Crack Problems Research Articles

An Experimental Investigation on Durability Properties of Fiber Reinforced Concrete for M25 Grade

In modern years Fibre reinforced concrete is cement based composite material has been developed. It has been successfully used in construction with its outstanding flexural tensile strength, resistance to splitting, impact resistance and outstanding permeability and frost resistance. It is a successful way to raise toughness, shock resistance and resistance to plastic shrinkage cracking of the mortar. Fibre is added as a reinforcing material possessing certain characteristic properties. Concrete is the most extensively used structural material in the world with an yearly production of over seven billion tons. For a multiplicity of reasons, much of this concrete is cracked. The reason for concrete to undergo cracking may be endorsed to structural, ecological or economic factors, but most of the cracks are formed due to the natural weakness of the material to resist tensile forces. Concrete normally shrinks and force crack when it is controlled. It is now well-known that steel fibre reinforcement offers a solution to the problem of cracking by making concrete tougher and more yielding. It has also been proved by wide investigation and field tests carried out over the past three decades. The present investigation focuses on introduction of steel, glass, carbon fibres, Polyvinyalcohol (PVA) fibres, of polypropylene fibres at the time of mixing and production improves a number of properties of concrete, particularly those related to strength, performance and durability. This review paper is an evaluative report of studies established in the recent years. It describes and gives an Experimental basis for the research.

Thermoelastic fracture of two-dimensional hexagonal quasicrystal media weakened by a penny-shaped crack subjected to uniformly antisymmetric heat fluxes

This study focuses on the thermoelastic fracture behavior of quasicrystals, a class of solids that exhibit unique properties between traditional crystals and amorphous materials. The complex atomic structure of quasicrystals poses challenges in understanding their fracture mechanisms under thermoelastic loading conditions. Central to our investigation is an analytical examination of a penny-shaped crack in an infinite three-dimensional body composed of two-dimensional hexagonal quasicrystals, where the upper and lower crack surfaces are applied to a pair of uniformly antisymmetric heat fluxes. This crack problem requires simultaneous consideration of thermal-phason-phonon multiple field coupling. According to the symmetry of field variables with respect to the crack plane, the thermal-phason-phonon coupled crack problem is transformed into a mixed boundary value problem in the upper half space. The extended displacement discontinuities, encompassing both phonon and phason displacement discontinuities, as well as the temperature discontinuity, are chosen as the basic unknown variables to construct the boundary integral-differential equations governing the mixed boundary value problem. Based on these boundary governing equations and Fabrikant's potential theory method, the problem with the crack surface subjected to uniform antisymmetric heat fluxes is solved. The solutions of thermal-phason-phonon fields on the crack plane, and in the full space are given in closed-form. Numerical results are employed to validate the obtained analytical solutions and visually illustrate the spatial distribution of thermal-phonon-phason coupling fields in the vicinity of the crack. The study provides fundamental insights into the behavior of cracks in quasicrystals under thermal loading, with potential implications for the design of new materials and structures.

Full field crack solutions in anti-plane flexoelectricity

In flexoelectric materials, strain gradients can induce electrical polarization. However, internal defects such as cracks profoundly affect the electromechanical coupling properties of flexoelectric solids. In particular, anti-plane cracks involve less physical fields, which are easier to study. In this study, we present a comprehensive and innovative investigation of the anti-plane crack problems in flexoelectric materials, including semi-infinite and finite-length anti-plane cracks. For the first time, we formulate a full-field solution for semi-infinite anti-plane cracks in flexoelectric media by applying the Wiener–Hopf technique. Furthermore, the collocation method and the Chebyshev polynomial expansion are used for the first time to derive the full-field hypersingular integral equation solution for finite-length anti-plane cracks in flexoelectric solids. In addition, a comparative analysis between the full-field and asymptotic solutions for semi-infinite cracks is performed, shedding light on the discrepancies in the representation of the electromechanical coupling behavior near the crack tip. The mixed finite element method is used to compare with the full-field solutions of finite-length cracks. The agreement between the numerical results and the full-field solutions demonstrates the rigor of our study. This research advances the knowledge of defects in flexoelectricity and provides significant insight into relevant failure mechanisms.

