Crack Propagation In Brittle Materials Research Articles

A peridynamic-informed deep learning model for brittle damage prediction

Physics-informed Neural Network (PINN) has been introduced recently to predict and understand complex physical phenomena by directly incorporating feedback from governing equations. While PINNs offer remarkable capabilities, challenges arise when addressing discontinuities and heterogeneity, potentially compromising accuracy and reliability in prediction outcomes. In this study, a novel approach that combines the principles of peridynamic (PD) theory with PINN is presented to predict quasi-static damage and crack propagation in brittle materials. To achieve high prediction accuracy and convergence rate, the linearized PD governing equation is enforced in the PINN’s residual-based loss function. The proposed PD-INN is able to learn and capture complicated displacement patterns associated with different geometrical parameters, such as pre-crack position and length. The computational method presented in this study can be implemented to any PD constitutive model like Bond-Based PD or State-Based PD as well as any horizon factor. Several enhancements like cyclical annealing schedule and deformation gradient aware optimization technique are proposed to ensure the model would not get stuck in its trivial solution. The model’s performance assessment is conducted by monitoring the behavior of loss function throughout the training process. The results obtained through PD-INN demonstrate a satisfactory level of agreement in 2D and 3D when compared with the ground truth deformation from high-fidelity techniques like PD direct numerical method and Extended finite element method (X-FEM). Our results show the ability of the nonlocal PD-INN to predict damage and crack propagation accurately and efficiently.

The influence of boundary effects on explosive damage and crack propagation in brittle materials

To investigate the influence of boundary effects on the damage and fracture characteristics of brittle materials under explosive loads, studies were conducted using explosive model experiments and simulation methods. The results indicate that the damage outcomes of single and double boundary models are significantly affected by the variation in the distance (Δl) between the explosion source and the boundary. When Δl is the same, more fragments are generated by the double boundaries. The circumferential tensile stress, produced by the superposition of incident and reflected stress waves at the boundary, is the primary cause for the continuation of crack propagation.

Phase-field simulation of fracture in Polymethyl Methacrylate

Significant interest and developments in phase-field fracture modeling have emerged. It approximates fracture continuously using a length-scale parameter, accurately simulating fracture initiation and crack propagation in brittle materials like Polymethyl Methacrylate (PMMA) with nonlinear elasticity. This study proposes a phase-field approach for simulating PMMA fracture behavior using ABAQUS with a nonlinear elastic material model (UMAT) and a three-layered element composition (UEL). The staggered approach sequentially solves displacements and phase-field variables. Numerical results are validated against experiments considering various geometries, stress concentrators, and pre-cracks. The computational approach accurately predicts fracture initiation and crack growth in complex patterns and diverse loading conditions.

On the choice of a phase field model for describing fracture behavior of concrete

Numerical modeling of concrete fractures is of prime importance in the durability assessment of civil engineering structures. The phase field model has been demonstrated as a promising framework to simulate crack propagation in brittle material while using the many existing techniques. In this paper, we discuss choosing the most appropriate phase field model for describing the fracture behavior of concrete. More specifically, we present a detailed analysis of the existing models, which have been created by combining different spectral decompositions and crack density functions. The numerical simulation predictions are confronted with the experimental observation of a benchmark problem from the literature. The obtained results showed that the extensive/compressive decomposition and the quadratic crack density function are the most suitable models to study concrete cracking behavior. The investigation’s size effects demonstrated heterogeneities played an important role in concrete’s post-cracking behavior and softening branches, especially for the small concrete structure.

Physics informed neural networks for phase field fracture modeling enhanced by length-scale decoupling degradation functions

The paper proposed a novel framework for efficient simulation of crack propagation in brittle materials. In the present work, the phase field represents the sharp crack surface with a diffuse fracture zone and captures the crack path implicitly. The partial differential equations of the phase field models are solved with physics informed neural networks (PINN) by minimizing the variational energy. We introduce to the PINN-based phase field model the degradation function that decouples the phase-field and physical length scales, whereby reducing the mesh density for resolving diffuse fracture zones. The numerical results demonstrate the accuracy and efficiency of the proposed algorithm.

Experimental study on 3D internal penny‐shaped crack propagation in brittle materials under uniaxial compression

AbstractFractures are widely present in geomaterials of civil engineering and deep underground engineering. Given that geomaterials are usually brittle, the fractures can significantly affect the evaluation of underground engineering construction safety and the early warning of rock failure. However, the crack initiation and propagation in brittle materials under composite loading remain unknown so far. In this study, a three‐dimensional internal laser‐engraved cracking technique was applied to produce internal cracks without causing damage to the surfaces. The uniaxial compression tests were performed on a brittle material with internal cracks to investigate the propagation of these internal cracks at different dip angles under compression and shear. The test results show that the wing crack propagation mainly occurs in the specimen with an inclined internal crack, which is a mixed‐Mode I–II–III fracture; in contrast, Mode I fracture is present in the specimen with a vertical internal crack. The fractography characteristics of Mode III fracture display a lance‐like pattern. The fracture mechanism in the brittle material under compression is that the internal wing cracks propagate to the ends of the whole sample and cause the final failure. The initial deflection angle of the wing crack is determined by the participation ratio of stress intensity factors KII to KI at the tip of the internal crack.

