Problem Of Brittle Fracture Research Articles

A non-local 3D lattice particle framework for elastic solids

A novel non-local lattice particle method for three-dimensional elasticity and fracture simulation of isotropic solids is proposed in this paper. First, the basic concept and detailed derivation of the proposed model are given. Three cubic lattice packing are investigated using the proposed model and simulation results are compared with classical finite element method solutions. The performance of these lattice structures are assessed using several benchmarks, for both deformation and brittle fracture problems. From the simulation results, good agreements with both analytical solution and experimental data are observed. Conclusions and future work are drawn based on this study.

Size effects in finish machining of porous powdered metal for engineered surface quality

Porous tungsten is conventionally machined with the aid of a plastic infiltrant to achieve acceptable surface finish. For dispenser cathode application, both high surface porosity and low surface roughness are necessary. Cryogenic machining has already been demonstrated to be capable of eliminating the need for plastic infiltration by greatly reducing smearing of pores. In order to address the problem of undesirable brittle fracture during cryogenic machining, the importance of uncut chip geometry is investigated. The value of critical chip thickness, beyond which brittle fracture occurs, is found to be closely linked to the microstructure of the workpiece material. While machining with very low uncut chip thickness leads to ploughing and spalling of the workpiece surface, ductile mode machining of porous tungsten with cryogenic cooling is found to yield excellent surface quality. When the maximum uncut chip thickness is approximately equal to the average ligament diameter of 80% density porous tungsten (d≈8–9μm), ductile mode machining is possible under both dry and cryogenic conditions. Changes in shock compaction behavior of the workpiece material, leading to altered physical properties, is hypothesized to be the underlying mechanism of ductile mode machining of porous tungsten.

The Volume Strain Energy Density Factor Criterion for Sharp V-Notches under Mixed-Mode I and II

This paper presents a new energy approach based on the concept of a volume stain-energy-density factor useful to deal with the general problem of brittle fracture for sharp V-notches under mixed-mode I and II. The basic assumption is that the fracture occurs when the volume strain energy density factor arrive at its critical value in the direction of crack initiation where the deviator strain energy density factor is minimum. The method is validated taking into account experiment data already reported in the literature and the analytical predictions are in good agreement with experiment data. It indicates that the accuracy of the new approach is undoubtedly very satisfactory and can be applied in engineering.

Embrittlement study of electroplated nickel films by microindentation

Electroplated nickel is known to suffer from a brittle fracture problem. This phenomenon originates from small amounts of impurities such as hydrogen, sulfur and phosphorus which are incorporated during the plating process and improve the mechanical properties (hardness) through grain refinement. In this study, the correlation between the impurities and brittle fracture of electroplated Ni films was systematically investigated via microindentation in the temperature range 673–973 K. The measured KC values ranged between 2.6 and 3.2, and the activation energy for the grain growth was determined to be 234 kJ mol−1.

Mechanical properties and fracture toughness of rail steels and thermite welds at low temperature

Brittle fracture occurs frequently in rails and thermite welded joints, which intimidates the security and reliability of railway service. Railways in cold regions, such as Qinghai-Tibet Railway, make the problem of brittle fracture in rails even worse. A series of tests such as uniaxial tensile tests, Charpy impact tests, and three-point bending tests were carried out at low temperature to investigate the mechanical properties and fracture toughness of U71Mn and U75V rail steels and their thermite welds. Fracture micromechanisms were analyzed by scanning electron microscopy (SEM) on the fracture surfaces of the tested specimens. The ductility indices (percentage elongation after fracture and percentage reduction of area) and the toughness indices (Charpy impact energy Ak and plane-strain fracture toughness KIC) of the two kinds of rail steels and the corresponding thermite welds all decrease as the temperature decreases. The thermite welds are more critical to fracture than the rail steel base metals, as indicated by a higher yield-to-ultimate ratio and a much lower Charpy impact energy. U71Mn rail steel is relatively higher in toughness than U75V, as demonstrated by larger Ak and KIC values. Therefore, U71Mn rail steel and the corresponding thermite weld are recommended in railway construction and maintenance in cold regions.

