Crack Propagation Model Research Articles

Multiaxial fatigue behavior and modelling of additive manufactured Ti-6Al-4V parts: The effects of layer orientation and surface texture

Additive manufacturing (AM) technologies have enabled industries to create and manufacture highly intricate parts with designs that have previously been deemed impossible via subtractive means. Analogous to conventionally fabricated parts, additively manufactured (AM) parts are often subjected to cyclic loadings throughout their service life. Consequently, fatigue performance becomes an important consideration in design and qualification. The geometric complexity of AM parts is accompanied by varying thermal histories which affect microstructure, porosity, surface texture, and residual stresses. The aforementioned factors influence fatigue performance and possibly introduce multiaxial stress states even when the loading is uniaxial. Therefore, understanding the fatigue behavior under multiaxial loadings is necessary to assess reliable in-service part performance. In this study, the effects of build layer orientation and surface texture on the multiaxial fatigue behavior of unmachined Ti-6Al-4V parts fabricated via a laser beam powder bed fusion process are investigated. Fatigue tests include axial, torsion, in-phase, and 90° out-of-phase axial/torsion loadings. Results indicate that the fatigue cracks in unmachined Ti-6Al-4V start from surface defects and are oriented along the maximum tensile stress plane. Accordingly, fatigue results are correlated using the tensile-based Maximum Principal Stress (MPS) approach. Finally, the influence of surface defects on the fatigue performance is incorporated by evaluating the surface micro-notches along the MPS using Murakami’s area parameter to obtain an initial crack size, which is then used with the NASGRO crack propagation model to predict fatigue lives.

Ordinary state-based peri‑ultrasound modeling for monitoring crack propagation in plate structures using sideband peak count-index technique

This work presents a nonlocal theory based on ordinary state-based (OSB) peridynamics for numerical modeling of crack propagation under loadings and peri‑ultrasound modeling for elastic wave propagation that interacts with generated cracks in 3-D plate structures. Propagating cracks in plate structures for two types of loading – tensile and shear are considered. For both loading cases, at six different times after the start of the loading the analysis is carried out to investigate how the results vary for these six different stages of crack propagation. An ultrasonic excitation is applied at a point on the surface of the plate to generate guided waves propagating through the plate structure and interacting with generated cracks at different stages of crack formation. The out-of-plane velocity fields are recorded at the receiving material point for further analysis. A relatively new and promising nonlinear ultrasonic (NLU) technique called sideband peak count-index (or SPC-I) is adopted to extract the nonlinear response due to the generated cracks. Results show that when the crack propagation is at its early stage the SPC-I value first increases, and then decreases with time at the advanced stages of crack propagation. This is because for both types of loading (tensile or shear) the newly generated cracks are small cracks (or micro-cracks) in the beginning and then they evolve into macro-cracks under increasing loadings. The observation for SPC-I trends is consistent with other numerical modelings and experimental observations reported in the literature, and such qualitative matching gives confidence in the proposed method. The proposed method combining the peri‑ultrasound modeling and SPC-I technique presented in this paper can provide a new insight for monitoring crack propagation and give some guidance for experimental structural health monitoring (SHM) applications.

Bridging Law Application to Fracture of Fiber Concrete Containing Oil Shale Ash

Concrete is a widely used material in various industries, including hazardous waste management. At the same time, its production creates a significant carbon footprint. Therefore, intensive research is being conducted to create more eco-friendly concrete, for example, partially replacing cement with by-products such as oil shale ash (OSA) or improving properties by adding dispersed fibers such as basalt fibers (BFs). The article consists of experimental testing of nine types of concrete and the modeling of crack propagation in bending. The basic trends of crack propagation in samples of concrete with OSA and BFs are simulated using a two-dimensional Finite Element (FE) model considering only material degradation on the opening crack surface and experimental data of three- and four-point bending tests. Crack propagation is modeled using the bridging law approach. A surrogate model for predicting the peak loading as a function of tensile strength and fracture work was created. An examination of the results of the FE model shows that the bilinear and nonlinear bridging law functions best describe the crack growth in the analyzed material. A comparison of experimental and modeled results showed that the length of the composite BF strongly affects the accuracy of the numerical model.

