Dynamic Stress Intensity Factor Research Articles

Mechanics of crack initiation, propagation and crack grain boundary interaction in bicrystal silicon using near-tip localized stress calculation

Crack propagation and arrest are important phenomena in polycrystalline silicon. This phenomenon considerably affects the effectiveness of solar cells made up of polycrystalline silicon. To understand the crack propagation in polycrystalline silicon, it is essential to study the bicrystal first. Earlier, crack propagation has been studied in bicrystal materials primarily from the perspective of material behaviour. However, the mechanics part is largely missing. In the present work, crack propagation of bicrystal silicon during uniaxial tension has been studied at the atomistic scale. The silicon bicrystal was formed by joining two single crystals: crystal 1 and crystal 2 of different orientations. Various states like crack initiation, propagation, arrest, re-initiation and crack grain boundary (GB) interaction have been analysed using Stress Intensity Factor (SIF), calculated from the local crack tip virial stress field. Considering the effect of crack tip velocity, the dynamic SIFs at crack propagation state have been converted to the SIF of an equivalent static crack using the generalized expression for anisotropic material. It has been found that for the propagation state, crack propagation continues as long as the equivalent static SIF is greater than the critical SIF (CSIF). In crystal 1, crack propagation is along the low CSIF direction. Therefore, the crack did not change its path and propagated along a straight line. On the other hand, when the crack enters to crystal 2, it follows a zigzag path. Both of these observations have been justified in terms of near-tip calculated SIFs.

Dynamic response of semi-cylindrical depression, cylindrical cavity and type-III crack to SH wave in half-space anisotropic media

In this study, the anti-plane dynamic response of an elastic half-space anisotropic medium containing surface semi-cylindrical depressions and internal cylindrical cavity and type-III crack is solved analytically. The wave function expansion method, the complex function method and the Green's function method can be used to effectively construct the free wave field equation and the scattered wave field equation in the case of SH wave incidence, in which the scattered wave field generated by the crack is constructed by the Green's function method and the "crack cut" method. For the scattered wave field generated by a circular cavity is constructed using the mirror method, where the positional offset coefficient in the mirror method of a half-space anisotropic medium is introduced, which well solves the problem of the asymmetry of the scattered wave field. Finally, the effects of anisotropic strength of the medium, SH wave incidence angle and dimensionless incident wave number on the surface displacement amplitude (|W|), dynamic stress concentration factor (DSCF) at the boundary of the circular cavity and dynamic stress intensity factor (DSIF) at the crack tip are investigated in both frequency and time domains under different working conditions, and conclusions different from those of isotropic medium are obtained, which provide some theoretical references for the earthquake-resistant design of the underground structure with canyon topography and the surface building.

A stable numerical framework for long-time dynamic crack analysis

This paper introduces a stable numerical framework designed to address dynamic crack problems over long-time intervals. The initial step involves the temporal discretization of the governing dynamic equilibrium equations using the arbitrary order Krylov deferred correction method. To ensure precise boundary condition matching, a novel numerical implementation is incorporated into the Krylov deferred correction technique. Subsequently, the resulting system of spatial partial differential equations at each time node is solved using the meshless generalized finite difference method with 4th-order expansions in regions close to the crack-tips and 2nd-order expansions in areas far from the crack-tips. This combined approach capitalizes on the strengths of both the Krylov deferred correction technique and the generalized finite difference method, enabling stable simulations of dynamic cracks with the large time step and without the need for mesh generation. Notably, we refine the collocation nodes near crack tips to attain accurate numerical results for displacement and stress field. Several numerical experiments involving diverse impact loadings are conducted to validate the developed framework. Furthermore, a comparison is made between the dynamic stress intensity factors obtained using our approach and those from existing methods.

Fracture behavior in blasting under different static stresses and high stress unloading

AbstractIn this paper, the effects of static stresses on the blast‐induced crack in polymethyl methacrylate specimens with an empty hole were investigated by caustic system. The propagation behavior and re‐initiation process of blast‐induced crack under initial static stress and high stress unloading were investigated. The results show that when the direction of the empty hole is perpendicular to the static stress, the static stress reduces the length of the main crack. However, when the static stress is very high, the length of main cracks does not decrease. In addition, the static stress reduces the crack velocity and dynamic stress intensity factor (DSIF) and suppresses the increase of DSIFs and crack velocity due to reflected wave. The crack arrested under high stress unloading propagates again in the later stage. Moreover, the duration of high stress unloading lasts approximately 1 ms.

