Dynamic Fracture Mechanics Research Articles

Hierarchical Dynamic Bayesian Network-Based Fatigue Crack Propagation Modeling Considering Initial Defects.

Orthotropic steel decks (OSDs) are inevitably subjected to fatigue damage caused by cycled vehicle loads in long-span bridges. This study establishes a probabilistic analysis framework integrating the dynamic Bayesian network (DBN) and fracture mechanics to model the fatigue crack propagation considering mutual correlations among multiple fatigue details. Both the observations of fatigue crack length from field inspection and monitoring data of vehicle loads from the weight-in-motion (WIM) system are utilized. First, fracture mechanics-based uncertainty analysis is performed to determine the multiple uncertainty sources in the Paris crack propagation model, material property, and observation data of crack length. The uncertainty of monitoring data of vehicle loads is ignored because of its high accuracy; consequently, the vehicle-load-related uncertainty is spontaneously ignored, which is also demonstrated to be very small on the investigated actual bridges. Second, a hierarchical DBN model is introduced to construct mutual dependencies among various uncertainties and intra-correlations in the propagation process of multiple fatigue cracks at different components. Third, a stochastic traffic model is established based on the WIM monitoring data and multi-scale finite element analysis via substructure techniques to determine the probability distribution of vehicle-load-related parameters. After variable discretization, a refined exact inference algorithm in a forward–backward–forward manner is adopted to estimate the posterior distribution of equivalent initial crack length and update the established DBN model. Finally, the proposed method is demonstrated by a numerical case study and a typical application on an actual cable-stayed bridge with steel box girders using OSDs in China. The results show that the probability distribution of equivalent initial crack size can be spontaneously derived with a larger mean value than the results of conventional empirical analysis. Furthermore, the component-level fatigue reliability is tracked and predicted based on the established crack propagation model.

A rate-dependent damage model to characterize dynamic fracture behavior of Ti6Al4V under high strain rate loading

Material damage and fracture behavior are affected by loading rates. This paper aims to investigate dynamic deformation and fracture mechanisms of Ti6Al4V over a wide strain rate range from quasi-static to 104 /s. A high strain rate test apparatus is developed and a new rate-dependent material damage law is proposed. The damage energy of Ti6Al4V keeps nearly constant at the strain rate lower than 10 /s, while it declines dramatically under the strain rate high than 103 /s. Ductile to brittle transition of Ti6Al4V occurs at the strain rate of 16,000 /s, which leads to the transition of material fracture mechanism from adiabatic shear to embrittlement fracture. The research proves that developing appropriate damage evolution law is important to improve prediction accuracy of material deformation and guarantee structural design safety especially for dynamic loading components.

Atomistic simulation and continuum modeling of the dynamic tensile fracture and damage evolution of solid single crystalline Al with He bubble

The dynamic tensile fracture mechanism and damage evolution characteristics of solid single crystalline Al with He bubble are investigated by molecular dynamics (MD) simulations and continuum modeling. The physical mechanism leading to fracture is found to be dominated by He bubble growth, in wide ranges of strain rate and initial bubble volume fraction. The bubble growth process can be divided into three stages and the microscopic mechanism is related to the plastic deformation of surrounding metallic material predominated by dislocation growth and movement. It is further revealed that the evolution characteristics of He bubble are independent on strain rate or initial bubble volume fraction, but the growth rate increases significantly with increasing strain rate or decreasing bubble fraction. Additionally, the critical stress for bubble growth and dynamic tensile strength at the strain rates from 106 /s to 1010 /s are obtained, showing strain rate hardening effect. Finally, a continuum model based on the understanding derived from MD simulations is proposed to describe the damage evolution of the metal with He bubble, including the new strength softening effect induced by bubble growth. The dynamic tensile processes at the strain rates from 104 /s to 1010 /s are calculated by this model, and the obtained pressure and bubble evolutions and dynamic tensile strength are in good agreement with available MD results. We suppose that the present study sheds some light on the dynamic fracture of solid metals containing He bubble.