Crack propagation and fatigue life estimation of spur gear with and without spalling failure

Spur gears are most commonly used to transmit power, and speed variation from one shaft to another shaft. Spalling more frequently occurs surface fault in the gears and sometimes it causes severe damage to the gear tooth. This paper focuses on the effect of spalling on the fatigue life of spur gear. The simulation study is conducted in two parts. In the first part, the Johnson-Cook Damage model is used for the spall generation on the tooth surface. After that, the spalling results are imported as input into the crack initiation /crack propagation model and calculated the rate of crack growth of fatigue crack is based on Paris law implemented in user-defined subroutine Abaqus software. User-defined subroutine code is also validated with the comparison of the numerical and experimental results available in the literature. Cracks with different initial lengths are placed in the deeper cavities of spalling and the crack propagation analysis is conducted using XFEM. The study is conducted for four different backup ratios with cracks of three different initial lengths. The fatigue crack growth life of spur gears is investigated using different crack lengths and backup ratios. Further, a comparison has been made between the fatigue life of a spur having a spalling fault with the fatigue life of spur gear that does not have spalling fault present on its surface. It has also been found in this study that spur gear having cracks originating from the spall region have a less fatigue life as compared to the spur gear without spalling. With the increase in backup ratio from 0.3 to 3.3, an exponential increase in fatigue life is observed. However, the fatigue life of spur gear without the presence of spalling fault has higher fatigue for all backup ratios.

Numerical study on fatigue behavior and strengthening of steel pipes with a surface crack

Recently, metallic pipes have been extensively utilized in civil and marine engineering, whereas surface cracks are quintessential flaws of steel pipes, the emergence of which may trigger fatigue failure. The work of this paper is mainly a numerical study on the fatigue behavior and strengthening of steel pipes with a part-through circumferential crack under four-point bending. A crack propagation model was proposed, and the corresponding surface crack growth simulation was subsequently implemented through finite element method (FEM) in conjunction with Python scripting. The numerical models, including unrepaired and carbon fiber reinforced polymer (CFRP)-repaired pipes, were further validated by evaluating the fatigue life and stress intensity factor (SIF). Based on the verified models, case studies were conducted, and two parameters, which are initial crack sizes and CFRP layer number, were quantitatively analyzed to assess their influence on SIFs along the crack tip, surface crack propagation, and the development of crack aspect ratio. The results reveal that initial crack sizes have an impact on the fatigue behavior of steel pipe to varying extents, especially on the SIF, crack propagation rate, and tendency of crack aspect ratio development, however, the final crack aspect ratio is largely unaffected. Moreover, reinforcing with CFRP can substantially reduce the SIF, enlarge the crack aspect ratio, and reduce the crack propagation rate, thereby dramatically extending the fatigue life. This study can serve as a reference for future research or design regarding the fatigue of steel pipe.

Numerical Study on the Dynamic Propagation Model of Cracks from Different Angles under the Effect of Circular Hole Explosion

A dynamic disturbance will induce cracks around the tunnel in tunnel blasting or shield construction. To investigate the overall stability of cracks with various angles during a fixed borehole (round hole explosion) blasting, models containing an individual crack with different angles were introduced for simulation research. The research set up a thin sheet model with a length of 350 mm and a width of 150 mm, with a 7 mm diameter hole and a pre-existing crack of 75 mm and 5 mm in the middle. The evolution of the stress wave propagation model and the crack propagation model were simulated using the AUTODYN software. And in this study, the theory of stress wave is used to creatively explain the dynamic load under the action of formation and reasons for the danger zone. The results indicate that pre-existing cracks from different angles will have an impact on the blast hole and the new cracks generated around itself. At 45–90°, pre-existing cracks will direct reflected stress waves to promote some cracks around the hole to have faster growth rates than others, and these special cracks with faster growths and longer lengths will more easily connect with the free surface or other cracks, resulting in overall instability. And these conditions are consistent with the prediction made by the stress wave propagation simulation study. The research results have certain guiding significance for the stability analysis and hazardous area prediction of tunnel blasting with existing cracks.

