Crack Initiation Criterion Research Articles

Dynamic Study on Fracture Problems in Viscoelastic Sedimentary Rocks Using the Numerical Manifold Method

The viscoelastic deformation behavior of a sedimentary rock under different loading rates is numerically modeled and investigated by the numerical manifold method (NMM). By incorporating a modified 3-element viscoelastic constitutive mode in the NMM, crack initiation and propagation criteria, and crack identification and evolution techniques, the effects of the loading rates on the cracking behavior of a sedimentary rock, such as crack open displacement, crack sliding displacement, crack initiation, crack propagation and final failure mode, are successfully modeled. The numerical results reveal that under a high loading rate (>1,000 MPa/s), due to the viscoelastic property of the sedimentary rock, not only the structural behavior deviates from that of elastic model, but also different cracking processes and final failure modes are obtained.

Evolution Procedure of Multiple Rock Cracks under Seepage Pressure

In practical geotechnical engineering, most of rock masses with multiple cracks exist in water environment. Under such circumstance, these adjacent cracks could interact with each other. Moreover, the seepage pressure, produced by the high water pressure, can change cracks’ status and have an impact on the stress state of fragile rocks. According to the theory of fracture mechanics, this paper discusses the law of crack initiation and the evolution law of stress intensity factor at the tip of a wing crack caused by compression-shear stress and seepage pressure. Subsequently, considering the interaction of the wing cracks and the additional stress caused by rock bridge damage, this paper proposes the intensity factor evolution equation under the combined action of compression-shear stress and seepage pressure. In addition, this paper analyzes the propagation of cracks under different seepage pressure which reveals that the existence of seepage pressure facilitates the wing crack’s growth. The result indicates that the high seepage pressure converts wing crack growth from stable form to unstable form. Meanwhile, based on the criterion and mechanism for crack initiation and propagation, this paper puts forward the mechanical model for different fracture transfixion failure modes of the crag bridge under the combined action of seepage pressure and compression-shear stress. At the last part, this paper, through investigating the flexibility tensor of the rock mass’s initial damage and its damage evolution in terms of jointed rock mass's damage mechanics, deduces the damage evolution equation for the rock mass with multiple cracks under the combined action of compression-shear stress and seepage pressure. The achievement of this investigation provides a reliable theoretical principle for quantitative research of the fractured rock mass failure under seepage pressure.

Elastic–plastic cracking analysis for brittle–ductile rocks using manifold method

In this study, the formation of localized deformation band and failure processes of brittle–ductile materials (coarse and medium marbles) containing pre-existing flaws under various loading conditions are simulated numerically. By incorporating the modified Mohr–Coulomb crack initiation criterion and the crack evolution techniques, the cracking processes, such as crack initiation, propagation and coalescence are successfully modeled by the developed numerical manifold method. According to the results, the development of macro-shear cracks is preceded by the development of localized deformation bands, which are underlain by damage accumulation and material deterioration. The numerical results are comparable to the laboratory test results.

Estimation and comparative study of JIC using different methods for 20MnMoNi55 steel

Fracture toughness is one of the key input variables to compute critical load of the structural components. The resistance against ductile fracture can be quantified either by the initiation value or by the entire resistance curve. Different standard methods like JSZW, JSME and ASTM: E1820 etc. are mainly used to estimate the critical crack initiation value from the resistance curve developed by the J-integral test. However, the results vary from method to method and are even inconsistent for the same method. Pehrson and Landes suggested a simple method for estimation of the critical fracture toughness by identifying the critical point corresponding to the maximum load on load–displacement curve. In the present study, different standard methods along with the one suggested by Pehrson and Landes are used to find out the critical fracture toughness using 1T–CT and ½T–CT specimens of the material 20MnMoNi55 steel for varying temperatures and crack size. The results are analyzed to compare the merits of the different methods of estimation of fracture toughness.

