Examples Of Crack Propagation Research Articles

A 3D peridynamic model for fracture analysis of transversely isotropic solids

The classical continuum mechanics (CCM) has limitations in simulating crack initiation and propagation, and the peridynamic (PD) theory overcomes these shortcomings. This study proposed a 3D transversely isotropic PD model based on the micro-beam bond model. Firstly, the micromoduli of the micro-beam bond applied to the transversely isotropic 3D solid model are derived based on the elastic matrix relationship between the different coordinate systems. Secondly, the strain energy density expressions of arbitrary material points are expressed in both the PD theory and the CCM theory using strain and elastic matrix under the assumption of homogenization, respectively. Finally, by equating the strain energy density expressions under the two theories based on the conservation of energy, the constitutive model parameters of the 3D transversely isotropic PD model are solved. Numerical examples of crack propagation demonstrate the effectiveness of the proposed model in addressing dynamic 3D fracture problems.

Influence of material microstructure on fracture development in deformable bodies

The problem of predicting the location and direction of local fracture and estimating the ultimate load of composite material is one of the practically important problems of fracture mechanics. With a wide variety of composite materials, it is natural to expect the presence of a large number of failure criteria, each of which should be valid for a certain class of materials and reflect most completely its physical and mechanical properties, structural defects, operating conditions, etc. The choice of effective assessment of the bearing capacity of modern composite material under extreme conditions is at present the main task of researchers. In this paper, the criterion of fracture of composite materials based on simple and quite effective theory of macrostresses by M.Ya. Leonov and K.M. Rusynka is preferred. The macrostress theory effectiveness is shown in the papers by V.V. Panasiuk, L.T. Berezhnytskyi, S.Ya. Yarema, L.V. Ratych, and M.H. Stashchuk. In our paper, we clarify and extend the advantages of macrostress concept criterion in comparison with other fracture criteria in deformable bodies. Examples of crack propagation in the process of body tension are given in this paper.

Efficient Runge–Kutta solver for stochastic crack growth analysis

Stochastic crack growth analysis by simulation may easily require a significant amount of computational effort. The Initial Value ordinary differential equations appearing in crack propagation problems may be solved by the Runge–Kutta (RK) family of solvers. However, crack propagation considering uncertainties imposes additional challenges for RK solvers: possibility of vectorized and/or parallelized computation of sample realizations; and adaptation of time discretization for each sample, to handle changes and discontinuities in the derivatives of crack growth curves, caused by changes in loads and in crack propagation rates. Existing adaptive RK methods, with change in time step length during crack growth computation, struggle with these challenges. In this setting, the present paper proposes a modified adaptive RK method which allows for simultaneous crack growth computations with different time-step discretizations, and aims at efficiently dealing with cases where discontinuities are present in the derivative of the crack growth curve. Application of the proposed method to three crack propagation examples, including one related to weld flaws in pipes, indicates that it is as accurate as other adaptive methods from the literature, while requiring only a fraction of the computational time.

An orthotropic peridynamic shell model for linear elastic deformation and crack propagation

Peridynamics is a non-local mechanics theory that can handle discontinuities such as cracks. This study presents an orthotropic peridynamic (PD) shell model based on the micro-beam bond. Under the homogenization assumption, eight PD material parameters expressed by four independent material constants are used to describe the axial, bending, and torsional deformations of the micro-beam bond. The eight PD material parameters can be derived by the rule of equating the strain energy density (SED) of the PD shell model and that of the classical continuum mechanics (CCM) shell model. To improve the computational efficiency and solve the surface effects of PD models, the morphing method is used to establish the PD-CCM shell coupling model. Several numerical examples of crack propagation in orthotropic materials are executed, and the results demonstrate the effectiveness of the proposed model.

