Simulation Of Crack Growth Research Articles

Numerical Simulation of Fatigue Crack Growth and Fracture in Welded Joints Using XFEM—A Review of Case Studies

Numerical simulation of fatigue crack growth in welded joints is not well represented in the literature, especially from the point of view of material heterogeneity in a welded joint. Thus, several case studies are presented here, including some focusing on fracture, presented by two case studies of mismatched high-strength low-alloyed (HSLA) steel welded joints, with cracks in the heat affected zone (HAZ) or in weld metal (WM). For fatigue crack growth, the extended finite element method FEM (XFEM) was used, built in ABAQUS and ANSYS R19.2, as presented by four case studies, two of them without modelling different properties of the welded joint (WJ). In the first one, fatigue crack growth (FCG) in integral (welded) wing spar was simulated by XFEM to show that its path is partly along welded joints and provides a significantly longer fatigue life than riveted spars of the same geometry. In the second one, an integral skin-stringer panel, produced by means of laser beam welding (LBW), was analysed by XFEM in its usual form with stringers and additional welded clips. It was shown that the effect of the welded joint is not significant. In the remaining two papers, different zones in welded joints (base metal—BM, WM, and HAZ) were represented by different coefficients of the Paris law to simulate different resistances to FCG in the two cases; one welded joint was made of high-strength low-alloyed steel (P460NL1) and the other one of armour steel (Protac 500). Since neither ABAQUS nor ANSYS provide an option for defining different fatigue properties in different zones of the WJ, an innovative procedure was introduced and applied to simulate fatigue crack growth through different zones of the WJ and evaluate fatigue life more precisely than if the WJ is treated as a homogeneous material.

Simulation of fatigue crack growth in aluminium alloy 7075-T7351 under spike overload and aircraft spectrum loading

The trend towards virtual testing and digital-twin assisted management means that the accurate and reliable simulation of fatigue crack propagation behaviour is more important than ever. Reliable but conservative approaches to support this are in widespread use in the aerospace industry. Nevertheless, the conservatism comes at a significant cost in terms of reduced structural life and an increased ongoing inspection requirement and, as such leads to questions about the economic burden of these approaches. Recent comparisons between blind predictions and test results revealed the extent of the issue for cracking in aluminium alloy 7075-T7351 coupons with configuration and loading representative of military transport aircraft wing skins. The current models were generally conservative by a factor of two or more in terms of crack propagation life. This suggested that there was significant scope to improve the modelling to better reflect all the complex contributing factors. The current work has investigated the issue of changes in the crack front constraint as the crack progresses from a state of high constraint (close to plane strain) to a lower constraint (approaching plane stress). This issue was investigated both experimentally and with the development of an improved analytical model. A test program was conducted on several specimens, loaded under constant-amplitude, constant-amplitude with spike-overloads and a variable amplitude spectrum. Crack-opening stress levels were measured at key points in the tests and the results were used to develop and evaluate improved modelling approaches. The improved model was generally able to predict crack growth within about ± 30 % of that demonstrated along with the correct form of the crack growth, which is a significant advance and will lead to reduced costs and increased safety.

Numerical and experimental crack-tip cohesive zone laws with physics-informed neural networks

The cohesive zone law represents the constitutive traction versus separation response along the crack-tip process zone of a material, which bridges the microscopic fracture process to the macroscopic failure behavior. Elucidating the exact functional form of the cohesive zone law is a challenging inverse problem since it can only be inferred indirectly from the far-field in experiments. Here, we construct the full functional form of the cohesive traction and separation relationship along the fracture process zone from far-field stresses and displacements using a physics-informed neural network (PINN), which is constrained to satisfy the Maxwell-Betti's reciprocal theorem with a reciprocity gap to account for the plastically deforming background material. Our numerical studies simulating crack growth under small-scale yielding, mode I loading, show that the PINN is robust in inversely extracting the cohesive traction and separation distributions across a wide range of simulated cohesive zone shapes, even for those with sharp transitions in the traction-separation relationships. Using the far-field elastic strain and residual elastic strain measurements associated with a fatigue crack for a ZK60 magnesium alloy specimen from synchrotron X-ray diffraction experiments, we reconstruct the cohesive traction-separation relationship and observe distinct regimes corresponding to transitions in the micromechanical damage mechanisms.

Numerical Fatigue Crack Growth on Compact Tension Specimens under Mode I and Mixed-Mode (I+II) Loading.

