Cracked Body Research Articles

Novel cell-based smoothed extended finite element method for simulating the interactions of ultrasonic waves with randomly distributed cracks in solid structures

The conventional extended finite element method (XFEM) is a powerful tool for simulating crack-related problems in materials; however, several limitations exist, such as numerical instabilities and convergence issues. These problems arise because enriched elements have higher stiffness than standard elements, and this difference can cause computational difficulties. To overcome these limitations, we developed the cell-based smoothed extended finite element method (CS-XFEM), an advanced computational technique designed to simulate the intricate interactions between ultrasonic waves and randomly distributed cracks within solid materials. This innovative approach integrates a cell-based smoothing technique into the XFEM, effectively softening the stiffness of the enriched elements around crack tips. Therefore, the CS-XFEM eliminates numerical instability, providing a more stable and reliable computational framework. In this study, numerical experiments were conducted in which plasticity properties were assigned to both the crack bodies and tips to reflect crack yielding. Further, frictional contact in the crack body elements was formulated using the Heaviside function, and deformation around the crack tips was approximated using a singular function. Through comprehensive numerical investigations, we demonstrated that the conventional XFEM fails to converge and, instead, diverges when ultrasonic waves interact with randomly distributed cracks. By contrast, our proposed CS-XFEM method demonstrates strong convergence capabilities, rendering it well-suited for exploring the interactions between ultrasonic waves and randomly distributed cracks under varying crack quantities, lengths, and friction coefficients. Overall, the proposed CS-XFEM is an efficient, accurate, and robust method for investigating the acoustic nonlinearity induced by randomly distributed cracks with frictional contact in solid structures.

Misconception of the Use of 2D Plane Stress Solutions for Free Surfaces of Cracked Bodies and Its Significance for Full Field Measurement Techniques

Although 2D fracture mechanics solutions have been successfully applied, many analyses are affected by the wrong presumption of the 2D plane stress state at the free surface intersected by a crack front. The significance of this presumption and the related confusion have grown rapidly with the progress of strain field measurement techniques, such as the digital image correlation. The article demonstrates this wrong presumption on two of the most commonly measured and studied entities, which are the plastic zone in front of the crack tip and the crack tip opening displacement. 3D stress and strain solution is necessary to be performed. A realistic crack front curvature is required to be considered. Only such solutions can be used for comparison with the experimentally obtained strain fields. Other solutions are wrong and can bring confusion, wrong conclusions about material behavior, and slow down the progress in the field of fracture mechanics due to the incompatibility of the presumed stress state and the stress state present in experiments.

An Over-the-Counter Healing Ointment: Benefits in Dry Skin and Wound Healing.

The use of ointments can be beneficial for dry, chapped, or cracked skin and also for supporting wound healing. We describe the results of 2 studies with an over-the-counter healing ointment (HO) to evaluate the effects on skin hydration and in the setting of wound healing after dermatologic procedures.  Methods: Study 1 was a single-center, in-use study using HO on qualified areas at least once daily for 4 weeks in subjects with dry, cracked body skin and self-perceived sensitive skin. Study 2 was a multi-center study of wound healing in subjects using HO on a daily basis after having dermatologic surgical procedures.  Results: In Study 1, there was a significant reduction in skin dryness after 1 and 4 weeks of HO use (P<0.05). Image analysis of the skin revealed a significant increase in skin smoothness after the first application of HO in 100% of subjects (P<0.05). Tolerability and safety were excellent, and HO was well-perceived by subjects throughout the study. In Study 2, HO improved clinical assessments at all time points compared with baseline with a decrease in erythema, edema, scabbing/crusting, and an improvement in overall wound appearance (P<0.05). There was no worsening or significant increase in measures for tolerability parameters at any study visits. Additionally, HO achieved a favorable perception by study subjects.  Conclusions: HO has a well-established safety profile and has been shown to improve both skin hydration and the overall wound healing process after dermatologic surgical procedures. J Drugs Dermatol. 2024;23(5):360-365. doi:10.36849/JDD.8224.

