Crack Front Research Articles

Cracking time and prediction model of low-alloy steel reinforced seawater sea-sand concrete based on DIC technology

The cracking of seawater sea-sand concrete (SSC) cover due to the corrosion of low-alloy steel (LS) is a critical factor affecting its serviceability and durability. To analyze the cracking behavior of the SSC cover, a thick-walled cylinder model was developed in this study. The cylinder was divided into multiple coaxial rings of equal thickness, and damage variables were introduced to determine the extent of damage for each cracked ring based on the position of the rust expansion crack front. A predictive model for the cracking time of SSC cover was established by using the displacement compatibility equation at the interface of reinforcing steel and cover concrete, in combination with Faraday's law. To verify the accuracy of the model, the Digital Image Correlation (DIC) technique was utilized to determine the timings of two pivotal stages: the initial cracking and complete cracking of the cover. The comparison between the predictive outcomes and experimental results showed an error range of 4 %–10 %, indicating that the predictive model is relatively accurate.

Study of fatigue fracture characteristics for duplex stainless steel STHE welded joint specimen

A shell and tube heat exchanger (STHE) welded joint is considered for fatigue fracture mechanism. The joint is made up of a protruding tube fabricated to a tubesheet by means of welding. A super duplex stainless steel (DSS) material is used for the tube and tubesheet. Fatigue test was newly conducted using the single tube test specimen. The initial cracking plane was moved from the minimum sectional-area plane that was perpendicular to the loading direction, and the crack growth was almost planar. Stress analysis is carried out using finite element method (FEM) and the stress distributions are carefully studied by comparing the simple perforated plate. In addition, three-dimensional crack propagation (CP) simulation is performed employing extended finite element method (X-FEM). Fracture phenomenon is verified using the experimental and numerical crack front geometries. The fracture mechanics parameter is evaluated and verified with empirical formulae. CP behaviors are carefully discussed based on the fracture mechanics parameter. The CP life is presented for three loading amplitudes. The FAT class of the STHE welded joint is studied based on the available design standards such as BS, IIW and JSSC. Finally, the fatigue fracture characteristics of the STHE welded joint specimen are shown through the experimental and numerical methods.

Experimental analysis and modeling of subsurface cracks with random propagation for ceramic material on rolling contact fatigue

During the degradation of critical rotating components using ceramic materials, due to the uncertainty of the failure generation mechanism, the high nonlinearity of failure evolution and the diversity of failure modes, the unpredictability of sudden failure triggered by random propagation of subsurface cracks poses a great challenge to the operation and maintenance. Based on the finite element model reconstructed from fatigue tests, an early failure evolution model for ceramic bearings considering random propagation of subsurface cracks is constructed in this paper. Throughout the work, the position coordinates of critical nodes characterizing the degree of crack propagation (α, β, γ) are introduced to visualize the influence of propagation on the finite element of crack front during the whole rolling contact process, whose errors (ɛ) are stabilized at 10%. Then Monte Carlo Simulation is used to generate the randomness events of crack propagation, which satisfies the uncertainty characteristics of early failure initiation and propagation under actual working conditions. The results show that the first deflection shows strong randomness. Afterwards, the main cracks move away from the surface in mixed fracture mode, and finally form abrupt spall after several deflections. The proposed model not only reveals the sudden failure mechanism of ceramic bearing under uncertain crack propagation, but also effectively evaluates performance degradation of critical rotating components using ceramic materials.

Numerical Study of the Plastic Zone at the Crack Front in Cylindrical Aluminum Specimens Subjected to Tensile Loads.

Cylindrical specimens are of great interest in analyzing mechanical elements' behavior and investigating phenomena with biaxial loads. It is necessary to identify the behavior of the crack front along the thickness to interpret these results, which are usually based on the hypothesis of a straight crack and the observation of the outer face of the crack front. Based on the work carried out on compact tension type specimens, this work proposes adapting this methodology to cylindrical specimens, adapting the previous finite element models. Cylindrical specimens provide an asymmetric behavior influenced by the radius, where the CT (compact tensile) specimen can be considered the extreme infinite radius case. Combinations of the load level and radius values help us simulate the crack's behavior under intermediate hypotheses between a plane crack theory and a three-dimensional one. The plastic strain around the crack front will be analyzed as a function of the thickness and the load level applied. The results allow us to validate the numerical methodology and establish the differentiated behaviors of the plastic zones close to the outer and inner radii.