This study focused on standard Compact Tension (CT) specimens and two loading modes during the numerical analyses carried out, namely: pure mode I and mixed-mode loading (Modes I+II). Numerical stress intensity factors, KI, were calculated using Abaqus® 2022 and compared with those given analytically under pure mode I loading, showing very good agreement. Additionally, KI, KII, and KIII results obtained from Abaqus® were presented for mixed-mode loading, analyzing crack growth and variation through the thickness of the CT specimen. Moreover, fatigue crack growth simulations under mode I loading were conducted on standard CT specimens using the Extended Finite Element Method (XFEM) and the Paris Law parameters of an AISI 316L stainless steel. It was shown that XFEM effectively determines crack propagation direction and growth, provided that an appropriate mesh is implemented.

Influences of Pre-Existing Fissure Angles and Bridge Angles on Concrete Tensile Failure Characteristics: Insights from Meshless Numerical Simulations.

The existence of cracks is a key factor affecting the strength of concrete. However, traditional numerical methods still have some limitations in the simulation of crack growth in fissured concrete structures. Based on this background, the numerical treatment method of particle failure in smoothed particle hydrodynamics (SPH) is proposed, and the generation method for concrete meso-structures under the smoothed particle hydrodynamics (SPH) framework is developed. The concrete meso-models under different pre-existing micro-fissure inclinations and bridge angles (the inner tip line of the double pre-existing micro-fissure is defined as a bridge, and the angle between the bridge and the horizontal direction is defined as the bridge angle) were established, and numerical simulations of the crack propagation processes of concrete structures under tensile stress were carried out. The main findings were as follows: The concrete meso-structures and the pre-existing micro-fissures all have great impacts on the final failure modes of concrete. The stress-strain curve of the concrete model presents four typical stages. Finally, the crack initiation and propagation mechanisms of fissured concrete are discussed, and the application of smoothed particle hydrodynamics (SPH) in crack simulations of fissured concrete is prospected.

Phase-field modeling of crack growth under coupled creep-fatigue

Crack growth under coupled creep-fatigue strongly influences service life of metallic components operating at high temperatures. However, there lack numerical models that enable direct simulations of crack growth and plasticity development under coupled creep-fatigue. In this study, a unified phase-field model is developed for simulating crack growth under fatigue, creep, and coupled creep-fatigue. This model is able to reproduce the Paris laws for both brittle and ductile materials in pure fatigue mode, which shows that the degradation rate due to cyclic stress in ductile materials is generally larger than that in brittle materials. Fatigue simulations with different yield strengths demonstrate that plasticity facilitates crack growth in typical ductile materials. High-throughput simulations are performed under coupled creep-fatigue conditions, with varying hold-stress levels and hold-time. By analyzing crack growth rate under different hold-time, a creep-fatigue interaction term is obtained. Simulation results demonstrate that the creep-fatigue interaction is caused by smaller stress gradient and enhanced degradation rate ahead of the crack tips under coupled creep-fatigue, compared to the situation of pure fatigue. This work reveals the origin of different Paris-law exponents in brittle and ductile materials and demonstrates how the interplay between creep and fatigue affects crack growth.

Effect of stress ratio and welding residual stresses on the fatigue crack growth behaviour of Weldox-700 steel using LGDM

In this work, numerical simulations of high-cycle fatigue and fatigue crack growth have been performed using localizing gradient damage methodology (LGDM) for base and welded weldox-700 steel. LGDM models crack growth phenomenon by avoiding any non-physical widening of damage bands. The effect of stress ratio is included in the strain-based damage evolution in the present work. Accordingly, the generalized expressions of damage parameters have been derived. Experimental fatigue tests are performed on the base material and the welded joints. In order to numerically investigate the welded joints, residual stresses developed during welding are obtained through sequentially coupled thermo-mechanical finite element analysis. Subsequently, the fatigue-life and crack-propagation are simulated by applying the residual stresses as a pre-existing field in the LGDM framework, which uses full coupling between deformations and non-local equivalent strains in the finite element analysis. The simulated results and experimental fatigue data are found to be in good agreement.

