Fracture Mechanics Studies Research Articles

A fracture mechanics study of the phase separating planar electrodes: Phase field modeling and analytical results

Abstract It is well known that phase separation could severely intensify mechanical degradation and expedite capacity fading in lithium-ion battery electrodes during electrochemical cycling. Experiments have frequently revealed that such degradation effects could be substantially mitigated via reducing the electrode feature size to the nanoscale. The purpose of this work is to present a fracture mechanics study of the phase separating planar electrodes. To this end, a phase field model is utilized to predict how phase separation affects evolution of the solute distribution and stress profile in a planar electrode. Behavior of the preexisting flaws in the electrode in response to the diffusion induced stresses is then examined via computing the time dependent stress intensity factor arising at the tip of flaws during both the insertion and extraction half-cycles. Further, adopting a sharp-interphase approximation of the system, a critical electrode thickness is derived below which the phase separating electrode becomes flaw tolerant. Numerical results of the phase field model are also compared against analytical predictions of the sharp-interphase model. The results are further discussed with reference to the available experiments in the literature. Finally, some of the limitations of the model are cautioned.

A Fracture Mechanics Study of a Compact Tension Specimen: Digital Image Correlation, Finite Element and Meshless Methods

This study mainly aims to determine the stress intensity factor range (SIF) for a compact tension (CT) specimen under uniaxial tensile fatigue loading state. A 2D full-field optical technique, Digital Image Correlation (DIC), is used to acquire the experimental solution. Therefore, the deformation contour is measured for several crack growth lengths. In addition, SIF is experimentally characterized together with a numerical overdetermined algorithm for different crack lengths. Besides, the strain variation with respect to the notch tip is captured. The innovation of this study is the combination of an experimental DIC procedure with a numerical overdetermined algorithm. Moreover, to assess the performance of the proposed fracture model, the problem is resolved using advanced discretization techniques, such as the Finite Element Method (FEM) and the Meshless Radial Point Interpolation Method (RPIM). Thus, the cracked CT specimen is elasto-statically modeled using above-mentioned numerical approaches. Hence, the FEM model is analyzed with ABAQUS ©, allowing to compute the mode I SIF results for different crack lengths in addition to strain contours. Likewise, the foregoing procedure is repeated for the RPIM analysis and encouraging numerical results are achieved. The SIF is determined with a maximum energy release rate criterion in front of the crack tip in FEM study, while in RPIM study, it is calculated within the same overdetermined algorithm used in the DIC study. Overall, the experimental and numerical SIF results are compared with the reported solution (ASTM E647) exhibiting a reasonable agreement.

Technical Problem Identification for the Failures of the Liberty Ships

The U.S. Liberty Ship Building Program in World War II set a record—a total of 2700 Liberty Ships were built in 6 years, in order to support the battle against Nazi-Germany. However, numerous vessels suffered sudden fracture, some of them being split in half. This paper demonstrates and investigation of the Liberty Ships failure and problems, which reveals that the failures are caused by a combination of three factors. The welds produced by largely unskilled work force contain crack type flaws. Beyond these cracks, another important reason for failure associated with welding is the hydrogen embitterment; most of the fractures initiate at deck square hatch corners where there is a stress concentration; and the ship steel has fairly poor Charpy-Impact tested fracture toughness. It has been admitted that, although the numerous catastrophic failures were a painful experience, the failures of the Liberty Ships caused significant progress in the study of fracture mechanics. Considering their effect, the Liberty Ships are still a success.

Mixed-mode fracture modeling with smoothed particle hydrodynamics

In this work, we describe a coupled Drucker–Prager and Grady–Kipp SPH framework in order to simulate mode I, mode II and mixed mode failure under the same formulation. This framework is then applied to study failure in uniaxial compression of gypsum samples containing a single angled flaw.To validate the model, results are compared with the experimental analysis and shows good agreement, where fracture initiation positions and angles are well represented. This trend of agreement continues beyond initiation, through to propagation, and finally post-failure behavior.The methodology and results shown here describe a powerful tool for study of fracture mechanics.

Study on subsurface-inclined crack propagation during machining of brittle crystal materials

There is an immense need to obtain high-quality surface and subsurface on brittle material owing to the advantage of its improved performance. Thus, in this paper, we proposed a mechanical and numerical study of fracture mechanics from the perspective of external loading and indentation geometry in brittle machining. Stress intensity factors are computed to analyze various impacts of external loading and indentation configuration on subsurface crack propagation. Results indicate that the main fracture mode for inclined crack is shear rather than opening and the apex angle of the indentation plays an important role in fracture behavior. As a certain external loading is exerted to the surface of the silicon, a large apex angle of indentation may lead to strong shielding effect on mode II crack propagation. A relationship between critical value of external loading to the crack propagation and the apex angle of the indentation is given in this paper that shows quantitative indication for suppression of crack growth.

