Crack Path Prediction Research Articles

Incorporation of gradient-enhanced microplane damage model into isogeometric analysis

PurposeThis study aims to develop a new analysis approach devised by incorporating a gradient-enhanced microplane damage model (GeMpDM) into isogeometric analysis (IGA), which shows computational stability and capability in accurately predicting crack propagations in structures with complex geometries.Design/methodology/approachFor the non-local microplane damage modeling, the maximum modified von-Mises equivalent strain among all microplanes is regularized as a representative quantity. This characterization implies that only one additional governing equation is considered, which improves computational efficiency dramatically. By combined use of GeMpDM and IGA, quasi-static and dynamic numerical analyses are conducted to demonstrate the capability in predicting crack paths of complex geometries in comparison to FEM and experimental results.FindingsThe implicit scheme with the adopted damage model shows favorable numerical stability and the numerical results exhibit appropriate convergence characteristics concerning the mesh size. The damage evolution is successfully controlled by a tension-compression damage factor. Thanks to the advanced geometric design capability of IGA, the details of crack patterns can be predicted reliably, which are somewhat difficult to be acquired by FEM. Additionally, the damage distribution obtained in the dynamic analysis is in close agreement with experimental results.Originality/valueThe paper originally incorporates GeMpDM into IGA. Especially, only one non-local variable is considered besides the displacement field, which improves the computational efficiency and favorable convergence characteristics within the IGA framework. Also, enjoying the geometric design ability of IGA, the proposed analysis method is capable of accurately predicting crack paths reflecting the complex geometries of target structures.

Nonlocal FEM Simulations of Ductile Damage with Regularized Crack Path Predictions

Constitutive equations of finite strain elasto-plasticity are coupled to continuum damage mechanics to simulate the initiation and propagation of cracks in ductile materials. The diffuse deterioration of material’s strength is modelled using porosity as a damage parameter. We show that the local damage model yields simulation results, pathologically dependent on the FEM mesh upon mesh refinement: (i) the structural behaviour becomes unrealistically brittle; (ii) the FEM mesh determines the crack path. To solve these problems, an integral-based approach to nonlocal damage is implemented. It enables physically sound results by introducing the linear size of the microstructure into the model’s formulation. To prevent the effect of unrealistic diffusion of damage, the averaging operator is applied not to the porosity, but to its dual parameter, material’s continuity. Solutions of test problems for crack propagation in a compact tension specimen are presented. The convergence of FEM solutions is demonstrated for different slopes of the mesh with fine and coarse discretizations.

A novel damage model in the peridynamics-based cohesive zone method (PD-CZM) for mixed mode fracture with its implicit implementation

Peridynamics (PD) becomes increasingly promising in computational fracture mechanics for its powerful ability to capture complex crack problems. Nevertheless, the PD applications are mainly limited to brittle fracture, and a robust PD model for predicting mixed mode fracture of quasi-brittle materials is still lacking. In this work, a novel damage model is proposed in the PD-CZM to accurately predict quasi-brittle failure under quasi-static mixed-mode loading, especially shear-dominated loading. In order to establish the damage criterion of quasi-brittle materials, the bond potential in bond based peridynamics (BBPD) is firstly separated into the dilatational part and deviatoric part. Instead of using existing bond stretch-based failure criterion, a new damage criterion obtained by combining bond stretch and dilatational bond potential is firstly proposed to determine the damage initiation. Also, the tension softening behavior of quasi-brittle materials is described in the damage model by a well-established degradation curve based on an energy-equivalence principle. Besides, to robustly solve the physical nonlinear characteristics, especially tension softening-induced snap-back phenomenon, the implicit implementation of the PD-CZM is performed with different implicit solution methods. Three challenging benchmarks are simulated to validate the proposed damage model, including Schlangen’s single-edge notched beam test, Nooru-Mohamed’s double edge-notched concrete specimen (DENS) test and Arrea and Ingraffea’s single notched shear beam test with severe snap-back behavior. Both the predicted crack paths and the load–displacement curves are in perfect agreement with the experimental observations and other numerical results, clearly demonstrating the validity of the proposed damage model and the robustness of the implicit implementation.

