Dimensional Crack Research Articles

New crack front enrichment for XFEM modeling

The extended finite element method (XFEM) using a new crack front enrichment is proposed for the crack modeling in this study. The discontinuity of displacement in the element including the crack tip or front is modeled by combining the Heaviside function with a step function. The proposed enrichment scheme avoids the calculation of the geometrical characteristic lengths in the element containing the crack tip or front when using the Ramp function, and the step function only depending on the level set function is defined to activate the discontinuity. Thus, both two dimensional (2D) and three dimensional (3D) cracks can be modeled more effectively by the new crack front enrichment. The Conjunction Gradient Method (CGM) that can reduce the burden of storage and manipulation is utilized to solve the global linear algebraic system of 3D XFEM. In addition, two kinds of 3D variable-node elements are used to connect the coarse and fine elements to save the number of nodes and elements. The Westergaard’s crack problem is analyzed to test the convergence rate of the proposed method, and it is found that the new crack front enrichment can match the theoretical convergence rate of the finite element method (FEM) in the presence of a dominant r-singularity. The proposed method is applied to determine the stress intensity factors (SIFs) of straight, inclined, edge and curved cracks. Comparing with the reference solutions demonstrates that the proposed crack front enrichment exhibits significant advantages for the 3D crack modeling.

MEASURES TO IMPROVE THE EFFICIENCY OF HYDRAULIC FRACTURING AND SKIN FRACTURING

Due to the increasing problems of aging of the field, the annual increase in waterlogging, the decrease in the number of wells reaching the planned increase and the increase in the cost of additional measures, it is recommended to revise the number of hydraulic fracturing operations carried out in the downward direction. The article presents the selection of candidate wells of the rolling stock, when considering wells from drilling and immediately before hydraulic fracturing, recommendations for preparatory and final work are issued according to GIS conclusions. The data of the calculation of a 3-dimensional crack model, including the use of a variety of theoretical relationships to simplify computer calculations, and its results are presented. In an ordinary process, despite the large amount of data, some of their values cannot be obtained. It is suggested that the missing data should be supplemented with estimates, when selecting which you need to be extremely careful.

The influence of bending loading on surface fatigue crack growth life

Engineering structures often serve under complex fatigue loading and the most common of which are tension and bending loading, or their combination. Fatigue cracks always initiate as surface and other three dimensional (3D) cracks and most of the fatigue life of structures spends on 3D crack growth, but fatigue crack propagation curves of materials are widely obtained using through-the-thickness specimens. In this work, a 3D fracture mechanics based method is developed to evaluate surface crack propagation life under combined tension and bending loadings by considering the plasticity induced fatigue crack closure. The method is validated firstly against available experimental data of surface fatigue cracked plates under the combined loadings, and then applied to predict fatigue crack propagation life of surface cracked railway axles under rotating bending. It is shown that the method can make prediction of life within 0.80 to 1.08 of the test life, and the predicted shape evolution of surface crack agrees well with experimental observation. With a modification of short crack closure being made and an equivalent initial crack being assumed, the proposed method can be extended to fatigue life prediction. It is found that the influence of bending loading on fatigue life increasing for larger initial cracks, especially in the submillimeter range. This fracture mechanics based method can serve as a unified way to calculate fatigue crack growth life as well as fatigue life of practical structures under both tension and bending loadings by use of the material crack growth curves obtained with straight-through cracked standard specimens.

A new enrichment scheme for the interfacial crack modeling using the XFEM

A new enrichment scheme is proposed for the interfacial crack modeling in the framework of extended finite element method (XFEM), in which the approximation of displacement in the element including the crack tip is reconstructed by only the Heaviside function and the material interface enrichment function. The proposed enrichment scheme can model not only the discontinuity of displacement across the crack surface but also the discontinuity of displacement gradient across the material interface in the crack tip element with the weight functions. In addition, no blending elements are introduced and it is unnecessary to define the ramp function in the new XFEM formulation. The static and dynamic stress intensity factors (SIFs) of interfacial cracks are analyzed by the new enrichment scheme and the results show that the effect of material interface in the crack tip element plays a significant role in the accuracy of fracture mechanics parameters and the proposed method can predict the deformation more accurately and obtain a more stable dynamic SIFs. The proposed new enrichment scheme can be extended to three dimensional crack modeling in future works.