Two‐dimensional meso‐structural simulation of concrete fracture by the implementation of zero‐thickness cohesive interface elements

AbstractConcrete is considered as a non‐homogeneous material and from a mesoscopic point of view is constituted of three main phases, namely aggregates, mortar matrix and interfacial transition zone (ITZ). To investigate the damage process of concrete materials at the mesoscale due to mechanical loading, an explicit numerical model with full representation of the three mesoscopic phases is required. To this end, in this work, a Python code is developed to generate zero‐thickness cohesive interface elements in two‐dimensions (2D). The generated code is capable of generating two‐dimensional quadratic cohesive interface elements (i) within the mortar elements, (ii) within the aggregates elements and (iii) at interfaces between mortar and aggregates. To simulate the crack propagation, the generated zero thickness‐cohesive elements are preinserted at the interface of solid elements and different traction‐separation laws are assigned to them to simulate all potential crack paths. The implemented algorithms to generate the cohesive elements are discussed in detail and numerical examples of crack propagation in concrete is presented using Abaqus/CAE. The numerical results are compared with those in the literature qualitatively to validate the performance of the model. The developed method provides the possibility to investigate the damage processes in meso‐and micro‐scales underlying the macroscopic behavior of the semi‐brittle materials.

Peridynamic Shell Model Based on Micro-Beam Bond

Peridynamics (PD) is a non-local mechanics theory that overcomes the limitations of classical continuum mechanics (CCM) in predicting the initiation and propagation of cracks. However, the calculation efficiency of PD models is generally lower than that of the traditional finite element method (FEM). Structural idealization can greatly improve the calculation efficiency of PD models for complex structures. This study presents a PD shell model based on the micro-beam bond via the homogenization assumption. First, the deformations of each endpoint of the micro-beam bond are calculated through the interpolation method. Second, the micro-potential energy of the axial, torsional, and bending deformations of the bond can be established from the deformations of endpoints. Finally, the micro moduli of the shell model can be obtained via the equivalence principle of strain energy density (SED). In addition, a new fracture criterion based on the SED of the micro-beam bond is adopted for crack simulation. Numerical examples of crack propagation are provided, and the results demonstrate the effectiveness of the proposed PD shell model.

Warped Gaussian processes for predicting the degradation of aerospace structures

Gaussian processes (GPs) can be used to predict future states of a system with credible intervals when considering multiple previous trajectories for training. For example, predicting the degradation of mechanical structures is one application in which they have shown their usefulness. In modeling the system output as a GP, the output is presumed to be normally distributed—assuming the predictions to be defined from negative to positive infinity. However, this assumption does not hold in many applications as, for example, crack lengths and damage indices can only assume positive values. Moreover, several degradation trajectories for training are rare in real-world applications, and the current state of a monitored system, which is used to update the prediction, can often be not directly measured. This paper presents an approach that utilizes warped GPs for treating data that is not normally distributed while considering multiple degradation trajectories for training. The approach is successfully applied to two different crack propagation examples: first, an analytically computed pre-cracked infinite plate, and second, two equally manufactured aluminum structures that resemble a lower section of a wing. For the investigated aerospace structures, we use finite element (FE) simulations to generate multiple degradation trajectories for training. To estimate their hidden degradation states, we infer the current crack length from strain measurements by using Bayesian inference. The results show that the approach of warped GPs provides more accurate predictions than using standard ones for non-normally distributed data, as is the case for crack growth problems. The approach enables quick training of warped GPs while considering multiple training trajectories. Additionally, the crack lengths estimated from strain measurements agree well with the visually inspected ones. Ultimately, the presented approach enables estimating the current and future degradation states with credible intervals that can be used to improve maintenance scheduling.

Use of a rotation-invariant linear strain measure for linear elastic crack propagation calculations

The classical stress intensity factor concept requires linear elastic calculations based on infinitesimal strains in order to create the correct stress and strain singularity at the crack tip. Infinitesimal strains, however, are not rotation-invariant and cannot be used in structures undergoing large rotations even if the stretch is small. Therefore, a new strain measure is proposed based on a linearization of the Lagrange strain tensor written in terms of the right stretch tensor instead of the deformation gradient. In that way the local rotation is removed from the linear strain measure. An example of crack propagation of a rotating beam shows the effectiveness of the method.

