Crack Path Simulation Research Articles

Multiple discrete crack initiation and propagation in Material Point Method

Cracks in MPM (CRAMP) is one of the most prominent discrete crack simulation methods in the Material Point Method (MPM) due to its simplicity and versatility. However, CRAMP is yet to include the capability to simulate concurrent crack initiations and propagations, as well as propagation to the edge of the material domain. The method proposed in this paper enables the simulation of multiple crack paths with CRAMP via the dynamic assignment of particles to separate grids while minimizing the number of necessary grids. It also proposes methods of evaluating crack initiation and propagation via the Rankine criterion. The proposed methods are then implemented in an in-house Convected Particle Domain Interpolation (CPDI) MPM developed at Aalto University.To verify the integrity of the CPDI algorithm, our CPDI code with the proposed method implemented simulated a CPDI vortex. Furthermore, six fracture-simulation verification test cases were carried out: (1) through-crack in an infinite plate; (2) mode-I propagation; (3) initiation; (4) initiation with large deformations; (5) merging; (6) multiple initial cracks; and (7) radially-cracked thick ring. All these verification tests show successful initiation, propagation, merging, crack opening, and agreement with the results from the literature, as well as the convergence of various parameters with the expected rates.

Modeling of crack path in layered architectures composed of dissimilar materials

AbstractIn order to make full use of the potential fatigue crack growth resistance provided by layered architectures, a validated crack path simulation algorithm for crack propagation through different elements of the layered architectures was established. The crack path approaching a material interface was predicted by using the maximum tangential strain (MTSN) criterion and the crack behavior at the interface was simulated by a developed two‐step method (a modified stress‐and‐energy‐based cohesive zone method considering the change in direction of an interface penetrating crack). The crack path simulation by using this algorithm in layered example architectures indicates (1) there are two criteria zones for the transition between crack deflection and penetration in terms of the relationship between interfacial strength and toughness; (2) the likelihood of a crack deflecting out of the interface will increase with the propagation of an interfacial crack; and (3) the architecture difference which affects shielding or anti‐shielding behavior has a significant effect on crack deflection or penetration events.

Numerical simulation of fatigue crack paths in orthopedic plates

This study is aimed to explain the behaviour of different orthopedic plate designs, under uniaxial bending, with cracks initiated in the stress concentration areas. Extended finite element method (XFEM) in ANSYS software was used for simulating the fatigue crack growth in 5 orthopedic plates with different geometries. Results for crack length vs, plate geometry indicated plate D as the best option regarding residual life. Crack paths are analysed in all 5 plates to explain such a behaviour, indicating benefits of initial crack growth into length, followed by growth into depth.

Simulation of bridging mechanisms in complex laminates using a hybrid PF-CZM method

Delamination and cracking of matrix/fiber is a common failure phenomena reported in fiber reinforced composite materials. As complex stress states develop in laminated structures, they are prone to develop fracture phenomena. Therefore, designs with large damage tolerance are currently implemented in most of the industrial sectors. This can be achieved by designing such materials with superior fracture resistance, which requires a comprehensive understanding of failure mechanisms. Cohesive Zone Models (CZM) are a popular technique to study debonding and decohesion in composite structures. Furthermore, due to the accurate simulation of complex crack paths including crack branching, the Phase Field (PF) approach has gained notable relevance in fracture studies, including the interplay between debonding and crack propagation in the matrix. In order to get a further insight into these intricate scenarios, involving bridging mechanisms in intralayer and interlayer, crack simulation coupling the phase field approach and the cohesive zone model is herein exploited for identifying crack migration through material layers. The crack paths and the related force–displacement curves of 2D multilayered material models of complex laminates are predicted and compared.

Numerical simulation of crack paths in asphalt mixture using ordinary state-based peridynamics

Cracking creates major distress in asphalt pavements. Because of mathematical complications, existing simulation efforts are incapable of simulating the crack branching and crack coalescence in asphalt mixtures. To overcome this deficiency, this paper developed a two-dimensional (2D) ordinary state-based peridynamics (OSB-PD) method to simulate the entire crack propagation phase, which includes crack propagation, crack branching and crack coalescence. The 2D asphalt mixture digital image was acquired via the X-ray computed tomography method. The Prony series coefficients of the fine aggregate mixture (FAM) were obtained from the dynamic modulus test. The fracture energy of the FAM was determined from the semicircular bending (SCB) test. The measured mixture properties were then input into the 2D OSB-PD numerical method to simulate the crack paths under the SCB test and the three-point bending (TPB) test conditions. The simulated crack paths matched well with those observed from the experiments (at 5% level of significance), thus validating the accuracy of the proposed 2D numerical simulation method. The validated method was finally implemented into the simulation of the crack paths in the laboratory-used asphalt mixture and subjected to compressive loading. The simulation results indicated that the diagonal crack exists when the crack propagates in an asphalt mixture. The diagonal crack then continues to branch and coalesce through the following possible paths until the failure of the asphalt mixture: (a) penetrating through the aggregate; (b) branching along the surface of aggregate in different directions; and (c) coalescing with each other.