A study on the evolution mechanism of small diameter thin-walled stainless steel bellows during a bending process

In order to accurately construct the evolution mechanism of the matrix during the bending process, this paper combines finite element simulation and material characterization methods to study the evolution process of the matrix in detail. Firstly, a repeated bending model of the bellows was constructed by ABAQUS finite element software. The deformation hardening, geometry evolution, stress and strain evolution of the matrix were analyzed in depth. At the same time, by characterizing the microstructure of the trough under different bending times, the evolution of the microstructure during the fracture process was obtained. Combined with the fracture characteristics, it can be seen that the deformation hardening of the trough is significant and the stress is large, so it is most likely to become the failure zone. The waveform distortion increases the deformation inhomogeneity of the trough at different positions, resulting in local large strain accumulation and further aggravating the fracture failure of the trough. During the bending process, a large number of martensite tissue appears in the central area of the bellow wall thickness, and the dislocation gradually moves from the inner and outer surfaces to the center. The crack initiates first at the bellow outer surface and propagates along the circumference and wall thickness direction. Bending four times is the key node of crack propagation. Moreover, the crack propagation models of the trough in the wall thickness and circumferential direction are established, and the fracture failure mechanism of the trough during repeated bending is revealed.

New model of crack propagation of aluminium wire bonds in IGBT power modules under low temperature variations

In this paper, a new model for wirebond degradation during power cycling in IGBT power module is proposed. This model is based on experimental crack propagation analyses and on a plastic strain empirical law. For the experiments, two power cycling tests in switching mode under high voltage were carried out respectively with junction temperature swings of ∆ Tj=30°C and 40°C at a minimal temperature of Tj,min=55°C. The DUTs and the test conditions were chosen so that only degradations of chip top-side interconnections could occur. The on-state voltage (VCE) was measured online during the tests as an indicator of wire and metallization degradations, moreover, the samples were removed at different aging stages. The removed samples were cross-sectioned in order to observe the crack propagation evolution with cycling. Concerning the plastic strain law, we used results from literature giving the evolution of the plastic strain variation (∆εpl) with bond-wire contact crack growth. As results, this new lifetime prediction model based on a modified Paris's law for aluminium wire bonds fatigue of IGBTs shows a good fitting of the test results and is it can be used to predict the lifetime under other load conditions. Finally, the lifetime of tested IGBT modules are estimated and used to verify the effectiveness of the proposed model.

Calculation of fracture number and length formed by methane deflagration fracturing technology

The innovative Methane in-situ deflagration fracturing technology offers several benefits. It can prevent formation pollution and eliminates the need for complex treatment procedures for backflow materials. Additionally, it reduces ground transportation expenses and is poised to become a highly effective and eco-friendly waterless fracturing technology. This paper suggests methods for determining the number and length of fractures in oil and gas well stimulation, considering the main influencing factors. The fracture number is calculated using mass conservation principles, while the fracture length is determined using the crack propagation model. The fracturing experiments with large-sized samples were conducted to verify the technical feasibility of the new fracturing technology and fill the gap in large-scale physical model experimental research for deflagration fracturing technology. Following the experiment, compare experimental data with calculated data, and analyze the factors that affect the fracture number and length. The results indicate that both methods are highly feasible and possess strong predictive accuracy. It is advised that to enhance the fracturing effect on formations with high crustal stress, it is beneficial to appropriately increase the peak pressure, reduce the pressure rate, and increase the fracturing time while ensuring that the wellbore remains undamaged. Moreover, these proposed methods are versatile and adaptable, making them suitable for explosive fracturing within hydraulically fractured formations and high-energy gas fracturing technology.

Study on sealing integrity of cement sheath in ultra deep well reservoir reconstruction

AbstractThis article mainly studies the influence of high temperature, high pressure, and ultra‐deep well reservoir renovation construction on wellbore barriers, and explores the impact of reservoir renovation on cement sheath under high temperature and high‐pressure conditions. Combining the coupling effect of casing, cement, and formation rock, a three‐dimensional numerical model is established to analyze the stress changes and distribution of the cement sheath during the volume fracturing process. By establishing a numerical model for the analysis of the integrity of the wellbore during the fracturing process of the ultra‐deep well vertical section, the stress changes and distribution of the cement sheath during the fracturing process are analyzed. A numerical calculation model for crack propagation during perforation and cement sheath reservoir renovation is constructed, and the model results are verified through laboratory experiments and computed tomography scans. The shear failure of the cement sheath interface under different conditions such as different casing pressure, cement sheath thickness, elastic modulus, and Poisson's ratio is analyzed during the fracturing process. The research results can provide technical support for the integrity of the wellbore and the design of the well structure in similar ultra‐deep well development processes.