Mixed finite element implementation of plane crack problems within strain gradient elasticity

AbstractAn approach is proposed and applied to solve boundary value problems within the strain gradient elasticity theory. A mixed variation formulation of the finite element method is used, where stresses, strains, and displacements are considered as independent variables. This significantly simplifies the pre‐requirement for approximating functions and allows one to use the simplest triangular finite elements with a linear approximation of displacements. Global unknowns in a discrete problem are nodal displacements, while the strains and stresses in nodes are treated as local unknowns. This discrete problem is solved by a modified iteration procedure, where the global stiffness matrix for classical elasticity problems is treated as a preconditioning matrix with fictitious elastic moduli. The modeling plane crack problem (tension of a square plate with a central crack) is solved. The obtained solution agrees with the results available in the literature. Good convergence is achieved by refining the mesh for all scale parameters.

Multi-objective optimization design for anti-fatigue lightweight of dump truck carriage combined with machine learning

As urbanization continues to accelerate, dump trucks assume an increasingly important role in the transportation and construction of infrastructure. The carriage represents a critical structural assembly of dump trucks. One of the primary failure modes of the carriage is weld fatigue failure, which frequently gives rise to the problem of weld fatigue cracking during transportation. To increase the fatigue life of welds and enhance the degree of structural lightweight of a heavy dump truck carriage, a method for anti-fatigue lightweight design based on machine learning and multi-objective optimization is proposed. A high-fidelity finite element model of the carriage is established for static simulation analysis of the typical conditions. Based on the virtual reliability simulation test of the dump truck and the equivalent structural stress method, the fatigue life of the critical welds in the carriage is calculated. The important part thicknesses are selected as design variables through the comprehensive contribution analysis method. The maximum displacement and maximum stress under the dangerous condition are considered as constraints. The mass of the carriage and the minimum fatigue life of the critical welds are considered as optimization objectives. The GA-XGBoost machine learning approximation models (GA-XGBoost-MLAM) and NSGA-II algorithm are employed for multi-objective optimization design of the carriage. The entropy weighted TOPSIS method is utilized for multi-objective decision-making of Pareto solutions. The design after optimization and decision-making shows that, while satisfying the requirements of static structural performance, the minimum fatigue life mileage of the critical welds of the carriage is increased by 157,570 km, representing an increase of 36.58%. Additionally, the mass of the carriage is reduced by 295.69 kg, representing a decrease of 9.47%. Therefore, the proposed design method achieves a good effect in the anti-fatigue lightweight of dump truck carriage.

Properties and hydration mechanism of slow-setting and expansive cement based on CFB ash and slag

Aiming at the problems of long construction time and easy shrinkage cracking of pavement base, the slow-setting and expansive cement (SEC) was prepared using circulating fluidized bed ash and slag (CFBA and CFBS), S95 ground granulated blast furnace slag (GGBFS), and silica fume (SF) as supplementary cementitious material in this paper. By adjusting the content of supplementary cementitious material, the ratio of ash and slag, the performance of SEC was evaluated by the indexes of water consumption of standard consistency, setting time, flexural and compressive strength. The hydration products of mortar samples and the influence mechanism were studied by means of XRD, TG-DTG, FTIR, and SEM-EDS. The results showed that when the SF content was 6 %, the compressive strength of the mortar specimens reached its maximum (35.19 MPa) at 28 days, which increased by 23.04 % compared to the control group. Meanwhile, the free calcium oxide and gypsum in CFBA reacted under alkaline conditions to form ettringite (AFt) and C-S-H gel, which caused the volume expansion of cement and led to a decrease in shrinkage within the cement system. SEC has higher mechanical properties and much smaller shrinkage cracks than ordinary cement. Therefore, replacing part of the cement by solid waste such as CFBS to prepare SEC to compensate for the shrinkage of the pavement base is an effective way to reduce pavement cracking.