A plane stress model of bond-based Cosserat peridynamics and the effects of material parameters on crack patterns

A plane stress model of bond-based Cosserat peridynamics is proposed, of which the constitutive equations of Cosserat continuum are implemented. The rotation of the proposed bond-based Cosserat peridynamic model is independent with the translational displacement, and the couple stress is considered in the material points’ interaction. The proposed model can degenerate into bond-based peridynamics and micropolar peridynamics under certain conditions. Several examples of crack propagation are designed to investigate the effect of material parameters on crack patterns. The numerical results are compared with other peridynamic models and experimental results to validate the proposed model. The numerical results show that the Cosserat shear modulus and the tangential stiffness of bond have an impact on crack propagation, including crack branching and crack pattern.

A generalized cover renewal strategy for multiple crack propagation in two-dimensional numerical manifold method

Partition of unity based numerical manifold method can solve continuous and discontinuous problems in a unified framework with a two-cover system, i.e., the mathematical cover and physical cover. However, renewal of the topology of the two-cover system poses a challenge for multiple crack propagation problems and there are few references. In this study, a robust and efficient strategy is proposed to update the cover system of the numerical manifold method in simulation of multiple crack propagation problems. The proposed algorithm updates the cover system with a bottom-up process: 1) identification of fractured manifold elements according to the previous and latest crack tip position; and 2) local topological update of the manifold elements, physical patches, block boundary loops, and non-persistent joint loops according to the scenario classification of the propagating crack. The proposed crack tracking strategy and classification of the renewal cases promote a robust and efficient cover renewal algorithm for multiple crack propagation analysis. Three crack propagation examples show that the proposed algorithm performs well in updating the cover system. This cover renewal methodology can be extended for numerical manifold method with polygonal mathematical covers.

Hybrid FEM and peridynamic simulation of hydraulic fracture propagation in saturated porous media

This paper presents a hybrid modeling approach for simulating hydraulic fracture propagation in saturated porous media: ordinary state-based peridynamics is used to describe the behavior of the solid phase, including the deformation and crack propagation, while FEM is used to describe the fluid flow and to evaluate the pore pressure. Classical Biot poroelasticity theory is adopted. The proposed approach is first verified by comparing its results with the exact solutions of two examples. Subsequently, a series of pressure- and fluid-driven crack propagation examples are solved and presented. The phenomenon of fluid pressure oscillation is observed in the fluid-driven crack propagation examples, which is consistent with previous experimental and numerical evidences. All the presented examples demonstrate the capability of the proposed approach in solving problems of hydraulic fracture propagation in saturated porous media.

MODELLING OF CRACK PROPAGATION: COMPARISON OF DISCRETE LATTICE SYSTEM AND COHESIVE ZONE MODEL

Lattice models are often used to analyze materials with discrete micro-structures mainly due to their ability to accurately reflect behaviour of individual fibres or struts and capture macroscopic phenomena such as crack initiation, propagation, or branching. Due to the excessive number of discrete interactions, however, such models are often computationally expensive or even intractable for realistic problem dimensions. Simplifications therefore need to be adopted, which allow for efficient yet accurate modelling of engineering applications. For crack propagation modelling, the underlying discrete microstructure is typically replaced with an effective continuum, whereas the crack is inserted as an infinitely thin cohesive zone with a specific traction-separation law. In this work, the accuracy and efficiency of such an effective cohesive zone model is evaluated against the full lattice representation for an example of crack propagation in a three-point bending test. The variational formulation of both models is provided, and obtained results are compared for brittle and ductile behaviour of the underlying lattice in terms of force-displacement curves, crack opening diagrams, and crack length evolutions. The influence of the thickness of the process zone, which is present in the full lattice model but neglected in the effective cohesive zone model, is studied in detail.

