Vicinity Of Crack Tip Research Articles

Viscous solvent effect on fracture of predamaged double-network gels examined by pre-notch and post-notch crack tests

Double network (DN) gels, composed of two interpenetrating polymer networks with contrasting properties, garnered considerable attention since their invention due to large resistances to crack initiation and propagation. This study systematically investigates the effect of viscous solvent on the fracture behavior of DN gels through pre-notch and post-notch crack tests conducted on both water-swollen and ethylene glycol (EG)-swollen DN gels. Fracture energy analysis reveals that the chain dynamics changed by viscous solvent EG would remarkably reduce the two individual fracture energy contributions Γbulk and Γtip, originating from the energy dissipation in the bulk and in the crack tip vicinity, respectively. Furthermore, we observed that chain dynamics influence crack propagation behaviors and the molecular orientation of network strands ahead of crack tips in DN gels. Examination of the retardation patterns ahead of propagating crack tips allows for the analysis of the molecular orientation of network strands. Unusual butterfly-like retardation patterns were observed for the EG-swollen DN gels, in stark contrast to the conventional damage zone patterns seen in water-swollen DN gels. This suggests that the slowed chain dynamics induced by the viscous solvent EG lead to significant viscoelastic mechanical responses ahead of crack tips, which governs the stress/strain fields at the crack tip. This study offers valuable insights into the underlying toughening mechanism of DN gels, particularly regarding the effect of polymer chain dynamics. The experimental analysis, integrating findings on fracture energy contributions, crack propagation behaviors, and retardation observations from both pre-notch and post-notch crack tests, could be applied to characterize other soft materials with diverse toughening mechanisms, thereby aiding in the design and application of future soft materials.

Crack propagation arrest by the Joule heating in micro/nano-sized structures

The Joule heating technique is utilized to arrest the crack propagation so to protect some important structures being further damaged. In this approach there are created compression stresses at the crack tip vicinity due to a specific temperature distribution induced by the electric current. The Joule heating is amulti-physical problem which is applied here to micro/nano-sized structures. The size-effects are considered for description of both the elastic and the thermal fields. The heat conduction can’t be well described by classical Fourier’s law in nano-sized structures. A novel gradient theory is developed in such structures adopting the size effect of heat conduction. Besides, the strain gradients and double stresses are introduced into the constitutive laws. Then, the governing equations are given by partial differential equations with order of derivatives being higher than in classical theory. The principle of virtual work is the base of weak formulation and derivation of the discretized finite element equations for ageneral 2d boundary value problem with cracks. The collocation mixed FEM with large strain gradients is developed for numerical solution, where the C0 continuous approximation is applied independently to displacements and strains and also to temperature and temperature gradients. Kinematic constraints between strains and displacements are satisfied by the collocation method at selected interior points. The collocation mixed FEM is applied to solve 2D crack problems with Joule heating.

Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation?

The analytical solution of an elliptic dielectric cavity in an infinite dielectric plate is taken as basis to investigate a Griffith crack problem which is obtained by letting the semi-minor axis tend towards zero. In the course of this, an erroneous conformal mapping, commonly employed in literature and correctly reproducing the electric field only in a part of the physical space, is rectified. Interpreting the elliptic interface as faces of a mechanically opened crack which is exposed to an oblique remote electric field, surface charges and electrostatic tractions are calculated. In contrast to the established capacitor analogy model, approximately yielding electric charge densities and Coulombic tractions from displacements and electric potentials in the undeformed crack configuration, the work at hand provides exact solutions accounting for different implications of the crack curvature and for the inclination of the electric field. Crack weight functions are finally used to calculate stress and electric displacement intensity factors. As turns out, the surface charges of the capacitor analogy represent an excellent substitute for the exact electric boundary conditions within a relevant range of parameters, whereas inaccurate Coulombic tractions in the vicinity of crack tips may lead to a significantly overestimated mode I stress intensity factor.