On optimization of heterogeneous materials for enhanced resistance to bulk fracture

We propose a novel approach to optimize the design of heterogeneous materials, with the goal of enhancing their effective fracture toughness under mode-I loading. The method employs a Gaussian processes-based Bayesian optimization framework to determine the optimal shapes and locations of stiff elliptical inclusions within a periodic microstructure in two dimensions. To model crack propagation, the phase-field fracture method with an efficient interior-point monolithic solver and adaptive mesh refinement, is used. To account for the high sensitivity of fracture properties to initial crack location with respect to heterogeneities, we consider multiple cases of initial crack and optimize the material for the worst-case scenario. We also impose a minimum clearance constraint between the inclusions to ensure design feasibility. Numerical experiments demonstrate that the method significantly improves the fracture toughness of the material compared to the homogeneous case.

Calculations of crack stress intensity factors based on FEM and XFEM models

ABSTRACT The basis of describing stress intensity factor and predicting residual life of structure is the right numerical model of dynamic crack propagation. ‘FEM+M integral’ and ‘XFEM+M integral’ methods were, respectively, adopted. Difficulties of ‘FEM+M integral’ method were solved, such as the singularity of crack tip, nodal uncoincidence of rubber layer unit and plate unit during mesh repartition and calculation convergence. In addition, difficulties of ‘XFEM+M integral’ method were overcome, such as difficult crack tip coordinates, difficult cutting point of crack and element and crack deflection in the element. On this basis, the effective calculation of stress intensity factor was realised. Through simulation and calculation, it is found that the error value is within 5%. The model reliability is further verified within the allowable error range.

A peridynamic model for electromechanical fracture and crack propagation in piezoelectric solids

This paper presents for the first time an approach to the problem of electromechanical fracture and crack propagation in piezoelectric solids with peridynamics. Fracture in piezoelectric ceramics is an important problem in engineering due to its complexity. The majority of the computational models available on the literature rely on sharp crack representations, which have difficulties dealing with complex crack patterns, or rely on diffusive crack models, such as the phase-field fracture model, that can predict complex patterns but does not represent cracks in a discrete way. On the other hand, peridynamics has been designed to solve this problems and is able to simulate discrete cracks as well as complex crack phenomena like fragmentation and branching. We present a novel approach to the implementation of different electric crack face boundary conditions in a peridynamic way, by a field selective bond breaking approach. Moreover, it is also presented the first electromechanical failure criterion for fracture in piezoelectric ceramics. We develop an energy based failure criterion due to its generality and wide range of applications. These approaches are presented in a way such that they are valid for any type of peridynamic formulation. The used numerical model is implemented using correspondence-based peridynamics with the linear piezoelectricity constitutive setting, using a meshfree discretization and solved quasi-statically with an implicit incremental-iterative scheme. Numerical examples are presented to demonstrate the capabilities of these new approaches and assess the performance of the model against experimental results. The model is capable of numerically predicting complicated fracture behaviour and crack propagation in an intrinsic/autonomous way, as demonstrated by the results.

A new mixed-mode phase-field model for crack propagation of brittle rock

A new mixed-mode phase-field model for crack propagation of brittle rock

Performance of acceleration techniques for staggered phase-field solutions

The staggered phase field formulation has proved to be a robust formulation for the modeling of crack nucleation and propagation, but it suffers from a very slow convergence rate. Here, we summarize some of the methods that were proposed in the literature to accelerate staggered schemes and numerically investigate their performances in staggered hybrid quasi-static phase field modeling. Between the studied methods, we found that Anderson’s method was the most robust in terms of the mean number of iterations that were required for convergence and the stability of the solution.

Stochastic selection of fatigue crack growth model for a damaged bridge gusset plate

Damage tolerance-based fatigue assessment of operational structures is often rationalized by integrating the simple Paris model with fixed parameters, which often do not represent the unique geometrical, boundary, and loading conditions of the structure. This paper has implemented a stochastic approach which involves different crack growth models, from the simple Paris model to the complex NASGRO model, and estimates the parameters which truly fit the structural condition and crack propagation models. The case study for this paper is a steel riveted railway bridge, where an edge fatigue crack was observed in one of the gusset plates. The most suitable models are recognized at different damage states of the plate and the influence of the measurement uncertainties on the model selection process is highlighted.

