Dynamic Stress Intensity Factor Research Articles

Crack arrest characteristics and dynamic fracture parameters of moving cracks encountering double holes under impact loads

Brittle materials such as rock or concrete contain a large number of micro-cracks, voids, and other defects. Under external impacting loads, the interaction between fissures and holes affects the bearing capacity and stability of Engineering structures. To study the interaction mechanism between moving cracks and circular holes, A large-size semi-circular notched with a fissure and double circular hole (SNFDH) specimen was suggested in this research, and the dynamic fracture tests were carried out on the SNFDH specimens with different double circular hole spacing (35mm, 40 mm, 45 mm, 50 mm, 55 mm, 60 mm, and 70 mm) using a drop hammer impact test device. Crack propagation gauges were employed to track the time and velocity at which the crack propagated along its trajectory. Dynamic Drucker-Prager yield criterion and the cumulative damage failure criterion were used in the numerical simulation of SNFDH concrete materials. The program AUTODYN was employed to simulate the crack growth characteristics when a crack encounters the double hole. The program ABAQUS was applied to calculate the dynamic fracture parameter of cracks. The test results manifest that the crack propagating trajectory has three different characteristics according to the double hole spacing; the double circular hole has an arresting function for a moving crack; the size of the double hole spacing has a significant effect on the crack propagating velocity, crack propagating length, dynamic stress intensity factor and dynamic energy release rate; the configuration of the SNFDH specimen can be used to investigate the crack arrest mechanism when moving crack encountering double holes.

Interfacial dynamic impermeable crack analysis in dissimilar piezoelectric materials by a new interaction integral

Dynamic intensity factors (IFs) provide an important parameter for assessing the failure risk of an interfacial crack for piezoelectric composites exposed to electromechanical impact loadings. In the present research, a new dynamic interaction integral (I-integral) is built for computing the dynamic stress IFs (SIFs) and electric displacement IF (EDIF) of an interfacial crack located in dissimilar inhomogeneous piezoelectric media. Through proper selection of auxiliary variables, the domain expression of I-integral for the inhomogeneous piezoelectric bi-materials does not need to take into account any derivative term for any piezoelectric material property. Further, after rigorous theoretical derivation, the resulting I-integral is still valid for complex models where the integration domain contains other multiple interfaces, regardless of whether the extra materials are straight or curved. Incorporating the modified extended finite element approach, the accuracy is confirmed by checking the dynamic IFs extracted from the I-integral with referenced results. The domain-independence is tested by varying ranges of integration domains for inhomogeneous piezoelectric bi-materials and multi-interface piezoelectric composites. Finally, typical examples are employed to discuss the influences of the direction and magnitude of electric impact loading, combination of polarizations, inhomogeneous degree of piezoelectric bi-materials and complex distribution of diverse material properties on the dynamic IFs.

Study on the influence of slit pipe wall thickness on the rock breaking effect of slit charge explosion

AbstractIn this study, the influence of slit pipe wall thickness on shaped charge blasting efficiency was investigated. The influence of different slit pipe wall thicknesses on the dynamic behavior of slotted charge blasting was analyzed by a combination of experimental observations and numerical simulations. Polymethyl methacrylate (PMMA) was used as a rock simulation material to prepare slit pipes with different slit pipe wall thicknesses (0.5, 1.0, and 1.5 mm). A dynamic caustics system is used to capture the crack propagation process. ANSYS/LS‐DYNA was used for the numerical simulation analysis. The experimental results show that there is a positive correlation between the slit pipe wall thickness and the crack propagation length, velocity, and dynamic stress intensity factor. With increasing slit pipe wall thickness, the directional propagation and energy concentration ability of cracks are significantly improved, but an increase in the slit pipe wall thickness will also promote the propagation of secondary cracks. In addition, the numerical simulation results support the experimental observations and reveal the existence of an optimal slit pipe wall thickness that can maximize the blasting efficiency while maintaining structural integrity. This study not only deepens the understanding of the physical laws of the blasting process but also provides a practical reference for the optimal design of slotted charges in engineering applications.