Analytical solutions to Mode I penny-shaped crack problems in two-dimensional hexagonal quasicrystals with piezoelectric effect

The paper studies a penny-shaped crack in an infinite three-dimensional body of two-dimensional hexagonal quasicrystal media with piezoelectric effect. The crack surfaces are applied combined electric and normal phonon loadings. Such a Model I crack problem is transformed into a mixed boundary value problem in the upper half-space, which is analytically solved using Fabrikant's potential theory method. The boundary integral-differential equations governing Model I crack problems are presented for two-dimensional hexagonal piezoelectric quasicrystals. The normal phonon displacement discontinuity and electric potential discontinuity across crack surfaces are taken as the unknown variables of boundary governing equations. Analytical solutions of all field variables are derived not only for the crack plane but also for the full space. Solutions in integral form are provided for the penny-shaped crack under arbitrarily distributed electric and normal phonon loadings. Closed-form solutions in terms of elementary functions are given for concentrated point loadings and uniformly distributed loadings, respectively. Key fracture mechanics parameters, such as crack surface extended displacements (i.e., normal phonon displacement, electric potential), crack tip extended stresses (i.e., normal phonon stress, electric displacement) distribution, and corresponding extended stress intensity factors, are clearly derived. Numerical results are utilized to verify the present analytical solutions and graphically illustrate the distribution of phonon-phason-electric coupling fields around the crack. The present solution can serve as a benchmark for both experimental and numerical investigations.

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.

Numerical solution for the interior electric displacement of the moving DBY‐PS model for semi‐permeable cracked piezoelectric material

AbstractIn this study, we analysed a moving crack at the interface of an infinitely long piezoelectric bilayer using the Dugdale–Barenblatt yield (DBY) model and the polarisation saturation (PS) model. To model the moving crack problem, a Yoffe‐type crack moves at a constant subsonic speed on the interface of an infinitely long piezoelectric bilayer. The crack faces are assumed to be semi‐permeable, and at the boundary of the bilayer, in‐plane electrical and out‐of‐plane mechanical stresses are applied. Due to the application of electro‐mechanical loads, cracks propagate, mechanical yielding zones and electric saturation zones are developed. To arrest the crack from further propagation, mechanical yield stress and saturation electric displacement are applied at the developed zones. To address this problem analytically and numerically, the mixed boundary value problem is transformed into a set of coupled Fredholm integral equations (FIEs) of the second kind using the Fourier transform and the Copson method. The closed‐form analytical expressions for the length of the electrical saturation zone (ESZ), whether longer, shorter or equal to the mechanical yielding zone (MYZ), show dependence on external electro‐mechanical loads under semi‐permeable crack conditions. The algorithm to solve the electric crack condition parameter (ECCP) has been defined using numerical discretization and the bisection method. Illustrative examples demonstrate the proposed technique's effectiveness and suitability for Yoffe‐type moving cracks. The numerical results show the convergence of the ECCP. Furthermore, the numerical results show how mechanical and electrical zone lengths and energy release rate (ERR) are affected by electrical and mechanical loads, strip thickness and crack velocity. In addition, the size of the mechanical yielding zone is consistently promoted by electrical load, while the promotion or prevention of the electrical saturation zone by mechanical load depends on the relative sizes of the nonlinear zones.

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.

A combined displacement discontinuity-interaction integral method for computing stress intensity factors and T-stress

In this paper, the displacement discontinuity method (DDM) is combined with interaction integral to simultaneously evaluate stress intensity factors and T-stress for analyzing two-dimensional mixed-mode crack problems. The displacement discontinuity method has been proved to be one of the most efficient boundary element methods for solving crack problems with boundary-only discretization character. However, there is a lack of efficient methods collaborating with the displacement discontinuity method to evaluate fracture parameters. The available geometrical extrapolation method and J-integral technique for calculating fracture parameters in combination with the displacement discontinuity method are imprecise and difficult to be implemented into mixed-mode crack analysis. The present combined displacement discontinuity method and interaction integral approach can easily extract stress intensity factors and T-stress for mixed-mode crack problems without needing any decomposition of elastic field into symmetric and antisymmetric components. The fundamental basis lies in introducing auxiliary fields for the proper defined single mode crack, then calculating fracture parameters by evaluating the formulated interaction integral in terms of displacement discontinuity solutions and auxiliary elastic fields. In this paper, the basis of the displacement discontinuity method is illustrated firstly, then the explicit expressions for auxiliary fields of displacement gradients are derived. Next, the interaction integral can be determined by being converted to an equivalent area integral. Finally, several numerical examples are examined to demonstrate the correctness of the present method.