Isogeometric smooth crack-band model (isCBM) using spress–sprain relations adapted to microplane theory

Recent optimum fitting of the data from eleven different types of distinctive fracture tests of quasibrittle materials, including the gap tests and the size effect tests, revealed that the crack band model (CBM) with the M7 damage constitutive law outperforms all the other existing computational fracture models for concrete. This is attributed to physically correct boundary conditions, especially those at the crack faces,to the crack front of finite width which allows using a triaxial tensorial damage constitutive law, and to choosing for this law a realistic material behavior description, the M7. Nevertheless the CBM has limitations—the width of the crack band cannot be varied, the statistically smooth damage distribution across the band cannot be resolved, and the propagation direction is biased by the mesh orientation when a regular mesh is used. These limitations have been overcome by the smooth crack band model (sCBM), which uses unconventional homogenization of damage mechanics to yield an additional Helmholtz free energy density, called the “sprain energy”. This energy is a function of the curvature tensor (or a hessian) of the vectorial displacement field, called the “sprain curvature tensor” (or sprain tensor for brevity), which is a sum of the strain gradient tensor and, importantly, the rotation gradient tensor. But, in a previous study, difficulties arose in computational implementation—the use of constant-strain elements required the curvature to be resisted by sprain forces that represented the derivatives of sprain energy with respect to nodal displacements and had to be applied on the nodes of adjacent elements. The need for adjacent nodes is here avoided by a variational derivation of the Isogeometric Smooth Crack-Band Model (isCBM). The microplane damage constitutive model M7 for concrete is adopted, which is made possible by establishing the relations of the sprain stress (or spress, for brevity) and sprain on microplanes of arbitrary orientations. Using Isogeometric Analysis (IGA) based on non-uniform rational B-Splines (NURBS), the excessive displacement curvature and its resistance (spress) can be described by the shape functions with C1-continuity. Computational results show that the orientation bias of regular meshes is eliminated while keeping the constitutive law intact, which is important for compatibility with the existing material laws in general. In addition, comparisons with experimental data reveal that isCBM with M7 can reproduce the correspondence between the size of the fracture process zone and the fracture energy, as indicated by gap tests. Finally, the isCBM does not compromise the strain-path-dependence of material response.

A local surface roughness mapping method for post-failure interpretation of brittle fracture propagation

Tensile fractures in brittle materials may exhibit striation features running along the surface that indicate the trajectory of fracture propagation. Because of the directional persistence of these features, directional roughness characterization methods can be used on subsampled fracture surface data to map localized roughness features that follow these striations. These maps can aid in the interpretation of fracture initiation sites and crack front positions with the use of post-processing visualization techniques such as vector maps and streamlines. Tensile fractures in rock and synthetic rock analogues are used to demonstrate the various fracture propagation patterns that emerge following this analysis. This mapping method and streamline analysis can be further used to analyze elevation profiles that follow fracture propagation along non-linear paths which may inform about the mechanisms that can associate surface features with the fracture process.

Three-dimensional numerical study of thickness effect on plastic CTOD and monotonic plastic zone in an aluminium CT specimen

This work is a numerical study of CT specimens with straight cracks and different thickness values submitted to different load levels, which aims to analyse the shape and dimension variations of the monotonic yielded area near the crack tip, examining the impact of variables such as load magnitude, thickness of the specimen and position along the crack front. Additionally, it intends to explore the correlation between the size of the monotonic plastic zone and the plastic CTOD (Crack Tip Opening Displacement) to determine if a well-defined relationship exists. Furthermore, the impact of specimen thickness and load level on plastic CTOD will be explored. A complex plastic zone was found along the crack front, with the maximum area positioned at some distance from the crack front. A plane stress scale was determined considering the size of the equivalent bi-dimensional yielded area. When examining the behaviour across the thickness, no conclusive correlation was identified between the plastic CTOD and the monotonic yielded area. This suggests that utilising this parameter may not be appropriate for studies related to fatigue crack growth. However, when considering average values, a good correlation was found. The increase in thickness decreased the plastic CTOD values at the surface, while the interior values were unaffected.