Numerical Study of Finite Fracture Growth in an Epoxy Resin

In the last decades, the study of fracture mechanics has been increase as tool capable to analyze the mechanical strength for structures without the occurrence of failure. The presence of small cracks can reduce the structural strength of the component enabling, in some cases, the collapse of the structure under a lower stress than the structural ultimate strength. Currently, the use of numerical methodologies, as finite element method (FEM), that address the problem of fracture in structural components to representing the macroscopic regime of the structure has been also used becoming increasing. The goal of the article, through the analysis of fracture and grounds of FEM, determine the fracture growth for a polymeric material (epoxy resin). Through ASTM E399 were established experimental procedures for obtaining fracture toughness (GC), the mechanical fracture bending SE (B) testing was choose, for its simplicity of design and manufacture. Three different numerical models were used to analyze the behavior the material and the fracture process. The results obtained from the numerical simulation were close to the literature results, confirming the effectiveness of the numerical tool used in predicting fracture phenomena in the material and its evolution associated with the loads application.

超高サイクル疲労域を含む変動振幅応力下におけるTi-6Al-4V合金の疲労寿命評価

In this study, the application of cumulative damage rule under variable amplitude stressing in very high cycle fatigue regime was investigated. Ultrasonic fatigue tests were conducted using Ti-6Al-4V alloy under constant amplitude loading and variable amplitude loading. Under constant amplitude loading, both internal fatigue failure and surface failure are observed. Under variable amplitude containing LCF and HCF loading with surface origin and VHCF loading with internal origin, the application of cumulative damage rule was not confirmed. Additional test results to confirm the application and study of fracture mechanism under variable amplitude stressing in the very high cycle fatigue regime are needed.

The Behavior of Ductile Damage Model on Steel Structure Failure

Damage of materials means the progressive or sudden deterioration of their mechanical strength due to loading, thermal or chemical effects. It could cover all related phenomena that occur from the virgin or reference state up to a mesocrack initiation. The continuum mechanical simulation of micro structural damage process is important in the study of ductile fracture mechanics. Material degradation has been widely modelled by continuum damage mechanics and it is accepted as a reliable methodology. In this paper, finite element simulation of damage evolution and fracture initiation in ductile solids will be investigated. Simulations are performed and the results are compared with the numerical and experimental ones addressed in the literature and good agreements were found between them. For this model, damage propagation and crack initiation, and ductile fracture behavior of notched specimens are predicted. The model can also quickly capture both deformation and damage behavior of the part by using 3D stress algorithm. Experiments are also carried out to validate the results. It is concluded that finite element analysis (FEA) in conjunction with continuum damage mechanics (CDM) can be used as a reliable tool to predict ductile damage. By means of examples, it has been demonstrated that the effect of softening cause by damage influences the global behavior of the structures and that the damage variable itself may give useful insights on failure analysis.

Design and fabrication of a cryostat for low temperature mechanical testing for the Mechanical and Materials Engineering group at CERN

Mechanical testing of materials at low temperatures is one of the cornerstones of the Mechanical and Materials Engineering (MME) group at CERN. A long tradition of more than 20 years and a unique know - how of such tests has been developed with an 18 kN double-walled cryostat. Large campaigns of material qualification have been carried out and the mechanical behaviour of materials at 4 K has been vastly studied in sub - size samples for projects like LEP, LHC and its experiments. With the aim of assessing the mechanical properties of materials of higher strength and/or issued from heavy gauge products for which testing standardized specimens of larger cross section might be more adapted, a new 100 kN cryostat capable of hosting different shapes of normalized samples has been carefully designed and fabricated inhouse together with the associated tooling and measurement instrumentation. It has been conceived to be able to adapt to different test frames both dynamic and static, which will be of paramount importance for future studies of fracture mechanics at low temperatures.The cryostat features a double-walled vessel consisting of a central cylindrical section with a convex lower end and a flat top end closure. The transmission of the load is guaranteed by a 4 column system and its precise monitoring is assured by an internal load cell positioned next to the sample in the load train. This innovative approach will be discussed together with other nonconventional instrumentation solutions.A validation of the whole system has been carried out, where bending efforts on instrumented samples have been measured. Additionally, dedicated tooling has been fabricated for the device's optimization. The preliminary results obtained confirm an excellent performance of the system and enhance the analysis of materials under extreme conditions with state of the art instrumentation.