Corrosion-Induced Cracking Model of Concrete Considering a Transverse Constraint.

The performance of corrosion-induced cracking of reinforced concrete members under transverse constraints was studied. Based on the theory of elastic-plastic mechanics and the hypothesis of uniform corrosion of a steel bar, a three-layer hollow cylinder model was established to predict the critical corrosion of the steel bar at the time of the cracking of the concrete cover. Taking the constraint of stirrups on surrounding concrete into consideration, it can be used to predict the corrosion rate of members with stirrups at the time of the cracking of the concrete cover, which further expands the application range of the corrosion-induced cracking models of concrete. On this basis, the critical corrosion rate of concrete under different stirrup ratios at the time of cracking was measured. The calculated results of the model are in accordance with experimental data. For corner steel bars, when the stirrup spacing is less than 100 mm, the existence of stirrups can effectively delay the occurrence of rust expansion cracks and enhance the durability of the structure. On the basis of this study, the problem of corrosion expansion and cracking of the concrete cover caused by non-uniform corrosion of steel bars along longitudinal and radial directions needs to be further studied in the future.

Numerical Simulation and ANN Prediction of Crack Problems within Corrosion Defects.

Buried pipelines are widely used, so it is necessary to analyze and study their fracture characteristics. The locations of corrosion defects on the pipe are more susceptible to fracture under the influence of internal pressure generated during material transportation. In the open literature, a large number of studies have been conducted on the failure pressure or residual strength of corroded pipelines. On this basis, this study conducts a fracture analysis on buried pipelines with corrosion areas under seismic loads. The extended finite element method was used to model and analyze the buried pipeline under seismic load, and it was found that the stress value at the crack tip was maximum when the circumferential angle of the crack was near 5° in the corrosion area. The changes in the stress field at the crack tip in the corrosion zone of the pipeline under different loads were compared. Based on the BP algorithm, a neural network model that can predict the stress field at the pipe crack tip is established. The neural network is trained using numerical model data, and a prediction model with a prediction error of less than 10% is constructed. The crack tip characteristics were further studied using the BP neural network model, and it was determined that the tip stress fluctuation range is between 450 MPa and 500 MPa. The neural network model is optimized based on the GA algorithm, which solves the problem of convergence difficulties and improves the prediction accuracy. According to the prediction results, it is found that when the internal pressure increases, the corrosion depth will significantly affect the crack tip stress field. The maximum error of the optimized neural network is 5.32%. The calculation data of the optimized neural network model were compared with the calculation data of other models, and it was determined that GA-BPNN has better adaptability in this research problem.

Methods and means of ensuring the accuracy of bending deformation measurements of connecting pipe between the VVER reactor and the steam generator in the conditions of a fuel campaign

The welded joint zone (WJ) No. 111 is a welding unit for the "hot" collector of the primary coolant to the DN1200 steam generator nozzle. The experience of operation of steam generators PGV-1000M of NPP power units with VVER-1000 shows that the WJ zone No. 111 is prone to the formation and development of operational defects. According to the results of periodic non-destructive testing of the WJ No. 111 zone performed at the PG of various power units of the VVER-1000 NPP, cases of detection of extended planar-type discontinuities, including through ones, were repeatedly recorded. Thus, this zone is one of the most critical zones of the reactor plant (RU) with VVER -1000. The root cause of the formation and development of operational defects has not yet been identified. Solving the problem of cracking of WJ No. 111 steam generators of nuclear power plants with VVER-1000 is one of the priority areas for improving the safety of operation of the power unit during the over-design service life. This problem is determined by a complex combination of temperature conditions, mechanical and corrosive effects, is relevant and has not yet been definitively solved. Therefore, it is very important to ensure the collection of reliable data on the actual stress-strain state of the WJ No. 111 zone in various operating modes (pressure loading of steam generators, heating/cooling of the power unit, hydraulic testing of the 1st and 2nd circuits). The article reveals the approaches and stages of creating and applying a strain gauge installation to ensure metrological suitability in the conditions of a campaign fuel company at an NPP power unit by using an adequate physical model to obtain additive and multiplicative correction coefficients.