A study of concrete cover separation failure in FRP-plated RC beams via an inter-element fracture approach

The phenomenon of concrete cover separation failure in FRP strengthened RC elements, unlike plate-end and mid-span debonding failure modes, has been not analyzed in depth in the literature and simplified strength models are mainly available, which possess a limited predictive capability. To this end in the present work, a novel numerical approach to investigate cover separation in FRP-plated RC beams is proposed, based on an inter-element cohesive fracture approach able to simulate multiple crack onset, propagation and coalescence in concrete structures, used in combination with an embedded truss model for taking into account the interaction between concrete cracks and tensile steel rebars. This approach has been validated by performing complete failure simulations for benchmark crack propagation examples, and subsequently has been exploited for predicting the load-carrying capacity and the related failure mode of real-scale retrofitted RC elements. Suitable comparisons with available experimental results have clearly shown the reliability and the effectiveness (in terms of numerical accuracy) of the proposed fracture approach.

The Natural Neighbor Radial Point Interpolation Method in Computational Fracture Mechanics: A 2D Preliminary Study

In this work, the natural neighbor radial point interpolation method (NNRPIM) is extended to the numeric analysis of crack propagation problems. Here, the advanced discretization meshless technique is combined with a linear elastic crack growth algorithm. The algorithm simulates the crack propagation by displacing iteratively the crack tip, which consequently requires a local remeshing. In each iteration, it is estimated the stress state in the crack tip and afterwards the direction of the crack propagation is obtained considering the maximum circumferential stress criterion.The required local remeshing does not represent a numeric difficulty for the NNRPIM. The main advantage of the NNRPIM is its capability to fully discretize the problem domain using only an unstructured nodal distribution. Being a truly meshless method, the NNRPIM is able to define autonomously the nodal connectivity and the background integration mesh.The classic NNRPIM formulation permits to enforce the nodal connectivity by means of two kind of influence-cells: first degree influence-cells or second degree influence-cells. This work investigates the influence of the nodal connectivity on the simulated crack propagation path. Thus, demanding benchmark crack propagation examples are studied and the obtained results are compared with reference solutions available in the literature.

Micro-crack propagation on a biomimetic bone like composite material studied with the extended finite element method

Cortical bone contributes to about 80% of the weight of the human skeleton. Along its other properties, cortical bone presents a high resistance to fracture propagation. With this paper the authors aim to model this material using the Extended Finite Element Method (X-FEM) and to understand the mechanism that allow this material to have such a property. A numerical model was developed, considering a biomimetic bone like composite material, modelling the primary anatomical and functional unit of cortical bone, the osteon, as a fiber, the interstitial lamellae as the matrix, and the cement line between them. Different properties were considered for all the above mention materials, and their influence on the micro-crack propagation was studied. The cracks introduced and their geometry allowed the authors to understand why the cracks are arresting their propagation, and why is this material so resistant to crack propagation. The results are presented using the calculated stress intensity factors, for different material and geometries, and also using several brittle fracture crack propagation examples calculated using X-FEM.

Crack propagation with adaptive grid refinement in 2D peridynamics

The most common technique for the numerical implementation of peridynamic theory is based on a mesh-free approach, in which the whole body is discretized with a uniform grid and a constant horizon. As a consequence of that computational resources may not be used efficiently. The present work proposes adaptive refinement algorithms for 2D peridynamic grids. That is an essential component to generate a concurrent multiscale model within a unified approach. Adaptive grid refinement is here applied to the study of dynamic crack propagation in two dimensional brittle materials. Refinement is activated by using a new trigger concept based on the damage state of the material, coupled with the more traditional energy based trigger, already proposed in the literature. We present as well a method, to generate the nodes in the refined zone, which is suitable for an efficient numerical implementation. Moreover, strategies for the mitigation of spurious reflections and distortions of elastic waves due to the use of a non-uniform grid are presented. Finally several examples of crack propagation in planar problems are presented, they illustrate the potentialities of the proposed algorithms and the good agreement of the numerical results with experimental data.

