Propagation Criterion Research Articles

A Psychoacoustic Quality Criterion for Path-Traced Sound Propagation.

In developing virtual acoustic environments, it is important to understand the relationship between the computation cost and the perceptual significance of the resultant numerical error. In this paper, we propose a quality criterion that evaluates the error significance of path-tracing-based sound propagation simulators. We present an analytical formula that estimates the error signal power spectrum. With this spectrum estimation, we can use a modified Zwicker's loudness model to calculate the relative loudness of the error signal masked by the ideal output. Our experimental results show that the proposed criterion can explain the human perception of simulation error in a variety of cases.

Reactivity-Guided Depercolation Processes Determine Fracture Behavior in End-Linked Polymer Networks.

The fracture of polymer networks is tied to the molecular behavior of strands within the network, yet the specific molecular-level processes that determine the mechanical limits of a network remain elusive. Here, the question of reactivity-guided fracture is explored in otherwise indistinguishable end-linked networks by tuning the relative composition of strands with two different mechanochemical reactivities. Increasing the substitution of less mechanochemically reactive ("strong") strands into a network comprising more reactive ("weak") strands has a negligible impact on the fracture energy until the strong strand content reaches approximately 45%, at which point the fracture energy sharply increases with strong strand content. This aligns with the measured strong strand percolation threshold of 48 ± 3%, revealing that depercolation, or the loss of a percolated network structure, is a necessary criterion for crack propagation in a polymer network. Coarse-grained fracture simulations agree closely with the tearing energy trend observed experimentally, confirming that weak strand scissions dominate the failure until the strong strands approach percolation. The simulations further show that twice as many strands break in a mixture than in a pure network.

Meso-crack propagation process of concrete based on macro-fracture parameters: Numerical and experimental

Formation and propagation of cracks along mortar-aggregate interfaces or penetration of cracks into aggregates highly influences the mechanical performance of concrete composites. This paper presents a numerical model to calculate the meso-crack propagation process of concrete based on the macro-material and interfacial parameters that can be directly measured by basic mechanical experiments. In the model, the issue of aggregate crack penetration versus interface crack propagation has been addressed by employing the stress intensity factor (SIF)-based criteria for crack propagation. After the validity of the numerical model is verified by test results on three-point bending concrete beams with single embedded cylindrical aggregate, the applicability of the model to meso-crack propagation in concrete with various geometrical dimensions, interfacial properties, and aggregate gradations is discussed through a series of numerical experiments. The results show that the proposed numerical model is capable of predicting the meso-crack propagation process of concrete with reasonable accuracy.

An efficient computational framework for height-contained growing and intersecting hydraulic fracturing simulation via SGBEM–FEM

An efficient computational framework to model the growth of intersecting height-contained hydraulic fractures is proposed. The fracture in solids is modeled by the classical theory of linear elastic fracture mechanics, whereas the injection flow in hydraulic fractures is treated as channel flow. The governing equations of fracture mechanics are formulated in terms of weakly-singular weak-form boundary integral equations, with the knowledge of the fracture surface geometry exploited to reduce the integral dimension. The fluid flow within the fracture is treated using finite element method as one dimensional flow in an arbitrarily curved channel. The symmetric Galerkin boundary element method and finite element method are coupled with the traction continuity condition. The model is then formulated in a variational form and augmented with Lagrange multipliers to prescribe displacement constraints on intersections of hydraulic fractures, while fluid constraints are enforced by a consolidation of associated pressure degrees of freedom. Pertinent numerical implementation techniques, including spatial and temporal discretizations, special crack tip element, crack propagation criteria and remeshing strategy, are presented. The proposed framework is verified by comparing to the numerical results from a three dimensional hydraulic fracturing simulator and then verified by comparing the stress intensity factors to the XFEM and Murakami’s results for both star shaped cracks and symmetric branched cracks. The verification shows the utility properly enforces the physical constraints on the intersections of fractures. Three numerical examples are shown to demonstrate the capability of the proposed computational framework modeling the intersecting hydraulic fracturing process in a single or separated height-contained pay zones.