Phase field modeling of ductile fracture at large plastic strains using adaptive isotropic remeshing

In this paper, a phase field model of ductile fracture is described within the framework of large plastic strains. Most results dealing with phase field modeling of ductile fracture are carried out on a fixed mesh, which requires a fine mesh throughout all the computation. The aim of this paper is to introduce an adaptive isotropic remeshing strategy coupled with a phase field model of ductile fracture to achieve accurate results with a major decrease in computational time. A mixed velocity/pressure finite element formulation is used for the solution of mechanical fields. The plastic strain field needs to be transferred to the new mesh after each remeshing operation. This field transfer requires the use of a suitable remeshing-transfer operator. Different field transfer operators are tested and results are reported. In order to reduce the numerical diffusion associated with the field transfer operation, a volume quality based metric has been introduced. This paper presents different numerical examples with both qualitative and quantitative analyses in order to show the ability of the developed strategy in predicting crack evolution in ductile materials. The proposed framework is also able to predict crack paths in highly ductile materials while benefiting from space-adaptivity.

Direction-dependent fracture in solids: Atomistically calibrated phase-field and cohesive zone model

We propose a new phase-field damage formulation which takes into account anisotropic damage evolution in solids. Such anisotropy projects itself in fracture energy values which depend on the direction of the crack surface. Therefore, instead of one constant scalar parameter for the fracture energy value, we use a direction-dependent fracture energy function. By incorporating a direction-dependent fracture energy function, only a single damage variable as well as a first order damage gradient need to be used within the standard phase-field damage model. This is in contrast to other available anisotropic phase-field models which typically use multiple variables or higher order gradient terms. To obtain values for the fracture energy function, atomistic calculations are performed. Here, molecular static simulations are utilized to calculate the energy of free surfaces within an Aluminum crystal. As a result, we report the fracture energy value as a function of the surface orientation. The obtained fracture energy function is passed directly to the phase-field damage formulation to investigate transgranular fracture within a single crystalline. Moreover, the grain boundary is represented via a cohesive zone model to take into account intergranular fracture in a bi-crystalline structure. The predicted crack path is in good agreement with obtained results from molecular dynamics simulations. Finally, by calibrating the length scale parameter in the phase-field damage model, it is possible to compare the reaction forces from finite element calculations with atomistic ones.

A combined adaptive phase field and discrete cutting method for the prediction of crack paths

Crack propagation is modelled in this contribution by combining different methods. The main idea is to use the newly developed virtual element method in combination with the phase-field methodology and a specific cutting technology. The idea is that the direction of a crack path can be easily predicted using the phase-field method. However this method needs a very fine mesh to resolve a real crack and thus this method has to be coupled with an adaptive approach. Due to the flexible virtual element method that allows to add arbitrary number of nodes to an element a robust cutting technique can be used to replace the refined mesh by a discrete crack. In total this combination of different methods allows a very efficient and robust solution of crack growth in solids.

An auto-adaptive sub-stepping algorithm for phase-field modeling of brittle fracture

In this work, we propose an auto-adaptive displacement stepping algorithm to auto-adaptively adjust the displacement step size while solving the quasi-static brittle fracture propagation problem with the phase-field method. We employ a step size controller based on an ‘a posteriori’ error estimator to achieve adaptivity in the displacement step size. To capture correct crack propagation behavior near peak load, we propose an energy-based conditional. The conditional is evaluated in a sub-step of the primary displacement step, and it decides whether to accept or reject the step. Based on the step size controller algorithm and the sub-stepping algorithm, we formulate the auto-adaptive sub-stepping algorithm. We investigate the accuracy and computational cost of the proposed algorithm on several benchmark problems from the literature and compare it to the standard alternate minimization (AM) approach. The algorithm auto-adaptively adjusts the size of the displacement step and allows us to use step sizes that may vary by even three orders of magnitude. As compared to the standard AM algorithm, this results in a reduction of 78–90% in the CPU time required to reach peak reaction force, and 56–78% reduction in the CPU time needed to complete analysis, and always maintains the accuracy in crack path prediction.