Effects of the Impurities on the Embrittlement Phenomena of Electroplated Nickel Films

Electroplated nickel has been known to have brittle fracture problem and the phenomena originated from the fact that the nickel films contained small amounts of impurities such as hydrogen, sulfur and phosphorus which enabled plating process and improved mechanical properties (hardness) through grain refinement effect. In this study, correlation between the impurities and brittle fractures of electroplated nickel films were systematically investigated at temperature range of 673–973K. Experimental results showed that the fracture toughnesses were closely related with the microstructures of the nickel films and their impurity content. The measured KC values were ranged between 2.0 and 4.5, which were one order of magnitude lower than those of pure nickel. Activation energy for the grain growth of the nickel films was determined as 234KJ/mole.

Brittle fracture: thermodynamic refinement of the Griffith problem

The purpose of the work is (a) a rigorous formulation of the brittle fracture problem from the thermodynamic point of view and (b) widening the theory by accounting for not only surface tension, but also the line tension of a crack. A proper thermodynamic formulation of the Griffith problem is attained by introducing generalized Gibbs energy as a thermodynamic potential, both the 2d and 3d cases being included. Thermodynamic line tension is introduced as a new characteristic of a crack originating from changing surface tension near the crack tip, which can be of certain significance for nanocracks. The criterion of rupture is reformulated in the context of line tension. As an example, a detailed calculation of the surface and line tensions of a crack is performed for a molecular solid with dispersion forces. The effect of line tension on the ultimate strength is shown to be twice as much in the 3d case as compared with the 2d case.

On a variational, free‐discontinuity formulation of brittle fracture: mean‐field relaxation and numerical solution

AbstractIn this paper we address the resolution of two important issues arising in the context of the relaxed variational formulation of the incremental free–boundary value problem of brittle fracture. First issue, is how by recasting the formulation into a discrete, minimum–maximum problem one can avoid the undesirable scale effects expressed in terms of the characteristic size and domain–shape dependence of the calculated minimum; second, how by a remeshing procedure in combination with a domain–shape update for tracking the propagating 0–th level set one can reconstruct the crack surface. We finally illustrate our approach by a geometrically linear 2–dimensional example for crack propagation in an initially isotropic brittle solid. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Full scale test and alnalytical evaluation on flexural behavior of tapered H-section beams with slender web

In December 2005, one(A) of the two pre-engineered warehouse buildings in the port of K City of Korea was completely destroyed and the other(B) was seriously damaged to be demolished. Over-loaded snow and unexpected blast of wind were the causes of the accident and destructive behavior was brittle fracture caused by web local buckling and lateral torsional buckling at the flange below rafter. However, the architectural design technology of today based on material non-linear method does not consider the tolerances to solve the problem of such brittle fracture. So, geometric non-linear evaluation which includes initial deformation, width-thickness ratio, web stiffener and unbraced length is required. This study evaluates the structural safety of 4 models in terms of width-thickness ratio and unbraced length using ANSYS 9.0 with parameters such as width-thickness ratio of web, existence/non-existence of stiffener and unbraced length. The purpose of this study is to analyze destructive mechanism of the above-mentioned two warehouse buildings and to provide ways to promote the safety of pre-engineered buildings.

Critical points of Ambrosio-Tortorelli converge to critical points of Mumford-Shah in the one-dimensional Dirichlet case

Critical points of a variant of the Ambrosio-Tortorelli functional, for which non-zero Dirichlet boundary conditions replace the fidelity term, are investigated. They are shown to con- verge to particular critical points of the corresponding variant of the Mumford-Shah functional; those exhibit many symmetries. That Dirichlet variant is the natural functional when addressing a problem of brittle fracture in an elastic material.