Unique continuation from a crack’s tip under Neumann boundary conditions

We derive local asymptotics of solutions to second order elliptic equations at the edge of a (N−1)-dimensional crack, with homogeneous Neumann boundary conditions prescribed on both sides of the crack. A combination of blow-up analysis and monotonicity arguments provides a classification of all possible asymptotic homogeneities of solutions at the crack’s tip, together with a strong unique continuation principle.

Investigation of two different size microplastic degradation ability of thermophilic bacteria using polyethylene polymers

There are several studies stating that many types of microplastics cannot be retained completely by conventional wastewater treatment systems. Therefore, it is necessary to prevent discharge of these microplastics to the ecological system. The objective of this study was to investigate the biodegradation ability of two different size of PE (50 and 150 µm) by using two Gram-positive, spore-forming, rod-shaped, and motile thermophilic bacteria, called strain Gecek4 and strain ST5, which can hydrolyze starch, were isolated from the soil’s samples of Gecek and Ömer hot-springs in Afyonkarahisar, Turkey, respectively. Phenotypic features and 16S rRNA analyzing of strains also studied. According to these results, Gecek4s and ST5 identified as Anoxybacillus flavithermus Gecek4s and Bacillus firmus ST5, respectively. Results showed that A. flavithermus Gecek4s can colonize the polymer surface and cause surface damage whereas B. firmus ST5 could not degrade bigger-sized particles efficiently. Moreover, morphological changes on microplastic surface were investigated by scanning electron microscopy (SEM) where dimensional changes, irregularities, crack, and/or holes were detected. This finding suggests that there is a high potential to develop an effective integrated method for plastic bags degradation by extracellular enzymes from bacteria.

On a new high order phase field model for brittle and cohesive fracture: numerical efficiency, length scale convergence and crack kinking

Being able to seamlessly deal with complex three dimensional crack patterns like branching and merging, phase field models (PFMs) are promising in the computational modelling of fracture of solids. Regarding the damage field, if only its second order derivative is present in the governing equation we have a second order PFM and if its fourth order derivative is also present we have a fourth order PFM. Previous studies have demonstrated that fourth order PFMs, with its smoother damage profile, are better in convergence and able to model strong anisotropic fracture energies. However, previous fourth order PFMs were developed only for brittle fracture and do not embed the material strength directly in the formulation. This paper presents a fourth order phase field regularised cohesive zone model (fourth order PF-CZM) for both brittle fracture and quasi-brittle fracture. We present a semi-analytical approach to compute the coefficients of the rational degradation function used in the fourth order PF-CZM. The proposed model is tested with multiple benchmark problems for mode I and mixed-mode fracture, and the results demonstrate that the fourth order PF-CZM: (1) provides results independent of the length scale and (2) is more efficient than its second order counterpart. The proposed model was then applied to modelling strong anisotropic fracture energies. A detailed study on sawtooth like crack patterns, which is a signature of strongly anisotropic fracture, is carried out with focus on periodicity and length scale sensitivity.

Industrial Thermal Insulation Properties above Sintering Temperatures.