Molecular dynamics simulation of crack growth in nanocrystalline nickel considering the effect of accumulated plastic deformation

Molecular dynamics simulations are conducted to investigate atomic stress and plastic strain distribution in pre-cracked crystalline nickel, along with microstructure evolution. The plastic strain calculation method is improved by refining neighboring atom selection. A new parameter for measuring plastic strain concentration allows for comparison across different crystallographic directions. The effects of temperature, strain rate, crystallographic direction, loading mode, grain boundary and grain size are evaluated. At elevated temperature, crack tip blunting becomes obvious, and crack propagation decelerates. The crack propagates through void nucleation, growth, and eventual linkage with the original crack. Higher temperature increases the plasticity limit of void nucleation. Strain rates show a positive correlation with plasticity limit but a negative correlation with crack growth rate and final length. Crystallographic direction influences crack propagation, with crystal 100 exhibiting significant crack propagation, while 110 and 111 demonstrating marked resistances to crack propagation. Crystal 100 has the highest plastic deformation concentration near the crack tip. Loading mode affects plastic deformation accumulation. In-plane shear results in less plastic deformation and less obvious crack propagation. In bi-crystals, the relative rotation angle between grains significantly influences crack propagation. X-rotation of the right grain most significantly impedes crack propagation, while y- and z-rotation tend to cause the crack to cross the grain boundary. In polycrystals, plastic deformation accumulation at grain boundaries is significant, with the crack tending to propagate along grain boundaries. Plastic strain and concentration parameter peaks are lower in grain boundaries than in single crystals, indicating weaker stability. The results demonstrate that the failure process of crystalline nickel is intricately linked to the stress and plastic strain distribution around the crack tip. The plastic strain and concentration parameter are more accurate predictors of crack propagation than atomic stress.

An adaptive phase field approach to 3D internal crack growth in rocks

Modeling the 3D internal crack under compression entails complex fracture mechanics (mode I-II-III fracture), resulting in substantial computational costs and challenges in characterizing fracture morphology characterization for Phase Field Method (PFM) simulations. In the present paper, we developed a 3D adaptive crack propagation model integrated into the PFM to study the internal cracks in rocks. The proposed locally refined solution was implemented within the isogeometric analysis (IGA) framework, utilizing PHT-splines and employing the phase field variable as an error indicator to accurately capture non-smooth crack surfaces. The simulation begins with a coarser mesh, and the spatial discretization is adaptively refined in real-time as the computation progresses and the phase variable threshold is reached. By comparing our results with previous numerical tests, we validated the effectiveness of our model in simulating crack growth. Notably, a smaller length scale parameter led to a higher peak force in notched square plates under tension, and our adaptive PFM successfully reduced errors caused by length scale parameters. We further validated our model by comparing it with uniaxial compression experiments on 3D-printed resin samples with internal penny-shaped cracks, achieving good agreement with the experimental data. Using the 3D adaptive PFM, we predicted changes in crack morphology and fracturing mechanisms by varying the inclination angles of internal penny-shaped cracks. Our numerical results showed that as the inclination angle increased, wing cracks initiated closer to the end tips of the original crack, and their length decreased due to the wings wrapping effect. The corresponding fracturing mechanisms transition from mode I-III fracture (0°) to mode I-II-III fracture (30°, 45°, 60°), and eventually to mode I fracture (90°) as inclination angles increase. Comparing 2D and 3D models, we found that the growth of wing cracks in 3D was significantly influenced by the intermediate principal stress. We conclude that the extended 3D adaptive PFM-based model accurately predicted complex mechanical behavior and crack growth patterns in rock.

Crack propagation simulation and overload fatigue life prediction via enhanced physics-informed neural networks

The fatigue crack growth simulation and life prediction of structures are implemented in this paper based on the physics-informed neural networks (PINNs). Firstly, the enhanced PINNs are proposed by introducing the crack tip asymptotic displacement fields, so that the crack tip stress intensity factors can be calculated accurately even when the number of collocation points is small and the distribution grid is regular. The enhanced PINNs essentially transform the solution of elastic body containing crack into the optimization of minimizing the constructed loss functions, and can invert the fracture parameters. Then, an automatic crack propagation simulation method is developed based on the enhanced PINNs. The network architecture and the overall node distribution can be unchanged during the crack propagation process, and only new crack surfaces need to be processed and corresponding loss functions need to be modified. Because the nodal refinement around crack-tip is not required, this simulation method is convenient and can accurately predict the mixed-mode crack propagation path. Finally, the fatigue crack growth life algorithm considering overload is developed, where the effect of each overload can be captured by the cycle-by-cycle method. Based on this algorithm, the retardation behavior can be characterized and the fatigue life of structure under the load spectrum with periodic overloads can be accurately predicted. The sufficient examples are given to verify the feasibility and accuracy of the method proposed in this paper.

