High Speed Crack Propagation Research Articles

Strategy for simulating high-speed crack propagation in 3D-plate structures based on S-version FEM

Plate structures serve as the fundamental components of many large structures; therefore, dynamic crack propagation in plates is a significant safety concern. This paper proposes a novel strategy based on the s-version finite element method (s-method) for simulating high-speed crack propagation in a 3D plate structure. We employed a combination of the nodal force release technique and local mesh update method to simulate a dynamically propagating crack front. The global mesh was generated based on the entire domain geometry without considering crack propagation, which significantly simplified the mesh generation procedure, whereas the local mesh was generated only in the vicinity of the crack front with fine elements to ensure high accuracy. In the proposed strategy, the local mesh completely covered the crack front beyond the surface of the 3D plate structure. Such an incompatibility between the surface of the target domain and boundaries of the local mesh causes non-negligible errors in the conventional s-method. Hence, we propose an approach based on Heaviside enrichment to eliminate these errors. To investigate the effectiveness of the proposed strategy, numerical examples to analyse the experimental results of high-speed crack propagation in double cantilever beam-type plate specimens made of polymethyl methacrylate are presented. The numerical results demonstrated the effectiveness of the proposed strategy for simulating high-speed crack propagation in 3D plate structures. Therefore, the proposed strategy has the potential to serve as a fundamental numerical framework for simulating dynamic crack propagation in engineering structures.

Development of a model for simulating high-speed crack propagation in a 3D solid based on the s-version FEM

Development of a model for simulating high-speed crack propagation in a 3D solid based on the s-version FEM

A Brief Review on Additive Manufacturing of Polymeric Composites and Nanocomposites.

In this research article, a mini-review study is performed on the additive manufacturing (AM) of the polymeric matrix composites (PMCs) and nanocomposites. In this regard, some methods for manufacturing and important and applied results are briefly introduced and presented. AM of polymeric matrix composites and nanocomposites has attracted great attention and is emerging as it can make extensively customized parts with appreciably modified and improved mechanical properties compared to the unreinforced polymer materials. However, some matters must be addressed containing reduced bonding of reinforcement and matrix, the slip between reinforcement and matrix, lower creep strength, void configurations, high-speed crack propagation, obstruction because of filler inclusion, enhanced curing time, simulation and modeling, and the cost of manufacturing. In this review, some selected and significant results regarding AM or three-dimensional (3D) printing of polymeric matrix composites and nanocomposites are summarized and discuss. In addition, this article discusses the difficulties in preparing composite feedstock filaments and printing issues with nanocomposites and short and continuous fiber composites. It is discussed how to print various thermoplastic composites ranging from amorphous to crystalline polymers. In addition, the analytical and numerical models used for simulating AM, including the Fused deposition modeling (FDM) printing process and estimating the mechanical properties of printed parts, are explained in detail. Particle, fiber, and nanomaterial-reinforced polymer composites are highlighted for their performance. Finally, key limitations are identified in order to stimulate further 3D printing research in the future.

Mechanism study of preventing crack propagation of fractured rockunder dynamic loads

To deeply understanding dynamic fracture properties and preventing crack propagation of fractured rock mass under dynamic loads, impact experiments were conducted using TWSRC (tunnel with single radial crack) samples, and sandstone were selected as the raw material to manufacture fractured rock samples. The crack initiation, propagation and obstructing behavior were measured by using a drop hammer impact test device and crack propagation gauge measuring system. The mechanism of preventing crack propagation and failure behavior during dynamic fracturing process was focused, and then the corresponding numerical simulation was conducted by using the finite difference code, which can be used to accurately estimate the experiment result. The results indicate that the whole dynamic fracturing process of fractured rock under dynamic loads is composed of the cyclic process of crack initiation, high-speed crack propagation, slowly deceleration, preventing crack propagation. In addition, the period of crack obstruction was approximate the microsecond level. The ratio of transgranular (TG) fracture at the crack obstruction point of fractured rock was smaller than that of the crack initiation point, and the ratio of TG fracture of green sandstone during the dynamic fracturing process was larger than that of black sandstone. The fracture energy for crack initiation again after crack obstruction was much less than the fracture energy required for the initial initiation of pre-existing crack.

Dynamic fracture and dealloying induced stress-corrosion cracking

Electrochemical dealloying is a corrosion process in which one elemental component of an alloy is selectively dissolved often resulting in the evolution of a bicontinuous nanoporous morphology composed of ligaments and pores. When such structures form on the surface of ductile face-centered cubic metals such as brass, stainless steels and gold-containing alloys, it has been proposed that they trigger stress-corrosion cracking as a result of their ability to support high-speed cracks that can be injected into the undealloyed parent phase alloy. Here we examine how the applied stress or stored strain energy control the dynamics of high-speed crack propagation and the relationship between the fracture plane orientation of cracks that have been injected into the undealloyed parent phase and that which forms during stress corrosion cracking of a single-crystal silver-gold alloy. In both cases, we observe exceptionally flat cleavage-like fracture surfaces, whose crystallographic orientation is determined by that of the tensile axis. We present a continuum formulation of the injection distance based upon a crack tip equation of motion that incorporates inertial effects in which the work of fracture is a decreasing function of crack speed.