Study on dynamic fracture properties of sandstone under the effect of high-temperature using large-scale sample

High temperatures are a crucial factor in the drilling of rock and the extraction of geothermal resources, to investigate the change rules of the dynamic fracture mechanism and physical parameters of sandstone under high temperature environment, this study conducted a series of physical parameter measurements on the sandstone treated in a range of temperatures (room temperature to 700 °C) using large single cleavage semicircle compression (LSCSC) sample. According to the experimental results, it can be observed that 400 °C is the threshold for the variation of the physical parameters of sandstone. The mass, P-wave velocity, S-wave velocity, elastic modulus and Poisson’ ratio have a significant downward trend with the temperature. The main mineral components of sandstone undergo thermochemical reactions and the variation of quartz is a fundamental cause for the deterioration of sandstone. The dynamic loading test was conducted using a drop hammer impact device and the fractured sample, the dynamic fracture test results indicate that the dynamic crack initiation time (CIT) of the samples is advanced with the temperature, but the crack speed and dynamic fracture toughness decreased with the temperature. Further discussions about SEM images and fractal box dimension of fracture surfaces can be found that with the temperature increases, the proportion of intergranular fractures of sandstone gradually increases, the effect of dynamic loads changes from destroying the grain structure of sandstone to orderly coalescing the micro-cracks in the sandstone.

Influence of hot-rolling on the microstructure and mechanical properties of a near β-type Ti-5.2Mo-4.8Al-2.5Zr-1.7Cr alloy

In this work, the 90° clock rolling and the uni-directionally rolling processes at high temperature were carried out on the near β-type Ti-5.2Mo-4.8Al-2.5Zr-1.7Cr titanium alloy cutting from an ingot, respectively. The corresponding microstructures were quantitatively characterized, and its effect on the dynamic mechanical properties and fracture mechanism were emphatically investigated. It was found that after 90° clock rolling, the microstructure composed of equiaxed primary α phase(αp) with an average size of about 2 ​μm and the β transformed regions containing the acicular secondary α phase(αs) with an average thickness of about 50 ​nm and the separated β phase was obtained. However, in the uni-directionally rolled titanium alloy, no acicular αs was observed, and the corresponding microstructure consisted elongated lamellar α phase (average thickness: about 1.3 ​μm), few equiaxed α phase (average grain size: about 300 ​nm) and the inlaid β phase. The microstructural difference of the hot-rolled titanium alloys was closely related to the deformation process. Moreover, a great number of αp and αs in the 90° clock rolled titanium alloy effectively enhanced the strength, and the dynamic compressive strength reached to 1730 ​MPa. Furthermore, equiaxed αp was conducive to the homogeneous deformation, which counteracted the localized deformation caused by acicular αs to a certain extent and made the 90° clock rolled titanium alloy exhibit an acceptable critical fracture strain of about 10.5%. Moreover, the fracture microstructures showed that the main failure mode of the 90° clock rolled and the uni-directionally rolled titanium alloy were ductile fracture and brittle fracture, respectively.

Dynamic fragmentation in steel cylindrical shells

The paper describes an experimental study of the influence of the composition and mechanical properties (ultimate and yield strength, reduction of area, impact toughness, and the fraction of fibrous fracture) of brittle, quasi-brittle, and ductile steels on the parameters of dynamic fragmentation and fracture mechanisms. The experiment showed that simple exponential functions could be used to describe cumulative mass distributions of shell fragments from the materials under study. The exponent of these functions is the reciprocal characteristic mass (1/μ) and it decreases as the fraction of fibrous fracture of shell fragments increases. It serves as a dynamic fracture criterion that is sensitive to changes in the composition and mechanical properties of the material. The relations between the fragmentation parameter 1/μ and mechanical properties and composition of shell materials were obtained. Reaching the critical value of the fragmentation criterion (1/μc) leads to changing the fracture mechanism from “ductile” to “brittle” mode which arises in a material with ∼40% of fibrous fracture at the fracture surface of impact specimens and ∼50% of shear fracture of fragments.The authors studied the structure and features of ductile and brittle fracture surfaces of shell fragments, compared the statistical distributions widely used to describe the fragmentation process (Mott, Weibull, and Grady-Odintsov) and the dependencies of their parameters on material properties. The study did not reveal any advantages of the parameters of these distributions over the 1/μ parameter of the exponential function. The analysis of the literature data on the fragmentation of shells of different steels showed that they did not contradict the obtained results, and the usage of simple exponential distributions makes it possible to reveal the physical meaning of parameters of statistical distributions. Several common patterns of fragmentation of solids are discussed.