On the role of vacancy-hydrogen complexes on dislocation nucleation and propagation in metals

New insights are provided into the role of vacancy-hydrogen (VaH) complexes, compared to the hydrogen atoms alone, on hydrogen embrittlement of nickel. The effect of the concentration of hydrogen atoms and VaH complexes is investigated in different crystal orientations on dislocation emission and propagation in single crystal of nickel using atomistic simulations. At first, embrittlement is studied on the basis of unstable and stable stacking fault energies as well as fracture energy to quantify the embrittlement ratio (unstable stacking fault energy/fracture energy). It is found that VaH complexes lead to high embrittlement compared to H atoms alone. Next, dislocation emission and propagation at pre-cracked single crystal crack-tip are investigated under Mode-I loading. Depending upon the elastic interaction energy and misfit volume, high local concentrations at the crack front lead to the formation of nickel-hydride and nickel-hydride with vacancies phases. These phases are shown to cause softening due to earlier and increased dislocation emission from the interface region. On the other hand, dislocation propagation under the random distribution of hydrogen atoms and VaH complexes at the crack front or along the slip plane shows that VaH complexes lead to hardening that corroborates well with the increased shear stresses observed along the slip plane. Further, VaH complexes lead to the disintegration of partial dislocation and a decrease in dislocation travel distance with respect to time. The softening during emission and hardening during propagation and disintegration of partial dislocation loops due to VaH complexes fit the experimental observations of various dislocation structures on fractured surfaces in the presence of hydrogen, as reported in literature.

Dynamics of crack front waves in three-dimensional material failure.

Crack front waves (FWs) are dynamic objects that propagate along moving crack fronts in three-dimensional (3D) materials. We study FW dynamics in the framework of a 3D phase-field platform that features a rate-dependent fracture energy Γ(v) (v is the crack propagation velocity) and intrinsic length scales, and quantitatively reproduces the high-speed oscillatory instability in the quasi-2D limit. We show that in-plane FWs feature a rather weak time dependence, with decay rate that increases with dΓ(v)/dv>0, and largely retain their properties upon FW-FW interactions, similarly to a related experimentally observed solitonic behavior. Driving in-plane FWs into the nonlinear regime, we find that they propagate slower than predicted by a linear perturbation theory. Finally, by introducing small out-of-plane symmetry-breaking perturbations, coupled in- and out-of-plane FWs are excited, but the out-of-plane component decays under pure tensile loading. Yet, including a small antiplane loading component gives rise to persistent coupled in- and out-of-plane FWs.

Numerical simulation and experimental verification of fatigue crack propagation in high-strength bolts based on fracture mechanics.

To investigate the fatigue crack propagation behavior of high-strength bolts for high-speed train brake discs, the fatigue crack propagation of high-strength bolts with initial defects under various load ratios was numerically simulated and experimentally verified based on fracture mechanics in this paper. Firstly, the fracture mechanics model of a three-dimensional hexahedral mesh with initial root defects was established using ABAQUS-FRANC3D interactive technology. Then the stress intensity factor (SIF) of the crack front was calculated by the stress superposition of the crack surface to simulate the coupling effect of preload and axial cyclic load. Based on it, fatigue crack propagation was simulated. Finally, the corresponding fatigue experiments on prefabricated crack bolts were carried out. The results show that mode I cracks dominate in the process of crack propagation. The stable crack propagation zones of the fractured high-strength bolts all show a semi-elliptical cross-section. The SIF of the crack front decreases with the increase of the load ratio, thus making the crack propagation life increase with the increase of the load ratio. The experimental outcomes are in great agreement with the simulation results, which verify that the numerical simulation method can effectively and accurately evaluate the fatigue life of high-strength bolts with initial defects and provides an effective means for predicting the fatigue crack propagation life of the same type high-strength bolts in engineering applications.