Adaptive concurrent multiscale model for fracture and crack propagation in heterogeneous media

We introduce an adaptive concurrent multiscale methodology (ACM2) to handle situations in which both macroscopic and microscopic deformation fields strongly interact near the tip of a crack. The method is based on the balance between numerical and homogenization error; while the first type of error states that elements should be refined in regions of high deformation gradients, the second implies that element size may not be smaller than a threshold determined by the size of the unit cell representing the material’s microstructure. In this context, we build a finite element framework in which unit cells can be embedded in continuum region through appropriate macro–micro boundary coupling conditions. By combining the idea of adaptive refinement with the embedded unit cell technique, the methodology ensures that appropriate descriptions of the material are used adequately, regardless of the severity of deformations. We will then show that our computational technique, in conjunction with the extended finite element method, is ideal to study the strong interactions between a crack and the microstructure of heterogeneous media. In particular, it enables an explicit description of microstructural features near the crack tip, while a computationally inexpensive coarse scale continuum description is used in the rest of the domain. The paper presents several examples of crack propagation in materials with random microstructures and discuss the potential of the multiscale technique in relating microstructural details to material strength and toughness.

Two-dimensional Numerical Estimation of Stress Intensity Factors and Crack Propagation in Linear Elastic Analysis

When the loading or the geometry of a structure is not symmetrical about the crack axis, rupture occurs in mixed mode loading and the crack does not propagate in a straight line. It is then necessary to use kinking criteria to determine the new direction of crack propagation. The aim of this work is to present a numerical modeling of crack propagation under mixed mode loading conditions. This work is based on the implementation of the displacement extrapolation method in a FE code and the strain energy density theory in a finite element code. At each crack increment length, the kinking angle is evaluated as a function of stress intensity factors. In this paper, we analyzed the mechanical behavior of inclined cracks by evaluating the stress intensity factors. Then, we presented the examples of crack propagation in structures containing inclusions and cavities.

Strain energy density prediction of crack propagation for 2D linear elastic materials

When the loading or the geometry of a structure is not symmetrical about the axis of the crack, the rupture occurs in mixed mode loading, and the crack does not propagate in a straight line. It is then necessary to use kinking criteria to determine the new direction of crack propagation.The aim of this work is to present a numerical modeling of crack propagation under mixed mode loading conditions. This work is based on the implementation of the displacement extrapolation method (DEM) and the strain energy density theory in a finite element code. At each crack increment length, the kinking angle is evaluated as a function of stress intensity factors (SIFs). In this paper, we analyzed the mechanical behavior of inclined cracks by evaluating the stress intensity factors. Then, we present the examples of crack propagation in structures containing inclusions and cavities.

On numerical aspects of phase field fracture modelling

Recently, a continuum model for crack propagation in brittle visco-elastic materials has been presented (M. Fleck et al., Phys. Rev. E 83, 046213 (2011)), in which fracture is described as an elastically induced nonequilibrium interfacial pattern formation process. The underlying mesoscopic description of a propagating crack results in a complicated moving boundary problem, that allows the self-consistent determination of the crack velocity as well as the entire time-dependent crack surface. Here we focus on the numerical aspects tied to the approximative solution of the arising moving boundary problem and discuss several strategies to develop efficient numerical schemes applying to it: i) a finite difference scheme, ii) a scheme based on the finite element method and iii) a scheme based on the multipole expansion method. The pros and cons of each method are elucidated in detail. Further, we present a comprehensive view on how the different approaches can be employed to validate each other in comparative studies, which is then illustrated for the example of crack propagation under mode I loading.