Crack Propagation Speed Research Articles

Study of rock dynamic fracture toughness by using VB-SCSC specimens under medium-low speed impacts

Dynamic fracture toughness, including initiation toughness, propagation toughness and arrest toughness, are important parameters for describing fracture behavior of rock materials. In order to study these parameters, a new V-shaped bottom single cleavage semi circle (VB-SCSC) specimen which has the arrest function for propagating cracks was proposed in this paper. The arrest function of this specimen is produced by the compressive waves set off from the two inclined bottoms, and the horizontal components of these compressive waves have the confining action on the propagating cracks. The experiments were performed by using a low & medium speed impact test system, and the crack propagation time and propagation speed were measured by using crack propagation gauges (CPG). The angle of the two inclined bottoms of the VB-SCSC specimens was designed as 120° or 150°, and both types of specimens have the arrest function on the propagating cracks. The finite difference code AUTODYN was applied in the simulation of crack propagation path, and the finite element code ABAQUS was applied in the calculation of stress intensity factors. Finally the dynamic fracture toughness was determined by using experimental-numerical method. The results show that the VB-SCSC specimen can be used to measure not only the initiation and propagation toughness, but also the arrest toughness. In the process of crack propagation, the crack may arrest for a period, and the arrest toughness is higher than both the initiation toughness and propagation toughness.

Chip formation mechanism in dry hard high-speed orthogonal turning of hardened AISI D2 tool steel with different hardness levels

Serrated chip formed in dry hard turning is considered one of the major chip types. In this paper, the main objective was to understand how the crack initiation and propagation, and thermo-plastic instability and pressure from force contribute to the formation mechanism of serrated chip in dry hard high-speed orthogonal turning (DHHOT) of the hardened steel with different hardness levels at cutting speed with 50, 450, and 850 m/min. The influences of the cutting speeds (50, 450, and 850 m/min) and workpiece hardness (40, 45, 50, 55, and 60 ± 1 Rockweel hardness (HRC)) on chip morphology, segment spacing, degree of segmentation, chip deformation coefficient, shear angle, and chip segmentation frequency also were experimentally investigated. Experimental results showed that the very high strain in the shear band does give rise to the high temperature in higher hardness material and at higher cutting speed and this makes the high-speed slip of the shear band much easier happen along existing micro-crack. The critical chip is produced at a cutting speed of 50 m/min and a hardness level of 50 ± 1 HRC. The strain rate increases with the increments of the cutting speed, which increases brittleness, and thus induces acceleration of the crack propagation speed in shear band. Moreover, the increments of the quenching hardness can increase the brittleness of the workpiece and thus lead to the large damage in shear band. The microstructure of the material within the bottom of chip showed that the elongated grains do appear due to thermo-mechanical effect between the chip back and the rake face of the cutting tool.

Laser shock peening induced residual stresses and the effect on crack propagation behavior

Laser shock peening (LSP), as a powerful surface engineering technique to improve the fatigue performance of metallic components, requires elaborately designed process pattern to maximize its benefits. In this study, a numerical method, combining finite element method (FEM) and residual stress intensity factor (SIF) analysis, was used to predict the effect of LSP pattern on the crack propagation behavior of the compact tension (CT) samples. The 3D FEM model was fully benchmarked using the mesh sensitivity study and time step calibration. The model was further validated using residual stresses data measured using the X-ray diffraction method. After that, the simulation of LSP of CT sample was conducted using five representative cases, and the corresponding residual stress fields were obtained. A mixed-mode SIF model was then applied to evaluate the effect of the residual stress field in resisting crack propagation. Based on the calculated residual SIFs from different LSP patterns, the best LSP patterns in terms slowing crack propagation speed were identified. To validate the simulation results, LSP experiments were conducted on CT samples using two identified LSP patterns and the crack growth rates were tested. The experiment results were consistent with the numerical prediction. This work demonstrates that FEM model combining residual SIF analysis can be applied to design appropriate LSP patterns on components with complex geometries.