Fast fracture in toughened glass when impacted randomly by Ice

Modelling the triggering of fracture at a pre-existing flaw is an evolving method of predicting ultimate failure in glass. This fracture mechanics approach of modelling has been shown to give more reliable predictions than a calibrated probabilistic distribution model (as is commonly adopted) when dealing with hail impact which is highly transient in nature. The dynamic stress intensity factor controlling fast crack growth is sensitive to the complex stress state surrounding the critical flaw. Finite element simulations of localised stresses in 3D could incur high computation cost which is compounded by the need to repeat computations until convergence and to simulate multiple strikes in emulating a storm scenario. In this study, closed-form expressions were developed to waive away the need of any simulations. With hail impact, boundary conditions of the glass panel need not be factored into the modelling, as the highly transient stresses are wave controlled. Input parameters are the thickness and level of prestress in glass; offset of position of strike from the known crack and its depth; and the size, velocity, and temperature of the ice impactor. Results from 40 test scenarios involving 5 offset distances, 3 crack depths, 2 glass thicknesses, and 2 sizes of ice were used to validate the prediction, and to reveal the sensitivity of the outcome of the impact to changes in the impact position relative to the known crack.

Transient thermal fracture investigation of a cracked functionally graded layer via Guyer-Krumhansl model

Recent experimental evidence proves the Guyer-Krumhansl (G-K) model’s capability of predicting the nonclassical transient heat transfer process in heterogeneous composites. The objective of this article is to explore the dynamic thermal and fracture behaviors of a cracked orthotropic functionally graded material (FGM) layer subject to abrupt thermal shocks via the G-K equation. The thermal and elastic governing equations determined by the G-K model are transformed into the singular integral equations, which are calculated numerically to assess the non-Fourier transient temperatures and the resultant dynamic thermal stress intensity factors. Parametric comparisons are carried out for the effects of the non-Fourier thermal lagging time and thermal nonlocal length on the transient thermoelastic responses. The findings would benefit the applications of unconventional heat conduction theories and shed light on the scientific understanding of FGM’s fracture behaviors.

Random Dynamic Responses of Two Parallel Interfacial Cracks Between A Functionally Graded Material Strip And Two Dissimilar Elastic Strips

Abstract An analytical approach is presented in this article for the random dynamic study of two parallel interfacial cracks in a functionally graded material (FGM) strip that is bonded between two distinct elastic strips. One of the parallel cracks is placed at the interface of the elastic strip I and the FGM strip, and another is at the interface of the FGM strip and elastic strip II. A stationary stochastic process of time is used to model the dynamic loadings that are applied to the crack faces. To find the solution, the FGM strip is splited into a number of sub-strips, and using an average method, the material properties of each sub-strip are reduced to random variables. A fundamental problem is formulated to find the solution. The boundary conditions are reduced to a set of singular integral equations employing the Fourier sine, Fourier cosine, and Laplace transforms, which are solved by using the Collocation method. Further, the analytical expressions of dynamic stress intensity factors (DSIFs) about the crack tips in the time domain are obtained with the help of the Improved Dubner and Abate's method. Finally, the Monte Carlo method is used to obtain the mathematical expectation and standard deviation of DSIFs. The outcomes of the present study are also verified. The unique aspect of this study is the pictorial illustration of mathematical expectation and standard deviation as functions of the number of sub-strips, functionally graded parameter, thickness of the strips, and length of parallel interfacial cracks.

Theoretical analysis of the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress

A mathematical model of blasting stress wave scattering at an arc-shaped interface crack is established to theoretically analyze and verify the scattering characteristics of blasting stress waves at an arc-shaped interface crack in a deep rock mass with high in-situ stress. Based on the continuum mechanics, finite deformation, and incremental stress theories and the geometric and physical characteristics of the arc-shaped interface crack, the mathematical model includes a set of the first class of singular integral equations with Hilbert kernels. The opening and dislocating displacements of the arc-shaped interface crack and the effective stress components of scattered stress waves are numerically calculated and discussed with the variation of the type, frequency, and incident angle of the blasting stress wave; the curvature radius and opening angle of the arc-shaped interface crack. The condition that the dynamic stress intensity factors and energy release rates at the upper and lower tips of the arc-shaped interface crack reach peak are also provided. It is found that when the frequency of the blasting stress wave and the curvature radius of the arc-shaped interface crack increase, the peaks of the above dynamic stress intensity factors will increase further, and the arc-shaped interface crack is more likely to expand or destabilize. Although the order of in-situ stress is much smaller than that of Young’s modulus of the deep rock mass, it increases the effective stress concentration of scattered stress waves and the opening and dislocating displacements of the arc-shaped interface crack. These findings will provide theoretical guidance for analyzing the cracking characteristics of blasting stress waves in deep rock masses with high in-situ stress.

