thin silicon wafers make it difficult for the industry to scale up and prevent novel technologies from entering the market. Thin wafers fail largely due to breakage during solar cell processing and handling. One of the root causes for breakage is sub-mm edge cracks in the silicon wafer, and these cracks cannot be reliably detected by most commercially-available crack detection tools. In this work, we first investigate the correlation between wafer thickness and critical crack length, and explain the importance of detecting sub-500-μm edge cracks as the wafer thickness is reduced. Secondly, we extend our previous work of micro-crack detection to demonstrate an edge illumination technique using a near-infrared laser to image edge cracks less than 500 μm in length in multicrystalline silicon. Thirdly, we investigate two fundamental edge illumination mechanisms based on dark-field imaging; namely, direct and vicinal illumination. We will then compare these methods to a state-of-the-art rear illumination method. The advantages and disadvantages of both illumination methods are presented and provide an in-depth analysis of light-crack interaction. In particular, we find that the robustness of vicinal illumination is due to diffuse reflectance. The diffuse reflectance has less dependence on crack configurations, while direct illumination has more dependence on the crack configurations because it utilizes specular reflectance. Our results show that our proposed prototype can detect sub-mm edge cracks in multicrystalline silicon wafers, which is an important step in enabling thin silicon wafer manufacturing.

Cost effectiveness of crack treatment methods: A field study

Abstract In the United States, more than 94% highways are paved with asphalt materials and placing crack sealant materials has been a common pavement maintenance for decades. Crack sealing treatment includes the use of a router to create a reservoir on the intended cracks whereas crack filling is given without doing any modification to the crack wall. Although the initial cost of crack sealing is higher, it is expected to have a longer service period compared to crack filling. There is little research on comparison of short and long term cost effectiveness between these two treatments using the real field cost data analysis. In this study four test sites in Texas were treated with crack filling and sealing using the same sealant material and finishing technique. Cost effectiveness of both treatments was measured in terms of initial, annual average and life cycle cost based on the cost inputs during construction. In general, the results of this study indicated that (1) on an average approximately 45% initial cost increase was estimated with the two routing configurations of crack sealing; (2) material and labor cost is found to have the most significant effect on the higher initial cost of crack sealing compared to other associated costs; (3) annual average and life cycle costs have shown that crack sealing is more cost effective pavement maintenance compared to crack filling over a long period of time; (4) agency cost is observed to be reduced by approximately 24% with crack sealing treatment based on the 35 year analysis period.

Analysis of crack geometry and location in notched bars by means of a three-probe potential drop technique

It is often necessary to define the crack initiation life of a fatigue tested component, generally at a given (short) crack length. The size of an initiated crack can be estimated by employing different experimental methods, one of which is the direct current potential drop (DCPD) technique. In the case of notched bars subjected to fatigue loadings, the crack configuration (i.e. circumferential or semi-elliptical) and location cannot be singled out by means of the potential drop method (PDM) operating with a single potential probe. In the present contribution, three potential probes are adopted to overcome this issue. The calibration curves reporting the three potential drops as a function of the crack size are derived by means of 3-dimensional electrical FE analyses. Two different crack configurations are analyzed: (i) circumferential and (ii) semi-elliptical surface cracks. The calibration curves have been validated by systematic comparison with experimental results, generated by fatigue testing of sharp as well as blunt notched specimens made of steel and a titanium alloy under pure axial loading. Finally, a procedure to assess the area, the configuration and the location of the initiated fatigue crack starting from the experimentally measured potential drops is discussed.

The effect of crack geometry on non-destructive fault detection of EN 8 and EN 47 cracked cantilever beam

Since long it has been observed that the size of the crack in structures increases with time, and finally, it may lead to its catastrophic failure. Hence, it is crucial to do the vibration study of cracked structures with regard to vibration-based crack detection and the classification of cracks. So far, vibration-based non-destructive testing method is applied to many spring steel cracked cantilever beams for its possible crack detection. However, the effect of various kinds of practical cracks, that is, V-shaped and U-shaped, on the applicability of these methods has been overlooked. To investigate this issue, artificially cracks are made on the cantilever beam. By free vibration analysis, the effect of crack geometry, crack depth, and crack location on natural frequency is investigated. The natural frequency results obtained from V-shaped and U-shaped models for the same crack configurations are compared with each other and it is revealed that the results are not much sensitive for the change of crack geometry. Hence, it is clear that free vibration-based crack detection method approximately predicts the crack parameters, that is, crack location and crack depth, in structures irrespective of the crack geometry. It is also found that for the same configuration, results of natural frequency are comparatively on the lower side for U-shaped crack models than V-shaped crack models. In this study, the natural frequency of each cracked case is computed by a theoretical method and numerical method and shows good agreement. Finally, it is also observed that structural integrity of a cracked cantilever beam is a function of crack location.