Experimental determination of critical thickness limitations of (010) β -(AlxGa1−x)2O3 heteroepitaxial films

The effect of heteroepitaxial β-(AlxGa1−x)2O3 film thickness and Al content on surface morphology was characterized to experimentally determine the critical thickness limitations of the (010) β-(AlxGa1−x)2O3/Ga2O3 heterostructure. High-resolution x-ray diffraction was used to assess the strain state of the films; reciprocal space mapping (RSM) revealed that even cracked films were still fully strained. In cracked films, diffuse scattering was observed in RSMs, indicating lattice tilting. Cracking of the films was investigated using atomic force microscopy (AFM), x-ray topography (XRT), bright-field scanning transmission electron microscopy (BF-STEM), and high-resolution transmission electron microscopy. Using both AFM and XRT, the [001] direction was observed to be the most prevalent crack direction; however, cracks were also observed in the [100] direction. In uncracked regions of the films, XRT revealed the alignment of threading dislocations along the [001] direction. Cross-sectional imaging of the crack geometry and propagation was performed using BF-STEM, and it was observed that the cracks in the [001] direction extended through the thickness of the β-(AlxGa1−x)2O3 film (∼205 nm) and a further ∼100–200 nm into the β-Ga2O3 substrate. Experimental data for critical film thickness showed good agreement with previous theoretical calculations based on the Griffith criterion for crack propagation.

A new method for predicting multi-crack fracture mechanism in the finite plate of red sandstone

A novel theoretical approach was put forth to forecast multi-crack propagation trajectories in a finite plate. First, a weighted residual approach and complex function are used to create the formula for computing the maximum (stress intensity factor) SIF of multi-crack in the finite plate. And then, three cracks were then chosen as a model for computation to determine how the plate size affects the SIF. The formula of multi-branch crack in finite plate is derived and the crack initiation and propagation criterion of multi-crack in finite plate was established. Finally, the propagation paths of three cracked red sandstone in a finite plate were predicted and verified by the uniaxial compression test. It demonstrates that the SIF of multiple cracks in a finite plate is consistently larger than that of an infinite plate. Under the uniaxial compression test, the first crack initiation point is often A2 or B2, and each specimen’s first crack initiation time increases and subsequently reduces when the relative horizontal spacing (Ds’) of cracks varies. The crack initiation stress increases and the unstable stress first increases and then decreases with Ds’. The total crack extension length initially goes down and then goes up. All of the fracture initiation and propagation mechanisms are Mode I. The effectiveness of the multi-crack propagation theory in finite plates is established by the good agreement between predicted and test findings.

Plane and axisymmetric problems of an interfacial crack in a power-law graded material

Plane and axisymmetric problems of interfacial cracks in a power-law graded infinite medium are examined. It is shown that the models are governed by integral equations of Mellin’s convolution type whose kernels are expressed through the hypergeometric function. Exact solutions are derived by the method of orthogonal Jacobi polynomials in a series form and by the Wiener–Hopf method by quadratures. Mode-I stress intensity factors and the associated weight functions for power-law graded materials in the plane and axisymmetric cases are introduced and evaluated. It is shown that, although the displacement jump and the normal traction component have power singularities at the crack tip different from 1/2, the strain energy variation is proportional to the crack length change as in the case of homogeneous materials. A Griffith-type criterion of crack propagation in power-law graded materials is proposed and results of numerical tests are reported.

High-cycle fatigue life assessment of welded cruciform joints of Q460D steel

In this paper, a reliable high-cycle fatigue life assessment method based on unified crack growth approach is presented for welded cruciform joints. Considering the ellipsoidal fracture model of structural steel as the instability propagation (fracture) criterion of fatigue crack, this study investigates the failure mode of the welded cruciform joint of Q460D steel subjected to a high-cycle fatigue test. Following the ellipsoidal fracture model, a set of theoretical calculation and numerical simulation were established to investigate the fatigue cracking of the welded cruciform joints. The theoretical model was further proposed for estimating the fatigue life of the welded cruciform joints of Q460D steel using the unified crack growth approach. Based on the theoretical and simulated results, the unified crack growth approach and the allowable stress fatigue life formula recommended in China's current code “Standard for design of steel structures, GB50017-2017” were then evaluated and compared. The calculation errors of the unified crack growth approach and the fatigue life formula recommended in China's current code are −48.2% ∼ +8.3% and −60.2% ∼ −34.8%, respectively.