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

Particle Discontinuous Deformation Analysis of Static and Dynamic Crack Propagation in Brittle Material

A dynamic description of material brittle failure using a hybrid phase-field model enhanced by adaptive isogeometric analysis

The objective of this work is to study dynamic crack propagation in brittle materials under time-dependent loading conditions by using the recently developed adaptive isogeometric phase-field approach. The current approach owns several ingredients including the advantages of the phase-field method (PFM), which can be used to model complex crack morphologies without any fracture criterion, and the isogeometric analysis, which possesses some excellent features such as exact geometry and high-order continuity. In addition, the model is further enhanced by employing the locally refined non-uniform rational B-spline (LR NURBS) basis, which is utilized for spatial discretization and phase-field discretization, while the generalized-α or HHT-α method is employed for the temporal discretization. For the coupled elasto-phase field system, a staggered approach is adopted to compute the unknown field variables. Moreover, a hybrid formulation of the PFM is employed to recover the linearity of momentum equation. The structured mesh adaptive refinement is conducted based on the prescribed threshold on the phase-field variable, thus it can effectively alleviate the burden of computational overhead, which is the main shortcoming of the PFM. Three problems involving dynamic crack growth is solved to show the robustness and the applicability of the proposed approach. It is shown that the proposed approach can obtain accurate results at a fraction of degrees-of-freedom without compromising accuracy in comparison with uniformly refined mesh.

Crack propagation in quasi-brittle materials by fourth-order phase-field cohesive zone model

A phase-field approach becomes a more popular candidate in modeling crack propagation. It uses a scalar auxiliary variable, namely a phase-field variable, to model a discontinuity zone in a continuity domain. Furthermore, the fourth-order phase-field approach produces a better convergence rate and more accurate solutions than the second-order one. However, it is available for modeling crack propagation in brittle material. This study addresses the fourth-order phase-field model combining the non-standard phase-field form with a cohesive zone model (CZM) to predict crack propagation in quasi-brittle material. A Cornelisson's softening law is used to capture the high precision of crack propagation prediction. The concrete material is considered as a quasi-brittle one. For computation efficiency using NURBS-based finite elements, Virtual Uncommon-Knot-Inserted Master-Slave (VUKIMS) technique is employed to derive a local refinement mesh. Numerical results are verified by the published ones from literature. It was found that the peak load and crack path are independent of the element size and insensitive to the length-scale number using the fourth-order phase-field CZM. Our proposed model shows the most significant advantage compared to the standard phase-field approach in terms of computational cost and solution accuracy.

2D finite elements for the computational analysis of crack propagation in brittle materials and the handling of double discontinuities

Crack growth simulations by way of the traditional Finite Element Method claim progressive remeshing to fit the geometry of the fracture, severely increasing the computational effort. Methods such as the eXtended Finite Element Method (XFEM) allow to overcome this limitation by means of nodal shape functions multiplied by Heaviside step function to enrich finite element nodes. Through the medium of a discontinuous field, the entire geometry of the discontinuity can be modelled regardless of the mesh, avoiding remeshing. In this paper two shell-type XFEM elements (a three-node triangular element and a four-node quadrangular element) to evaluate crack propagation in brittle materials are presented. These elements have been implemented into the widespread opensource framework OpenSees to evaluate crack propagation into a plane shell subjected to monotonically increasing loads. Moreover, in the perspective of fracture propagation simulations, the problem of managing multiple cracks without remeshing or operating subdivisions on the integration domain has been investigated and a four-node quadrangular finite element for the computational analysis of double crossed discontinuities by the means of equivalent polynomials is presented in this paper. Equivalent polynomials allow to overcome inaccuracies on the results when performing standard numerical integration (e.g. Gauss-Legendre quadrature rule) over the entire domain of XFEM elements, without the need of defining integration subdomains. The presented work and the computational strategy behind it may be extremely useful not only in the field of fracture mechanics, but also to solve complex geometry problems or material discontinuities.

Crack growth pattern analysis of monolithic glass ceramic on a titanium abutment for single crown implant restorations using smooth particle hydrodynamics algorithm.