Study of mixed-mode I/II fractures using single cleavage semicircle compression specimens under impacting loads

In order to study the fracture behavior of mixed-model I/II cracks under dynamic loads, a single cleavage semicircle compression (SCSC) specimen was proposed, and by using these specimens, rock dynamic fracture experiments for pure mode I and mixed-mode I/II under the impact of split Hopkinson pressure bar (SHPB) were conducted. Crack propagation speed was measured by using a crack propagation gauge (CPG) system and a high speed photography system, respectively. In order to confirm the experimental results, several numerical models for pure mode I and mixed mode I/II were established by using cumulative damage (CD) failure criterion, and by using these models, crack propagation behavior was simulated by using AUTODYN code. Generally, the results of crack propagation paths predicated by the numerical simulation agree well with the experimental results. This study shows that during crack propagation, the propagation speed is not a constant, and it may arrest for a moment. The new configuration specimen SCSC proposed in this paper is applicable in studying dynamic fractures by combining with SHPB device.

Shape sensitivity analysis for non-differentiable performance measures in multiscale crack propagation simulation using regression hybrid method

ABSTRACTIn this paper, we present a regression hybrid method that calculates shape sensitivity coefficients for multiscale crack propagation problems with performance measures that are non-differentiable in numerical implementation. These measures are crack propagation speed (or crack speed) defined at atomistic level obtained by solving coupled atomistic/continuum structures using the bridging scale method (BSM). The major contributions of this paper are: first, by analyzing the characteristics of the performance measures of crack speed in design space, this paper verifies for the first time that these measures are theoretically continuous and differentiable with respect to design variables, and as a result, the sensitivity coefficients exist in theory; second, to overcome the non-differentiability of the performance measures in numerical computation due to the finite size of integration time step, this paper proposes a regression hybrid method that calculates the shape sensitivity coefficients of crack speed through polynomial regression analysis based on the sensitivity of atomic responses, which is calculated through analytical shape design sensitivity analysis (DSA). And finally, the proposed method supports for 3D crack propagation problems with periodic boundary condition in one direction. A nano-beam example is used to demonstrate numerically the feasibility, accuracy, and efficiency of the proposed method.

Crack propagation and arrest simulation of X90 gas pipe

To determine whether X90 steel pipe has enough crack arrest toughness or not, a damage model was suggested as crack arrest criterion with material parameters of plastic uniform percentage elongation and damage strain energy per volume. Fracture characteristic length which characterizes fracture zone size was suggested to be the largest mesh size on expected cracking path. Plastic uniform percentage elongation, damage strain energy per volume and fracture characteristic length of X90 were obtained by five kinds of tensile tests. Based on this criterion, a length of 24 m, Φ1219 × 16.3 mm pipe segment model with 12 MPa internal gas pressure was built and computed with fluid-structure coupling method in ABAQUS. Ideal gas state equation was used to describe lean gas behavior. Euler grid was used to mesh gas zone inside the pipe while Lagrangian shell element was used to mesh pipe. Crack propagation speed and gas decompression speed were got after computation. The result shows that, when plastic uniform percentage elongation is equal to 0.054 and damage strain energy per volume is equal to 0.64 J/mm3, crack propagation speed is less than gas decompression speed, which means the simulated X90 gas pipe with 12 MPa internal pressure can arrest cracking itself.

Investigation of dynamic multi-cracking behavior in PVB laminated glass plates

Radial multi-cracking phenomenon can be observed in Polyvinyl Butyral (PVB) laminated glass subject to the dynamic loading which may contain abundant impact information along with the material properties of the plate. Firstly, the cracking problem is investigated experimentally based on the high-speed photography in terms of crack propagation speed and morphology. In the meantime, a numerical simulation 3D model describing the same setup is suggested and the extended finite element method (XFEM) is introduced to study the multi-crack problem after the validation from the experiment results. The length history of brittle dynamic stress intensity factors (DSIFs) of various failure modes and the crack propagation mechanism based on the displacement field of crack tip and the K criterion of brittle solid is unraveled. A parametric study is then carried out to investigate the influence of four impact and material variables on the DSIFs. It is shown that the PVB interlayer is proven to play a very important role in glass cracking DSIFs and thus governs the crack propagation behavior. Results may provide fundamental explanation to the basic crack propagation mechanism on radial multi-crack in PVB laminated glass, thus to offer guidance for impact information extraction and cracking-resistant structure design and material selection.