A consistent linearization scheme for KGD problems using fracture tip asymptotic solutions

AbstractRecently, a fluid volume enrichment strategy based on the asymptotic solutions near the crack tip was proposed for fluid‐driven fracture propagation problems. Despite its successes in various benchmark and field‐scale problems of hydraulic fracturing simulations, the aforementioned enrichment strategy has the following limitations. First, the tightly coupled solid‐fluid nonlinear system cannot be consistently linearized due to the fast marching method applied to solve the Eikonal equation for fracture tracking. As a result, an approximated Jacobian had to be deployed for the Newton‐Raphson iterations. This is particularly troublesome when the fracture front propagates into newly fractured cells, since a large number of nonlinear iterations are required for convergence because of the inconsistent linearization. Second, the existing method only focused on the viscosity‐dominated fracture propagation regime. Even though the extension of the method to the toughness‐dominated regime could be relatively straightforward, it is not immediately clear how to apply the enrichment technique to the transition regime. This work is dedicated to address the above two limitations. Specifically, a unified fracture propagation criterion is proposed, which not only works for the viscosity‐dominated regime, but also for the toughness‐dominated regime and the transition regime in between. The techniques to consistently linearize the coupled solid‐fluid system and properly initialize the primary unknowns are demonstrated, which result in the significant reduction of required number of nonlinear iterations for convergence. The proposed technique is demonstrated in the context of the Khristianovic‐Geertsma‐de Klerk (KGD) problems due to its relative simplicity.

Micro–macro approach of anisotropic damage: A semi-analytical constitutive model of porous cracked rock

A semi-analytical constitutive model of a porous cracked rock is proposed based on the micro–macro approach within a thermodynamic framework. The representative volume element (RVE) of a porous cracked rock is divided into two subproblems, P1 and P2. The porosity evolution equation of a spherical pore is proposed for P1, whereas P2 is an inelastic problem containing numerous anisotropic penny-shaped cracks. First, the relationship between microscopic and macroscopic strains is established through homogenization. This relationship is introduced into the macroscopic free energy equation. A crack propagation criterion based on the Griffith release rate is proposed, and the evolution equations of the shear and tensile crack densities are proposed based on the surface energy function. Subsequently, the Gaussian numerical integration method is used to obtain a semi-analytical explicit expression of the macroscopic stiffness tensor. Finally, based on the proposed crack propagation criterion, a strength-prediction method is developed. A series of uniaxial and triaxial experimental data for different rocks from other references is used to validate the proposed constitutive model and strength prediction method. The results obtained using the proposed model agree well with the experimental curves obtained from uniaxial tension and triaxial compression tests performed on different rocks. The macroscopic mechanical behavior and evolution of microscopic parameters for different rocks with an increase in confining pressure are effectively demonstrated by the proposed model. Strength prediction method can accurately describe the failure strength of different rocks. Furthermore, a sensibility analysis of model parameters revealed that initial porosity e0 and dilation coefficient ζ have a deteriorating effect on the failure strength, and material constant η has an enhancing effect on the failure strength.

An efficient model for predicting complex delamination front of elastic coupling laminates

This work proposes a simple and efficient model to predict the variable crack front with any shape. The model contains a propagation criterion which defines the local growth direction of the delamination crack front by the vector perpendicular to the connection line of two adjacent mesh points. The angle between this vector and the pre-crack direction is calculated by the coordinates of two delamination front points. Crack front can be obtained by the local direction changes of the historical crack front. This model avoids the computing time caused by a high-fidelity finite element model. Its applicability is verified for composite laminates without coupling and with different couplings. The predicted crack front shows good agreements with the numerical results obtained by a high-fidelity FE model with refined mesh. Factors controlling the crack front shape are further discussed by analyzing strain energy release rate and mode mixture distribution at the crack front.

Alpha-heating analysis of burning plasma and ignition experiments on the National Ignition Facility

A recent experiment conducted on the National Ignition Facility (NIF) described in the study by Abu-Shawareb et al. [Phys. Rev. Lett. 129, 075001 (2022)] achieved a fusion yield output of 1.3 MJ from ∼ 220 kJ of x-ray energy absorbed by the capsule, demonstrating remarkable progress in the field of laser driven inertial confinement fusion. In the study by A. R. Christopherson [“Effects of charged particle heating on the hydrodynamics of inertially confined plasmas,” Ph.D. thesis (2020)], the plasma conditions needed to claim the onset of ignition and burn propagation were outlined and multiple criterion were provided to assess progress in inertial fusion experiments. In this work, we modify the metrics from A. R. Christopherson [“Effects of charged particle heating on the hydrodynamics of inertially confined plasmas,” Ph.D. thesis (2020)] to accurately calculate performance metrics for indirect-drive experiments on the NIF. We also show that performance metric trends observed in NIF data are consistent with theory and simulations. This analysis indicates that all the identified criterion for ignition and burn propagation have been exceeded by experiment 210 808.