Artificial neural networks-based J-integral prediction for cracked bodies under elasto-plastic deformation state –cyclic loading

The study builds upon a prior modeling framework designed for monotonic loading to compute the cyclic J-integral encompassing a crack tip experiencing elastic–plastic deformation due to cyclic loads. The proposed modeling approach extends the authors' earlier time-efficient method for computing the J-integral by combining artificial neural networks (ANNs) with finite element (FE) analyses. The ANN-FE integration allows efficient and accurate prediction of elastic–plastic stresses, strains and displacement fields for a crack body under cyclic loadings from the linear elastic FE solution. In the context of cyclic loading, stress, strain, and displacement fields near the crack tip of stainless steel (SS304) are determined by FE analyses under both elastic and elasto-plastic states for various crack sizes and R-ratios. ANNs models are developed to establish the nonlinear relationship between these two states. Consequently, the proposed approach enables the prediction of the elasto-plastic cyclic J-integral through the equivalent domain integral method, based on the elastic FE solution bypassing the need of a complicated elasto-plastic FE solution under cyclic loadings. The results show that this approach can effectively predict elasto-plastic cyclic J-integral while avoiding the complex computation of elastic–plastic deformation fields around the crack tip during cyclic loadings.

A novel fracture criterion for elastic‐brittle cracked body under compression and shear conditions

AbstractWhen the elastic‐brittle cracked body is subjected to compressive‐shear loading, not only does the phenomenon of wing crack initiation and propagation occur, but there is also a notable incidence of secondary crack initiation and propagation due to shear stress. Moreover, the shear fracture toughness (KIIc) predicted by the fracture criterion in the framework of classical fracture mechanics is usually smaller than the tensile fracture toughness (KIc), which is inconsistent with the actual observations. Therefore, this research firstly establishes a mechanical model of an elastic‐brittle cracked body under biaxial compression considering three kinds of crack parameters and materials' mechanical properties. Then, the stress field characteristics at the crack tip are analyzed. Next, a compression‐shear mixed fracture criterion is proposed. Finally, the effects of the lateral pressure coefficient (λ), critical plastic zone size (rc), friction coefficient (f), and deformation parameters of the crack surface on the failure modes at the crack tip are investigated.

Stress corrosion cracking of leaded brass used in oil temperature sensor of vehicle

In today’s modern age, many kinds of sensors are used in cars. Sensors used in automobiles monitor the performance of the entire vehicle. They are used to control and process oil, temperature, emission level, coolant level, etc. In vehicle engine, oil is pumped under high-pressure throughout the engine system to lubricate the engine parts that are in constant friction. By doing so, it also transfers away heat from these engine parts. As the oil travels around the motor, large amount of heat keeps being absorbed and transferred. It eventually reaches engine sump where it is cooled using a coolant, and then again recirculated through the engine. In this process, overheating of this oil can greatly affect its viscosity and reduce its efficiency, eventually causing performance issue of the engine. To prevent overheating, temperature oil sensors are used, that continuously send data to the Electronic Control Unit (ECU) then subsequently ECU adjusts and regulates the fuel quantity and ignition timing. Oil Temperature Sensors (OTS) usually consists of three parts: brass body, thermistor unit and a coupler unit. For continuous temperature monitoring, the brass body is continuously in contact with the engine oil that are based on sulphates and ammoniate, under high pressure and elevated temperature. In present study, we observed leakage failure in the brass body of OTS and conducted root cause failure analysis. The basic objective of failure analysis is to identify the overall damage mode like: mechanical overload, environmental degradation / corrosion, fatigue etc. and its type and root-cause leading to the failure and its understanding help to mitigate similar failures in near future. In the present work, the failed / cracked brass body material was analyzed by using Scanning Electron Microscopy attached with Energy Dispersive Spectroscopy for identifying mechanisms of corrosion failures in OTS brass body components is highlighted. Failure analysis of cracked brass body showed the Stress Corrosion Cracking (SCC) failure which is further confirmed by multiple crack branching and Intergranular (IG) fracture.