Processing highly flammable products, the oil and gas (O&G) industry can experience major explosions and fires, which may expose pressurized equipment to high thermal loads. In 2020, oil fires occurred at two Norwegian O&G processing plants. To reduce the escalation risk, passive fire protection may serve as a consequence-reducing barrier. For heat or cold conservation, equipment and piping often require thermal insulation, which may offer some fire protection. In the present study, a representative thermal insulation (certified up to 700 °C) was examined with respect to dimensional changes and thermal transport properties after heat treatment to temperatures in the range of 700 °C to 1200 °C. Post heat treatment, the thermal conductivity of each test specimen was recorded at ambient temperature and up to 700 °C, which was the upper limit for the applied measurement method. Based on thermal transport theory for porous and/or amorphous materials, the thermal conductivity at the heat treatment temperature above 700 °C was estimated by extrapolation. The dimensional changes due to, e.g., sintering, were also analyzed. Empirical equations describing the thermal conductivity, the dimensional changes and possible crack formation were developed. It should be noted that the thermal insulation degradation, especially at temperatures approaching 1200 °C, is massive. Thus, future numerical modeling may be difficult above 1150 °C, due to abrupt changes in properties as well as crack development and crack tortuosity. However, if the thermal insulation is protected by a thin layer of more robust material, e.g., passive fire protection to keep the thermal insulation at temperatures below 1100 °C, future modeling seems promising.

An Improved Damage Mechanics Method for Solving Three Dimensional Crack Problems of Concrete

In this paper, a damage mechanical model is improved to simulate the three-dimensional (3D) mixed mode cracking process of quasi-brittle material such as concrete. The cracking and crack propagating in an element is reflected in the model by controlling the degraded stiffness matrix and the dissipated energy. The local tracking algorithm (LTA) is employed to preselect the element that will belong to the crack path to be damaged. The local tracking algorithm is extended to 3D by analyzing and overcoming defects in the previous 3D LTAs. The present LTA has very low computational cost and this fact is proved by comparison with well-known global tracking algorithm. The numerical results from the novel damage model added 3D local tracking algorithm show good agreement with the results of the previous researches, demonstrating the superior performance of the approach in predicting crack propagation and fracture strength.

Prediction of fatigue crack propagation in bulb-flat by experimental and numerical method

The fatigue crack propagation in the bulb-flat, which is widely used in ship and bridge engineer ing, is one of the basic parameters for structures'fatigue life prediction. In this paper, the shape of a three dimensional surface crack in full-scale bulb-flat was measured and estimated by Nominalization Crack Opening Displacement (NCOD) method. Then the obtained crack shape was used to predict the fatigue crack propagation in the bulb-flat based on the two dimensional Paris formula and the Linear Finite Element Analysis (LFEA) method. Finally, the predicted fatigue crack propagation was verified by the full-scale fa tigue test on a typical ship structure in detail. This method proposed in this paper may provide reference to the definition of failure criterion of bulb-flat.

Sensitivity of reliability-based fatigue analysis to crack shape development in cracked pipeline

An accurate prediction of crack shape development during fatigue propagation plays a key role in structural reliability assessment. To predict crack shape, aspect ratio variability (a/c; a: crack depth, c: half crack length) is wildly used and different correlations to estimate this later exist in literature. In this paper, reliability index of a pipeline with axially surface crack is evaluated. Initial aspect ratio was varied. Tow dimensional crack growth models based on Paris Law coupled to liner elastic fracture mechanics were used. The objective is to clarify the effect of initial aspect ratio and it variability during propagation on the life time prediction of cracked pipeline. Based on Importance sampling, reliability index is plotted against number of load cycle. Results show an important role of initial aspect ratio and crack growth model in reliability index estimation. Calculation of different sensitivity factors illustrates the effect of uncertainty and correlation of Paris law parameters on the predicted life time of the pipeline.