An extended peridynamic model for dynamic fracture of laminated glass considering interfacial debonding

In this work, an extended peridynamic (PD) model considering interfacial debonding is proposed to investigate the dynamic fracture behavior of laminated glass under low-velocity and high-velocity impacting loads. The interaction between different materials is described by adding an interfacial force term into the governing equations, which is derived from the energy density function of the interfacial bonds. A potential function term sourced from the cohesive zone model (CZM) is reconstructed and then introduced into the peridynamic model to describe the cohesive interfaces. The failure criterion of interfacial debonding is determined by the calculation of interface fracture energy and interfacial energy density. Two benchmark examples, a through-cracked tensile test and a drop-weight test, have been conducted to establish the validity of the proposed model. The proposed model and approach are then employed to investigate the dynamic fracture mechanism of laminated glass under high-velocity impacting loads.

Dynamic Fracture Analysis of Natural Gas Pipelines Based on a Cohesive Zone Model

Fracture research of natural gas pipelines with cracks is an important part of pipeline integrity evaluation. Based on the cohesive zone model (CZM), a numerical analysis is conducted of the dynamic fracture of X80 steel pipelines under explosion load. The factors considered include the crack propagation length, crack propagation velocity, dynamic crack tip opening angle (CTOA) and gas pressure. The results show that the whole cracking process can be divided into three stages: rapid cracking, stable propagation, and deceleration and stop cracking. When in the rapid cracking stage, the axial cracking of the pipeline is dominant. However, in the stable propagation stage, lateral expansion plays a more significant role. Besides, there exist upper limits on the length and velocity of crack propagation. In addition, it is also found that the time for the inflection point of rapid cracking and stable propagation is later than that to reach the velocity peak. The dynamic CTOA decreases with axial crack propagation, and the steady-state value of the CTOA is positively correlated with the load. The high-pressure gas escapes from the pipeline along the crack, resulting in the increase of air pressure outside the pipeline. Moreover, the peak pressure outside the pipeline is approximately linear its the initial crack length. The present research on the dynamic fracture mechanics behavior of the pipeline provides a necessary supplement for the test.

Dynamic Mechanics and Crystal Structure Fracture Characteristics of Rock-like Materials in Coal Mines

Deep rock bears dynamic loads such as machinery, blasting and disturbance in the mining process. The dynamic fracture mechanism of deep rock is a necessary prerequisite for engineering design and analysis. To study the dynamic fracture mechanism of rock under high in situ stress, deep mudstone and sandstone were selected as research objects. The dynamic mechanical properties and energy dissipation of mudstone sandstone were assessed by using a 50 mm diameter separated Hopkinson test device. According to the similarity criterion, the similarity of strength was assumed as primary factor to prepare similar model materials. Then, dynamic mechanical tests of these similar materials were carried out under dynamic compression splitting and active confining pressure. The results show that materials similar to mudstone and sandstone mainly show axial fracture tensile failure and crushing failure. Both the average strain rate dynamic strength and peak strain of these similar materials increase with increasing impact pressure, and the dynamic strength of similar materials increases exponentially with increasing strain rate. This result is consistent with the regularity of original rock. The dynamic splitting of mudstone-like materials is dominated by the failure of intermediate cracks, and sandstone-like materials also show secondary cracks in addition to intermediate splitting cracks. The dynamic peak strength of mudstone-like materials increases with increasing active confining pressure, and the dynamic peak strength of sandstone-like materials increases nearly twofold under the action of active confining pressure.