High speed crack propagation characteristics of functionally graded brittle materials under ultra-high loading rate

Functionally graded materials are considered to be a special composite material. By continuously changing the composition and structure of the material, the interface and delamination problems of the material can be eliminated, which causes the material properties to change slowly with the change of the composition and structure of the material. In this paper, a lattice spring model, which can accurately show the mechanical properties of brittle materials, is used to study the evolution law and mechanism of the crack path and crack velocity in functionally graded brittle materials under ultra-high loading rate. This model uses the quantitative parameter mapping method proposed by Gusev to solve the spring stiffness coefficient of the model accurately, and the fracture criterion of the model based on the energy balance principle of Griffith is set up, using the Fortran software construct the lattice spring model for functionally graded brittle materials and carry out the numerical simulation, the evolution of crack propagation path and velocity in functionally graded brittle materials under ultra-high loading rate is studied. The simulation results show that the propagation path of high speed cracks in functionally graded brittle materials under the action of ultra-high loading rate has two stages: single crack and bifurcation crack. Once the crack reaches the critical condition of crack initiation, it will start to crack and grow at a high speed. The crack propagation velocity suddenly jumps from 0 to more than 0.5 times the Rayleigh wave velocity(CR), followed by a process of speed decline and recovery; after the initial drastic change, the growth speed gradually reaches a stable platform. Thereafter, the growth rate slowly climbed and exceeded 0.69CR; due to the stress relaxation caused by the crack initiation, the maximum tensile stress at the crack tip also showed a process of declining and slowly rising. Through comparison, it is found that the change law of the crack tip has a significant correlation with the change law of crack growth rate (high-speed growth stage), which is helpful to reveal the internal mechanism that determines the crack growth rate. The study of crack propagation under different loading rates can predict the crack propagation speed, direction and distance in functionally graded brittle materials.

Self-emitted surface corrugations in dynamic fracture of silicon single crystal

When a dynamic crack front travels through material heterogeneities, elastic waves are emitted, which perturb the crack and change the morphology of the fracture surface. For asperity-free crystalline materials, crack propagation along preferential cleavage planes is expected to present a smooth crack front and form a mirror-like fracture surface. Surprisingly, we show here that in single crystalline silicon without material asperities, the crack front presents a local kink during high-speed crack propagation. Meanwhile, local oscillations of the crack front, which can move along the crack front, emerge at the front kink position and generate periodic fracture surface corrugations. They grow from angstrom amplitude to a few hundred nanometers and propagate with a long lifetime at a frequency-dependent speed, while keeping a scale-independent shape. In particular, the local front oscillations collide in a particle-like manner rather than proceeding with a linear superposition upon interaction, which presents the characteristic of solitary waves. We propose that such a propagating mode of the crack front, which results from the fracture energy fluctuation at a critical crack speed in the silicon crystal, can be considered as nonlinear elastic waves that we call "corrugation waves."

The characteristics of high speed crack propagation at ultra high loading rate

It is important to understand the characteristics of high speed crack in brittle materials under ultra high loading rate forming through impact loading condition, which is important for understanding the impact damage evolution of ceramics and solid explosives. In this paper, a lattice spring model, which can accurately show the mechanical properties of brittle materials, is used to study the evolution law and mechanism of crack path and crack velocity in brittle materials under ultra high loading rate. This model uses the quantitative parameter mapping method proposed by Gusev to solve the spring stiffness coefficient of the model accurately, and the fracture criterion of the model based on the energy balance principle of Griffith is set up. Simulations show that the path of high speed crack behave the evolution process of a single crack and then micro-branching crack and bifurcation crack finally under the influence of ultra high loading rate. The crack propagation distance between the beginning and the bifurcation decreases with the increase of the loading rate; the crack bifurcation is not immediately after the crack initiation, but as the crack propagation speed reaches the critical value, the expansion path produces more secondary cracks, and then the crack is bifurcated. With the increase of loading rate, the average velocity of cracks gradually increases in three stages, but it shows a different variation after reaching the stable value. In the single crack stage, the steady average velocity is 0.584 times the Rayleigh wave velocity (CR), and there exists only a very small velocity oscillation; the steady value of the average crack velocity corresponding to the differential fork phase is 0.5 times the Rayleigh wave velocity, accompanied by a certain oscillation; The average speed of the stable crack corresponding to the bifurcation stage is much higher than the value of the first two stages, and it can reach 0.638 times the Rayleigh wave speed. It is also accompanied by obvious speed oscillation. The study of the propagation of cracks under different loading rates can predict the internal crack growth rate, propagation direction, and extension distance of brittle materials such as ceramics and rocks.