Mechanical characterization and fractographic study of epoxy–kaolin polymer nanocomposites

In this work the mechanical behavior of composite materials formed by a diepoxy–diamine (epoxy) thermosetting matrix filled with kaolin intercalated with ethylenediamine (K–EDA) was studied. Fracture toughness experiments showed that an addition of 2wt% K–EDA to the epoxy matrix causes an approximately 24% increase in the critical stress intensity factor (KIC). The study of fracture mechanisms was completed using the double-notch four-point-bending test. The presence of kaolin particles in the matrix induces crack branching and deflection mechanisms. Furthermore, observation of the fracture surface revealed the presence of tails near kaolin particles, which is consistent with crack-pinning. The present study indicates that kaolin clay can be effective in toughening epoxy at small quantities if it is reasonably well dispersed.

A new body-fitted immersed volume method for the modeling of ductile fracture at the microscale: Analysis of void clusters and stress state effects on coalescence

In this work, a new finite element framework is developed and applied to the study and modeling of ductile fracture mechanisms at the microscale. More particularly, a body-fitted meshing and remeshing methodology is introduced and applications to void coalescence are investigated. Though most studies focus on periodic arrangements of voids, it was proven in experiments as in simulations that random void clusters have a major influence on void growth and coalescence. With the method proposed in this paper, various void arrangements can be addressed and their effect on void growth and coalescence can be studied at large plastic strain and various stress states.

Fracture Mechanics Modelling of an In Situ Concrete Spalling Experiment

During the operation of nuclear waste disposal facilities, some sprayed concrete reinforced underground spaces will be in use for approximately 100 years. During this time of use, the local stress regime will be altered by the radioactive decay heat. The change in the stress state will impose high demands on sprayed concrete, as it may suffer stress damage or lose its adhesion to the rock surface. It is also unclear what kind of support pressure the sprayed concrete layer will apply to the rock. To investigate this, an in situ experiment is planned in the ONKALO underground rock characterization facility at Olkiluoto, Finland. A vertical experimental hole will be concreted, and the surrounding rock mass will be instrumented with heat sources, in order to simulate an increase in the surrounding stress field. The experiment is instrumented with an acoustic emission system for the observation of rock failure and temperature, as well as strain gauges to observe the thermo-mechanical interactive behaviour of the concrete and rock at several levels, in both rock and concrete. A thermo-mechanical fracture mechanics study is necessary for the prediction of the damage before the experiment, in order to plan the experiment and instrumentation, and for generating a proper prediction/outcome study due to the special nature of the in situ experiment. The prediction of acoustic emission patterns is made by Fracod 2D and the model later compared to the actual observed acoustic emissions. The fracture mechanics model will be compared to a COMSOL Multiphysics 3D model to study the geometrical effects along the hole axis.

Analytical solutions of cracks emanating from an elliptic hole in an infinite plate under tension

It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering. However, the fracture mechanics studies of hole edge crack problems are not sufficient. The problem of an elliptical hole with two collinear edge cracks of unequal length in an infinite plate under uniform tension at infinity is investigated. Based on the complex variable method, the analytical solutions of stress functions and stress intensity factors are provided. The stress distribution along the axes and the edge of the elliptical hole is given graphically. The numerical results show that there is obvious stress concentration near the hole and cracks, and the stresses tend to applied loads at distances far from the defect, which conform to Saint-Venant’s principle. Hence, the stress functions are proved to be right. Under special conditions, the present configuration becomes the Griffith crack, two symmetrical cracks emanating from an elliptical hole, two cracks of unequal length emanating from a circular hole, a crack at the edge of a circular hole, or a crack emanating from an elliptical hole. Compared with available results, stress intensity factors for these special shapes of ellipses and cracks show good coincidence. The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the major-to-minor axis ratio of the elliptical hole. The stress distribution in an infinite plate containing an elliptic hole with unsymmetrical cracks is given for the first time.