Determination of Dynamic Crack Initiation and Propagation Toughness of a Rock Using a Hybrid Experimental-Numerical Approach

AbstractIn order to determine the mode-I (opening mode) dynamic fracture toughness of a rock, cracked-straight-through Brazilian disc (CSTBD) specimens with strain gauges glued on the specimen’s surface were diametrically impacted by a split Hopkinson pressure bar. A hybrid experimental-numerical approach was used to determine the dynamic initiation toughness, and it was also used in conjunction with a universal function to obtain the dynamic propagation toughness. Precautions were taken for getting the time history of dynamic stress intensity factors. Numerical accuracy, stability, and convergence to the solution were guaranteed by analyzing beforehand a widely-recognized benchmark dynamic crack problem. Using the numerical technique the result of the conducted trial analysis corresponded almost exactly with the classical result. The dynamic initiation toughness and dynamic propagation toughness of the rock increase with increasing dynamic loading rate and crack propagation speed, respectively, demonstra...

Cortical bone fracture analysis using XFEM - case study.

We aim to achieve an accurate simulation of human cortical bone fracture using the extended finite element method within a commercial finite element software abaqus. A two-dimensional unit cell model of cortical bone is built based on a microscopy image of the mid-diaphysis of tibia of a 70-year-old human male donor. Each phase of this model, an interstitial bone, a cement line, and an osteon, are considered linear elastic and isotropic with material properties obtained by nanoindentation, taken from literature. The effect of using fracture analysis methods (cohesive segment approach versus linear elastic fracture mechanics approach), finite element type, and boundary conditions (traction, displacement, and mixed) on cortical bone crack initiation and propagation are studied. In this study cohesive segment damage evolution for a traction separation law based on energy and displacement is used. In addition, effects of the increment size and mesh density on analysis results are investigated. We find that both cohesive segment and linear elastic fracture mechanics approaches within the extended finite element method can effectively simulate cortical bone fracture. Mesh density and simulation increment size can influence analysis results when employing either approach, and using finer mesh and/or smaller increment size does not always provide more accurate results. Both approaches provide close but not identical results, and crack propagation speed is found to be slower when using the cohesive segment approach. Also, using reduced integration elements along with the cohesive segment approach decreases crack propagation speed compared with using full integration elements. Copyright © 2016 John Wiley & Sons, Ltd.

Multiple moving interfacial cracks between two dissimilar piezoelectric layers under electromechanical loading

The dynamic problem of several moving cracks at the interface between two dissimilar piezoelectric materials is analyzed. The combined out-of-plane mechanical and in-plane electrical loads are applied to the layers. Fourier transforms are used to reduce the problem to a system of singular integral equations with simple Cauchy kernel. The integral equations are solved numerically by converting to a system of linear algebraic equations and by using a collocation technique. The results presented consist of the stress intensity factors and the electric displacement intensity factors. It is found that generally the field intensity factors increase with increasing crack propagation speed.

Investigation into size and strain rate effects on the strength of rock-like materials

Based on a relaxation model, the relationship between spatial and temporal properties of deformation and fracture of rock-like materials is established, the essence of which lies in the finiteness of crack propagation speed and the complex internal structural hierarchy. There exists one-to-one correlation between characteristic length scale and characteristic strain rate, i.e., in order to fracture a sample of size L or activate structural elements of size L, definite strain rate ε̇L must be applied, below which a sample of size L would not fracture or structural elements of size L would not be activated. From the viewpoint of structural hierarchy, the size effect may be considered as the realization of the structural surface strength of smaller scale structural elements with the decrease of the sample size. The essence of strain rate effect is that because of the finiteness of crack propagation speed, the increase of strain rate activates the deformation and fracture process of smaller scale elements before the complete fracture of the sample. The dynamic strength of material is the realization of size effect on strength at the activated smaller scale level of solid. Based on one-to-one correlation between characteristic scale level and characteristic strain rate, size effect equation is transformed into strain rate effect equation. This investigation examines the size and strain rate effects on strength of rock-like materials, which would give better understanding of dynamic phenomena of deformation and fracture of rock mass, including the Earth's crust.