Multi‐field formulation of large deformation ductile fracture

AbstractIn the present contribution we focus on a novel computational framework for the simulation of ductile fracture in elastoplastic solids. In particular, a fully non‐linear formulation of gradient plasticity is applied together with a higher order phase‐field approach to fracture to account for large elastic and plastic deformations along with three dimensional crack propagation. The proposed formulation is based on a multiplicative decomposition of the deformation gradient into elastic and plastic contributions and a subsequent multiplicative decomposition of the elastic part into a fracture sensitive and a fracture insensitive contribution, see [1]. Postulating that fracture requires a local state of tensile/shear deformation, the latter decomposition is used to formulate the isochoric and tensile contributions to the elastic strain energy, whereas the compressive contribution remains unaffected by the crack phase‐field and vice versa. The modification of the Griffith brittle fracture theory to ductile fracture is most crucial and has to be adjusted carefully. Within our framework, this adaptation is considered as dependency of the critical fracture energy density by the equivalent plastic strain. Concerning the elastic/plastic decomposition, we assume an isochoric plastic flow which requires special attention for the update procedure of the plastic deformation. To be specific, we apply an exponential time integration scheme such that we preserve the deviatoric state of the plastic deformation and obtain a correct evaluation of the phase‐field driving force. Eventually, a number of numerical examples will demonstrate the accuracy and capability of the proposed multi‐field approach to ductile fracture.

Penentuan Kehilangan Kekangan dalam Medan Tiga-dimensi Hujung-retak Tiada-pengerasan

Analysis of crack tip stress field is important in determining of the integrity of structures under the influence of cracks and defects. Current techniques to analyze crack tip stress fields are based on two-dimensional approach and very conservative. Efforts to develop three-dimensional crack tip stress analysis methods have been inconclusive with various drawbacks. In this paper, the structure of three-dimensional crack tip fields has been examined under non-hardening condition which will allow a detail examination of crack tip stresses in the absence of strain hardening effects. Three-dimensional crack tip analysis is based on three-dimensional bend and tension cracked models. The fields along the crack front were examined as a function of load level, J, and thickness, x3/t. The results showed that at the crack tip (r = 0), a group of asymptotic fields develop which feature a constant stress sector directly ahead of the crack tip. Within this sector the fields differ hydrostatically while being similar in respect of the maximum stress deviator. From the behavior of the crack tip stresses, explicit expression of crack tip constraints are given for constraint loss in terms of maximum stresses due to out-of plane effects at θ=0° and along the crack front 0  x3/t  0.5. Significantly, the results showed that constraint based fracture mechanics can be extended to fully three dimensional crack tip fields.

Simulation implementation of trajectory and intersections of three-dimensional crack growths with displacement discontinuity method

This paper presents some detailed implementation schemes of geometrical evolution of three dimensional crack growth for most scenarios. These include growth of isolated cracks, intersections of crack growth with body surface or another crack at interior or at front edge. The schemes have been implemented in a crack growth simulator FRACOD3D, which is based on displacement discontinuity method (DDM) for stress analysis and implements the geometrical evolution of crack growth by explicitly adding new elements along the crack front. For growth of isolated cracks, there is no need to re-mesh the old part of cracks and thus no need to recalculate the related influence coefficients in the new growth steps. For intersection of growth of a crack with body surface or interior of another crack, minimum re-mesh on the body surface or on the other crack is used by just subdividing three elements. Simulations with early versions of the explicit schemes showed that implementation of the geometrical evolution is very challenging in that the growth could lead to very unsmooth crack and affects the further numerical simulations. Some examples show that the new schemes give smooth growth. It is noted that these schemes can also be employed with other stress analysis methods which represents crack growth by adding new elements along the crack front.

Bond-based peridynamic modelling of singular and nonsingular crack-tip fields

A static meshfree implementation of the bond-based peridynamics formulation for linearly elastic solids is applied to the study of the transition from local to nonlocal behavior of the stress and displacement fields in the vicinity of a crack front and other sources of stress concentration. The long-range nature of the interactions between material points that is intrinsic to and can be modulated within peridynamics enables the smooth transition from the square-root singular stress fields predicted by the classical (local) linear theory of elasticity, to the nonsingular fields associated with nonlocal theories. The accuracy of the peridynamics scheme and the transition from local to nonlocal behavior, which are dictated by the lattice spacing and micromodulus function, are assessed by performing an analysis of the boundary layer that surrounds the front of a two dimensional crack subjected to mode-I loading and of a cracked plate subjected to far-field tension.