Dual boundary element method for comparative studies on fatigue crack growth models

Fatigue crack growth studies require models that accurately predict component life with low uncertainty. Despite the large number of proposed models, there is no clarity on their applicability, which justifies a comparative analysis between some of them. The dual boundary element method (DBEM) was applied for cracked bodies, whereby the stress intensity factors (SIF), the growth rate, and the number of cycles were computed. Three crack increment models were studied under constant amplitude fatigue loads: the Paris, the Klesnil-Lucas, and the Forman models. Results were validated with experimental literature and through the finite element method, indicating that each model represents a specific zone of the crack growth curve. Klesnil-Lucas model reproduces the region near the fracture threshold, Paris fits the controlled crack growth zone, whereas Forman’s model recreates the unstable fracture zone, i.e., when the stress intensity factor approaches the material’s fracture toughness. The J-integral with stress field decomposition gave errors below 0.8% for mode I. Results were similar for the propagation path and the number of cycles to those obtained with the finite element method, with errors of about 3% considering different K-effective approaches. Klesnil-Lucas accurately predicts the number of cycles with an error margin below 3%, considering the curved region in the growth rate at the propagation onset, while the Paris model becomes very conservative, predicting values up to 50% lower than experimental data. The Klesnil-Lukas model is advised for simulating the entire crack propagation.

Wave dispersion analysis and evaluation of dynamic stress intensity factors using peridynamics approach

The objective of this paper is to evaluate the dynamic stress intensity factors (DSIFs) of a cracked body using the bond-based peridynamics (BBPD) formulation. The peridynamics theory offers advantages over the classical continuum theory for solving partial differential equations in fracture mechanics. Nevertheless, some problems remain, such as its dispersion characteristics and constant micromodulus used in the classical BBPD. In this study, a Gaussian function is used to define the non-constant micromodulus. A wave dispersion analysis for a 1D problem was carried out and the influence of the horizon, mesh size and the kernel function on the dispersion properties were analyzed. On the other hand, a new approach to evaluate the DSIFs of a cracked body using the BBPD coupled with the displacement extrapolation technique is presented. Parameters that reduced the wave dispersion were kept for the DSIFs estimation. The proposed method is applied to analyze some benchmark examples. The obtained results are compared with the exact ones and they showed that the proposed approach can be used as an alternative method to evaluate DSIFs.

Modeling of contact interaction of crack banks based on finite element schemes

The problems of modeling the formation and propagation of cracks are relevant in a variety of applied fields: dynamics and strength of machines and mechanisms, mechanics of structural materials and structures, etc. When describing the fracture process, in addition to the fracture criteria, it is also important to correctly take into account changes in the rheology of the destroyed material, including the contact interaction between the surfaces of the cracks and fragments formed. This paper proposes a technique for calculating the stress-strain state of cracked bodies taking into account the contact interaction of crack banks in the normal direction. The technique is based on the transformation of a finite element grid with the introduction of double nodes, as well as an iterative algorithm for determining the contact zones of the crack banks. An example of calculating deformations of a shaft with a crack under the action of body weight at different angular positions of the shaft is given.

Mechanism of crack evolution and strength failure in chemo-mechanical induced fracture

Chemo-mechanical coupled fracture is ubiquitous among various application fields. Understanding the mechanism of crack propagation is critical to the prediction and control of fracture behavior. In this paper, mechanical damage and chemical erosion have been investigated by a combination of experiments and theoretical analysis. We developed a theoretical model to analyze the interface evolution and the mechanical state of the crack tip in chemically active environments based on the transition-state theory. This model enables us to predict mechanical failure and chemical corrosion of materials exposed to external acid attack. Theoretical predictions of the corrosion rate and fracture strength have been validated by fracture experiments performed in different concentrations of corrosive solutions. In particular, we discovered a non-monotonic and non-linear relationship between the degree of corrosion and fracture strength, which demonstrates that corrosion-induced crack tip blunting and mass loss of materials together affect the cracking critical state. We further conducted the thermodynamic analysis of a quasi-static cracked body to investigate the effect of corrosion on energy stored in the crack tip. Our theory-experiment-combined study reveals the mechanism of coupling chemical and mechanical damage and provides significant insight into corrosion-induced fracture behavior in aggressive environments.