Modelling of crack initiation in adhesively bonded Joint

In this paper, a review of some techniques proposed in the literature for modelling crackinitiation in adhesively bonded joints is presented. The techniques reviewed are: a) the singular intensityfactor, b) the inherent flaw size, c) Cohesive-zone model (CZM) and d) Continuum Damage Mechanics(CDM). The singular intensity factor characterizes the stress singularity at the corner point and can beused as a failure criterion to predict crack initiation. The inherent flaw method technique assumes that asmall crack having a fraction of millimetres is initiated at the singular point in order to develop a fracturemechanics criterion for crack initiation. The strain energy release rate for an un-cracked specimen is usedto determine the size of the inherent flaw. The cohesive zone model (CZM) technique is based ondefining parameters from fracture mechanics test specimens and using them to model failure of the joints.Continuum Damage Mechanics makes use of thermodynamics principles in order to derive a damageevolution law. In this damage evolution law the damage variable (D) is expressed as a function of numberof cycles, applied stress range and triaxiality function. Furthermore, the possibility of using the eXtendedFinite Element Method (XFEM) to predict crack initiation is elaborated.

A stress-based criterion for ductile crack initiation of pre-strained carbon steel

An attempt was made to represent the critical condition for ductile crack initiation by a stress-based parameter. First, tensile tests were conducted using notched bar specimens. Then, a stress-based criterion was derived from the stress and strain at onset of ductile cracking. Validity of the criterion was shown by comparison with the crack tip stress estimated for the fracture toughness tests. By using the stress-based criterion, the change in failure strain due to pre-straining could be reasonably explained. It was concluded that the stress was better than the plastic strain for representing the critical condition of the ductile crack initiation.

Crack initiation and fatigue life prediction on aluminum lug joints using statistical volume element–based multiscale modeling

This article presented the application of an energy-based multiscale damage criterion for crack initiation and life prediction in crystalline metallic aerospace structural components under fatigue loading. A novel meso statistical volume element model was developed to improve computational efficiency compared to traditional meso representative volume element models. The key microscale factors affecting the mechanical properties of crystalline materials, including grain orientation, misorientation, principal axis direction, size, aspect ratio, and shape were considered in the formation of the statistical volume element model. The effect of several factors was studied to assess the importance in the overall macroscopic response of the material. Fatigue tests of lug joint samples were performed to validate the damage criterion as well as the statistical volume element model. Crack initiation was predicted within 29% accuracy, and orientation was predicted within a 2° range, which was comparable to other methods. The simulation efficiency of the statistical volume element model was improved 15 times over the traditional representative volume element models.

Al–Mg合金およびAl–Si合金におけるAE法を用いた凝固割れ発生の判断基準

Detection of solidification cracking of JIS AC7A aluminum alloy and Al–7%Si alloy was attempted by using acoustic emission method. In order to detect AE of solidification cracking, we investigated about AE signals of gas porosity, shrinkage cavity, and fracture in the semi-solid tensile test. The frequency bands of these casting defects were 150 kHz or less, so the source characterization of AE signals were difficult by that. Therefore we discussed and suggested value of integrated AE peak volt as an indicator of crack initiation. As a result, we proved value of time integral (IAP) is beneficial for eutectic alloy and value of temperature integral (TIAP) is beneficial for noneutectic alloy. We also suggested value of time temperature integral (DIAP) as the criterion of crack initiation which is beneficial for eutectic and non-eutectic alloy.

SM490鋼の弾塑性破壊じん性に及ぼす塑性ひずみの影響（応力破壊基準による検討）

SM490鋼の弾塑性破壊じん性に及ぼす塑性ひずみの影響（応力破壊基準による検討）

In-Situ Observation and Mechanical Criterion on Interface Cracking in Nano-Components

ABSTRACTWe have investigated the criterion of interfacial crack initiation in nanometer-scale components (nano-components) by means of a loading facility built in a transmission electron microscope (TEM). Three types of experiments are conducted in this project. (1) In order to clarify the applicability of conventional continuum mechanics to the nano-components, we prepare cantilever specimens with different size, which introduce different stress fields, containing an interface between a 20 nm-thick copper (Cu) thin film and a silicon (Si) substrate. These demonstrate the validity of the “stress” criterion even for the nano-scale fracture. (2) In order to examine the effect of microscopic structure on the mechanical property, we fabricate a bending specimen in the nano-scale with thin Cu bi-crystal (the thickness of about 100 nm) formed on Si substrate, of which understructure can be observed in situ by means of a TEM during the mechanical experiment. The initial plastic deformation takes place near the interface edge in a grain with a high critical resolved shear stress and expands preferentially in the grain. Then, the plasticity appears near the between Cu grain boundary and Cu/Si interface, and this development brings about the interfacial cracking from the junction. These indicate the governing influence of understructure on the mechanical property in the nano-components. (3) In order to investigate the fatigue behavior of metal in a nano-component, a cyclic bending experiment is carried out using nano-cantilever specimens with a 20 nm-thick Cu constrained by highly rigid materials (Si and SiN). The high strain region is in the size of 20-40 nm near the interface edge. The specimen breaks along the Cu/Si interface before the maximum load under the fatigue loading. The load-displacement curve shows nonlinear behavior and a distinct hysteresis loop, indicating plasticity in the Cu film. Reverse yielding appearing after the 2nd cycle suggests the development of a cyclic substructure in the Cu film. These indicate that the crack is caused by characteristic understructure owing to fatigue cycles.