Analytical method for predicting mode I crack propagation process of concrete under low-cycle fatigue loading

The fatigue failure of concrete structures is preceded by the formation of microcracks and the propagation of macrocracks. Therefore, the fatigue fracture properties of concrete should be investigated thoroughly to guarantee the safety of structures. In this paper, an analytical method for predicting the mode I crack propagation in concrete under low-cycle fatigue loading is proposed according to the fictitious crack model, where the fatigue tension-softening constitutive relationship is introduced, and the initial fracture toughness-based crack propagation criterion is applied. The fatigue crack propagation process can be determined by solving two governing equations. To validate the effectiveness of the method, the fatigue crack propagation in three-point bending (TPB) beams is calculated, and the results are compared with the simulated and experimental results. It is shown that, although the linearization assumption of the crack opening displacement (COD) along the depth direction leads to slight differences between the analytical and simulated results, there is still a reasonable agreement between the analytical and experimental results. The effectiveness of the analytical method is verified. Therefore, when Young’s modulus, initial fracture toughness, and fatigue tension-softening constitutive relationship are determined, the mode I fatigue crack propagation in concrete can be predicted based on the analytical method. It is expected that the method will contribute to the safety assessment of concrete structures under low-cycle fatigue loading.

A new mixed type crack propagation criterion in shale reservoirs

Hydraulic fracturing is a mainstream technology for unconventional oil and gas reservoirs development all over the world. How to use this technology to achieve high-level oil and gas resource extraction and how to form complex fracture networks as hydrocarbon transportation channels in tight reservoirs, which depends to a large extent on the interaction between hydraulic and pre-existing cracks. For hydraulic fracturing of fractured reservoirs, the impact of natural fractures, perforation direction, stress disturbances, faults and other influencing factors will produce a mixed Ⅰ&Ⅱ mode hydraulic fracture. To forecast whether hydraulic fractures cross pre-existing fractures, according to elastic mechanics and fracture mechanics, a stress state of cracks under the combination of tensile (Ⅰ) and shear (Ⅱ) is presented. A simple mixed-mode Ⅰ&Ⅱ hydraulic fracture's crossing judgment criterion is established, and the propagation of hydraulic fractures after encountering natural fractures is analyzed. The results show that for a given approaching angle there exists a certain range of stress ratio when crossing occurs. Under high approaching angle and large stress ratio, it is likely that hydraulic cracks will go directly through pre-existing cracks. The reinitiated angle is always controlled within the range of approximately 30° among the main direction of penetration.

Coupled Two-Phase Flow and Elastodamage Modeling of Laboratory and In Situ Gas Injection Experiments in Saturated Claystone as a Potential Host Rock for Nuclear Waste Repository

Understanding gas migration behavior in host rocks is of importance to the safety evaluation of deep geological repositories for nuclear waste. Experimental results reported in the literature show that gas flow in saturated claystone is through a highly localized network of dilatant pathways and that water is barely displaced. To explain the specific gas migration behavior, a two-scale approach is developed. A subcritical criterion for microcrack propagation is proposed to represent the time-dependent damage at the macroscale. The passage from microscale to macroscale is implemented through an asymptotic homogenization method. The solid mechanics is coupled with the fluid flow through pore pressure variation and an intrinsic permeability model, which implicitly accounts for the fracture opening induced permeability change. The developed model is tested against both laboratory and in situ gas injection experiments in the literature. Some key experimental findings, such as the development of preferential gas pathways and the fully saturated state are explicitly captured by the poroelastic damage model. Model results explain that the highly localized fracture pathways are the major places where gas and water interact with each other, and as a result the whole rock is almost kept fully saturated, which helps us get in-depth understanding of this gas transport mechanism.

A mesoscopic numerical method for fracture energy of concrete

AbstractThis paper develops a mesoscopic numerical method for evaluating the fracture energy of concrete. In this method, concrete is modeled as a three‐phase composite material, composed of mortar, coarse aggregate, and the interface between them. The actual mixed‐mode I–II crack growth path in mode I fracture tests is traced by applying crack propagation criteria. After verifying the numerical method by a series of three‐point bending tests, the effects of aggregate location, aggregate size, and crack propagation path on the fracture energy of concrete are evaluated. It is found that for the fracture mode of crack bypassing aggregates, the actual fracture energy of concrete is significantly affected by the aggregate location but independent of the aggregate size and the crack propagation path.