Susceptibility of a Fe-Mn-Al-Ni-Cr shape memory alloy to environment-assisted corrosion cracking

In recent years, iron-based shape memory alloys (SMAs) have become increasingly interesting for application in civil engineering structures. Promising candidates in the field are iron-based Fe-Mn-Al-Ni-X (X = Ti, Cr) SMAs. These alloys have demonstrated the potential to be used in various types of applications. While the fully recoverable martensitic phase transformation can be used for structures where high damping capacities are required, i.e. for high rise buildings in earthquake prone areas, it has been successfully demonstrated that the material can also be used as prestressing element in concrete structures. However, for the application in civil engineering structures the problem of stress corrosion cracking and environment-assisted cracking has to be considered. The simultaneous occurrence of tensile stresses and unfavorable environmental conditions, such as carbonation of concrete or the penetration of salt, can lead to spontaneous failure of the building structure. In the present study, the susceptibility of Fe-Mn-Al-Ni-Cr to stress corrosion cracking was studied in neutral chloride containing solutions. For that purpose, tensile tests under constant load control at different stress levels have been conducted. The pitting corrosion that occurred during immersion in the electrolytic solution has a decisive influence on the martensitic phase transformation and the crack evolution. The high density of dislocations at the martensite-to-austenite interfaces promotes the formation of transgranular cracks as well as stress-induced corrosion cracks originating from corrosion pits. Assessment of the fracture surfaces revealed dominating intergranular crack growth, most likely induced by hydrogen embrittlement. The detrimental mechanisms lead to failure of the specimens well before the targeted test time of 1000 h.

Determination of Temperature Stresses during the Construction of Massive Monolithic Foundation Slabs, Taking into Account the Subgrade Compliance

Background The problem of early cracking caused by the heat of concrete hardening is relevant for massive reinforced concrete structures, including foundation slabs. The purpose of this work is to develop the methodology for determining temperature stresses during the construction of foundation slabs, taking into account the interaction with the subgrade. Methods The Pasternak elastic foundation model with two-bed coefficients is used for the soil. The temperature of the foundation slab is considered a function of only one coordinate z (temperature changes only along the thickness of the slab). As a result, to determine the stress-strain state of the slab, a fourth-order differential equation for deflection was obtained. A technique for numerically solving the resulting equation using the finite difference method is proposed. The calculation of the stress-strain state is preceded by the calculation of the temperature field, which is performed by the finite element method in a simplified one-dimensional formulation. Results The solution to the test problem is presented for a constant modulus of elasticity of concrete over time. The results were compared with finite element calculations in a three-dimensional formulation in the ASNYS software. The calculation was also performed taking into account the dependence of the mechanical characteristics of concrete on its degree of maturity. In this case, the picture of the stress-strain state changes significantly. The proposed method was also successfully tested on experimental data. Conclusion The proposed approach can significantly save calculation time compared to the finite element analysis in a three-dimensional setting.

Plastic deformation mechanism of TA1 pure titanium plate using SEM-EBSD in-situ tensile testing

As the core component of proton exchange membrane fuel cell (PEMFC), pure titanium bipolar plate has been faced with cracking and thinning problems in the forming process. It is considered that the stamping and tensile deformation of the bipolar plate have similar stress states. In this paper, the plastic deformation mechanism of TA1 pure titanium plate is analyzed from the aspects of twin, texture evolution and dislocation slip by in-situ tensile combined with SEM/EBSD. During tensile deformation, a large number of dislocation slips occur inside α grain, and obvious slip traces are produced on the surface of the sample. Within grains with different crystallographic orientations, the degree and direction of the trace are different, which leads to the increased disharmony between grains. Especially in the triple junction of grain boundary, soft/hard orientation grain junction and other deformation disharmony locations are easy to crack. The tensile deformation causes obvious changes in the texture, and the initial strong bimodal texture becomes weak bimodal texture. This phenomenon is explained by intragranular misorientation, crystal rotation and twins. The main mechanism of tensile deformation of titanium plate is slip and twinning. A large number of {11–22}<11-2-3> compression twins are formed due to most c-axis bearing compressive stress. The types of initiating slip systems are different in different stages. The cylindrical slip system is preferentially activated and occupies a dominant position before yielding, which is conducive to the plastic forming of the plate. After yielding, the start-up ratio of the pyramidal slip system is increased due to the deflection of the observed surface of sample during tensile process, which improves the deformation resistance of the thin plate.