Microstructural modeling of fatigue crack initiation in austenitic steel 304L

A methodology for modeling realistic microstructures of metallic polycrystalline material is presented. This approach is applied to the prediction of cyclic behavior of austenitic steel 304L in order to study the role of microstructural effects on fatigue crack initiation. The microscope observations show crack initiation and microcrack propagation are dependent on crystallographic orientations, indicating the need for such modeling approach. A representative volume of the material corresponding to a realistic microstructure, containing about 200 grains, has been numerically modeled with the crystal plasticity approach. This model takes account of dislocation densities on the 12 slip systems, isotropic and kinematic hardening, grain sizes, crystal orientations and elastic anisotropy. The material parameters used in this model were obtained through experimental measurements and the literature or identified through an inverse procedure, which give good predictions of stress- strain response at the macroscale. The field results of local strain, stress, slip-based and energy-based initiation metrics are simulated at grain scale. The results show that some of these metrics are in good agreements with experiments and can be used in fatigue crack initiation criteria.

Study on the Crack Initiation Criterion in Fretting Fatigue of LZ50 Steel

Fretting-fatigue often occurs at the contact area between two materials. There exist strong stress singularity exist at the contact edge, crack usually initiation at here. In this paper, the singular stress fields near the contact edge is obtained by using commercial code ABAQUS, then, the curve fitting method is used to determine the stress-singularity order and stress-strength parameter. Finally, the criterion of fretting-fatigue crack initiation in LZ50 steel is determined by using stress-strength parameters.

Frictional crack initiation and propagation analysis using the numerical manifold method

By employing both a physical mesh and a mathematical mesh to formulate a physical problem, the numerical manifold method (NMM) can lead to a very simple meshing task, which allows directly capturing the discontinuities across the crack surfaces without further incorporating unknowns to the related nodes through enrichment functions. These features enable the NMM to handle complex crack problems. In this study, based on the contact technique of the NMM and the incorporation of the Mohr–Coulomb crack initiation criterion, the effects of the friction and cohesion on the crack growth from a closed flaw (crack) under compression were investigated. A limited number of comparisons between the numerical results and the physical experiments show that with the Mohr–Coulomb crack initiation criterion, the NMM can not only accurately predict the pure tensile or pure shear crack growth, but the NMM can also satisfactorily predict the development of mixed shear–tensile crack types. Using a parametric analysis, the effects of the confining stress, the flaw inclination angle, the flaw friction angle and the material strengths on the crack development (crack initiation stress, crack initiation angle, crack type developed) have been investigated.

Crack propagation in multilayer thin-film structures of electronic packages using the peridynamic theory

This paper presents an application of the peridynamic theory to predict crack paths in multilayer thin-film structures of electronic packages. The peridynamic theory is a nonlocal continuum theory that has an inherent crack initiation and growth criterion. Specifically, the peridynamic theory is employed to model cross-sectional nanoindentation, an experimental technique used for characterizing interfacial adhesion and observing crack paths. Cross-sectional indentation experiments previously conducted on blanket and patterned thin-film structures were simulated. The predicted crack propagation paths in both blanket and patterned multilayer thin-film structures compare well with the results from cross-sectional nanoindentation experiments.

Modeling the Effects of Local Anodic Acidification on Stress Corrosion Cracking of Nickel

Abstract In the author's recent work, effects of pH, chlorides, and sulfides on local anodic acidification has been modeled by coupling electrochemical polarization and phase precipitation inside occluded cells of nickel and iron. In the present work, the model is experimentally verified and extended to demonstrate the capability of accumulated and reduced hydrogen ions to provide critical conditions for local hydrogen-assisted crack propagation. Based on experimentally determined crack critical hydrogen reduction charge densities and crack initiation strains from small scale slow strain rate testing (SSRT), the model explains quantitatively the effects of chlorides, hydrogen sulfide (H2S), pH, and global mechanical stress on cracking by hydrogen that is locally produced by ion reduction at the tip of an advancing anodic corrosion path. In particular, the known effects of pH, chlorides, and H2S on cracking of metallic materials applied in the oil and gas industry are reflected by the results of the calcul...