Wave dispersion analysis and simulation method for concrete SHPB test in peridynamics

The Split Hopkinson Pressure Bar (SHPB) technique is a widely used method for measuring mechanical properties of materials subjected to high-strain-rate loads, while it is difficult to simulate the whole testing process including high-rate deformation, local damage and failure of materials by the common numerical methods. In this paper, an improved numerical approach based on the non-local peridynamic (PD) theory is employed to study the elastic wave dispersion and propagation and the impact failure of concrete Brazilian discs in SHPB test. Meanwhile, an improved PMB (Prototype Microelastic Brittle) model and an implementation method of the contact-impact process are introduced. In PD, the nonlocal long-range force controls the numerical dispersion of wave through different material point sizes and horizon sizes. The numerical dispersion can result in a slight distortion of the wave speed and crack propagation speed, which is not conductive to failure analysis of solids. The improved PMB model can effectively lessen the numerical dispersion compared with the original PMB model. Furthermore, the PD simulation of concrete Brazilian disc SHPB test can reproduce damage accumulation and progressive failure of a specimen, and produce typical final failure pattern. The PD simulation method for SHPB test can be used to analyze the dynamic response of solids suffering impact load.

Crack propagation speed in ultra high performance concrete (UHPC)

This paper investigates crack speed in ultra-high performance concrete (UHPC) using pre-notched three-point bending specimens. The experimental parameters are fiber volume fraction and rate of loading. A hydraulic servo-controlled testing machine is used to apply lower notch tip strain rates, in the range of 0.025–1.01/s, while a newly developed impact testing system is used to achieve higher notch tip strain rates, ranging from 6.8 to 41.11/s. A high-speed camera is used to record images of the UHPC specimens during testing. Notch tip strain and crack speed are computed from the images, which show that crack speed increases asymptotically as the crack initiation strain rate increases. Crack speeds of up to 514m/s were achieved at the lower notch tip strain rates and up to 1454m/s for the higher notch tip strain rates. The achieved relationships are incorporated into a recently proposed crack-velocity dependent dynamic fracture model. The model is validated using published experimental data and used to show that, like conventional concrete, the strain rate sensitivity of UHPC is strongly associated with the characteristics of dynamic crack growth.

Modelling of stress-corrosion cracking by using peridynamics

We present for the first time a numerical multiphysics peridynamic framework for the modelling of adsorbed-hydrogen stress-corrosion cracking (SCC), based on the adsorption-induced decohesion mechanism. The material is modelled at the microscopic scale using microstructural data. First-principle studies available in the literature are used for characterizing the process of intergranular material strength degradation. The model consists of a polycrystalline AISI 4340 high-strength low-alloy (HSLA) thin, pre-cracked steel plate subjected to a constant displacement controlled loading and exposed to an aqueous solution. Different values of stress intensity factor (SIF) are considered, and the resulting crack propagation speed and branching behaviour are found to be in good agreement with experimental results available in the literature.

Molecular dynamics simulations of crack growth behavior in Al in the presence of vacancies

Fracture properties of a material are strongly influenced by the presence of defects. In view of this, molecular dynamics simulations were performed within the framework of embedded atom method to investigate the crack tip behavior under mode I loading in FCC Al with and without defects. Defects consisting of a random distribution of vacancies were introduced in the precracked matrix. The results reveal a significant change in the fracture behavior of Al with defects. The interactions between the crack tip and vacancies were found to modify the stress concentrations at the crack tip. Increase in vacancy content lead to increased crack tip blunting and reduced crack propagation speeds as compared to the vacancy-free material, thereby toughening the material to fracture. The significance of such studies towards gaining deeper insights into the fracture behavior at higher scales is highlighted.

Reflective Crack Propagation and Control in Asphalt Pavement Widening

Abstract To investigate the reflective crack-propagation behavior and provide control techniques for asphalt pavements widening, the finite-element models were built to simulate the widened asphalt pavement with a latent joint. The developed finite-element model considered the influence factors, including the loading modes (i.e., the symmetrical and unsymmetrical loading modes), the thickness and modulus of the asphalt concrete surface, the modulus of the new and existing stabilized bases, and the sheet stiffness of the reinforced geosynthetic. The finite-element simulation results show that increasing the thickness or reducing the modulus of the asphalt concrete surface effectively delays the propagation speed of the reflective cracks. The cracking potential reaches the minimum when the new and existing bases have a uniform modulus. Additionally, geosynthetic reinforcement across the joints significantly reduces the stress concentration around the crack tip and slows down the propagation of the reflective cracks. These benefits become greater when increasing the sheet stiffness of the geosynthetic. Finally, an experimental study was conducted to investigate the influence of the types of the asphalt overlay and the geosynthetic reinforcement on the reflective crack-propagation behavior. The experimental results indicate that the geosynthetic-reinforced structure with a lower modulus of the asphalt concrete surface significantly increases the fatigue life of widened pavements, and the polypropylene geotextile performs better than the glass-fiber grid in terms of the extension of the fatigue life.