Prefabricated crack propagation in translucent alumina ceramic sheets during flame thermal shock

The prefabricated cracks propagation of ceramic under flame thermal shock was studied by real-time observation. The experimental results show that wing cracks are generated from both tips of the prefabricated crack, and the complete failure of the samples is a high-speed process. The crack propagation speed is fast at first and then gradually slows down. The maximum propagation speed of the near flame tip increases with the prefabricated crack distance to the heated surface, while an inverse trend is observed for the far flame tip. The effect of prefabricated crack angle on thermal shock crack propagation was also considered. In addition, numerical simulations based on dynamic fracture mechanics were carried out to reproduce the entire cracking process. To this end, the relation between the dynamic stress intensity factors and the crack growth speed in the speed range of 100 m/s to 2600 m/s was identified by combing experiments and numerical simulations. The simulation results and the above-mentioned relation are consistent with the experimental observations. The numerical model can faithfully reproduce the crack evolution process of the thermal shock, which is difficult to observe in an experiment due to the high speed of the cracking process.

Dynamic Response and Numerical Interpretation of Three Kinds of Metals for EFP Liner under Explosive Loading

In order to study the dynamic response of tungsten heavy alloy materials under explosive loading, two kinds of typical tungsten alloys for explosively formed projectile (EFP) liner and one kind of existing EFP liner were tested in a flash X-ray experiment, with copper liner as a reference. Results showed that copper liner could form a coherent EFP, while 90W–9Ni–Co and W–25Re liners fractured to different extents. The microscopic features of the three kinds of metals were examined and compared with the original liner, and the microstructure evolutions under explosive loading were analyzed with the fracture model and mechanism of the two kinds of tungsten alloys’ fracture determined. Associated with the stress and strain conditions by numerical simulation, the fracture mechanism of tungsten heavy alloys can be analyzed. The crack-tip plastic zones of 90W–9Ni–Co and W–25Re are much smaller than copper, and due to the severe stress concentration at the tip of cracks, it is easy for cracks to propagate and trigger the cleavage in tungsten alloys. The value of a crack-tip plastic zone r(θ) can be used to explain the fracture phenomenon in explosive loading, which can be an alternative guideline for the material selection criteria of the EFP liner. The research results are significant in understanding the dynamic forming, microstructure evolution, and fracture mechanism of tungsten heavy alloys.

Experimental Study on Dynamic Mechanical Properties and Fracturing Behavior of Granite CSTFBD Specimens in SHPB Tests

Abstract The purpose of this paper is to study the dynamic fracture mechanics characteristics and fracturing behavior of cracked-straight-through flattened Brazilian disk specimens using the Split Hopkinson Pressure bar system. The researchers also used Particle Flow Code 2D for simulating the crack process and achieved consistent outcomes. In this experiment, rock specimens were made from Beijing Fangshan granite. The results of the experiment determined the effects of impact pressures and loading angles on the crack mode and mechanical properties of the specimens. These specimens have attained the stress equilibrium state prior to failure. With greater impact pressure, there will be faster changes in the corresponding equivalent tensile stress, while the peak value remains relatively high under the same loading angle. With different loading angles, the change rate of the equivalent tensile stress remains the same; however, the time required to reach the maximum stress becomes different. For a 30° loading angle, the energy dissipation ratio in accordance with the same impact pressure is lower than compared to that of a 0° loading angle. In this experiment, several cracks have been produced under a different range of impact pressures and loading angles, which can be classified into six types. They include two types of tensile cracks, shear cracks, and tensile-shear cracks. At a 0° loading angle, mode I fracture occurs, and at 15° and 30° loading angles, a mixed-mode I-II fracture occurs on the specimen. Furthermore, triangular fracture zones occur on the two end faces of the specimens under the loading force due to the concentration of local stress during the force process.