Random beam lattice modeling method for catastrophic crack growth simulation of brittle-like materials

A random and irregular beam lattice modeling method is developed to predict the crack growth process of brittle-like materials. The model representing the random degree of beam lattice model is defined, which is used to study the influence of lattice mesh on the crack path prediction results. In the simulation, the coupling interactionsamong cracks initiation and growth can be considered. Crack growth process of two double-edge notched specimens, respectively, under shear and tension and direct-tension were simulated and compared with the corresponding experimental results. By comparison of simulation and experimental results, effectiveness of the developed beam lattice modeling method is verified, and can be used to simulate crack growth for studying the fracture mechanisms of brittle-like materials. And the regular beam lattice model can affect the crack paths prediction, and random and irregular beam lattice model is more suitable for simulating crack growth.

Application of Response Surface Method in Probabilistic Fatigue Crack Propagation Life Assessment using 3D FEA

Fatigue crack growth life assessment is an important task in damage tolerant design practices. Being able to assess variability of crack propagation path and remaining useful life requires both deterministic and probabilistic modeling capabilities. Three-dimensional fatigue crack growth finite element modeling and Radial Basis Function based Response Surface modeling is shown to be an accurate and efficient route to predict crack propagation path in uncertainty quantification studies. A mixed-mode fatigue crack growth experimental measurement from literature is used for validation purposes and for quantifying crack path sensitivity due to off-nominal specimen geometry. Two sets of deterministic 3D crack propagation simulations are performed to relate geometric deviations to crack path predictions: first set is used to calibrate the response surface model while the second for verification purposes. Once verification requirements are satisfied, the response surface model can be employed in Monte Carlo type probabilistic simulations.

Corrosion effect, constraint and path orientation estimated in cracked gas turbine blade

The severe damage of gas turbine is due to the failure of the blade, in which the occurrence of a serious pitting occurred on the blade surfaces was evidence of fatigue marks in the fracture surface. This paper deals with the effect of semi-elliptical crack propagation on the crack path using a basic approach in predicting crack paths, namely, incremental methods. The crack position was chosen at the node coordinate where we have the maximum principal stresses. In this node, we have created a semi-elliptical crack and we have compared the results with the Stress Intensity Factors and T-stress values. The local fracture criterion of the maximum average tangential stress in the vicinity of fracture process zone including two terms of the Williams series solution for the mixed mode I/II loading has been used for predicting the angle of surface crack growth. The volumetric method (VM) for the compression-sensitive materials is described by a linear combination of the effective stress and the effective stress intensity factor. The results of our finite element computations based on a two-parameter fracture mechanics formulation showed that the T-stress has significant effects on the crack path.

Comprehensive Comparisons of Two-and Three-Dimensional Numerical Estimation of Stress Intensity Factors and Crack Propagation in Linear Elastic Analysis

This paper presents a comprehensive comparison of two finite element software in two and three dimensions. The first is a two-dimensional crack growth simulation program developed as source code by using Visual Fortran Language whereas the second is ANSYS mechanical program (3D structural analysis for fracture mechanic analysis). The procedure consists of computing stress intensity factors (SIFs), the crack growth path and the stresses and strain distributions via an incremental analysis of the crack extension, considering two and three-dimensional analysis. Comparisons between these two software were performed for different case studies for stress intensity factors as well as crack growth trajectory. This source code includes the mesh generator based on the advancing front method as well as all the pre and post process for the crack growth simulation under linear elastic fracture mechanics theory with a user-friendly interface. The maximum circumferential stress criterion was used for prediction of the crack growth in isotropic materials under mixed-mode loading. Furthermore, the equivalent domain integral method has been used for calculating the stress intensity factors values during crack growth. Verification of the predicted crack path and stress intensity factors values were validated with relevant experimental data and numerical results obtained by other researchers with a good agreement.