Experimental and numerical study of fracture mechanisms in UO2 nuclear fuel

In this paper we study the brittle behavior of UO2 nuclear fuel. Firstly, we present the interpretation of bending tests with three different approaches to assess rupture parameters (critical stress and surface energy). Secondly, we present Vickers’ indentation tests on fresh UO2 fuel. The comparison between bending and indentation tests on fresh fuel allows us to assess the parameters necessary to derive the critical stress and the surface energy from indentation tests. Vickers’ indentation is then used to evaluate rupture parameters of irradiated fuels. At the end, we present some applications to fuel rod modeling taking into account the different rupture mechanisms.

Integrity analysis of reactor pressure vessels subjected to pressurized thermal shocks by XFEM

The integrity of an reactor pressure vessel (RPV) related to Pressurized Thermal Shocks (PTSs) has been widely studied. However, due to the difficulties associated with the crack modeling with the 3-D finite element method (FEM), it is preferred to use models with simple geometries and crack configurations. In the last years new improved FEMs were developed which include the singularities and discontinuities and simplify the computational fracture mechanics studies. One of those methods, the eXtended Finite Element Method (XFEM) relies on the introduction of the crack effect with an enrichment of the finite element approximation space. This paper introduces the use of XFEM to the structural analysis of an RPV subjected to PTSs. The analysis compares the stress intensity factor (SIF) calculated with XFEM with results obtained by conventional FEM calculations.

Stresses Due to Intercalation in Layered and Non-Spherical Lithium Storage Particles

With an increase of the scope of use of the Lithium Ion batteries from small electronic devices to large automobiles, there has been a concomitant effort to increase both the capacity and lifetime of these energy storage devices. While newer materials such as silicon show a dramatic increase in energy densities and capacities, the large strains and resulting stresses within these particles lead to comminution and degradation of the particle. Experimental studies have shown that combining these materials with carbon nanotubes can help reduce these strains, mostly by using geometry to constrain the volumetric change of silicon particles. These, and other studies, highlight an important point: the effect of geometry on the intercalation of lithium ions into storage particles and the stress generated as a result are not very well understood. The goal of our current work is to study the effect of morphology of these storage particles on the stresses that are generated within.In our previous work [1,2] we developed a coupled stress-diffusion model for lithium intercalation into a storage particle due to the volumetric expansion of the particle. We identified three non-dimensional parameters that govern the stress response of these particles, the non-dimensionalized current, the non-dimensionalized partial molar volume and the maximum lithiation strain. Our work shows that the effect of the stress on the concentration within the particle can be quite significant and we identified certain combinations of material parameters that would lead to a decrease in the maximum stresses in these particles. We now take this idea one step further by introducing the bilayer spherical particle. This particle consists of an inner sphere, which is coated with a layer of a second material. Our results show that by controlling the rate of diffusion within the layers certain material combinations can be beneficial for the inner sphere. We also conduct a basic fracture mechanics study in order to identify the material parameters at which we particle degradation would be most likely. Due to computational considerations most models of intercalation particles tend to look at spherical particles. However most storage particles used in battery electrodes tend to be irregular in shape with sharp edges and extended aspect ratios. The change of the relative surface area to the volume of the particle can lead to a change in the stress response of the particle for the same material parameters. In order to study the effect of these edges on the stress response, we perform a parameter study on cubic particles as well as ellipsoidal particles with different aspect ratios. Our results show that a change in material properties can lead to differences in both the value of maximum stress as well as its location in the particle, due to the interplay of diffusion and stress responses. Our model highlights the fact that if storage particle geometry could be controlled by using the appropriate manufacturing techniques, then the stress response of the lithium intercalation particles can be improved. R Purkayastha, R.M McMeeking ‘A Linearized Model of Lithium Ion Batteries and Maps for their Performance and Failure’, Journal of Applied Mechanics, 79 (2012) 031021.1 – 031021.16R. Purkayastha, R.M. McMeeking, ‘A Parameter Study of Intercalation of Lithium into Storage Particles in a Lithium-Ion Battery’ Computational Materials Science, 80 (2013) 2-14