Influence of crack aperture and orientation on the uniaxial compressive behavior of rock

The pre-existing cracks with various geometric and physical properties significantly affect the mechanical behaviors of rock mass. In this study, uniaxial compressive tests are performed on numerical models of specimens containing a single pre-existing crack with different apertures and orientations based on PFC 2D to shed light on the impact of different crack apertures and orientations. The results reveal that the uniaxial peak strength and elastic modulus tend to decrease with increasing apertures, but they tend to increase with increasing inclination angles. Crack apertures can affect the stress intensity factor in the vicinity of the pre-existing crack tips, which further influences the crack initiation and crack type. Furthermore, shear cracks are more prone to occur in a pre-cracked specimen with a larger crack aperture and larger crack orientation. The crack initiation stress and strain initially show a slight decrease until the inclination angle reaches 45°, and then significantly increase with the further increase of angle from 45° to 90°. The microcracks occur earlier and easier when the inclination angle is 45°. As the inclination angle of the pre-existing crack increases, shear-sliding along the crack becomes more prominent, resulting in the formation of coplanar secondary cracks. The macro failure patterns switch from tensile failure to shear failure with increasing crack inclination angle, which is in good agreement with trend lines of displacement in the displacement field.

Joule heating analyses in electrically conductive micro/nano-sized structures

Joule heating is occurred in electrically conductive materials. In cracked structures with high concentration of electric current at the crack tip vicinity the Joule heating can be extremely high and even a melting of metal can be observed. It is interesting to investigate thermal stresses caused by this local heating. In micro/nano-sized structures the overheating of structures can be very fast and structure can be damaged. However, in these small structures it is observed the size effect for both heat transport and also for the mechanical balance equation. The thermal transport cannot be described by the classical Fourier’s equation in materials with an internal structure. For mechanical problem due to the size effect the strain gradients have to be considered in the constitutive equations. Then, governing equations for both problems are given by partial differential equations with order of derivatives being higher than in classical case. The collocation mixed FEM is developed here for this multi-physical problem. The present computational method is applied to some crack problem to illustrate compressive stresses at the crack tip vicinity, which are leading to the crack closure.

Configurational force method enables fracture assessment in soft materials

Configurational mechanics offers a framework for quantifying the tendency of defects to alter the material configuration. When applied to fracture mechanics, configurational forces can be used to quantify the propensity of cracks to propagate. An alternative, well-established approach involves analytical solutions for crack tip displacement fields. However, these solutions typically apply to a limited range of constitutive behaviors and oftentimes to the linear small strain regime. The ease of calculating configurational forces in a numerical Finite Element implementation, along with their applicability to soft fracture at large strains, motivates the study of their performance as a standalone fracture framework. In contrast to the majority of works that remain theoretical and numerical, our study includes a robust experimental approach to configurational forces at finite strains. We report tensile experiments on a soft elastomer with pre-cuts ante fracture initiation. In a first attempt to approach the J-integral via configurational forces, we explore the performance of the linear elastic fracture mechanics solutions on Pacman-shaped domains that reproduce the crack tip vicinity. Then, we implement the entire boundary value problem with three-dimensional simulations that replicate the empirical tensile deformation of the soft elastomer samples. Subsequently, the results are benchmarked against estimations of the J-integral obtained through a bespoke finite strain analytical crack tip solution. With the successful validation of the configurational force method at finite strains, we aim to establish a pipeline for the calculation of configurational forces in a standalone manner and circumventing the need for close-form analytical solutions.

Численное исследование направления роста трещины в квазихрупком материале в градиентном поле температуры

The elliptical crack growth in a quasi-brittle material located in a gradient field of temperature next to the melting temperature for the thermodynamic phases of the material is studied. The elastic properties of the material are assumed to have an obvious dependence on temperature. This is typical for materials located close to the melting point. To determine the direction of crack growth, a gradient strain criterion is introduced, which assumes crack growth from the point of maximum elastic strain of the material toward its minimum. Depending on the orientation of the crack axis relative to the direction of the temperature gradient, the crack retardation, the change of the crack growth direction, or the appearance of secondary lateral cracks in the vicinity of the main crack tip are possible. The calculated results and the admissibility of applying the introduced criterion have been successfully validated by an experiment with thermal fracture of freshwater ice blocks. As a result, the phenomena predicted by finite element calculations have also been discovered experimentally.