Numerical Simulation of Spatial Crack Growth and the Local Failure Process of Rock Using the SMDSM Empowered by Structured 3-D Hierarchical Meshes

Numerical Simulation of Spatial Crack Growth and the Local Failure Process of Rock Using the SMDSM Empowered by Structured 3-D Hierarchical Meshes

Fatigue crack growth simulation by extended finite element method: A review of case studies

AbstractNumerical simulation of fatigue crack growth (FCG) is presented, based on the application of the extended finite element method (XFEM). Couple of case studies are presented, as a review of recent experience of the Belgrade school of XFEM simulations, established at the Faculty of Mechanical Engineering. Case studies comprised Charpy specimen with initial crack at the notch tip, oil rig pipe with an axial surface crack, pressure vessels with a crack at the welded joint with connecting pipe, turbine shaft with a crack at the transition radius, optimization of a wing spar in respect to FCG, the effect of mesh size on fatigue life estimation of a stringer panel, fatigue life estimation of wing‐to‐fuselage connecting lug, geometry effect on fatigue life of orthopedic plates and fatigue life of hip implant. Based on these case studies, XFEM is discussed in respect to its accuracy and efficiency. It is concluded that XFEM is a versatile tool for simulation of FCG, providing an excellent option for precise and reliable fatigue life of a cracked component.

A model for modifying the S‐N curve considering the effect of boundary conditions on the fatigue crack growth of welded components

AbstractThe present study proposes a novel model to modify master S‐N curves of components according to their load redistribution capability reflected in different boundary conditions (BCs) based on the fracture mechanics analysis. To that end, a comprehensive numerical study was conducted on a Single Edge Notch Bend (SENB) specimen constrained with different kinematic BCs using discrete fatigue crack growth (FCG) simulation. It was observed that BCs indeed can have a significant effect on the crack growth behavior and consequently on the resulting fatigue life under the same nominal loading conditions. The proposed model was applied to the S‐N curve of a T‐welded joint, and the predicted fatigue life was validated against 3D FCG simulations. Finally, FCG tests were conducted on SENB specimens to experimentally corroborate the effect of BCs on the FCG rate.

Peridynamic simulation of fatigue crack growth in porous materials

Pores are a key type of concerns in additive manufacturing technology. They can significantly affect materials’ fatigue resistance and fatigue crack growth in the structures. In this paper, an intermediately-homogenized (IH) peridynamic (PD) fatigue crack model is introduced for simulating the fatigue crack growth in porous materials. The effect of micro-scale heterogeneity on fatigue failure is preserved in the IH-PD model, where stochastically-generated pre-damage matches materials’ porosity. The PD J-integral, a key parameter used to connect the fatigue simulation and the experimental measurements, is calculated under different porosities, and the independence of PD J-integral on its integration path is verified. Then, the PD fatigue crack model combined with the IH-PD material model is applied to study the dependence of the crack path and growth rate on porosity in compact tension alloy samples. The normalized fatigue life between experimental measurements and numerical results is compared. The normalized fatigue life-porosity relationship calculated from the IH-PD fatigue model matches the average trend of the experimental measurements.

A numerical framework based on localizing gradient damage methodology for high cycle fatigue crack growth simulations

A numerical framework based on localizing gradient damage methodology for high cycle fatigue crack growth simulations

Investigating the Influence of Holes as Crack Arrestors in Simulating Crack Growth Behavior Using Finite Element Method

The primary focus of this paper is to investigate the application of ANSYS Workbench 19.2 software’s advanced feature, known as Separating Morphing and Adaptive Remeshing Technology (SMART), in simulating the growth of cracks within structures that incorporate holes. Holes are strategically utilized as crack arrestors in engineering structures to prevent catastrophic failures. This technique redistributes stress concentrations and alters crack propagation paths, enhancing structural integrity and preventing crack propagation. This paper explores the concept of using holes as crack arrestors, highlighting their significance in increasing structural resilience and mitigating the risks associated with crack propagation. The crack growth path is estimated by applying the maximum circumferential stress criterion, while the calculation of the associated stress intensity factors is performed by applying the interaction integral technique. To analyze the impact of holes on the crack growth path and evaluate their effectiveness as crack arrestors, additional specimens with identical external dimensions but without any internal holes were tested. This comparison was conducted to provide a basis for assessing the role of holes in altering crack propagation behavior and their potential as effective crack arrestors. The results of this study demonstrated that the presence of a hole had a significant influence on the crack growth behavior. The crack was observed to be attracted towards the hole, leading to a deviation in its trajectory either towards the hole or deflecting around it. Conversely, in the absence of a hole, the crack propagated without any alteration in its path. To validate these findings, the computed crack growth paths and associated stress intensity factors were compared with experimental and numerical data available in the open literature. The remarkable consistency between the computational study results for crack growth path, stress intensity factors, and von Mises stress distribution, and the corresponding experimental and numerical data, is a testament to the accuracy and reliability of the computational simulations.