Analysis of Dynamic Response Behavior of Crack under Impact Stress Wave

The structural parts of construction machinery mostly fail due to impact load, but current research on the failure behavior of the impact load has not established a complete theoretical system. Based on wave theory and fracture mechanics, this paper analyzed the wave behavior of shock stress waves and established a model of shock stress wave propagation. Given the dynamic response behavior of the stress and strain field at the crack tip, dynamic fracture mechanics theory was used to solve the dynamic fracture strength stress factor and evaluate the dynamic fracture performance of the structure with crack damage under shock waves. Through dynamic response analysis and numerical calculation of the typical SHPB (split Hopkinson pressure bar) test standard compact tension (CT) specimens under the short-term strong shock stress wave, the stress and strain evolution law of the material under the shock wave was analyzed, and the correlation of the shock stress wave was verified. This research work can meet the requirements of engineering design and has practical engineering significance, playing an important role in material safety design.

Strain energy release rate under dynamic loading considering shear and crack tip root rotation effects

A closed form solution for the calculation of the strain energy release rate (SERR), at the initiation of a crack, for a double cantilever beam (DCB) test, under dynamic loading conditions, is presented. The dynamics of a Timoshenko beam are used in the analytical formulation. The equations of motion are obtained using a variational approach and the adhesively bonded region is modelled via a Lagrangian multiplier method. The SERR is calculated based on the contour integral method and is a function of the vibrational mode and the beam's eigenfrequencies. The analytical formulation is applied on two representative joint cases. One consists of isotropic and the other of composite sub-laminates. Finite element analysis was used to validate the analytical formulation. The results demonstrate the advantages of the use of the Timoshenko beam theory and the consideration of crack tip root rotations in dynamic fracture mechanics and emphasize that the localized vibration cannot be neglected in the SERR calculation.

Experimental study on the effect of loading angle on crack propagation in bedding shale

The dynamic fracture of rock materials is a basic problem in the field of rock mechanics, while the dynamic fracture mechanism of shale is more complex due to its anisotropic characteristics. In order to study the effect of bedding angle on dynamic fracture process of shale, a split Hopkinson pressure bar (SHPB) system was used to carry out impact tests on notched semi-circular bend (NSCB) specimens of shale. Additionally, a crack propagation gauge (CPG) was set at the crack tip, and the whole fracture process of the shale NSCB specimen was studied with the help of a high-speed photography system and the digital image correlation (DIC) method. The loading rate and Mode-I dynamic fracture toughness of the shale NSCB samples were obtained by the method recommended by the International Society for Rock Mechanics (ISRM). And the crack initiation time and crack propagation speed of the shale NSCB samples can be accurately obtained by CPG. It is found from the experimental results that the Mode-I dynamic fracture toughness of the shale NSCB samples has significant anisotropy, and the loading angle has a positive correlation with the Mode-I dynamic fracture toughness. Although the crack propagation of the C-0sample is not affected by the bedding, its crack propagation needs to cut through the shale matrix, hence the C-0 and 90° shale specimens have a high Mode-I dynamic fracture toughness. When the impact velocity is low, the bending stress on the dangerous section affects the fracture direction of the shale specimen, but with less effect on the bedding. The crack propagation path finally closes to the notch direction. With the increase of impact velocity, stress concentration and micro cracks may exist along the weak plane of bedding due to its relatively low strength. With the increase of impact velocity, the cracks between the weak planes of bedding begin to extend, and the failure planes along the direction of bedding and notch occurred simultaneously.

Dynamic fracture mechanism and fragmentation analysis of fine grained Al2O3/SiC composite

The Al2O3/SiC composite has an improved mechanical property compared with alumina matrix, and it can be used in the lightweight armour system. In this study, the dynamic tensile and compressive strength, strain rate sensitivity, fracture mechanism and fragments scale of the composite were carried out by experimental and theoretical analysis. Results showed that the dynamic strength of the Al2O3/SiC composite was sensitive to the strain rate, and it was controlled by its microstructure. The microfracture mechanism of the composite varied with the locations and stress states of specimen, which consisted of second phase particles effects, the intergranular and transcrystalline fracture mode, fractured core area, grain-boundary crack, grain distortion and splitting, cleavage fracture zones, slip bands et al. In the dynamic compression experiments, the statistic analysis results of recycled fragments were more agreed with the prediction of the modified DID model.