Crack arresting low-density porous materials with periodic microstructure

The problem of brittle fracture of a 2D periodic porous material is considered. For the considered relative density range the cellular material approximation with beam elements becomes invalid and a novel analysis technique based on the discrete Fourier transform is suggested. Mode I fracture toughness is derived from the continuum analysis of the stress state in a perforated elastic plane with a macroscopic crack composed of a number of microcracks between the neighboring voids. The crack length is proved to be sufficiently large such that the K-field of the linear elastic fracture mechanics takes place. The solution is obtained in the form of superposition of weighted Green functions every one of which corresponds to a unit displacement jump at a single microcrack. The Green function solutions are found by a combination of the representative cell technique and the finite element method. As a result the initial problem for infinite plane is solved by multiple analysis of the repetitive periodicity cell. An optimization of the voids shape for fixed relative density is performed in order to design the material with improved fracture toughness. Several types of voids arrangement are considered. In the limiting case of low density the results are compared with known data for cellular materials.

The materials and the design of the die in a critical manufacturing step of an automotive shock absorber cap

The industrial drawing of automotive shock absorber endcaps caused wear and radial brittle fractures of the tool steel dies. A finite element method (FEM) simulation of the process showed that this was caused by high contact and hoop stresses on the die. Such difficulties are usually solved by expensive changes in the die material, but a change in the punch design was proposed as a simpler and cheaper solution. The new punch geometries were employed in a FEM simulation of the drawing, indicating much lower contact and hoop stresses. The implementation of the solution eliminated the wear and brittle fracture problems.

Performance of time‐stepping schemes for discrete models in fracture dynamic analysis

AbstractIn this work we present a critical evaluation of different time integration schemes within the setting of non‐linear dynamic analysis of brittle fracture problem represented by a discrete model. The discrete model of this kind consists of Voronoi cells representing the grains of a heterogeneous structure, which are interconnected by cohesive forces modelled by beam‐like links capable of taking properly into account both brittle dynamic fracture and large displacement of a still connected pack of grains that might split from the structure. The brittle behaviour of cohesive links requires that the dynamic analysis of such a model be treated with care, and the best possible integration scheme be selected. Four different schemes are explored and compared in application to a dynamic traction test, including Newmark explicit and implicit schemes, HHT‐α scheme and energy‐decaying scheme. Copyright © 2005 John Wiley & Sons, Ltd.

Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency

AbstractIn this paper, two brittle fracture problems are numerically simulated: the failure of a ceramic ring under centrifugal loading and crack branching in a PMMA strip. A three‐dimensional finite element package in which cohesive elements are dynamically inserted has been developed. The cohesive elements' strength is chosen to follow a modified weakest link Weibull distribution. The probability of introducing a weak cohesive element is set to increase with the cohesive element size. This reflects the physically based effect according to which larger elements are more likely to contain defects. The calculations illustrate how the area dependence of the Weibull model can be used to effectively address mesh dependency. On the other hand, regular Weibull distributions have failed to reduce mesh dependency for the examples shown in this paper.The ceramic ring calculations revealed that two distinct phenomena appear depending on the magnitude of the Weibull modulus. For low Weibull modulus, the fragmentation of the ring is dominated by heterogeneities. Whereas many cracks were generated, few of them could propagate to the outer surface. Monte Carlo simulations revealed that for highly heterogeneous rings, the number of small fragments was large and that few large fragments were generated.For high Weibull modulus, signifying that the ring is close to being homogeneous, the fragmentation process was very different. Monte Carlo simulations highlighted that a larger number of large fragments are generated due to crack branching. Copyright © 2003 John Wiley & Sons, Ltd.

712 O(N)TB+Tersoff 連結分子動力学法によるシリコンのモード I き裂先端場の解析

In order to solve the brittle fracture problem as exactly as possible, the electronic charge distribution should be considered in the highly strained field like the crack tip. We have proposed the concurrent atomistic modeling for the crack problem, which is coupled with the linearly scaled tight-binding (O(N)TB) method and the empirical Tersoff potential. In this paper, it is applied to the crack propagation of silicon to understand an effect of the boundary condition of the atomic model to the local atomistic behavior in the crack tip field.