Investigation of dynamic three–point bending fracture properties of SCB sandstone

The stress intensity factor (SIF) is not only an important parameter in the field of fracture mechanics but also a key indicator reflecting the strength of the stress field at the crack tip. Therefore, this paper uses the Split–Hopkinson–Pressure–Bar (SHPB) device to conduct dynamic fracture experiments on semi–circular bend (SCB) sandstones of different fracture modes and then uses an experimental–numerical method to simulate the dynamic loading process to explore the changes law in SIF. Finally, combined with the high–speed digital image correlation (HS–DIC) technology, the fracture characteristics of SCB sandstones are studied. The results show that the rising rate of dissipated energy acting on the specimen fracture and damage increases rapidly when it is close to dynamic fracture, which makes the dynamic SIF also get a substantial increase, and the influence of dissipated energy on dynamic SIF is seen to be very strong. Moreover, prior to the occurrence of dynamic initiation fracture, the damage to the specimen is primarily triggered by microscopic tensile effects at the tip of the preset crack, which results in the value of KI always being greater than KII before the dynamic fracture occurs. Meanwhile, the distribution curve of dynamic SIF exhibits better symmetry or a trend towards symmetry compared to the distribution curve of static SIF. This suggests that the tip of the preset crack distributes with more uniform tensile and shear stresses during dynamic loading. Using the HS–DIC technique, when the specimen occurs dynamic pure mode I initiation fracture, there was a good symmetrical trend in both the vertical strain around the fracture crack and the horizontal displacement field at the specimen. However, when specimens occur dynamic mixed mode I/II initiation fracture, the horizontal displacement fields showed asymmetry, and the specimens all suffered varying degrees of shear damage.

An explicit improved meshless numerical manifold method for dynamic crack propagation

Accurately simulating the dynamic propagation of cracks is critical to investigating the mechanisms of rock fracture under dynamic loading. The meshless numerical manifold method, characterized by its node-based interpolation approximation akin to the meshless method and the dual-cover of numerical manifold method, is particularly suitable for crack analysis and has been successfully applied to quasi-static crack propagation. This paper aims to extend its application to the simulation of dynamic crack propagation. Initially, the meshless numerical manifold method's nodal arrangement and numerical integration scheme are enhanced to address dynamic problems more effectively, referred to as the Improved Meshless Numerical Manifold Method (iMNMM). Subsequently, we introduce a novel mass lumping method grounded in rigorous mathematical principles, an energy-conserving extended degrees of freedom inheritance strategy and a crack propagation criterion based on dynamic stress intensity factors. Additionally, the viscous artificial boundaries and the “large mass” acceleration method are incorporated to impose the acceleration and zero-displacement boundary conditions. Further, the improved explicit meshless numerical manifold method based on the central difference method is established for dynamic crack propagation. Finally, for verification, iMNMM is tested on several numerical examples. Numerical results manifest that iMNMM can enable the simulation of dynamic crack propagation with larger, constant time steps.

Effect of external magnetic field on electric current-induced fracture of notched thin metallic conductors: Part 2- High magnetic fields

In the companion report (Telpande et al., n.d.), we discussed the impact of a weak external magnetic field (up to 0.4 T) on the electric current-induced fracture of pre-notched thin metallic conductors, revealing a linear decrease in critical current density, jc, necessary for crack propagation. This study extends the investigation to explore the effects of stronger external magnetic fields (0.6–1 T) on the fracture of pre-notched, current-carrying metallic foils. The experimental analysis reveals a substantial, albeit linear, drop (up to 40 %) in jc under stronger magnetic fields. Interestingly, calculations of the dynamic stress intensity factor, KIE,t, which assesses the interplay between applied current density and external magnetic field, indicate crack growth under a strong magnetic field even when KIE,t is below the plane stress critical stress intensity factor, KIC. A remarkable phenomenon emerges: the application of electric current pulses combined with strong external magnetic fields induces observable surface undulations near the notch tip. A comprehensive 3D finite element model, integrating linear and nonlinear buckling analyses under multiphysics stimuli, attributes these undulations to localized buckling near the notch tip. This buckling-induced stress redistribution near the crack tip contributes to an overall reduction in fracture toughness due to mode mixity, leading to the fracture of the Al foil below KIC. This investigation, along with the companion report (Telpande et al., n.d.), significantly advances our understanding of the effects of magnetic fields on the fracture of current-carrying conductors.