The J and M integrals for a cylindrical cavity in a time-harmonic wave field

The invariant integrals are being widely used in the study of defects and fracture mechanics, mostly in elastostatics. However, the properties and the interpretation of these integrals in elastodynamics, especially in the case of time-harmonic excitation, remain unexplored. This contribution is focused on the derivation of the time average J integral for a cylindrical inhomogeneity and the M integral for a cylindrical cavity placed in a monochromatic plane elastic wave. It is shown in the context of antiplane linear elasticity that the J integral, or the material force acting on the inhomogeneity, resembles the radiation pressure force exerted on a dielectric cylinder by the normally incident electromagnetic wave. Based on the existing solution of this electrodynamic problem and the corresponding acoustic problem, the J integral is expressed as a function of the nondimensional wave number in the form of the partial wave expansion of the scattering theory. Employing the same classical method as with the J integral, the closed-form solution of the time average M integral for a traction-free cavity is also obtained as a function of the nondimensional wave number. The M integral, i.e., the expansion or scalar moment per unit length on an infinitely long circular cavity, is represented in terms of the scattering phase shifts as in the case of the J integral. Alternative expressions that are more convenient for numerical calculations for the cavity are also derived for both integrals. These calculations are carried out for the J and M integrals in a wide spectrum of frequencies. Asymptotic approximations of both integrals for low and high frequencies are presented. The long wavelength approximation, including the monopole and dipole contributions, has been provided for the J integral in the form of a simple analytical expression. The value of M integral in the vanishing frequency limit is also presented. In the opposite short wavelength limit, the corresponding asymptotic values are derived for both integrals. These solutions, which are valid for the empty cavity, are extended to the case of an inviscid fluid-filled cavity. The obtained results have a variety of engineering and geophysical implications. In particular, their applications to the flaw characterization of materials and further development of non-destructive evaluation techniques are briefly discussed in light of the frequency relationships derived for the J and M integrals.

A Study of Fracture Mechanisms in RAFM Steel in the Ductile to Brittle Transition Temperature Regime

The fracture behaviour of a Reduced Activation Ferritic Martensitic Steel (RAFM) has been studied within the Ductile to Brittle Transition Temperature (DBTT) regime. The DBTT has been determined by ASTM E 1921 based reference temperature approach under dynamic loading condition. The dynamic reference temperature (T0dy) was found to be − 33.8°C. The fracture mechanism has been studied by extracting TEM specimens precisely at the crack initiation sites using focused ion beam (FIB) technique in a high resolution dual beam scanning electron microscope. Detailed analytical TEM studies revealed that the morphology of carbides play a crucial role in the initiation of a crack. The larger ellipsoidal carbides, which were found to be Cr-rich, have been found to be responsible for dislocation piles ups. The shorter edge of these ellipsoidal carbides are areas of high stress concentration and were found to initiate cracks by decohesion of the particle-matrix interface. On the contrary, the iron rich carbides have been found to be smaller, more spherical, and thus less effective in blocking dislocation movement and therefore formation of pile ups. The results, which reveal an important mechanism towards crack initiation in ferritic-martensitic steels, will be presented in detail.

Detecting the Storm Movement by Sub Pixel Registration Approach of Newton Raphson Method

The change detection, storm detection and forecasting the weather condition consist of in the field of natural disaster management as the essential role. The detecting of the storm direction is provided to manage and to prevent the possible attacked region of the land. The sub pixel registration approach is applied for computing the movement of the interested cloud region. The direction of the storm can be tracked from these computations. Especially, the attacked region of Myanmar Land is forecasted from multi-date satellite image by using the digital image correlation based on the sub-pixel accuracy with Newton Raphson method. The proposed method is very effective because of its experiment and its result. Human can't be terminated the natural disaster. The weather prediction is very important for human daily life to prevent and reduce the attack of natural disaster. The storm direction detecting system is developed based on the sub-pixel accuracy with Newton Raphson method. The pixel correlation among the images is computed accurately by the Digital Image Correlation (DIC) for motion detection. The main application of DIC is in experimental mechanics. During the last two decades, various applications had been reported for two-dimensional measurement of displacement and strain field using the method of DIC. The most fundamental applications of two-dimensional DIC are found in fracture mechanics studies (1), (2), including measurement of strain field near crack-tips at high temperatures (3), strain measurement near stationary and growing crack-tips (4) and measurement of crack-tip opening displacement during crack growth (5), (6). H. A. Bruck et al. (1) proves that the computation of the digital image correlation using Newton Raphson method of partial differential correction. The integer pixel registration algorithm is used in their correlation computation. Moreover, DIC should serve as a valuable tool for biomedical research and the two-dimensional in-plane displacement and strain calculation problem and strain deformation (7)-(9). et al. (10) describes the performance of three different types of sub-pixel displacement registration algorithms in terms of the registration accuracy and the computational efficiency.

OS2101 軸受鋼の回転曲げ疲労における内部起点型破壊モードの疲労限度に関する破壊力学的考察

OS2101 軸受鋼の回転曲げ疲労における内部起点型破壊モードの疲労限度に関する破壊力学的考察