A FFT solver for variational phase-field modeling of brittle fracture

The variational phase-field method is an attractive non-local approach of modeling fracture in heterogeneous materials. However, these materials usually require a fine mesh to resolve the fracture process zone. Consequently, the standard finite element solver becomes cumbersome due to the large number of elements in applications with highly heterogeneous materials. Motivated by this limitation, an algorithm based on FFT methods has been introduced in this paper to solve the phase-field model of brittle fracture. Relying on a staggered update scheme, the proposed algorithm solves the fracture problem and mechanical problem separately, both using the FFT technique. It inherits the advantages of classical FFT methods in terms of simplicity of mesh generation and parallel implementation. Introduced within a FFT-based code “AMITEX”, it takes the advantage of massively parallel capabilities associated with a distributed memory implementation. The characteristics of the proposed method are analyzed in a single edge notched specimen benchmark. Representative numerical examples demonstrate that the proposed FFT solver is capable of predicting different crack modes and complex crack configuration, such as crack interaction, branching and coalescence. Finally, a model of an idealized continuous fiber composite with void involving over 32 million voxels is solved, illustrating the potential of the FFT solver in large-scale problems.

Failure investigation of liquefied petroleum gas cylinder using FAD and XFEM

To assess the reliability and performance of household liquefied petroleum gas (LPG) cylinder is important for safety standard. Such crack-like flaws in material of cylinder might lead to many serious catastrophes like fluid leakage and gas explosion. In this work, the failure assessment diagram (FAD) was determined according to the standard API 579 for inland produced LPG cylinders. A brand-new and used LPG cylinder of the same steel grade were investigated. Metallographic analyses, tensile tests and fracture mechanics tests using a single-edge tension SE(T) specimen were carried out. The direct current potential drop (DCPD) method was applied by the SE(T) test and the critical contour J-Integral for crack initiation was identified. Then, FE simulations of the cylinders afflicted with different crack configurations were performed under varying internal pressures. The corresponding critical pressure loads were determined and the level 3 FAD for a crack onset could be generated. It was found that the mechanical properties of used cylinder were obviously deteriorated that could therefore lead to an earlier failure when an unexpected certain pressure is given. In addition, FE simulations coupled with extended finite element method (XFEM) were conducted in order to describe the crack propagation in both cylinders. The results were firstly verified by comparing the load vs. crack mouth opening displacement (CMOD) curves. It was shown that the crack propagation in the aged LPG cylinder would become considerably stronger when unintended crack is present.

Weight functions and stress intensity factors for two unequal-length collinear cracks in an infinite sheet

The configuration of two unequal-length collinear cracks is common in aircraft structures containing multiple site damage. In this paper, the weight functions for this crack configuration are derived from the exact crack opening displacements under remote tension, and verified by reducing to the existing exact weight functions of two equal-length collinear cracks and by good agreement with finite element analysis. These weight functions are used to calculate the stress intensity factors and crack opening displacements for different load cases. The results agree very well with those from literature and finite element analysis. The weight functions for two unequal-length cracks provide a highly efficient and accurate tool for damage tolerance analysis of structure with multiple site damage.

Mode I fracture testing validation on non-plane strain zirconium foils

Mode I fracture testing was conducted on annealed pure zirconium sheet at room temperature to investigate material fracture performance with non-plane strain specimens. Finite element analysis (FEA) was used to determine geometry and size effects. The J-integrals at crack growth of 20 μm and fracture resistance curves were observed to be invariant for different cracked configurations including center cracked and edge cracked specimens. This implies that the influence of crack length on J-integral can be neglected. The out-of-plane dimension (thickness) plays a more important role than the in-plane dimension (crack length) for fracture testing using such small and thin samples. Digital image correlation (DIC) was used to measure the strain distribution near the crack tip at different loading levels. The strain distributions in front of the crack from FEA and DIC indicate that a J characterization region can still exist, even though large scale yielding has occurred.