Simulation of fatigue cracks growth processes of two parallel cracks in thin plate pulled by the constant amplitude cyclic loading

In the paper, the propagation processes of two parallel cracks in 2-mm-thick plate pulled by the cyclic loading were investigated by numerical simulation and experiment. The codes Abaqus and Franc3D were implemented jointly to predict the crack growth path, the stress distribution around the cracks tip and the fatigue life. The corresponding fatigue experiment was carried out on a servo-hydraulic fatigue testing machine. The investigation indicates that the predicted crack paths agree well with the experimental results at the crack propagation early stage, and the predicted crack growth rate is consistent with the findings in experiment, which validate the prediction of the mixed mode crack propagation processes.

The minimum shear stress range criterion and its application to crack orientation prediction in incomplete contact fretting problems

A proper prediction of crack paths is required when assessing accurately the fatigue crack propagation life. Recently, some authors have pointed out that the criterion of minimum shear stress range leads to inconsistent results when predicting fretting crack paths under incomplete contacts. In this paper, different fretting experiments with cylinder-to-flat contact found in the literature are reviewed, and the corresponding crack path prediction using the extended finite element method and the minimum shear stress range crack orientation criterion is performed. Results show the applicability of the criterion to predict the crack orientation during stage II in incomplete contact fretting problems.

A nonlocal fracture criterion and its effect on the mesh dependency of GraFEA

Recently, Khodabakhshi et al. (Meccanica 51(12):3129–3147, 2016. https://doi.org/10.1007/s11012-016-0560-6 ) presented a new method (by the name GraFEA) capable of studying fracture based on edge breakage within a classical FEA scheme which combines the best features of FEA and bond-breakage methods in a single framework. In this study, an attempt is made to investigate the mesh dependency of GraFEA by a set of numerical examples, and it is shown that using a local fracture criterion for edge failure will yield mesh-dependent results, as is already well known. A physically motivated nonlocal fracture criterion is implemented along with the edge breakage model, and its efficacy in eliminating the mesh sensitivity is investigated. The nonlocal criterion introduces a length scale into the problem. It is shown that by increasing the magnitude of the length scale parameter from zero, the damage pattern moves from localized fracture to diffuse damage pattern, yet with complete material separation (fracture) across a certain plane. It is shown by numerical results that, as expected, the introduction of the nonlocal fracture criterion eliminates the issue of mesh sensitivity, and thus predictions of the approximate crack paths and damage zone can be done within the classical FEA framework without the need for special formulations.

Fracture propagation using the radial point interpolation method

AbstractThis work presents a crack path prediction algorithm combined with the radial point interpolation method (RPIM), a meshless method. To allow easier implementation in existing structural analysis software, this algorithm is numerically compatible with finite element method (FEM) formulations. The proposed RPIM formulation uses the triangular elements of a FEM mesh as the background integration grid, allowing also to combine both formulations more easily. Thus, with the developed methodology, the RPIM can be integrated directly in a FEM software or use the same CAD tools to build the discretization meshes. Because the RPIM shape functions possess the delta Kronecker property, all the numerical techniques available for the FEM can be applied to enforce the natural and essential boundary conditions.The developed algorithm uses the maximum tangential stress criterion to determine the crack propagation direction, and the crack paths obtained with it corresponded well to previous research.

Predicting ductile tearing of additively manufactured 316L stainless steel

Predictions for ductile tearing of an additively-manufactured 316L metal structure were generated using a unified creep plasticity damage (UCPD) model and finite element models constructed using 4-node tetrahedral or 8-node hexahedral elements. Uniaxial tension and notched tension experiments were simulated to obtain material parameters for the UCPD model. Results from these simulations revealed that accurate prediction of material bifurcations prior to the initiation of ductile tears are critically important for generating accurate ductile tearing predictions. This occurs because material bifurcations lead to deformation localization which is followed by ductile tearing. Crack path predictions were found to be sensitive to the finite element mesh with cracks preferring to run along mesh lines. Finally, the unloading slope of the load displacement curve was found to be sensitive to element failure modeling.