A generalized finite difference method for 2D dynamic crack analysis

This paper presents a new framework for efficient and accurate analysis of transient elastodynamic cracks by using the generalized finite difference method (GFDM). The method first discretizes the solution domain into a set of overlapping small subdomains, and then in each of the subdomains, the unknown functions and their derivatives are approximated by using the local Taylor series expansions and moving-least square approximation. The degree of the Taylor series used in the local subdomain is increased automatically in the regions near the crack-tips, in order to appropriately describe the local asymptotic behavior of near-tip displacement and stress fields. The path-independent J-integral and sub-domain technique are adopted to compute the dynamic stress intensity factors (SIFs) of the cracked bodies. Preliminary numerical experiments for dynamic SIFs with both uniform and variable loading conditions are given to show the efficient and accuracy of the present method for transient elastodynamic crack analysis.

Study on multiple fatigue cracks growth in the web of a hollow compressor impeller

The fatigue crack growth characteristics of a hollow impeller whose thin-walled web has the propensity to nucleate multiple site damage (MSD) were investigated. To study its MSD crack growth, a simulation framework was proposed to accomplish noncoplanar crack coalescence and user-defined growth. It employed a modified linkup criterion and could account for the geometric constraints of cracked bodies, crack closure, and the kinking and twisting angle introduced by KII and KIII. Interaction features of the multisite crack growth were studied by simulating carefully designed cracking scenarios, and the crack cascade’s typical evolution over time and space was deduced. Results showed that larger adjacent cracks would introduce a stronger interaction effect. For crack colonies, the stress intensity factor would increase and remain higher between different merging positions. The crack growth was predominantly in tensile mode (greater than 95%) before coalescence, whereas the in-plane and out-of-plane shear modes increased noticeably to about 30% during and after coalescence. MSD will adversely affect the impeller fatigue evaluation due to faster crack growth, more complex crack profiles, and difficulty in determining the critical crack size due to the jump-like increase of crack colonies that makes applying damage tolerance difficult.

Partition-of-unity generalized node method based on isolated blocks for simulating multiple cracks

A partition-of-unity generalized node method (PUGNM) based on isolated blocks was developed to model multiple cracks. This study accommodates the extended finite element method (XFEM) and the numerical manifold method (NMM) within the same framework using the “path-connectivity” concept. In the PUGNM, (1) a cracked body is discretized by a structured square mesh; (2) the pre-assumed isolated blocks (or square elements) are partitioned into isolated sub-blocks by cracks and geometric boundaries; (3) the generalized nodes associated with each square node are defined on the isolated blocks; (4) the generalized nodes with actual independent deformations are obtained by merging all initial generalized nodes on the continuous blocks; (5) the displacement approximation based on the partition-of-unity (PU) method is constructed by a product of the standard quadrilateral finite element (FE) shape functions with the local functions associated with independently deformed generalized nodes. It was demonstrated that almost identical formulations can be derived for the classic XFEM, NMM, and PUGNM from the perspective of generalized nodes. Thus, construction of generalized nodes based on isolated blocks in the PUGNM is actually another implementation of the NMM based on the “path-connectivity” concept. The excellent numerical results show that the PUGNM can model multiple cracks.