Comprehensive damage and deformation mechanisms during out-of-phase thermal mechanical fatigue of the fourth-generation single crystal superalloy

To shed light on the stability and reliability of the fourth-generation single crystal (SX) superalloy during in-service operation, out-of-phase (OP)- thermal mechanical fatigue (TMF) experiments were systematically carried out. The TMF behavior, deformation and damage mechanisms were thoroughly investigated. The results showed that at comparatively low strain ranges (0.5% and 0.6%), the dislocation movements were basically concentrated in γ matrix and the TMF life was basically governed by high-temperature oxidation. More locally, the fatigue cracks initiated from the spalling of surface oxides, while the discontinuous Al2O3 layer could only provide limited protective resistance to crack propagation. Additionally, deformation twins could nucleate in the vicinity of micropores or crack tips, which further induced more complex defects and accelerated the fatigue fracture of the alloy. Nevertheless, as the strain range reached 0.8% and 0.9%, the nucleation and extension of micro-twins were independent on the defects, the mechanisms of twinning-shearing and anti-phase boundary (APB)-shearing were observed throughout the specimen. Under these conditions, the fatigue cracks basically initiated from the severe plastic deformation, which resulted in the much-reduced TMF life of the specimen. Ultimately, salutary guidance for the further application of fourth-generation SX superalloys was rationally summarized.

Toughening two dimensional materials through lattice disorder

Carbon-based two-dimensional (2D) materials, with graphene being the most prominent example, are some of the strongest materials existing today due to their covalent bonding but at the same time also the most fragile, with fracture toughness close to that of an ideally brittle solid, due to their intrinsic lack of effective dissipation mechanisms. Here, by investigating fracture mechanisms in monolayer amorphous carbon (MAC), we reveal a novel strategy to toughen 2D materials through lattice disorder. It is shown that lattice disorder results in rippling which can alleviate stress concentration in the vicinity of crack-tips and render MAC flaw tolerant. Consequently, MAC outperforms graphene in resisting brittle fracture and endures larger strain to failure in the presence of a preexisting crack. Our work sheds light on the mechanisms of crack propagation in MAC and also suggests that it might be generally possible to design tough 2D materials through lattice disorder.

Influence of flexoelectricity on interface crack problems under a dynamic load

In the present paper, the influence of flexoelectricity on behavior of the interface crack between two dissimilar dielectric materials under a dynamic mechanical load is investigated. The induced electric field affects the distribution and evolution of mechanical fields in dielectric materials. Large strain gradients induce the electric polarization in the direct flexoelectricity. Due to the large strain gradients at the crack tip vicinity it is needed to consider the strain gradient theory model. Governing equations in this theory contain higher-order derivatives than in the conventional continuum mechanics approach. The mixed finite element method (FEM) is developed here for a general boundary value problem, where the standard C0 continuous finite elements are applied for independent approximations of displacements and strains. The constraints between them are satisfied by collocation at appropriate internal points in elements. Interface cracks are observed in layered structures frequently due to a poor adhesion of layers. The incorporation of flexoelectricity and micro-inertial effects is needed into the failure analysis of interface cracks in nano-sized structures under dynamic loading. In numerical examples, we discuss the influence of flexoelectricity coefficients as well as the ratio of elastic coefficients and the geometrical size to microstructural (micro-stiffness and micro-inertia) length scale parameters of the bilayer composite on the crack opening displacement, stresses ahead the crack tip and induced electric intensity vector.