An alternative and robust formulation of the fatigue crack growth rate curve for long cracks

Crack growth simulations are an important method for estimating the remaining service life of components and structures with cracks under cyclic loading. In particular, the evaluation of cracks emanating from clinched joints is a major challenge because the fracture mechanical properties of the sheet materials can change locally due to the joining process. Special specimens are used to determine the relevant crack growth rate curves. For the application of these curves within simulation programs, they are described using crack propagation equations. This requires an accurate formulaic description of the entire crack curve with clearly identifiable parameters that unambiguously describe certain characteristics of the crack growth rate curve. Known approaches either describe only parts of the crack growth rate curve or the single parameters affect different characteristics of the curve and thus influence each other. Therefore, a new alternative and robust mathematical fit of the crack growth rate curve is developed and validated with experimental results.

Экспериментальная оценка адекватности численного моделирования межслоевой трещиностойкости слоистого стеклоэпоксикомпозита при комбинированной моде нагружения I/II

The reliability of numerical simulation of crack growth in a laminate glass-epoxy composite under mixed-mode loading by opening (mode I) and shear (mode II) of an interlayer crack is verified. According to the experimentally determined standard (DCB and ENF) and nonstandard (SLB and OLB) methods, the values of the parameters of interlayer crack resistance under individual and mixed-mode loading modes I and II calculated the exponent in the Benzeggagh-Kenane equation as a material constant of the laminate epoxy glass composite. Using this parameter and the ANSYS software package, within the framework of linear elastic fracture mechanics and the method of virtual crack closure, numerical finite element modeling of the growth of interlayer cracks in samples of a laminate glass-epoxy composite of the SLB and OLB types was carried out under a mixed-mode loading with a different fraction of modes. With the optimal number of elements in the finite element mesh per given length of the crack growth trajectory, numerical simulation provides sufficient accuracy of calculations of the limit load of the beginning of crack growth with a minimum amount of calculations and good agreement between the experimentally determined and calculated crack resistance parameters.

Quasi-static and fatigue crack growth simulation in co-consolidated thermoplastic joints containing crack arrest features

In the present article, quasi-static and fatigue crack growth in co-consolidated thermoplastic Crack-Lap Shear (CLS) specimens containing two different Crack Arrest Features (CAFs) have been numerically simulated. The substrates have been manufactured from unidirectional T700 carbon fiber reinforced Low-Melt PAEK thermoplastic material. The Friction Stir Spot Welding (RFSSW) and the Induction Low Stir Friction Riveting (ILSFSR) CAFs were studied. Crack growth simulation has been based on the cohesive zone modeling method and has been implemented via the LS-Dyna FE software. Both static and fatigue crack growth models have been successfully validated against results from respective mechanical tests. Both CAFs have been proven capable of delaying crack growth, especially for fatigue loading. An evaluation of various installation parameters of the two features, such as the diameter, the distance to the crack tip, and the installation depth, was performed for the quasi-static loading cases. All parameters have been found to affect the crack stopping efficiency, but the most important effect comes from the diameter of the CAF. Furthermore, a series of quasi-static and fatigue simulations have been run on a mono-stiffener element, representative of an aeronautical structural assembly, in order to evaluate numerically the efficiency of the CAFs at a higher scale. The results showed no crack stopping for the ILSFSR and a low crack stopping for the RFSSW for fatigue loading.

Adaptive PD-FEM coupling method for modeling pseudo-static crack growth in orthotropic media

In this study bond-based peridynamic formulation is developed and coupled with the finite element method (FEM) to simulate crack growth in orthotropic materials. The coupled PD-FEM formulation gives an opportunity to use both peridynamic and finite element method advantages simultaneously. The Legendre functions are implemented to define varying bond properties according to the material orientation. Pseudo-static crack propagation in the composite materials is simulated and it is shown that the proposed method is able to predict crack growth in orthotropic materials faster than the conventional PD methods. Accuracy of the proposed method is demonstrated through comparison of the results against those of numerical studies which are available in the literature.