Assessment of crack face contact using a weight function with application to fatigue crack growth in residual stress bearing bodies

This work develops a method to predict crack face contact under linear elastic conditions with application to fatigue crack growth in a residual stress bearing body. Residual stress changes the shape of the crack faces in a cracked body and can cause crack face contact that affects fatigue crack growth. Earlier work shows that the weight function can predict crack face shapes for applied or residual stress fields. The present work applies the weight function to compute a system of linear equations that can determine crack face contact pressure via quadratic programming. We validate the new method against the finite element method (FEM) in the context of fatigue crack growth in a single edge cracked beam having residual stress from prior elastic–plastic bending. The new method agrees with FEM over a range of crack sizes. Crack opening profiles agree when crack face contact is ignored (where the crack exhibits unrealistic over-closure) and when crack face contact is included. Stress intensity factors are also in agreement, comprising those due to applied loads, residual stress, and contact pressure. Being more efficient than FEM, the new crack face contract assessment method is useful for predicting residual stress effects in fatigue crack growth.

Analysis of near-interface cracks in three-dimensional anisotropic multi-materials by efficient BIEM

This paper presents the full analysis of near-interface cracks in three-dimensional linear elastic multimaterial bodies by a weakly singular boundary integral equation method (BIEM). The proposed technique was implemented in a general framework that allowed the treatment of finite cracked bodies with general configurations, material anisotropy, and mode-mixity. A system of integral equations governing unknown data on the boundary, crack surface, and material interface was established using a pair of weakly singular weak-form displacement and traction integral equations together with continuity along the material interface. A symmetric Galerkin boundary element method along with the finite element technique were implemented to solve the governing integral equations. In addition, the special near-front interpolation was employed to enhance the approximation of the relative crack-face displacement in the neighborhood of the crack front. The solved crack-face data were used directly to post-process the stress intensity factors and T-stresses along the crack front. An extensive numerical study was carried out not only to demonstrate the accuracy, convergence, and capability of the proposed technique, but also to explore the influence of material stiffness and distance to the material interface on fracture data along the crack front.

Analogy between Turbulent-to-Vortex Shedding Flow Transition in Fluids and Ductile-to-Brittle Failure Transition in Solids

By using complex potentials, some light is shed on the analogy between the singularity problems arising in fluid and fracture mechanics—in particular, those concerning plane irrotational flows around sharp obstacles and plane elasticity in cracked bodies. Applications to two equivalent geometries are shown: a thin plate transversally immersed in a uniform flow and a crack subjected to uniform out-of-plane shearing stress at infinity (Mode III). The matching between the fluid velocity field and the shearing stress field is consistent with the hydrodynamic analogy. Aside from the Reynolds criterion for the natural laminar-to-turbulent transition, a velocity-intensity factor criterion is defined to predict the forced turbulent-to-vortex-shedding fluid-flow transition (forced transitional flow) generated by a transversal plate obstacle. It is interesting to remark that the velocity-intensity factor presents physical dimensions intermediate between those of a velocity and a kinematic viscosity. In addition, it will be demonstrated that size affects the occurrence of natural-to-forced transitional phenomena in fluids, in a strict analogy to the scale-dependent ductile-to-brittle failure transitions in solids.

Analysis of Stress Intensity Factor of a Fibre Embedded in a Matrix

The analytical or numerical determination of the stress intensity factor (SIF) in cracked bodies usually assumes the body to be isolated. However, in fibre-reinforced composites, the fibre, which is the main load-carrying component, is embedded in a matrix. To clarify the effect the embedding matrix has on the SIF of the fibre, we propose a 3D computational model of an orthotropic fibre embedded in an isotropic matrix, and compute the SIF using the J-integral method. A parametric analysis based on dimensionless variables explores the effect of the fibre–matrix stiffness ratio as well as the effect of the degree of elastic orthotropy of the fibre. The results show that the SIF is strongly influenced by both factors, and that the matrix reduces the SIF by limiting the crack opening.