Failure characteristics and meso-deterioration mechanism of pre-stressed coal subjected to different dynamic loads

The study of dynamic fracture mechanism of pre-stressed coal is of great importance to the coal bursts prevention and the coal pillar reinforcement subjected to the dynamic disturbance. In this paper, the effect of pre-static load and dynamic load on the initiation fracture evolution and destruction states of coal were studied using experimental and theoretical approaches. The results show that the coal usually splits into several blocks along the dominant fractures when subjected to the static load. The increase of pre-static load can make the post-peak dynamic stress–strain curve of the specimen gradually transform from type II to type I. The dynamic load plays the same role as that of pre-static load in terms of the effect on the dynamic stress–strain curve, but different in dynamic failure state of the coal. The enhancement of the former will make the dominant fracture expansion and leading the dynamic failure of coal gradually transform from the surface peeling to failure into several large pieces along the dominant fractures, while the increase of the latter will provid increasing kinetic energy to activate the internal fracture expansion of the specimen, and causing the failure state of the specimen transform from the surface peeling to the complete destruction into pieces. For the specimen with the surface peeling failure form, the peeling degree of the specimen depend on both the length of the fracture and the distance of the fracture to the free surface. Based on these results, the dynamic instability mechanism and protection focus of coal pillars under coupled static and dynamic loads were further discussed.

Experimental investigation on dynamic mechanical characteristics and fracture mechanism of coal under repeated impact loads

Experimental investigation on dynamic mechanical characteristics and fracture mechanism of coal under repeated impact loads

Dynamic fracture mechanics and energy distribution rate response characteristics of coal containing bedding structure.

To investigate the influence of bedding structure and different loading rates on the dynamic fracture characteristics and energy dissipation of Datong coal, a split Hopkinson bar was used to obtain the fracture characteristics of coal samples with different bedding angles. The process of crack initiation and propagation in Datong coal was recorded by the high-speed camera. The formula for the model I fracture toughness of the transversely isotropic material is obtained on the basis of the finite element method (FEM) together with the J-integral. By comparing the incident energy, absorbed energy, fracture energy and residual kinetic energy of Datong coal samples under various impact speeds, the energy dissipation characteristics during the dynamic fracture process of coal considering the bedding structure is acquired. The experimental results indicate that the fracture pattern of notched semi-circular bending (NSCB) Datong coal is tensile failure. After splitting into two parts, the coal sample rotates approximately uniformly around the contact point between the sample and the incident rod. The dynamic fracture toughness is 3.52~8.64 times of the quasi-static fracture toughness for Datong coal. Dynamic fracture toughness increases with increasing impact velocity, and the effect of bedding angle on fracture toughness then decreases. In addition, the residual kinetic energy of coal samples with the same bedding angle increases with the increase of impact speed. The energy utilization rate decreases continuously, and the overall dispersion of statistical data decreases gradually. In rock fragmentation engineering, the optimum loading condition is low-speed loading regardless of energy utilization efficiency or fracture toughness. These conclusions may have significant implications for the optimization of hydraulic fracturing process in coal mass and the further understanding of crack propagation mechanisms in coalbed methane extraction (CME). The anisotropic effect of coal should be fully considered in both these cases.

A novel model of Z-pin insertion in prepreg based on fracture mechanics

Through-thickness reinforcement is a promising solution to the problem of delamination susceptibility in laminated composites. Modeling Z-pin–prepreg interaction is essential for accurate robotics-assisted Z-pin insertion. In this paper, a novel Z-pin insertion force model combining the classical cohesive finite element (FE) method with a dynamic analytical fracture mechanics model is proposed. The velocity-dependent cohesive elements, in which the fracture toughness is provided by the analytical model, are implemented in Z-pin insertion FE model to predict the crack initiation and propagation. Then Z-pin insertion experiments are performed on prepreg sample with metallic Z-pins at different velocities to identify the analytical model parameters and validate the simulation predictions offered by the model. Dynamics of Z-pin interaction with inhomogeneous prepreg is described and the effects of insertion velocity on prepreg contact force are studied. Results show that the force model agrees well with experiments and the fracture toughness rises with the increasing Z-pin insertion velocity.