Thermal shock fracture in a cracked strip: Incorporating convective heat transfer between lateral surfaces and ambient environment

This paper presents a comprehensive analysis of transient temperature and thermal stress around a thermal insulated crack in a finite thermoelastic strip subjected to thermal shock based on the dual-phase-lag (DPL) heat conduction. A detailed investigation of the effect of convective heat exchange between the lateral surfaces of the strip and the ambient environment is conducted. By employing integral transform technique, the thermoelastic crack problem is reduced to a set of singular integral equations, and solutions for the transient temperature distribution and dynamic stress intensity factors (SIFs) at the crack tips are then obtained. Numerical results reveal a considerable temperature gradient near the heating surface when both the high convective heat transfer coefficient and thin strip are involved. Consequently, the SIFs in such scenarios where cracks are located close to the heating surface are significantly larger compared to those calculated by neglecting the convective heat loss. Furthermore, during the initial period following a thermal shock, the SIFs may exhibit higher magnitudes than the steady-state values. These findings emphasize the importance of accounting for the influence of convective heat exchange with the ambient environment in material design and optimization to enhance fracture resistance under transient thermal loading.

Meshless variational method applied to Mixed-mode dynamic stress intensity factors

For linear elastic fracture mechanics, the variational technique with a path independent contour integral is used to determine the stress intensity factors (SIFs) for functionally graded materials (FGMs) under static and dynamic loads in this work. Utilizing the interpolation of the Chebyshev polynomials and the finite block method (FBM) to deal with two-dimensional fracture problems. The Quadratic form block is transformed from Cartesian coordinates to normalized coordinates with 8 nodes by technology of mapping. The new equilibrium equations in terms of displacements are derived in a normalized coordinate system. All coefficients of the Chebyshev polynomials are determined by considering the governing equations, boundary conditions and connecting conditions of the two blocks. The accuracy and convergence of the FBM with Chebyshev polynomials are illustrated through several examples and comparison has been implemented with analytical solutions and different numerical approaches.

Fatigue crack driving force of railway bogie frames using rigid-flexible coupled dynamics: A case for beam model

The stress intensity factor is essential to determine the residual fatigue lifetime of cracked components. However, the traditional method used to determine the stress intensity factor is very difficult to characterize the dynamic behaviors of structure arising from the fatigue crack. This paper proposed a methodology to determine the dynamic stress intensity factor (DSIF) of a crack incorporating with the rigid-flexible coupled dynamics. Firstly, a rigid-flexible coupled dynamic model of cantilever beam representing the typical structure of bogie frame with a straight crack was developed based on SIMPACK platform. In the model, the equivalent spring - contact element was employed to model the contact behaviors of crack interface. Subsequently, the DSIF considering the crack closure effect was calculated by the node displacement extrapolation. The validity of proposed method was demonstrated through comparing the DSIF with those obtained by other analytical methods. The results suggest that the proposed methodology can characterize the closure effect of crack, and yield more accurate estimation for the DSIF. This method establishes a link between the multibody system dynamics and the fracture mechanics, which enable us to calculate the DSIF of crack under the operating condition using a rigid-flexible coupled dynamic model.

Propagation and scattering of Rayleigh wave from an interfacial crack in a viscoelastic waveguide layer bonded to a piezoelectric substrate

In this article, the propagation and scattering of Rayleigh wave from an interfacial crack in a bilayer structure, a viscoelastic waveguide layer attached to a piezoelectric substrate, have been examined. The Principle of Superposition is used to formulate the problem. The Fourier transform method and stiffness matrix formulation have been used to arrive at singular integral equations. These singular integral equations are then reduced to a system of linear algebraic equations by applying the Gauss-Jacobi quadrature technique. A parametric study has been examined for phase velocity, attenuation, and dynamic stress intensity factor of mode-I and mode-II at both crack-tip.

A generalized finite difference method for 2D dynamic crack analysis

This paper presents a new framework for efficient and accurate analysis of transient elastodynamic cracks by using the generalized finite difference method (GFDM). The method first discretizes the solution domain into a set of overlapping small subdomains, and then in each of the subdomains, the unknown functions and their derivatives are approximated by using the local Taylor series expansions and moving-least square approximation. The degree of the Taylor series used in the local subdomain is increased automatically in the regions near the crack-tips, in order to appropriately describe the local asymptotic behavior of near-tip displacement and stress fields. The path-independent J-integral and sub-domain technique are adopted to compute the dynamic stress intensity factors (SIFs) of the cracked bodies. Preliminary numerical experiments for dynamic SIFs with both uniform and variable loading conditions are given to show the efficient and accuracy of the present method for transient elastodynamic crack analysis.