The third Sandia Fracture Challenge: peridynamic blind prediction of ductile fracture characterization in additively manufactured metal

In the context of the third Sandia Fracture Challenge (SFC3), the details of the blind predictions performed by the University of Texas team are provided in this article. Over the past two decades, the peridynamic theory has shown great promise in modeling autonomous crack nucleation and growth in materials. While peridynamics has been commonly applied to simulate failure of brittle materials, its ability in predicting ductile fracture has remained mostly untested. This fracture challenge was seen as an opportunity to assess the state of the art of the peridynamic theory in predicting the response of an additively manufactured 316L stainless steel bar with a complex geometry under the dynamic tensile experiments performed by Sandia National Laboratories. The performance of a recently proposed, generalized, ordinary finite deformation constitutive correspondence model, coupled with a recent state-based damage correspondence model was explored over this problem. For finite deformation material modeling, the classical elastoplastic framework of Simo was implemented within the ordinary correspondence theory. Damage modeling was achieved by incorporating the Johnson-Cook failure criterion using the damage correspondence framework. An iterative inverse technique was applied to calibrate the model parameters using the longitudinal and notched tensile tests data provided by Sandia National Laboratories. A blind prediction of the deformation and failure behavior of the SFC3 geometry was performed by embedding the calibrated model in a peridynamic simulation. Uncertainty was introduced into the model parameters to quantify material variability. The results are compared to the experiments conducted at Sandia National Laboratories. While our modeling approach led to qualitatively good results and a correctly predicted crack path, it underpredicted the load-carrying capacity of the structure and simulated an early fracture. Our post-experiment analysis identifies material instability issues associated with the model as the primary sources of error.

Predicting the crack path in a wedge under a concentrated tensile force by means of variational principle

Variational principle of brittle fracture mechanics is employed to predict the crack path in an infinite wedge under a concentrated tensile force. The weight function in basic equation of variational problem is assumed to be proportional to the maximum strain in the uncracked wedge. Obtained equation for solving the variational problem allowed predicting the crack path in general. The predicted crack path is in agreement with experimental results obtained in the case of the truncated wedge.

Fracture analysis of thin films on compliant substrates: A numerical study using the phase field approach of fracture

In this work, the phase field (PF) approach for brittle fracture in the bulk coupled with the cohesive zone model (CZM) for pre-existing interfaces is exploited for the simulation of fracture of thin films on compliant substrates, which are structural configurations of extensive use in many engineering systems such as protecting layers for vessels, stretchable electronic devices, among many others. Due to the coupling between the two aforementioned models for fracture, the proposed approach enables capturing bulk damage and crack deflection or penetration at the prescribed interfaces in a robust and reliable manner, these scenarios depending on the particular mechanical properties of the system via a sensitivity analysis. In this concern, it is shown that the proposed approach is capable of predicting several complex crack paths for different fracture modes, concerning the 2D and 3D thin film fracture problems herein investigated: (i) deflection/delamination, (ii) penetration and (iii) deflection/delamination at the prescribed interface in combination with penetration. Moreover, the effect of the interface fracture energy on the predicted crack path has been carefully investigated.

Critical analysis of the suitability of crack propagation direction criteria for 2D cylindrical plain fretting contact

In this work the suitability of the criterion of maximum effective amplitude of the normal stress (Δσn,eff)max and the criterion of minimum shear stress range (Δτ)min for 2D cylindrical plain fretting contact condition has been analysed. The numerical analysis has been performed by means of the extended finite element method, which takes into account the contact between crack faces during the closing part, and the results have been compared with experiments reported in the literature. Results show that overall the (Δτ)min criterion predominates in intermediate stage, while the (Δσn,eff)max shows less deviation in the final stage. However, the predicted crack path by the latter criterion shifts toward the outer side, which do not correlate with the experimental results reported in the literature. Additional studies should investigate the variables that are affecting this change in the behaviour along the crack in order to set a criteria that is able to predict the plain fretting condition crack paths accurately.