Background Glass ceramic materials have multiple applications in various prosthetic fields. Despite the many advantages of these materials, they still have limitations such as fragility and surface machining and ease of repairing. Crack propagation has been a typical concern in fullceramic crowns, for which many successful numerical simulations have been carried out using the extended finite element method (XFEM). However, XFEM cannot correctly predict a primary crack growth direction under dynamic loading on the implant crown. Methods In this work, the dental implant crown and abutment were modeled in CATIA V5R19 software using a CT-scan technique based on the human first molar. The crown was approximated with 39514 spherical particles to reach a reasonable convergence in the results. In the present work, glass ceramic was considered the crown material on a titanium abutment. The simulation was performed for an impactor with an initial velocity of 25 m/s in the implant-abutment axis direction. We took advantage of smooth particle hydrodynamics (SPH) such that the burden of defining a primary crack growth direction was suppressed. Results The simulation results demonstrated that the micro-crack onset due to the impact wave in the ceramic crown first began from the crown incisal edge and then extended to the margin due to increased stress concentration near the contact region. At 23.36 µs, the crack growth was observed in two different directions based on the crown geometry, and at the end of the simulation, some micro-cracks were also initiated from the crown margin. Moreover, the results showed that the SPH algorithm could be considered an alternative robust tool to predict crack propagation in brittle materials, particularly for the implant crown under dynamic loading. Conclusion The main achievement of the present study was that the SPH algorithm is a helpful tool to predict the crack growth pattern in brittle materials, especially for ceramic crowns under dynamic loading. The predicted crack direction showed that the initial crack was divided into two branches after its impact, leading to the crown fracture. The micro-crack initiated from the crown incisal edge and then extended to the crown margin due to the stress concentration near the contact area.

Adaptive phase field method using novel physics based refinement criteria

Amongst the available methods to model fracture processes, the phase field approach has proved to be efficient and has received extensive attention. However, the approach is computationally demanding as it requires a very high resolution, both in space and time to resolve the fracture characteristics. In this paper, a novel adaptive phase field method is proposed for modelling quasi-static crack propagation in brittle materials. The adaptive refinement is based on the stability analysis which is combined with the quadtree decomposition. The stability analysis is based on a linear perturbation method that is used herein to determine the onset of fracture initiation on the fly. Three standard benchmark problems are solved to show the efficiency and the robustness of the proposed method. It is shown that the proposed framework does not require any post processing technique for adaptive refinement and yet is effective.

A dynamic adaptive eigenfracture method for failure in brittle materials

We present a dynamic adaptive eigenfracture algorithm for the study of crack propagation in brittle materials. The original eigenfracture method is an variational approximation of the Griffith-type fracture with convergence as the element size vanishes. To improve its convergence rate, we extend the eigenfracture approach by using the effective energy release rate as the adaptive refinement criteria. Elements are subdivided based on nested refinement method with a pull-back operation. The dynamic adaptive eigenfracture method is validated by comparing to three-point bending tests of concrete and pure-tension tests of the material PMMA. The predicted crack angle in concrete and the simulation results of fracture propagation speed in PMMA show excellent agreement with experimental measurements. Even through a relatively coarse mesh employed in the simulations, the dynamic adaptive eigenfracture method can address the problem of mesh biased crack path.

Extended Voronoi cell finite element method for multiple crack propagation in brittle materials

This paper introduces a new extended Voronoi cell finite-element method (X-VCFEM) for modelling the propagation of multiple cracks in brittle materials. The direction of the crack propagation is adaptively determined in terms of the maximum energy release rate near the crack tip, and we apply a remeshing strategy that a node at a last incremental crack tip in the crack advance process is replaced by a node pairs to realize the gradual crack propagation. In order to accurately capture crack-tip stress concentrations, some singular stress terms of Williams expansion in the vicinity of crack tips are introduced in the assumed stress hybrid formulation which also includes the polynomial terms and the reciprocal terms. Then several numerical examples are used to demonstrate the effectiveness and accuracy of X-VCFEM enriched by some singular stress terms of Williams expansion by comparing X-VCFEM results with those computed by the commercial finite element package ABAQUS or established results in the literature. At last, two numerical examples are given to simulate multiple crack propagation in brittle media. The effects of morphological distributions such as length, orientation and dispersion on the crack propagation are studied. It is obvious that the X-VCFEM has great advantage of analyzing large regions of the microstructure with multiple growing and interacting cracks.