An extended multiphase hybrid-stress finite element method for modelling interface crack propagation between two dissimilar materials

In this work, an extended multiphase hybrid-stress finite element method (X-MHSFEM) is developed to investigate the stress intensity factor, kinking angle, and propagation path of an interface crack. Further, we have simulated the propagation of the interface crack by using the X-MHSFEM. Several types of element models containing the interface and matrix cracks are introduced in the propagation process of the interface crack. The derivation of the functional of the element containing the two materials, one interface, and all types of cracks, is performed. Stress functions are enriched by the asymptotic singular items that accounts for the oscillatory behavior to describe the stress concentration in the vicinity of the interface crack-tip, and the stress concentration near the matrix crack-tip are also captured by inserting certain singular stress terms of Williams expansion into the physical field of whole model. The stress intensity factors of the tips of the interface and matrix cracks are calculated by the least square method. The maximum and relative maximum circumferential stress criterion are employed as the fracture criteria for predicting the interface crack propagation along the interface or the deflection into layers. Further, the matrix crack propagation angle within the layers is determined by the maximum energy release rate criterion. A remeshing algorithm is employed to implement the propagation of the interface and matrix cracks. The effectiveness and accuracy of the present method are validated by comparing the results, obtained by the new method, with the experimental observation and other numerical results. Therefore, the extended multiphase hybrid-stress finite element method can provide an effective medium to deal with the interface crack fracture problems.

白色X線応力測定法の基礎と応用

The X-ray diffraction method has been already established as one of the most effective nondestructive evaluation method of a stress in crystalline materials. Since white X-ray beam has a wide wavelength range, a diffraction angle has to fix during a measurement to obtain a lattice spacing using the Bragg’s low. Therefore, the white X-ray method has some different features from the characteristic X-ray method. For example, the information of lattice spacing of many lattice planes in a material can be obtained simultaneously on the same diffraction angle. Because all equipment are held fixed position during a measurement, it is advantageous to in-situ measurement under the special environment such as high temperature or high pressure. In the present review article, a brief history of development of the white X-ray method is covered and some factors related to the measurement accuracy is explained. Fundamentals of the measurement system using white X-ray and the energy dispersive method are presented. Applications of the method using white X-ray obtained from a rotating target type X-ray generator to the measurement of residual stress of a surface ground material and a coating material are described. Furthermore, applications of the method using high energy white X-ray generated in the synchrotron radiation facility SPring-8 to the measurement of internal strain of a material loaded by four-point bending and strain distribution in the vicinity of crack tip in a material introduced a fatigue crack are also described.

Emergent failure transition of pearlitic steel at extremely high strain rates

It is a common wisdom that metallic materials become brittle once being deformed quickly. However, here we reveal an abnormal strain-rate-induced brittle-ductile-delamination transition in a widely used pearlitic steel with unique structure of alternative arrangement of nanoscale ductile ferrite and brittle cementite through extensive molecular dynamics simulations. In contrast to the brittle cleavage fracture in conventional crystalline alloys, the brittle fracture in pearlitic steel at relatively low strain rate is mediated by the nanoscale cavitation ahead of crack tip, akin to the widely observed fracture mode in metallic glasses. As the strain rate increases, fracture mode transforms to a dislocation nucleation mediated ductile mechanism. At extremely high strain rate, it is found that the fracture mode turns to be collective delamination at the interfaces, leading to a surprising “delamination toughening”. The abnormal brittle-to-ductile transition with increasing deformation rate is physically rationalized by a mechanistic model, which is based on a scenario of energetic competition between the interface cleavage and the dislocation nucleation in the vicinity of crack tip. Once the strain rate exceeds a critical value, fracture transitions to dislocation nucleation dominated. When strain rate increases to extremely high values, there is no enough time for either crack propagation or dislocation nucleation, and the collective delamination of interfaces occurs which involves only instantaneous bond breaking at weakly bonded regions, i.e. the interface. The unravelled phenomenon challenges the conventional knowledge of materials deformation and failure which might shed light on coordinating unanticipated utilities of the ultrastrong pearlitic steels in extreme environments.