Fracturing pump head body failure analysis and improvement measures

The head body of fracturing pump is one of the most easily damaged parts in fracturing equipment. Due to its own structure and working environment, it is easy to cause stress concentration, fatigue cracking and other problems. The working time of a batch of fracturing pump head body used in an oilfield is more than 300 h, and the pump head body is designed by the manufacturer for the oilfield.In this paper, the five-cylinder fracturing pump head body of this batch of cracking occurred as the research object. Firstly, the macro fracture analysis, physical and chemical properties analysis and micro fracture analysis were carried out at the cracking place. Secondly, the finite element analysis and fatigue life analysis were carried out by using ANSYS Workbench software and nCode software to explore the cause of pump head cracking failure. The results show that the crack originates from the sharp corner of the outer corner and spreads to the inner cavity. The chemical composition and mechanical properties of the pump head meet the requirements of the technical agreement. The grain size of the material does not meet the requirements of the technical agreement. The primary fracture morphology observed is indicative of fatigue streaking, while stress concentration can be identified at the location of this crack. There are two reasons for the cracking. First, the structure design is unreasonable and there is a large stress concentration at the cracking location. Second, the grain size of the material is large, resulting in a significant reduction in fatigue life, which is mainly related to the chemical composition of the material, forging process and heat treatment process, and ultimately lead to the pump head body cracking at the outside right Angle shoulder, expanding to the inner cavity, and cracking. According to the analysis results, the improvement measures of pump head body can improve the stress distribution and relieve fatigue. The results can provide a reference for the structural design and optimization of the pump head body.

Dynamic Thermal Response of Multiple Interface Cracks between a Half-Plane and a Coating Layer under General Transient Temperature Loading.

This paper explores the thermal behavior of multiple interface cracks situated between a half-plane and a thermal coating layer when subjected to transient thermal loading. The temperature distribution is analyzed using the hyperbolic heat conduction theory. In this model, cracks are represented as arrays of thermal dislocations, with densities calculated via Fourier and Laplace transformations. The methodology involves determining the temperature gradient within the uncracked region, and these calculations contribute to formulating a singular integral equation specific to the crack problem. This equation is subsequently utilized to ascertain the dislocation densities at the crack surface, which facilitates the estimation of temperature gradient intensity factors for the interface cracks experiencing transient thermal loading. This paper further explores how the relaxation time, loading parameters, and crack dimensions impact the temperature gradient intensity factors. The results can be used in fracture analysis of structures operating at high temperatures and can also assist in the selection and design of coating materials for specific applications, to minimize the damage caused by temperature loading.

Modeling of the Complexity Propagation of Crack in a Ductile Material Under Complex Solicitation in Crack Tip: Introduction of a Matrix of Stress Intensity Factors of Bifurcation

In fracture and damage mechanics, modeling of crack propagation has always been a source of difficulties. Numerous works have been carried out on this case at the crack tip, introducing new parameters: the Stress Intensity Factor (K); which is the local Irwin parameter, and also the Rice integral (J), the Griffith&amp;apos;s energizing method, in which J and G are the global parameters around the crack tip. The problem of the crack remains very complex and difficult problem to be solved. Several methods are used to investigate the crack problem, namely the method of gradient, the numerical methods by finite elements, as well as the thermodynamic approach and the classical methods of Irwin, Griffith or Rice, according to the Intensity Stress Factor. This study adds to the work already carried out. Using the analytical analysis method of equations, we manage to show that the Stress Intensity Factor has a matrix of rank 3 at the crack tip, which is a better form since it includes complex combination cases of crack mode and bifurcation. Furthermore, when the material is subjected to complex stress, after analysis we emerge from a new singularity in (r) which is different from the classical mode. Finally, we are shown the new form of singularity, which is frequency dependent. This work can explain many situations, for example, the case of certain structural disasters showing the presence of cracks for complex or uncontrollable stress.