In situ characterization of fracture toughness and dynamics of nanocrystalline titanium nitride films

Abstract

Modeling of dynamic crack propagation using rate dependent interface model

Influence of crack tip separation rate-dependent cohesive zone modeling at mesoscale and macroscale behaviors are investigated for sub-Rayleigh, intersonic and sub-Rayleigh to intersonic dynamic delamination growth speeds. A simple rate-dependency factor, k, is proposed for bilinear cohesive zone model (CZM) using the interface model of Corigliano et al. (2006). The factor is defined by the ratio of dynamic to static fracture toughness which is found to be related to the square of the ratio of pure-mode interfacial strengths for the selected bilinear CZM. Experimental cases from the literature with different loading rates are parametrically studied by varying the rate-dependency factor from unity, which is rate-independent, to infinity, a non-physical but theoretical condition. The first case is the three-point impact bending test that exemplifies the low-speed mode-I dynamic fracture. Next, asymmetric impact loading of polymer–composite experiment providing a mode-II dominated high speed intersonic propagation is simulated with various k. After comparing with mode-I low speed and mode-II dominated high-speed dynamic fracture experiments, an parametric analysis is carried out for a mixed-mode sub-Rayleigh to intersonic dynamic delamination in composite L-beams and compared with the experiments from Gozluklu et al. (2015). For this case, it is observed that the macroscopic aspects of fracture do not change with the rate-dependency factor. The effect of rate-dependency on crack growth kinetics is also found to be negligible for crack initiation and early stages of propagation, although the energy release rate increases. For one of the crack tips growing at intersonic speeds, the crack tip slows to sub-Rayleigh as the rate-dependency factor goes to infinity. The crack tip speeds for k>1 provides slightly better results compared with the experiments. In conclusion, rate-dependency is observed to be necessary in accurately modeling low speed, and low-to-high speed crack propagation cases but not in high-speed intersonic crack propagation.

Numerical simulation of thermal fatigue behavior in a cracked disc of AISI H-11 tool steel

Thermal fatigue is one of the key reasons of material failure in components which are exposed to high temperature cycles. Prediction of crack initiation site and crack propagation speed during thermal cycling helps us predict the life of a component in service. In this research numerical simulation of crack propagation due to thermal cycling on a circular disc has been carried out. The thermal profiles used in the simulation are taken from actual thermal fatigue experiments. The effect of the length of cracks and interaction between adjacent cracks has been investigated. 50 sets of numerical simulation models with different crack numbers and crack lengths have been simulated. The variation in Stress Intensity Factor (SIF), hoop stress and Crack Mouth Opening Displacement (CMOD) has been plotted as a function of primary/secondary crack lengths and number of cracks. Envelopes of possible crack growth have been identified and correspond well to the experimental observations. Results show a significant drop in hoop stress, SIF and CMOD with increase in number of cracks, thus limiting the number of cracks possible in a thermal fatigue crack network.

An Observation of Brittle Crack Propagation in Coarse Grained 3% Silicon Steel

Brittle fracture in carbon steel affects serious impact for the safety of fracture of in steel. Especially, the arresting technology of crack propagation is the last stand for the structure. It is so important issue that the conditions which can be stopped reliably crack propagation should be clarified thoroughly. On the background of such social importance, lots of experimental and theoretical researches have been conducted from both mechanical and microstructural viewpoints.Though it has been reported that the limit speed of brittle crack propagation is the Rayleigh wave speed and the speed is about 2,900 m/s in steels, the real speed of brittle crack propagation in steels is about 1,000 m/s and lower. The reason for that is considered braking effects with crack propagation, for example unevenness in the facet, tear ridge, microcrack, twin deformation and side ligament, namely the elements that dominate the arresting toughness.In this study, the 3% silicon steel where microstructure is ferrite single phase and its grain size is 4-5mm of very large is used. It is assumed that the brittle crack propagation speed in single crystal grain is very fast because there is no need to consider tear ridge between crystal grains. In this experiment, it is succeeded in shooting of brittle fracture of steel by high speed camera. As a result of that, it was revealed that the brittle crack propagation rate of 3% silicon steel is much lower than ordinary carbon steel. Also, twin deformation and unevenness in the facet are observed by scanning electron microscope (SEM).