Regularities of plastic deformation development in the crack tip vicinity

When determining the service life of cyclically loaded metal structures at the stage of fatigue crack development, an important role is played by the accuracy of assessing the plastic deformation zone size at the crack tip formed by the tensile overload. Within this zone, after reducing the load to the initial level, the fatigue crack development slows down. Despite the large number of studies in this area, none of the proposed dependencies is currently fully confirmed by experimental results in determining the plasticity zone size. The aim of the work is to assess the size of the plastic deformation zone formed by a single tensile overload. In the work of the finite element method for central-notch specimens and compact tension specimens, an analysis of the stress-strain state in the crack top vicinity is performed. As a calculation, a flat and three-dimensional model was used. Calculations are performed in the Ansys 14.0. Data on the mechanical properties of steels were used: St20, VSt3sp, 09G2S, 15G2SF. With increasing load, the plastic zone size in front of the crack tip was estimated, in the process of reduction, the distribution and length of the fields of residual compressive stresses and the size of the cyclic plastic zone were recorded, the length of which was also determined experimentally using strain gauges with a base of 0.5 mm. To assess the plastic zone size formed by a single tensile overload, a dependence is proposed that takes into account the patterns of plastic deformation development in the vicinity of the fatigue crack tip, and the results of the calculation agree well with the experimental data given in the literature. The obtained expression makes it possible to predict with greater reliability the development of fatigue cracks at variable load amplitudes.

Artificial neural networks-based [formula omitted]-integral prediction for cracked bodies under elasto-plastic deformation state –monotonic loading

Artificial neural networks (ANNs) integrated with a finite element (FE)-based equivalent domain integral method are developed to compute J-integral at the vicinity of crack tips through a time-efficient approach. Robust ANN models are trained to establish nonlinear relationships between FE predicted elastic and elasto-plastic stress, strain, and displacement fields of stainless steel (SS304). Subsequently, elastic–plastic J-integral can be determined by using only elastic FE analysis solution rather than computationally expensive elasto-plastic FE analysis solution. The results show that well-trained ANN models can efficiently and accurately determine J-integral around the crack tips on the basis of numerical elastic FE analysis solution.

Fracture propagation based on meshless method and energy release rate criterion extended to the Double Cantilever Beam adhesive joint test

In this work, a numerical methodology based on a meshless technique is proposed to predict the fracture propagation in Double Cantilever Beam (DCB) adhesive joints. The Radial Point Interpolation Method (RPIM) is used to approximate the field variable at each crack increment step. The meshless method permits a flexible discretization of the problem domain in a set of unstructured field nodes and eases the implementation of the geometric crack propagation algorithm. Regarding the fracture propagation algorithm, a recent adaptative remeshing technique is used combined with the RPIM. The crack tip is explicitly propagated by locally remeshing the field nodes and triangular integration cells in the crack tip vicinity. To predict the crack initiation, a fracture mechanics criterion based on the energy release rate in DCB is implemented. The proposed numerical methodology is validated with experimental data.

Mode III analysis of a piezoelectric rectangular plane weakened by multiple cracks and cavities

This study presents an analytical model for a piezoelectric rectangular plane weakened by multiple cracks and cavities, under in-plane electric displacement and anti-plane shear stress. The defects are considered either electrically permeable or impermeable. First, the piezoelectric rectangular plane is weakened by a Volterra-type screw dislocation. The electric and stress displacement fields of the domain under consideration are determined using finite Fourier transform. Then, the problem is reduced into a set of Cauchy integral equations in the piezoelectric rectangular plane using the distributed dislocation approach. The solution to these integral equations determines electric displacement and stress intensity factors and hoop stress around cavities in the piezoelectric rectangular plane. Also, the boundary of the plastic zone is found using the stress field in the vicinity of crack tips and the Von Mises yield criterion. Finally, multiple numerical results are provided to illustrate the capability of the dislocation method in handling different cases of crack and cavity configurations and arrangements.