Nonplanar Crack Growth Simulation of Multiple Cracks Using Finite Element Method

This work deals with a 2D finite element simulation of nonplanar multiple cracks using fracture and crack propagation analysis. This analysis was performed by using the developed source code software written by Visual Fortran Language. This source code includes the adaptive mesh generation utilizing the advanced front method and also the mesh refinement process. In order to correctly represent the field singularity, the quarter‐point singular elements are constructed around the tip of the crack. The crack growth criteria are used to predict the crack growth direction by utilizing the circumferential stress factor in calculating the yielding stress in elastic fracture assumptions. The stress intensity factor determination is one of the most critical procedures as it determines the crack initiation and propagation mechanism. Moreover, the stress intensity factor histories during the crack growth are measured with the use of equivalent domain integral methods. The crack path simulation and stress intensity factor calculations are compared with the literature and revealed that the results are in agreement with research carried in this domain.

Phase field modeling of brittle fracture in materials with anisotropic fracture resistance

AbstractMaterials which reveal a directionality in terms of the fracture resistance motivate the integration of anisotropic behavior within approaches for crack growth simulations. Within a variational phase field model for fracture, this kind of anisotropy is included by the enhancement of the non‐local part of the crack energy functional. Results of a numerical crack path simulation are presented and discussed to illustrate the properties of the applied model.

Application of Singular Integral Equation to a Crack Moving near a Hole in a Two-Dimensional Infinite Plate

In this study, crack path simulation was conducted based on a singular integral equation formulated by a continuous distributed dislocation technique. The problem investigated in this study was to predict the propagation path of a crack moving in an infinite elastic plate with a circular hole, under uniform tensile loading. In order to perform this prediction, a probing method was developed to search for a crack moving direction where the mode II stress intensity factor would be almost zero, enabling the crack to automatically extend in that direction. Some cases for different locations of an initial straight crack were simulated using the program developed.

Experimental Study and Numerical Modeling of Fracture Propagation in Shale Rocks During Brazilian Disk Test

Reliable prediction of fracture process in shale-gas rocks remains one of the most significant challenges for establishing sustained economic oil and gas production. This paper presents a modeling framework for simulation of crack propagation in heterogeneous shale rocks. The framework is on the basis of a variational approach, consistent with Griffith’s theory. The modeling framework is used to reproduce the fracture propagation process in shale rock samples under standard Brazilian disk test conditions. Data collected from the experiments are employed to determine the testing specimens’ tensile strength and fracture toughness. To incorporate the effects of shale formation heterogeneity in the simulation of crack paths, fracture properties of the specimens are defined as spatially random fields. A computational strategy on the basis of stochastic finite element theory is developed that allows to incorporate the effects of heterogeneity of shale rocks on the fracture evolution. A parametric study has been carried out to better understand how anisotropy and heterogeneity of the mechanical properties affect both direction of cracks and rock strength.

Crack path simulation in a particle-toughened interlayer within a polymer composite laminate

With recent advances in computational resources and the development of arbitrary cracking methods, such as the Augmented Finite Element Method (A-FEM), more complex simulations can now be represented featuring multiple interacting cracks. It has been established that Mode I crack propagation in particle-toughened interlayers within some toughened Carbon Fibre Reinforced Polymer (CFRP) laminates involves a discontinuous process zone, rather than a distinct crack tip. This results from multiple cracks forming ahead of the main crack that subsequently coalesce, leaving behind bridging ligaments that may then provide traction across the crack flanks. An idealised two-dimensional A-FEM model is presented in this work, which represents the ‘particles’ as one-dimensional cohesive regions. The model shows that variables such as particle spacing, distribution, strength and toughness, and fibre interface strength can be tailored in order to maintain the crack path within the interlayer. This competition between crack paths is important, as a reduction in composite toughness is reported when the crack path migrates to the fibre interface. The simulations are complemented by time-resolved Synchrotron Radiation Computed Tomography (SRCT) data, which identify the chronology of the damage processes, along with the effects of particle distribution on the crack path and the formation of bridging ligaments.