Two-scale modeling of particle crack initiation and propagation in particle-reinforced composites by using microscale analysis based on Voronoi cell finite element model

In this study, a two-scale finite element model has been developed for the elastic analysis of composite materials. The coarse finite element mesh was assumed for the macroscale analysis, while Voronoi cell finite element model (VCFEM) was used for the microscale analysis of heterogeneous domains. The adaptive coupling between the two scales in non-critical and critical regions was accomplished through the master–slave nodes method. Two scale elements were connected together through the use of shared nodes and the order of the edge displacement interpolation. A new extended VCFEM was proposed to simulate particle damage generation, and a remeshing algorithm was constructed to simulate particle crack generation and propagation in particle-reinforced composites. For crack propagation analysis, four new combined Voronoi elements were developed and analyzed at the microscale. The obtained results for the stresses, stress intensity factors, and crack path were compared with those calculated using the commercial calculation software Abaqus. The two sets of results are in very good agreement, confirming the accuracy of the proposed method used for determining the stress concentrations and also for coarse-mesh discretization.

A fast adaptive PD-FEM coupling model for predicting cohesive crack growth

In this study, nonlocal theory of peridynamic (PD) is coupled with finite element method (FEM) to simulate cohesive crack growth in quasi-brittle materials. The adaptive dynamic relaxation method is adopted to implement quasi-static loading conditions. The advantage of peridynamic method in the modeling of crack propagation is taken into consideration to be coupled with that of finite elements which is computationally less expensive and covers various boundary value problems. In this novel method, the whole domain of the problem is initially dominated by FEM solver with coarse mesh grids. Coupling process is then introduced to those regions which have critical conditions according to damage criterion. The capability of the proposed coupling method in the modeling of cohesive crack growth in quasi-brittle materials is demonstrated. In comparison to other conventional PD-FEM coupling methods, the computational cost of the proposed method is considerably improved and total running time of the solution is significantly attenuated. The validity of the method is confirmed through comparing the results with experimental ones.

Modelling crack propagation during relaxation of viscoelastic material

A viscoelastic material which is stretched and is then held at constant elongation, normally results in decreasing stresses till the equilibrium has been reached. With the decreasing stresses a crack propagation is not expected as the energy of the system is decreasing. However, an initial damage could lead to an increase in the mechanical load on the undamaged chains during relaxation, leading to material degradation and crack propagation. While experimental investigations have been presented in the literature, modelling such an effect has not been thoroughly investigated. In this work, an initial framework for modelling the damage evolution during relaxation is presented. A mechanical model is coupled with a phase field to model the crack propagation. For simplicity, a linear viscoelastic model is implemented for the mechanical part. A mobility constant is employed to model the evolution of the phase field with the changing mechanical energy during relaxation. The evolution of phase field can be interpreted as the evolution with which the polymer chains get damaged. Different load conditions and geometries are simulated, which shows that the proposed framework is able to model the damage evolution during viscoelastic relaxation. Thus, with the help of the numerical model a physical explanation for the failure during relaxation is presented.Graphical abstract

A consistent ordinary state-based peridynamic formulation with high accuracy

Peridynamics has shown great potential in numerical analysis of various engineering problems. However, its accuracy is still not quite satisfactory. In this paper, a consistent ordinary state-based peridynamic formulation (OSB-PD) is presented and significant improvement in computational accuracy is achieved. The starting point of the method is the investigation of the difference between the theoretical horizon and its counterpart in numerical implementation. Due to this difference, the original OSB-PD is inconsistent. The idea of modifying the theoretical horizon to eliminate such difference is proposed, based on which the consistent OSB-PD is developed. Numerical results show that the proposed method remarkably improves the accuracy of the original OSB-PD. Particularly, in calculating strain energy density, it almost achieves machine precision for constant strain field; for linear strain field, it shows orders higher accuracy than the original method. It is worth noting that such high accuracy is achieved with very small horizon and thus the proposed method is very fast. Capability of the proposed method in modeling crack propagation and fragmentation is also demonstrated.