Grain boundary melting of hafnium containing Ni3Al intermetallic compounds

The Ni[sub 3]Al intermetallic compound possesses the L1[sub 2]-type ordered structure below the melting temperature. Its yield strength has been shown to increase with increasing temperature. Also, it is the principal strengthening phase ([gamma][prime]) of the commercial nickelbase superalloys. However, there exists a serious problem of brittle intergranular fracture in polycrystalline Ni[sub 3]Al. By macroalloying with hafnium, Liu and White showed that the yield stress of Ni[sub 3]Al increases and raises the peak-strength temperature with hafnium additions. Taniguchi et al. found that hafnium alloying effectively decreases the oxidation rate and improves oxide scale adherence. In addition, hafnium additions improved other properties of Ni[sub 3]Al, such as creep resistance and high-cycle fatigue life. Although ternary or quaternary alloying additions have been shown to improve the thermomechanical properties of Ni[sub 3]Al, some alloying elements might segregate to the grain boundary to cause grain boundary melting at elevated temperatures below 1,395 C. The present study shows that the increase of hafnium content decreases the melting temperature of this alloy and, thus, increases the tendency for grain boundaries to melt.

Powder metallurgically produced Ni-35 at.% al compacts — A first assessment

The intermetallic phase [beta] NiAl to be an alloy with high heat resistance and good oxidation resistance and is being developed as a potential material for high temperature applications. In addition, off-stoichiometric nickel rich [beta] Ni-Al compositions are known to undergo a thermoelastic martensitic transformation and exhibit shape memory effect at relatively high temperatures. There is no major difficulty in processing these alloys at elevated temperatures. However, thy suffer a major problem of brittle fracture and poor ductility at ambient temperature. In this regard it has been suggested that finer grained NiAl can exhibit enhanced ductility. Moreover, in quenched alloys containing [>=]35at.% Al there is a problem with reversibility of the martensitic transformation. This is because, martensite decomposes on heating by temperate and this suppresses subsequent transformation to martensite on cooling. The aim of this work was to investigate the possibility of producing nickel rich Ni-Al alloys by P/M route. It will also be shown that the tendency for martensite to temper is suppressed with such a method of preparation.

Hydrogen permeation characteristics of incoloy907 alloy

The problem of brittle fracture induced by hydrogen ingress from environment must be considered for some high-strength alloys, particularly for the superalloys strengthened by [gamma][prime] precipitation, used in fields such as aerospace and nuclear power. Therefore, a number of studies on hydrogen performance of superalloys have been recently carried out. The understanding of hydrogen transport characteristics in these alloys is important to clarify the hydrogen embrittlement mechanism. Although hydrogen permeabilities and diffusivities of some superalloys have been reported, the study of the hydrogen permeation and diffusion in Incoloy 907 alloy, a type of Fe-Ni-Co based superalloy, is still absent to date. In the present work, a gaseous permeation technique was employed to measure hydrogen permeability and diffusivity in this alloy, in order to understand the relationship between hydrogen permeation and microstructure.

A new formulated method of a quasi-compatible finite element and its application in fracture mechanics

Based on the local properties of a singular field, the displacement pattern of an isoparametric element is improved and a new formulated method of a quasi-compatible finite element is proposed in this paper. This method can be used to solve various engineering problems containing singular distribution, especially, the singular field existing at the tip of cracks. The singular quasi-compatible element (SQCE) is constructed. The characteristics of the element are analysed from various angles and many examples of calculations are performed. The results show that this method has many significant advantages, by which, the numerical analysis of brittle fracture problems can be solved.

On non-glide stresses and their influence on the screw dislocation core in body-centred cubic metals I. The Peierls stress

The response of the screw dislocation core in a body-centred cubic model lattice to a general applied stress tensor is examined by means of computer simulation. The Peierls stress is found to have the symmetry required by Neumann’s principle but is found also to have a very strong dependence on shear components of the applied stress which should not interact with the screw dislocation. Rather than having the constant value suggested by the Schmid law of critical resolved shear stress, the Peierls stress can vary from zero to the theoretical shear strength of the lattice, depending upon the exact nature of the critical applied stress components. Calculations with different interatomic binding potentials show that the Peierls stress variation, while different in detail, remains broadly the same, suggesting an origin in the dislocation core geometry rather than the specific charac­teristics of the force laws. Specialization to the case of uniaxial applied stress shows that the similar Peierls stress variation can nevertheless lead to quite different orientation dependences of the flow stress in different materials. Applications to the problem of brittle fracture and possible sources of the Peierls stress variation are discussed briefly.