Использование накопленной энергии деформирования при численном моделировании разрушения конструкций из стали

В данной работе предложена модель баланса энергии в неупруго деформируемом металле. Ее отличительной чертой является учет структурных изменений в материале при помощи введения тензорного параметра плотности дефектов, совпадающего по смыслу с деформацией, обусловленной дефектами. Введение такого параметра позволило авторам работы предложить способ расчета величины накопленной энергии и сформулировать на ее основе критерий разрушения. Рассмотрены два способа вывода определяющих соотношений, позволяющих рассчитывать эволюцию пластической и структурной деформации. Первый способ основан на применении принципов линейной неравновесной термодинамики, второй способ представляет собой аналог теории пластического течения. Предложенная модель позволяет не только описывать напряженно-деформированное состояние, но и открывает возможности для использования энергетических критериев разрушения. На основе анализа экспериментальных исследований процесса накопления скрытой энергии деформирования в металлах предполагается, что разрушение в материале происходит при достижении накопленной энергией некоторого критического значения. Применение этого подхода к описанию разрушения проиллюстрировано на двух примерах. Первый пример посвящен моделированию распространения трещины при циклическом кручении трех цилиндрических образцов с трещинами, ориентированными к оси цилиндра под разными углами, второй пример описывает процессы зарождения и распространение трещины в опоре подшипника. При решении этих задач использовался расширенный метод конечных элементов. Полученные результаты согласуются с ранее опубликованными результатами.

Crack path simulation for cylindrical contact under fretting conditions

In this work different strategies to estimate crack path for cylindrical contacts under fretting conditions are carried out. The main goal is to propose and to evaluate methodologies not only to estimate the direction of crack initiation but also the subsequent propagation in its earlier stages, where the stress field is multiaxial, non-proportional and decays very fast due to the proximity with the contact interface. Such complex conditions pose a substantial challenge to the modelling of crack path. The numerical simulations are provided by a 2D Finite Element Analysis taking into account interactions between the crack faces. The results show that, under fretting conditions, models based on the critical plane method are not effective to estimate the crack initiation orientation, while models based on a so called “critical direction” applied along a critical distance provide better results. Regarding the subsequent crack propagation orientation, it was possible to see that stress intensity factor based models where one considers an infinitesimal virtual crack emerging from an original preexistent crack are powerful mechanisms of crack orientation estimation

Fatigue failure analysis of pin-loaded lugs

In the present paper, mathematical models are proposed in order to analyze the strength of pinloaded lugs with semi-elliptical crack and through-the-thickness crack. The crack growth investigation of considered crack configurations tackles the fatigue life evaluation and the crack path simulation of semi-elliptical crack. The residual strength is estimated by applying the two-parameter driving force model. The numerical and analytical approaches are employed for the stress intensity factor calculation. Experimental fatigue crack growth data are used in order to verify efficiency of the developed models. A good correlation between fatigue crack growth estimations and experimental observations is obtained.

Crack path predictions and experiments in plane structures considering anisotropic properties and material interfaces

In many engineering applications special requirements are directed to a material's fracture behavior and the prediction of crack paths. Especially if the material exhibits anisotropic elastic properties or fracture toughnesses, e.g. in textured or composite materials, the simulation of crack paths is challenging. Here, the application of path independent interaction integrals (I-integrals), J-, L- and M-integrals is beneficial for an accurate crack tip loading analysis. Numerical tools for the calculation of loading quantities using these path-invariant integrals are implemented into the commercial finite element (FE)-code ABAQUS. Global approaches of the integrals are convenient considering crack tips approaching other crack faces, internal boundaries or material interfaces. Curved crack faces require special treatment with respect to integration contours. Numerical crack paths are predicted based on FE calculations of the boundary value problem in connection with an intelligent adaptive re-meshing algorithm. Considering fracture toughness anisotropy and accounting for inelastic effects due to small plastic zones in the crack tip region, the numerically predicted crack paths of different types of specimens with material interfaces and internal boundaries are compared to subcritically grown paths obtained from experiments.

Simulation of crack paths at three-dimensional corners of laminated structures

A fracture mechanics-based approach focused on modelling the shape of such interface cracks and calculating the critical stress for steady-state propagation has been developed. The crack propagation is investigated by estimating the fracture mechanics parameters including the energy release rate and the three-dimensional mode-mixity along the crack front allowing determining the shape of the crack front profiles. A numerical approach is applied for coupling the far field solutions utilising the capability of the finite element method to the near field solutions at the crack front based on the J-integral. The developed two-dimensional numerical approach for the calculation of fracture mechanical properties has been validated with three-dimensional models for varying crack front shapes. A quantitative approach was formulated based on the finite element method with iterative adjustment of the crack front to estimate the critical delamination stress as a function of the fracture criterion and corner angles. The implication of the results on the delamination is discussed in terms of crack front profiles and the critical stresses.