Analytical analysis of the interaction between cavities and a crack in bonded isotropic and anisotropic half spaces under SH wave

Interaction between two cavities and a linear crack subjected to elastic shear horizontally (SH) wave is investigated analytically in this work. Two cavities are buried in two bounded half spaces respectively and the cross-section of each cavity has a different shape. The media of two half spaces are isotropic and anisotropic respectively, and the complex function method is applied to first solve the wave equation in each medium. Then, with the help of image principle, Green’s functions and wave field expressions in each separated half space are constructed. Subsequently, utilizing “conjunction” technique, a series of Fredholm integral equations containing undetermined forces at the interface are obtained and reduced in order to be solved. Dynamic stress distribution is mainly considered to discuss the interaction between the cavities and the crack. Finally, a parametric study on dynamic stress concentration factor (DSCF) and dynamic stress intensity factor (DSIF) presents the interaction is affected by several dimensionless factors simultaneously.

A Study on Crack Initiation and Propagation of Welded Joints under Explosive Load

Welded joints in naval ship hull structures are weak areas under explosive load, but there are relatively few studies investigating the failure characteristics of welded joints through dynamic fracture and explosion tests. In order to explore and predict the failure characteristics of welded joints under explosive load, instrumented Charpy impact tests, explosion tests, and numerical simulations were carried out. The dynamic fracture toughness of ultra-high strength ship hull structural steel welded joints was obtained, and the dynamic stress intensity factors, together with the correlation between stress wave and crack propagation at different positions, were acquired. The results showed that the stress state at the crack tip of a Charpy impact specimen was consistent with that of a welded joint under explosive loads, and the crack initiated when the dynamic stress intensity factor exceeded the dynamic fracture toughness. The results indicated that the dynamic fracture toughness obtained by instrumented Charpy impact tests could be used to predict the crack initiation characteristics of welded structures under explosive load, and the stress wave at the crack tip was basically perpendicular to the crack propagation surface and promoted the rapid propagation of cracks.

Dynamic propagation of moving cracks in brittle materials by field-enriched finite element method

We propose a field-enriched finite element model to simulate the dynamic growth of moving cracks in brittle solids. The paper introduces the dynamic model and verifies its accuracy by analyzing dynamic stress intensity factors during the propagation of a mode-I moving crack. We also simulate crack bifurcation using a specific criterion. Our numerical method successfully reproduces experiments, including the Kalthoff-Winkler experiment, three-point bending test under impact load, and compact compression specimen (CCS) experiment. Finally, we investigate how the location of a circular hole influences the propagation paths of a pre-existing straight crack using a numerical model including both the hole and the crack (COSSCC). Several numerical examples demonstrate the ability of dynamic field-enriched finite element method in simulating dynamic moving cracks.

Scattering of SH waves by elliptical cavity and type-III crack in deep anisotropic geology

Most of the underground rock formations are anisotropic, and the study of the dynamic response of anisotropic geology containing internal defects is necessary for the development of underground tunnels or caverns. In this paper, the wave function expansion method, the complex function method, and the Green's function method are used to solve the problem of scattering of SH waves in anisotropic rock in the presence of elliptical cavity and type-III crack. Boundary conditions for solving the problem are given using the conformal transformation method, and crack in the medium is constructed using the "crack cutting" technique. The scattered wave field generated by the crack is constructed based on the Green function method, and the displacement and stress fields in the model are obtained by the wave field superposition principle in the case of SH wave incidence. The dynamic stress concentration factor (DSCF) on the boundary of the elliptical cavity and the dynamic stress intensity factor (DSIF) at the crack tip are derived. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, the effects of the anisotropic strength of the rock mass, the dimensions of the cavern, and the incidence angle and wave number of the SH wave on the DSCF and DSIF are analyzed by numerical calculations in both the frequency and time domains. The results show that the anisotropy of the rock mass, the shape of the cavern and the defects of the surrounding medium have a great influence on the dynamic response of the underground structures, which should be given enough attention in the development and design of deep underground caverns or tunnels.

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.

Transient analysis of multiple arbitrarily oriented cracks under antiplane shear wave

ABSTRACT Most works in the literature on interactions of cracks and stress waves were for collinear or parallel cracks. However, in reality, cracks are usually randomly oriented. In this work, the problem of a homogeneous linear elastic body containing arbitrarily oriented cracks under dynamic antiplane shear loading is considered. Distribution of dynamic dislocations is used to simulate the cracks and the corresponding integral equation is derived. The integral equation is utilized to calculate the dynamic stress intensity factors. Numerical examples are provided to demonstrate the effectiveness of the present method.