A review of mixed mode I-II fracture criteria and their applications in brittle or quasi-brittle fracture analysis

Fracture criteria play a very important role in predicting crack propagation behavior and life evaluation of cracked bodies. In this paper, mixed mode I-II fracture criteria in the framework of linear elastic fracture mechanics and their applications in brittle or quasi-brittle fracture analysis are systematically reviewed. Meanwhile, the advantages and shortcomings of these criteria are briefly discussed. Furthermore, the effects of T-stresses on brittle fracture characteristics are also studied and some suggestions are given to select appropriate fracture criteria. The results show that different types of fracture criteria differ greatly in predicting the crack propagation behavior, and a suitable criterion can be chosen according to the crack types, loading modes and failure characteristics. Tension-based fracture criteria are applicable for the opening cracks under tensile-based failure, but not for the closed cracks under shear-based failure. T-stresses around the crack tip have significant effects on crack initiation angle, fracture resistance and crack tip plastic zone, which should be introduced into the classical fracture criteria only determined by singular terms for providing more accurate predictions. Moreover, the variable fracture process zone radius can be further considered in these modified criteria considering stress intensity factors and T-stresses, which are not only suitable for brittle materials, but also for plastic materials under small scale yielding. This review will contribute to the development of mixed mode fracture criteria.

An extended Bueckner–Rice theory for arbitrary geometric perturbations of cracks

The aim of this paper is to define a new, simple and efficient method of solution of elasticity problems for 3D bodies containing cracks slightly perturbed out of their original plane or surface. This method extends that proposed by Rice (1985, 1989), from a re-formulation of Bueckner (1987)’s 3D weight function theory, for the treatment of coplanar crack perturbations. First, a general formula is derived for the variation of total energy of a cracked elastic body, resulting from some small but otherwise arbitrary geometric perturbation of the embedded crack(s). This formula, which involves integrals over both the front and the surface of the crack, is derived from an expression of deLorenzi (1982) and Destuynder et al. (1983) in the form of a volumic integral, originally limited to purely tangential crack perturbations but duly extended here to arbitrary perturbations having both tangential and normal components. It is then used to derive a general expression of the variation of displacement arising from a general perturbation of the crack(s), anywhere in the cracked body. The reasoning here basically follows the same lines as in the works of Rice (1985, 1989), but for the presence of an additional normal component of the crack perturbation. The possible use of the formalism developed to treat problems of out-of-plane, or out-of-surface perturbations of cracks is finally briefly evoked; the straightforwardness of the new method proposed is hoped to permit future applications to non-coplanar crack problems too complex to be accessible by more conventional methods.

Effect of constraint on cyclic plastic behaviours of cracked bodies and the establishment of unified constraint correlation

Constraint effect existing in the cracked structures plays a vital role in monotonic loading conditions and affects the material fracture behaviour, it is not clear whether the constraint affects the cyclic plastic responses in the cyclic loading condition. In this research, the laboratory compact tension (CT) and central-cracked tension (CCT) specimens with different in-plane and out-of-plane constraints were selected to explore the constraint effect on the ratchet limit and cyclic plastic behaviour numerically by the Linear Matching Method (LMM). The results show that the plastic shakedown load domain and low cycle fatigue (LCF) life are compressed dramatically by increasing the in-plane constraint effect, while the out-of-plane constraint effect elevates the capability to resist ratcheting failure. In addition, the ratcheting boundary of the cracked specimen is much more sensitive and vulnerable under the influence of the high in-plane constraint effect. Moreover, the unified constraint parameter Ap is suitable to measure the strength of compound constraint under cyclic loading conditions, and there is a salient linear relation between constraint parameter Ap and cyclic plastic responses (including ratchet limit and alternating plastic strain range) of the cracked specimen. This correlation is very meaningful for evaluating the ratchet limit and low cycle fatigue (LCF) life of cracked structures in terms of different levels of constraint conditions (including different in-plane, out-of-plane, and compound constraint conditions), where the constraint effect is calibrated based on the unified constraint parameter Ap.