Enhancement of thermal shock resistance of Al2O3–MgAl2O4 composites by controlling the content and distribution of spinel phase

Herein, the Al2O3–MgAl2O4 composites were prepared using magnesite as variate and bauxite and alumina as main raw materials through a solid oxide reaction at 1500 °C. The content and distribution of MgAl2O4 on Al2O3–MgAl2O4 composites were adjusted with the aim of altering the microstructure and mechanical property, thereby enhancing their thermal shock resistance. The studies observed that by adding 5 wt% magnesite, a limited amount of MgAl2O4 particles can be generated, partially distributing on the microstructure; thus, the crack's propagation cannot be hinder with ease, which leads to a more limited residual strength ratio (68.97%). When 10 wt% of magnesite is added, the solid-solution (Mg1-xAl2x/3)Al2O4 is formed, and the apparent growth and wide distribution of spinel grains is induced, which pins the propagated front crack and enhances the toughening mechanism. The essential fracture path is altered from the predominantly transgranular mode to the mostly intergranular mode, and the residual strength ratio attains the highest value (94.36%).

Improved XFEM for 3D interfacial crack modeling

The conventional extended finite element method (XFEM) usually suffers from the crack tip enrichment for removing the blending elements. This may be inconvenient when treating the three dimensional (3D) and curved crack modeling since the crack tip enrichment is usually defined in the local coordinate system depending on the crack front. To avoid these shortcomings of the XFEM, an improved enrichment scheme is proposed for the 3D interfacial crack modeling. The proposed enrichment scheme removes the crack tip enrichment and two weight functions are introduced to capture the strong and weak discontinuities in the element including the crack front. The new enrichment scheme has advantages for the 3D curved interfacial cracks since all the enrichment functions are defined in the global system and it is unnecessary to introduce additional coordinate systems. Several benchmark problems including the mixed mode stress intensity factors (SIFs), anti-plane load and curved cracks are analyzed by the proposed method with the local refinement technology. Numerical results demonstrate that the proposed method can obtain accurate 3D energy release rate and SIFs. In addition, the proposed method enhances the applications of XFEM and has the potential abilities to the multiple-fields coupling and interfacial crack growth phenomena due to the fact that compatible enrichment functions are utilized.

Prediction of the durability of a plate with a through crack taking into account biaxial constraints of deformations along the front of a normal rupture crack

A methodology for evaluating the durability of plate elements of structures taking into account biaxial constraints of deformations along the front of a normal rupture crack (Mode I crack) is presented. The absence of the available literature data in which the prediction of the crack growth is carried out using Txx- and Tzz-stresses which are non-singular terms in the Williams expansion for stresses at the crack tip is noted. The calculation of the fatigue crack growth rate is based on the Paris equation in which the range of the effective SIF is used instead of the range of the usual stress intensity factor (SIF). In this case, the expression for the effective SIF includes Txx- and Tzz-stresses in addition to the usual SIF. This approach provides taking into account, for example, the thickness of the plate for predicting the durability, which is impossible when only the SIF and Txx-stresses are used. The formula for the effective SIF is derived proceeding from the assumption that tangential stresses in the pre-fracture zone are equal to the local strength of the material. In this case, the size of the pre-fracture zone and the local strength of the material are determined taking into account Txx- and Tzz-stresses. The numerical simulation is based on the proprietary finite-element program which allows calculating Txx- and Tzz-stresses at the front of a through crack in a plate subjected to cyclic uniaxial and biaxial tension. It is shown that nonsingular Txx-stresses primarily describe the effect of biaxial loading on the survivability, whereas Tzz-stresses describe the effect of the plate thickness on the survivability. It is shown that with increasing thic kness of the plate the value of the effective SIF increases due to the increased constraint along the crack front, thus increasing the crack growth rate and decreasing the survivability. With an increase in the stress ratio R, under the condition of a constant stress range, the maximum effective SIF reaches the critical value equal to the fracture toughness much faster thus reducing the durability. It is shown that for uniaxial cyclic tension, the durability predicted by the proposed methodology is higher than that in the classical approach, when the conventional SIF is used in the Paris equation. For biaxial cyclic tension of a plate, an increase in stresses directed parallel to the crack banks leads to an increase of crack front constraints and therefore to a decrease in the durability compared to the classical approach. In other words, the classical theory does not always provide a conservative estimate of the durability, which indicates the expediency of using the developed method for calculating the durability taking into account biaxial constraints of deformations along the crack front.