Using Deep Learning to Predict Fracture Patterns in Crystalline Solids

Summary Fracture is a catastrophic process whose understanding is critical for evaluating the integrity and sustainability of engineering materials. Here, we present a machine-learning approach to predict fracture processes connecting molecular simulation into a physics-based data-driven multiscale model. Based on atomistic modeling and a novel image-processing approach, we compile a comprehensive training dataset featuring fracture patterns and toughness values for different crystal orientations. Assessments of the predictive power of the machine-learning model shows excellent agreement not only regarding the computed fracture patterns but also the fracture toughness values and is examined for both mode I and mode II loading conditions. We further examine the ability of predicting fracture patterns in bicrystalline materials and material with gradients of microstructural crystal orientation. These results further underscore the excellent predictive power of our model. Potential applications of this model could be widely applied in material design.

Relationship between fractography, fractal analysis and crack branching

A critical part of failure analysis is to understand the fracture process from initiation through crack propagation. Crack propagation in brittle materials can produce crack branching patterns that are fractal in nature, i.e., the crack branching coefficient (CBC). There is a direct correlation between the CBC and strength, σf: σf∝CBC. This appears to be in conflict with the fractal dimensional increment of the fracture surface, D*, which is independent of strength and related to the fracture toughness of the material, Kc: Kc=E a01/2D* 1/2, where E is the elastic modulus and a0, a characteristic dimension. How can D* be constant in one case and CBC be a variable in another case? This paper demonstrates the relationship between D* and CBC in terms of fractographic parameters. Examples of fractal analysis in analyzing field failures, e.g., that involve comminution, incomplete fractures of components, and potential processing problems will be demonstrated.

Damage Zone Size Limit During the Crack Propagation

The principal goal of this work is to limit the damage zone length during the crack propagation in brittle materials. This study is based on the determination of stress fields by varying the distance between a semi-infinite crack and a neighboring dislocation. The model suggested is a rectangular element (a dish), having a semi-infinite crack in one of its ends and a dislocation located in the vicinity of a crack-tip, subjected to a tensile stress on mode I. The problem is treated numerically using Finite Element Method.For each distance between the two cracks (semi-infinite crack and dislocation), stress fields are given. On the basis of these stress fields, a limiting damage zone length is obtained.

Rock Dynamic Crack Propagation under Different Loading Rates Using Improved Single Cleavage Semi-Circle Specimen

The objective of this paper is to investigate the complete process of dynamic crack propagation in brittle materials under different loading rates. By using Improved Single Cleavage Semi-Circle (ISCSC) specimens and Split Hopkinson Pressure Bar equipment, experiments were conducted, with the fracture phenomenon and crack propagation of tight sandstone investigated. Meanwhile, the process of crack propagation behaviour was simulated. Moreover, with the experimental–numerical method, the crack propagation dynamic stress intensity factor (DSIF) was also calculated. Then, the crack propagation toughness of tight sandstone under different loading rates was investigated and illustrated elaborately. Investigation results demonstrate that ISCSC specimens can achieve the crack arrest position unchanged, and the numerical simulation could effectively deduce the actual crack propagation, as their results were well matched. During crack propagation, the crack propagation DSIF in the whole process increases with the rising loading rate, and so does the crack propagation velocity. Several significant dynamic material parameters of tight sandstone are also given, for engineering reference.

A Proper Generalized Decomposition (PGD) approach to crack propagation in brittle materials: with application to random field material properties

Understanding the failure of brittle heterogeneous materials is essential in many applications. Heterogeneities in material properties are frequently modeled through random fields, which typically induces the need to solve finite element problems for a large number of realizations. In this context, we make use of reduced order modeling to solve these problems at an affordable computational cost. This paper proposes a reduced order modeling framework to predict crack propagation in brittle materials with random heterogeneities. The framework is based on a combination of the Proper Generalized Decomposition (PGD) method with Griffith’s global energy criterion. The PGD framework provides an explicit parametric solution for the physical response of the system. We illustrate that a non-intrusive sampling-based technique can be applied as a post-processing operation on the explicit solution provided by PGD. We first validate the framework using a global energy approach on a deterministic two-dimensional linear elastic fracture mechanics benchmark. Subsequently, we apply the reduced order modeling approach to a stochastic fracture propagation problem.

Adaptive phase field method for quasi-static brittle fracture using a recovery based error indicator and quadtree decomposition

An adaptive phase field method is proposed for crack propagation in brittle materials under quasi-static loading. The adaptive refinement is based on the recovery type error indicator, which is combined with the quadtree decomposition. Such a decomposition leads to elements with hanging nodes. Thanks to the polygonal finite element method, the elements with hanging nodes are treated as polygonal elements and hence do not require any special treatment. The mean value coordinates are used to approximate the unknown field variables and a staggered solution scheme is adopted to compute the displacement and the evolution of the phase field variable. A few standard benchmark problems are solved to show the efficiency of the proposed framework. It is seen that the proposed framework yields comparable results at a fraction of the computational cost when compared to standard approaches reported in the literature.