Simulation of crack-paths formed in concrete around deformed tension bar

Simulation of crack-paths formed in concrete around deformed tension bar

Mixed mode crack growth simulation with/without overloads

In the present paper, mathematical models/procedures are developed in order to investigate the mixed mode crack growth process. The proposed procedures examine the fatigue life estimation and the crack path simulation under either constant amplitude loading or single overload. The fatigue life up to failure is calculated by employing two-parameter driving force model together with the equivalent stress intensity factor. The overload effect is theoretically analyzed by introducing the Wheeler’s retardation parameter. Further, the crack extension under Mode I/II conditions is experimentally investigated for two cracks emanating from two holes in the plate. Then, for the same mixed mode situation with two cracks, the crack growth paths are modeled by using the maximum principal stress criterion and the finite element method. The authors employ analytical and numerical approaches for the stress intensity factor calculations. The numerical investigation is performed by applying quarter-point (Q-P) singular finite elements. The efficiency of proposed procedures is verified through available crack growth data. The different mixed mode calculations are in a good correlation with crack growth observations.

Analysis of the crack growth propagation process under mixed-mode loading

In the present paper, a computational model for crack growth analysis under Mode I/II conditions is formulated. The focus is on two issues – crack path simulation and fatigue life estimation. The finite element method is used together with the maximum principal stress criterion and the crack growth rate equation based on the equivalent stress intensity factor. To determine the mixed-mode stress intensity factors, quarter-point (Q-P) singular finite elements are employed. For verification purposes, a plate with crack emanating from the edge of a hole is examined. The crack path of the plate made of 2024 T3 Al Alloy is investigated experimentally and simulated by using the finite element method with the maximum tangential stress criterion. Then, the validation of the procedure is illustrated by applying the numerical evaluation of the curvilinear crack propagation in the polymethyl methacrylate (PMMA) beam and the Arcan specimen made of Al Alloy for which experimental results are available in the literature. In order to estimate fatigue life up to failure of the plate with crack emanating from the edge of a hole, the polynomial expression is evaluated for the equivalent stress intensity factor using values of stress intensity factors obtained from the finite element analysis. Additionally, the fatigue life up to failure of the Arcan specimen is analyzed for different loading angles and compared with experimental data. Excellent correlations between the computed and experimental results are obtained.

Towards optimization of crack resistance of composite materials by adjustment of fiber shapes

We investigate the evolution and propagation of cracks in 2-d elastic domains, which are subjected to quasi-static loading scenarios. In addition to the classical variational formulation, where the standard potential energy is minimized over the cracked domain under physical conditions characterizing the behavior of the material close to the crack (e.g. non-penetration conditions), we include a ‘cohesive traction term’ in the energy expression. In this way we obtain a mathematically concise set of partial differential equations with non-linear boundary conditions at the crack interfaces. We perform a finite element discretization using a combination of standard continuous finite elements and so-called cohesive elements. During the simulation process cohesive elements are adaptively inserted at positions where a certain stress bound is exceeded. In our numerical studies we consider domains consisting of a matrix material with fiber inclusions. Beyond pure crack path simulation, our ultimate goal is to determine an optimal shape of the fibers resulting in a crack path that releases for a given load scenario as much energy as possible without destroying the specimen completely. We develop a corresponding optimization model and propose a solution algorithm for the same. The article is concluded by numerical results.

Reliability Evaluation on Deterioration of Power Device Using Coupled Electrical-Thermal-Mechanical Analysis

This paper presents a simulation method to evaluate the thermal fatigue life of a power module. A coupled electrical-thermal analysis was performed to obtain the nonuniform temperature distribution of electric current. Then, a thermomechanical analysis was carried out based on the temperature distribution from the electrical-thermal analysis. Since crack propagation can change the route of heat transfer, a crack path simulation technique was used to investigate the fracture behavior of the power module. The crack initiates in the solder joint below the Al bonding wire of the insulated gate bipolar transistor module and propagates by increasing the diameter. The effect of the bonding type on power cycling fatigue life is also discussed. The fracture process was found to depend on the type of bonding. Lead frame bonding was found to be more effective than wire bonding.