Numerical 3D‐bifurcation analysis of star‐shaped crack patterns using the energy method

AbstractThe present research deals with a three‐dimensional (3D) Finite Element Method (FEM) bifurcation analysis based on the global mechanical potential that can be used to find the parameters at which a crack pattern changes. In our case we want to analyze at which point the star‐shaped shrinkage cracks in an aqueous colloidal suspension filled in a glass cylinder change from four to three or two cracks growing. The driving force for the crack growth is shrinkage caused by diffusion controlled drying. The 3D crack front geometry is described efficiently by using a Fourier series approach. Based on steady‐state crack growth, the Fourier coefficients are determined in a first step using an optimization algorithm. As a result, the time dependent crack growth can be determined. In a second step, the bifurcation point is determined by an eigenvalue analysis of the second order derivatives of the potential energy of the system. If the lowest eigenvalue reaches zero the fundamental solution becomes unstable and a transition will occur. Our analysis shows that the transition from four to two cracks is preferred over the transition from four to three cracks.

Analytical prediction of fatigue resistance of additively manufactured aluminium alloy based on Murakami method

This research is devoted to analyze the stress state and fatigue strength of two specimens made by a newly developed high-strength aluminium alloy produced by the wire arc additive manufacturing (WAAM) process. The relationship between fatigue strength and flaw size was calculated based on the root squared area – a parameter by conventional Murakami’s equation which is a widely used analytical approach for predicting fatigue resistance in metallic materials. The research involves the metallographic preparation process on two aluminum alloy labeled HS-Al-A and HS-Al-B followed by Vickers hardness measurement. Further, the image of the observed pores was processed and dimensioned using an open-sourced software ImageJ by considering pixels and actual distance as well as by defining image threshold value for measuring pore sizes. The analytical approach is conducted in order to describe the maximum stress intensity factor Kmax at the crack front and to assess the fatigue strength σFS. As final results, specimen A has an average pore area of ≈65 µm with Kmax of 333.75 MPa∙√m and σFS of 137 MPa, while specimen B has an average pore area of ≈42 µm with Kmax of 325.13 MPa∙√m and σFS of 153 MPa. Overall, this research allows the formulation of a method for estimating fatigue strength of large defects leading to a conclusion that flaws can influence the fatigue resistance of the material so that the bigger the flaw size is, the lower σFS and the higher the Kmax.

Influence of heterogeneity due to toughness variations on weakest-link modeling for brittle failure

The effect of heterogeneous microstructures on the macroscopic probability of failure is studied by use of weakest-link modeling. Heterogeneity is here associated with a local variation of toughness, where a size scale characteristic of this variation defines a length parameter. The ratio between this length parameter and the size of the active fracture process zone, defined as the heterogeneity ratio, is key to evaluating the impact of a heterogeneous microstructure. Two extremes are identified; small-scale heterogeneity (SSH) and large-scale heterogeneity (LSH). For these cases, it is possible to formulate analytical expressions based on the weakest-link concept, and references are made to existing models in the literature. Typically, heterogeneity along the crack front, where gradients of the mechanical fields are small, falls under the category of SSH. On the other hand, the effect of heterogeneity in a plane perpendicular to the crack front depends strongly on the heterogeneity ratio. Cases that can neither be identified with SSH nor LSH must be addressed with care. How this can be done is discussed, and examples are given for four different microstructure configurations of interest. The investigation is carried out by numerical analysis of a modified boundary layer model. The cumulative probability of failure by cleavage fracture is evaluated in a post-processing step, where two different statistical models are examined; the Beremin model and the Kroon–Faleskog model. Both models render the same conclusion about the alteration of the overall failure probability distributions caused by heterogeneity.