Experimental, analytical and numerical analyses of constant and variable amplitude loadings in the very high cycle fatigue regime

Mechanical components often exceed a very high number of cycles in their fatigue life. Within the very high cycle fatigue (VHCF) regime, different damage mechanisms occur and the conventional fatigue limit is not valid any more, which has to be considered in a safety–relevant design. Especially in reference to operation loads or variable amplitude loading insufficient knowledge exists. Therefore, within the scope of this paper, the cumulative frequency distributions Felix/28 and WISPER are applied by blocks on a high strength steel by means of an ultrasonic fatigue testing system. The results are compared to those of constant amplitude loading at different stress ratios. Due to the variable amplitude loadings arrest marks are produced within the fish–eye surrounding the inclusion. The sizes and the area, where arrest marks are observable, as well as the spacings between the arrest marks are influenced by the different load sequences. By counting and measuring the arrest marks an average crack growth rate for the crack propagation within the fish eye can be calculated. For further studies a three–dimensional finite element model is created to work out the stress distribution surrounding internal inclusions or cavities and to compare the obtained stress intensity factors of a circumferential crack initiating at the imperfection with analytical solutions. Because VHCF failure is highly dependent on the type of the imperfection and also on the interaction to the surrounding matrix, the stiffness of the inclusion as well as the contact formulation between the matrix and the inclusion in the finite element model are modified. Finally, three–dimensional crack propagation simulations are performed to investigate the influence of crack closure behaviour and the mean stresses.

Three dimensional crack propagation through mesh-based explicit representation for arbitrarily shaped cracks using the extended finite element method

In this study a three-dimensional extended finite element modeling work is developed for crack propagation analysis of arbitrarily shaped crack(s) under mixed mode loading conditions. An explicit method is proposed for crack geometry characterizations, slicing of the enriched elements, and crack propagations. The method can be used to model multiple cracks propagation and allows for crack geometry transition from internal to surface, and further to through-thickness modalities under arbitrary loading conditions. Benchmark cases are studied and satisfactory agreement between theoretical and numerical results is observed. In addition, comparison between fully explicit and conventional implicit methods is made at different finite element mesh densities. The results show that compared to the conventional implicit method, there is a significant improvement in the obtained stress intensity factors for the fully explicit method at coarse linear hexahedral and quadratic tetrahedral meshes.

3次元平面き裂の拡大シミュレーション

3次元平面き裂の拡大シミュレーション

Fracture Analysis of Three Dimensional Elliptical Crack for Al7075-T651 Plate with Holes

Objectives: The paper deals with the study on analysis of Elliptical Crack for Al7075-T651 for three Dimensional Elliptical crack emanating from hole of the plate. Methods/Statistical Analysis: The impact of Crack shape and location with respect to various tensile loads on stress intensity factor is analysed. The crack in two holes of the plate is differentiated into different cases and they are analyzed for stress intensity factor. The crack case is formed with respect to the location of the through and part through crack in the model. Findings: The stress intensity factor of the crack geometry is attained by Ansys and the results are compared with Polynomial equation derived by displacement Extrapolation method. The paper also analyses the stress intensity factor along with parametric angle and Beta function of through elliptical crack model for various loads. Application/Improvements: The Stress Intensity factor value obtained can be used in finding the fatigue behaviour of materials under various loading conditions and improvements can be made by further improvement in the geometry of the plate.

Fracture propagation in brittle materials as a standard dissipative process: General theorems and crack tracking algorithms

The present work frames the problem of three-dimensional quasi-static crack propagation in brittle materials into the theory of standard dissipative processes. Variational formulations are stated. They characterize the three dimensional crack front “quasi-static velocity” as minimizer of constrained quadratic functionals. An implicit in time crack tracking algorithm that computationally handles the constraint via the penalty method algorithm is introduced and proof of concept is provided.