A multiple rolling-point loading method for low-stress equal-radial-depth cropping

A multiple rolling-point loading method for low-stress equal-radial-depth cropping is proposed considering the eccentricity of transient fracture areas of metal bars. The crack propagation criterion under single rolling-point loading is provided. The extended finite element method (XFEM) is used to simulate the longest contiguous propagation of crack fragment and polycyclic propagation of annular crack under multiple rolling-point loading. The bar can then transiently fracture with high-quality section. The cropping experiments of multiple rolling-point loading curves obtained in this paper reveals that the instantaneous fracture area can be reduced by up to 65% and the eccentricity of bars can be avoided.

Fatigue Phase‐field Modeling for Elastomeric Materials

AbstractFatigue failure prediction of elastomeric materials plays a crucial role in engineering applications, e.g., rolling tires. Experimental investigations, as a straightforward evaluation of fatigue failure, do not enable an efficient insight due to significant time consumption. Therefore, several numerical approaches are developed to model fatigue fracture or damage behavior of material components subjected to cyclic loading. Inspired by [1], the work at hand incorporates a degrading fracture toughness into a promising phase‐field method. As a smeared crack representation, the phase‐field model does not depend upon any explicit criterion for crack evolution, e.g., crack initiation and propagation. Furthermore, this work proposes a novel algorithm, which is based on a post‐processing technique, to evaluate the energy release rate for PARIS' parameters during the stable crack propagation regime. The methodology is implemented into the Finite Element framework and a demonstrative numerical example is simulated.

Аналитическая модель квазихрупкого разрушения пластины с трещиной

The paper considers a rectangular plate with the edge crack of mode I of normal separation from the elastoplastic material with the ultimate strain. This class of materials includes, for example, the low-alloy steels used in structures operating at temperatures below the cold brittleness threshold. The strength of the plate was studied within the framework of the Neuber --- Novozhilov approach. The crack propagation criterion was formulated using the modified Leonov --- Panasyuk --- Dugdale model using an additional parameter, i.e., the plasticity zone diameter (pre-fracture zone width). Under conditions of small-scale yielding in the presence of the stress field singular feature in the vicinity of the crack tip, the two-parameter (dual) criterion for quasi-brittle fracture was formulated for mode I cracks in the elastoplastic material. The fracture dual criterion included deformation criterion at the crack tip, as well as the force criterion at the fictitious crack tip. The lengths of the original and fictitious cracks were differing by the length of the pre-fracture zone. Diagrams of the plate quasi-brittle fracture under conditions of plane deformation and plane stress were constructed. The parameters included in the proposed quasi-brittle fracture model were analyzed. It was proposed to select model parameters according to the approximation (σ--ε)-diagram of uniaxial tension and the KIc critical stress intensity factor

A micromechanics‐based approach to damage propagation criterion in viscoelastic fractured materials regarded as homogenized media

AbstractThis paper aims to formulate a damage propagation criterion in microfractured viscoelastic materials, relying upon a micromechanics reasoning together with thermodynamics concepts. The fracture density is regarded as damage parameter at macroscopic scale. The equivalent behavior of the heterogeneous material (solid matrix + fractures) is first formulated within the framework of viscoelastic homogenization theory. In this context, relevant relationships relating local fields to macroscopic fields are derived, thus allowing a clear micromechanical interpretation of quantities involved in the upscaling process, such as the residual or viscous strains. Based on thermodynamic concepts, the energy dissipation and the free energy of the homogenized viscoelastic material are deduced at the macroscopic scale. The formulation of an energetic‐based criterion for damage propagation in viscoelastic fractured materials is then achieved by viewing the macroscopic energy release rate as the thermodynamic force responsible for propagation. Due to the delayed deformation component, the formulation is time‐dependent. Since it is formulated directly at the homogenized material level, the main advantage of the approach developed in this work is the rigorous determination of the energy release rate expression, without neglecting any residual term. In the last part of the paper, several numerical applications are performed to illustrate the main features of the modeling and to provide comparison with available simplified formulations. Finally, the proposed damage propagation criterion is applied to give qualitative insights on fracturing process of sedimentary layered rocks at geological times scale viewed as a long‐term mechanical damage problem, emphasizing the viscosity effects in preventing fracture propagation.