The Effect of Sintering Temperature on the Phase Composition, Microstructure, and Mechanical Properties of Yttria-Stabilized Zirconia.

It is known that the yttria-stabilized zirconia (YSZ) material has superior thermal, mechanical, and electrical properties. This material is used for manufacturing products and components of air heaters, hydrogen reformers, cracking furnaces, fired heaters, etc. This work is aimed at searching for the optimal sintering mode of YSZ ceramics that provides a high crack growth resistance. Beam specimens of ZrO2 ceramics doped with 6, 7, and 8 mol% Y2O3 (hereinafter: 6YSZ, 7YSZ, and 8YSZ) were prepared using a conventional sintering technique. Four sintering temperatures (1450 °C, 1500 °C, 1550 °C, and 1600 °C) were used for the 6YSZ series and two sintering temperatures (1550 °C and 1600 °C) were used for the 7YSZ and 8YSZ series. The series of sintered specimens were ground and polished to reach a good surface quality. Several mechanical tests of the materials were performed, namely, the microhardness test, fracture toughness test by the indentation method, and single-edge notch beam (SENB) test under three-point bending. Based on XRD analysis, the phase balance (percentages of tetragonal, cubic, and monoclinic ZrO2 phases) of each composition was substantiated. The morphology of the fracture surfaces of specimens after both the fracture toughness tests was studied in relation to the mechanical behavior of the specimens and the microstructure of corresponding materials. SEM-EDX analysis was used for microstructural characterization. It was found that both the yttria percentage and sintering temperature affect the mechanical behavior of the ceramics. Optimal chemical composition and sintering temperature were determined for the studied series of ceramics. The maximum transformation toughening effect was revealed for ZrO2-6 mol% Y2O3 ceramics during indentation. However, in the case of a SENB test, the maximum transformation toughening effect in the crack tip vicinity was found in ZrO2-7 mol% Y2O3 ceramics. The conditions for obtaining YSZ ceramics with high fracture toughness are discussed.

Model description of hydrogen-induced damage evolution in high-strength steel weld metal based on results of a novel test method

In this paper, the development of a novel method for testing welded tensile specimens under two-stage external tensile loading is presented. The test method is intended to investigate the susceptibility of submerged arc welded high-strength steel specimens of type S690QL-S3Ni2.5CrMo to hydrogen-induced damage. Multiple cracking events within one specimen prove that the locally prevailing boundary conditions decisively determine the hydrogen-induced damage sequences.By means of SEM and EBSD analyses on specimens after test completion, interrelationships about the microstructural damage behavior are being examined. The crack tip environments are of particular importance here, since complex stress and strain conditions tend to cause hydrogen accumulation and further propagation of inter- and transgranular cracks here. In the vicinity of crack tips, retained austenite is of special importance. This metastable phase might undergo a deformation-induced transformation into crack-sensitive martensite and simultaneously release high local hydrogen contents as a former hydrogen trap. Finally, a model description including various sections of the stress- and hydrogen-induced damage evolution is derived from the empirical-analytical results.

Fatigue crack propagation behavior of a micro-bainitic TRIP steel

Controlling the grain size of steels is an effective way for tailoring their mechanical properties, such as yield strength, impact toughness, and ductility. In this study, a new industrial thermomechanical treatment was applied to a low-alloyed TRIP-assisted bainitic steel 13MnSiCr7 to achieve a substantial microstructural refinement. In this way the average grain size of the new micro-bainitic steel was decreased from ∼25 μm to ∼5 μm. Fatigue tests were carried out in order to investigate the influence of this new thermomechanical treatment on crack propagation behavior. Besides electron backscatter diffraction (EBSD), vibrating sample magnetometry (VSM), and high-energy synchrotron X-ray diffraction (HEXRD) were used to study the microstructure in the vicinity of the fatigue crack tip. The applicability of each method for detecting the martensitic transformation is discussed. In addition, the contribution of the martensitic transformation to fracture toughness was assessed on the basis of the results obtained by HEXRD.