An XFEM model of cracked functionally graded materials under different dynamic loadings

The behavior of cracked structures made of functionally graded materials (FGMs) under different types of dynamic loading is investigated by calculating the dynamic stress intensity factor (DSIF). Material properties, i.e. Young’s modulus E and mass density ρ vary exponentially and continuously along a given direction, but Poisson’s ratio υ is assumed to be constant. Therefore, this work addresses the effect of FGM grading orientation as well as the effect of dynamic loading properties on DSIF. To achieve this goal, a computer code based on the extended finite element method (XFEM) combined with the Level-Set method was developed. DSIF is assessed using an interaction integral technique. To validate the developed code, the results were compared with other work in the literature on structures under step function loading. The good correlation between the results demonstrates the efficiency of the code. Then, as part of a parametric study, the structure is subjected to triangular and rectangular loadings, which change the graded value and orientation of the FGM. The quality of the results demonstrates the robustness of the developed code.

Transient analysis of a cracked functionally graded magneto‐electro‐elastic rectangular finite plane under anti‐plane mechanical and in‐plane electric and magnetic impacts

AbstractThe transient anti‐plane problem of a functionally graded magneto‐electro‐elastic (FGMEE) rectangular plane weakened by several embedded and edge cracks under various boundary conditions is solved. First, the solutions to the dynamic magneto‐electro‐elastic dislocation in the finite rectangular domain are derived by employing Laplace and finite Fourier cosine transforms. The solutions can be utilized to construct the singular integral equations in Laplace transform domain for FGMEE rectangular plane with multiple embedded and edge cracks. The integral equations arising from dislocation solutions have Cauchy‐type singularities with unknown dislocation density functions. These unknown functions may be obtained by reducing the integral equations into a system of linear algebraic equations, hereby, the dynamic stress intensity factors (DSIFs) for several arbitrarily embedded and edge cracks are obtained. The overshoots of dynamic stress intensity factors are shown to be intensely affected by the rectangular plane dimensions, length and position of the cracks, loading parameter, and negative or positive gradient index.

The Effect of Preloaded Compressive Stress and Curvature of Defect on Blast-Induced Fracture Behavior by Caustic and Numerical Models

In this study, the effects of preloaded uniaxial compressive stress and defect (prefabricated by laser cutting) curvature on blast-induced cracks and stress wave propagation were investigated in polymethyl methacrylate (PMMA) specimens using caustics theory. Based on the mathematical relationship between stress and optics, the fracture behavior (the propagation path, dynamic stress intensity factors (DSIFs), propagation velocity, initiation angle of the main crack, and damage degree between the defect and the blasthole) was calculated and analyzed quantitatively. The results show that the preloaded stress could mainly restrain the main crack propagation in the horizontal direction and reduce the initiation angle and damage degree at the defects. Meanwhile, the crack initiation position of the positive curvature defect was not at the end of the defect. In addition, the curvature of the defect significantly affected the blast-induced fracture compared to preloaded stresses. Comparing the main crack with other curvature defects, the DSIFs, velocity, crack arrest time, crack length, and horizontal offset distance of the main crack with negative curvature defect were the largest. The variation in the full stress field in the specimen under blasting and preloaded stress was simulated by a numerical model. The results show that the curvature of the defect has a significant effect on tensile waves at the end of defects, and the tensile stress from high to low was C-25, C0, and C25, in that order.

Prediction of pipeline fatigue crack propagation under rockfall impact based on multilayer perceptron

Recently, the artificial intelligence technologies have been widely used in the field of pipeline integrity management. When crossing mountains, pipelines would inevitably encounter rockfall impact, which will potentially affect the growth of crack. However, previous research barely investigated the effect of sudden rockfall impact on health management of pipelines with fatigue cracks. To overcome this limitation, a novel crack propagation prediction algorithm based is proposed for pipelines subjected to rockfall impact. The stress intensity factor (SIF) rockfall impact ratio is introduced to describe the interaction effect of rockfall on the fatigue crack of pipelines. And the dynamic SIF values are acquired by finite element modeling (FEM) where 354 models with different parameters are analyzed. To more accurately forecast the crack growth under the rockfall impact, a method integrates multilayer perceptron (MLP) with Paris’ law is proposed based on the above reliable database. Two parameters impacting the performance of the network including the number of neurons in the hidden layer and the hidden layer's activation function are evaluated and network with the most precise prediction results is selected. Quantitative analyses are performed for key factors including rockfall mass, impact velocity, impact position and crack size. The prediction results using dynamic SIF values are compared with the static ones to indicate the effect of rockfall on the crack propagation. The proposed method is valuable to support decision-making in pipeline reliability assessment and integrity management.