A novel approach to compute the spatial gradients of enriching functions in the X-FEM with a hybrid representation of cracks

The eXtended Finite Element Method (X-FEM) is a versatile technique to model discontinuities by enriching the trial functions with a prior solution. In the X-FEM, a crack can be explicitly represented by a set of triangles or implicit signed distances, i.e., level set functions, of the points of interest from the crack surface and the crack front. In the explicit representations, it is crucial to accurately evaluate surface normal, conormal, and tangent vectors along crack fronts for computations of the gradients of the enriching functions. The solution is very sensitive to these directional vectors, especially for non-planar 3D cracks. We here propose a novel approach to compute these gradients without evaluating the directional vectors. Level set functions are first set up in a hexahedral grid independent of the background mesh in the X-FEM. We can thus implement the Weight Essentially Non-Oscillatory (WENO) scheme to compute the gradients of level sets. The gradients of the enriching functions at any integration point can therefore be computed by interpolations and chain rules. We compare the implementation procedures of the explicit representation and the proposed hybrid representation in detail. A three-dimensional lens crack problem is studied to demonstrate the accuracy of the proposed method, especially for coarse meshes.

Dynamic Crack-Front Deformations in Cohesive Materials.

Crack fronts deform due to heterogeneities, and inspecting these deformations can reveal local variations of material properties, and help predict out-of-plane damage. Current models neglect the influence of a finite dissipation length scale behind the crack tip, called the process zone size. The latter introduces scale effects in the deformation of the crack front, that are mitigated by the dynamics of the crack. We provide and numerically validate a theoretical framework for dynamic crack-front deformations in heterogeneous cohesive materials, a key step toward identifying the effective properties of a microstructure.

Micromechanics of cleavage fracture and the associated tongue formation in ferritic steel

The present work investigates the micro-mechanisms of cleavage fracture in a low carbon ferritic steel, subjected to Charpy impact test at low temperature. EBSD crack path analysis reveals {100} crystallographic plane as the predominant cleavage plane in ferrite, with occasional cracking along the secondary {110} cleavage plane. {110} cleavage cracking is particularly feasible when the {100} planes within a given grain exhibit significant twist angles with the preceding crack plane. Moreover, the fracture surface also exhibited numerous “tongue” like features that are intermittently aligned parallel to a common <110> crack front, as evidenced from the point EBSD analysis directly on the fracture surface. To illuminate the origin of such intermittent tongues, we performed molecular dynamics fracture simulation on a pure Fe single crystal, considering a (001) edge crack with a large [110] crack front. It was found that the development of intermittent tongues mainly originates from the intermittent nucleation of symmetric {112}<111> type twins across the entire crack front. Such intermittent twin nucleation results in a sinusoidal crack front, characterized by twin boundary cracking in one region and radial expansion of cleavage cracking in the adjacent regions, which can ultimately lead to the formation of tongues on the fracture surface. Finally, based on the simulation results and experimental observations, we propose a step by step mechanism that potentially explains the formation of intermittent tongues when a sufficiently large <110> straight crack front propagates along a {001} cleavage crack plane.

A novel correlation models for predicting stress intensity factor of semi-elliptical crack in welded pipelines under cyclic internal pressure based on Bézier base XIGA

Pipelines are strategic infrastructures that are used for energy transfer in the world. Cracks in the residual stress field are the common defects in welded pipelines. These defects with cyclic internal pressure cause crack growth and decrease the fatigue life of pipelines. In this study, a novel correlation model is proposed to predict the stress intensity factor (SIF) of the semi-elliptical crack front in welded steel pipeline subjected to cyclic internal pressure. For this purpose, the Bézier extraction base extended isogeometric method is applied for numerical analysis and preparing a database of results based on the thermo elastic-plastic equation. Taguchi standard L25 orthogonal array was used as the analysis design to create the simulations. New correlations were proposed for SIF prediction using the multivariate linear regression method. These correlations were obtained based on a parametric study that included three parameters. These parameters are dimensionless crack geometry (a/c), pipe geometry (D/t), and loading (P/Pb) or (σres/E). The R-Square (R2) values of the presented model for the welding residual stress and cyclic internal pressure were obtained as 0.989 and 0.992, respectively. The results of FEM analysis with similar conditions were compared to the results of XIGA and correlation models to validate the presented method. The maximum difference between them is approximately 3.71% for the cyclic internal pressure, and 2.94% for the welding residual stress. RMSD for the cyclic internal pressure model is 0.49, and for the welding residual stress model is 0.51. Therefore, the proposed correlation models have acceptable accuracy in predicting the SIF and fatigue crack propagation rate of the semi-elliptical crack in the steel pipes.