Deformation and fracture of materials near spheroidal inclusions

We have proposed a model of the deformation and fracture of an elastoplastic body with an elastic spheroidal inclusion. The problem has been reduced to the solution of an integro-differential equation, and its numeral solution has been obtained by the method of mechanical quadratures. Using the strain criterion of crack initiation in the neighborhood of an inclusion, we have established the main parameters affecting local fracture. The results of investigations are presented in the form of plots.

Finite element model of the contact between a vibrating conductor and a suspension clamp

Aeolian vibrations may lead to failure of the overhead conductors of electrical transmission lines. Damages are caused by fretting fatigue at the attachment position of pieces of hardware. This phenomenon depends much on contact mechanics. The contact between a wire and a suspension clamp, a critical location, was modelled using the finite element method. Results from strain measurements on vibrating conductors served as input. The numerical results gave estimates of stresses and slip amplitudes. We can use these results to compute crack initiation criteria. The Ruiz and Chen criterion was chosen here and results compared well with experimental data.

An energy-based microstructure model to account for fatigue scatter in polycrystals

Scatter observed in the fatigue response of a nickel-based superalloy, U720, is linked to the variability in the microstructure. Our approach is to model the energy of a persistent slip band (PSB) structure and use its stability with respect to dislocation motion as our failure criterion for fatigue crack initiation. The components that contribute to the energy of the PSB are identified, namely, the stress field resulting from the applied external forces, dislocation pile-ups, and work-hardening of the material is calculated at the continuum scale. Further, energies for dislocations creating slip in the matrix/precipitates, interacting with the GBs, and nucleating/agglomerating within the PSB are computed via molecular dynamics simulations. Through this methodology, fatigue life is predicted based on the energy of the PSB, which inherently accounts for the microstructure of the material. The present approach circumvents the introduction of uncertainty principles in material properties. It builds a framework based on mechanics of microstructure, and from this framework, we construct simulated microstructures based on the measured distributions of grain size, orientation, neighbor information, and grain boundary character, which allows us to calculate fatigue scatter using a deterministic approach. The uniqueness of the approach is that it avoids the large number of parameters prevalent in previous fatigue models. The predicted lives are in excellent agreement with the experimental data validating the model capabilities.

Processing of polymer-derived porous SiC body using allylhydridopolycarbosilane (AHPCS) and PMMA microbeads

A simple method for making a porous SiC body through a polymeric route at one firing processing was demonstrated by the sacrificial filler template approach. By incorporating sacrificial pore-forming plastic powder, PMMA microbeads, into liquid preceramic polymer, AHPCS, and losing it after the polymer was hardened, a preceramic porous body was formed. As a consequence of systematic examination of the effects of particle size and mixture ratio of the powder, an AHPCS-derived porous SiC body was reproducibly formed without critical crack initiation. It was enabled only when the polymer was sufficiently contained to make a strong skeletal structure with the sacrificial plastic particles closely distributed. The porous microstructure would contribute to efficient gas emission and uniform thermal shrinkage during polymer pyrolysis, which reduced internal pressure and crack-causing thermal stress.

Coupling of peridynamic theory and the finite element method

The finite element method is widely utilized for the numerical solution of structural problems. However, damage prediction using the finite element method can be very cumbersome because the derivatives of displacements are undefined at the discontinuities. In contrast, the peridynamic theory uses displacements rather than displacement derivatives in its formulation. Hence, peridynamic equations are valid everywhere, including discontinuities. Furthermore, the peridynamic theory does not require external criteria for crack initiation and propagation since material failure is invoked through the material response. However, the finite element method is numerically more efficient than the peridynamic theory. Hence, this study presents a method to couple the peridynamic theory and finite element analysis to take advantage of both methods. Peridynamics is used in the regions where failure is expected and the remaining regions are modeled utilizing the finite element method. Then, the present approach is demonstrated through a simple problem and predictions of the present approach are compared against both the peridynamic theory and finite element method. The damage simulation results for the present method are demonstrated by considering a plate with a circular cutout.