Study of crack extension and branching behavior of layered materials under impact loading

This study utilized a digital laser dynamic caustics experimental system to conduct three-point bending impact experiments on layered epoxy specimens with different values of angle α between the bedding and the prefabricated crack, as well as the epoxy specimen without bedding. A high speed camera was employed to record the dynamic caustic spot at the crack tip during specimen extension and branching, analyze the dynamic stress intensity factor for crack tip for Mode I and II, crack extension speed, and exploration of the influence of angle α on crack extension and branching behavior. Numerical simulations were performed using the cohesive element method. The findings indicate an increase in crack initiation toughness as the angle α increases. After the initiation of the main crack, the failure mode was Mode I-dominated damage. When it extended near the bedding, the failure mode of the main crack changed to Mode II-dominated damage due to the influence of the bedding, resulting in the formation of branching cracks and microcracks. The main crack again exhibited Mode I-dominated damage after branching. Notably, the branching cracks primarily exhibited Mode II-dominated damage. The occurrence of branching cracks and microcracks intensifies with higher α. The variation of α significantly influences the speed of crack extension.

Interaction of anti‐plane shear waves with two collinear cracks in 1D hexagonal piezoelectric quasicrystals

AbstractThe present article presents the interaction of anti‐plane shear waves by two collinear cracks in one dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs). With the aid of Fourier transform, the mixed boundary value problem (MBVP) is transformed into three pairs of dual integral equations, which are solved analytically by Hilbert transform. The explicit expressions for dynamic stress intensity factors (DSIFs) of phonon and phason fields, crack opening displacement (COD) and electric displacement (ED) are derived in closed form and some special cases are studied. Numerical values of DSIFs of phonon and phason fields, COD and ED are plotted to show the effect of crack length and electric boundary condition. Moreover, the DSIFs of phonon field and COD are represented graphically for single crack.

Rate-dependent strength and crack damage thresholds of rocks at intermediate strain rate

To investigate the rate dependence on the mechanical behaviours of rocks under intermediate strain rate, three types of rock were loaded by using a newly developed servo-controlled dynamic triaxial apparatus. In this study, the dynamic strength and crack damage thresholds of rocks under different confinements were investigated at the strain rate range of 10−3∼100s−1, which is of significance to understand the rock damage subjected to earthquakes or far-field blasts. The results indicate that the apparatus could ensure the rock samples being loaded under a stable strain rate without causing prominent disturbance on the confining stress. In addition, the strength and damage thresholds are dependent on the strain rate, i.e., the increasing strain rate would result in the increase of dynamic strength and crack damage thresholds. The increase of confinement leads to a higher failure strength, the crack initiation and damage stresses are also positively correlated to the confining pressure under dynamic loads. Based on the theory of fracture mechanics that considers the crack growth velocity, it is found that the dynamic stress intensity factor exhibits a negative correlation with both the strain rate and confining pressure, whilst the fracture toughness presents an inverse trend. Therefore, the larger axial stress is required to initiate the cracks, which might further induce the variation of crack initiation stress.

Dynamic fracture behavior for hole-initiated cracks in functionally graded magneto-electro-elastic bi-materials

In this article, the dynamic fracture behavior of hole-initiated cracks in functionally graded magneto-electro-elastic (FGMEE) bi-materials with exponential variation is studied by Green’s function method, and SH-wave is considered as an external load acting on the bi-materials. The mechanical model of the cracks is constructed through interface-conjunction and crack-deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips is expressed. Numerical results clarified the factors that affect the DSIF, including wave number, incident angle, the geometry of the defect, and the gradient of the bi-materials. The accuracy of the present methods is examined by comparing the obtained results with the reference solutions. Compared with previous traditional numerical and analytical methods, the methods proposed in this paper are relatively more effective and applicable, and provide a new perspective for studying the fracture problems of FGMEE materials with more complex defects in practical engineering.