Controlling factors for roughness increases on cleavage fracture surfaces and crack branching in polycrystalline steel

Brittle fracture in carbon steel has serious impact on the fracture safety of steel structures. Thus, technology that arrests crack propagation is the final defence for these structures. Conditions that can reliably stop crack propagation should be thoroughly clarified. Considering the background of the social importance of the issue, many experimental and theoretical studies have been conducted from both the mechanical and microstructural viewpoints.Fracture surface roughness is an important factor in studying the physics of dynamic high-speed crack propagation. For example, in resin materials, fracture surface roughness increases with crack propagation speed, called mirror-mist-hackle, and when the crack propagation speed further accelerates, cracks macroscopically branch off. In this study, the authors conclude that crack branching occurs under conditions of high stress triaxiality, not under the high-speed conditions seen in resin materials, and the critical conditions for branching in steel are revealed. To elucidate the controlling factors that increase fracture surface roughness and branching, detailed discussion using numerical analysis is carried out.

Crack plane deflection and shear wave effects in the dynamic fracture of silicon single crystal

Fracture paths in crystalline solid can be significantly altered upon encountering stress perturbations. Here, we investigate the dynamic cleavage deflection in (001) silicon single crystal wafers under three-line bending load. It is found that the crack propagates preferentially along the (110) cleavage plane. However, when the crack front interacts with shear waves induced by the line-contact, it tends to deflect onto the (111) cleavage plane and forms secondary Wallner lines. Yet, the crack deflection is not permanent and a recovery process to the (110) plane is observed, suggesting that the (110) cleavage plane remains energetically prevailing during the high-speed crack propagation. We show that the ratio between the dynamic fracture energy of the (111) plane and that of the (110) plane at the deflection position is invariably larger than the one when the local crack velocity is lower than 40% of the Rayleigh wave speed. This confirms that the crack deflection is triggered by shear waves. Therefore the theory of crystallographic direction dependence of dynamic fracture toughness evolutions proposed in earlier literature needs to be further assessed before generalization.

Investigation on Acoustic Emission Characteristics from Q345R during Fatigue Crack Propagation

The fatigue crack propagation process of specimen made from Q345R was monitored by acoustic emission (AE) equipment. The AE characteristic of the specimen generated during the fatigue crack propagation was obtained by parameter analysis method and wavelet transform method .The results show that the fatigue crack growth curve comprises four phases of the crack generation phase, the low-speed crack propagation phase, the high-speed crack propagation phase and the fracture phase, and the variation of signal parameters presents the similar tendency to the fatigue crack growth rate. The values of signal parameters, such as count, energy, and amplitude, are stable and low in the crack generation phase and low-speed crack propagation phase, and relatively unstable and high in the high-speed crack propagation phase and fracture phase. The type of signals is burst emission and the frequency ranges from 100kHz to 180kHz. From these correlations, it may be possible to predict the remaining service life of a pressure vessel from the results of short-term AE monitoring of crack propagation.

Measuring high speed crack propagation in concrete fracture test using mechanoluminescent material

Measuring crack length in concrete fracture test is not a trivial problem due to high speed crack propagation. In this study, mechanoluminascent (ML) material, which emits visible light under stress condition, was employed to visualize crack propagation during concrete fracture test. Three-point bending test was conducted with a notched concrete beam specimen. The cracking images due to ML phenomenon were recorded by using a high speed camera as a function of time and external loadings. The experimental results successfully demonstrated the capability of ML material as a promising visualization tool for concrete crack propagation. In addition, an interesting cracking behavior of concrete bending fracture was observed in which the crack propagated fast while the load decreased slowly at early fracture stage.

Memorizing and detecting an arrested crack in a foam-core sandwich structure using embedded plastic materials and fiber-optic sensors

The authors recently established the ‘smart crack arrester’ concept to improve the damage tolerance of composite foam-core sandwich structures. The smart crack arrester can simultaneously arrest and detect a crack propagating along the interface between the facesheet and the core. Two fiber Bragg grating (FBG) sensors are embedded at both edges of the arrester to monitor the internal strain change induced by crack propagation. However, since the developed detection technique utilized transient elastic strain change during high-speed crack propagation, the system required a high-cost measurement system and could fail to detect a fatal interface crack in a practical noisy environment. Thus, this study advances the previous approach. Metal wires are additionally embedded alongside the FBG sensors, resulting in a more easily applicable and reliable crack-detection system with a new technical concept. Specifically, the characteristic strain state induced by arresting the interface crack is first ‘memorized’ by plastic deformation of the metal wire, and the consequent residual strain is then ‘statically’ picked up by the FBG sensor as a damage signal. This study begins by simulating deformation of the metal wires and the sensors to evaluate the feasibility of the proposed technique. The significant advantage of adding the metal wires is then demonstrated by comparing data from the new and previous approaches. Finally, a verification test is conducted to confirm that an FBG spectral shape statically obtained after unloading can indicate the propagation direction and tip location of an arrested crack.

ぜい性高速破壊停止用ストップホール(クラックアレスタ)に関する基礎研究 : 第2報,移動有限要素解析によるき裂再進展状態の考察

The stop hole is one of the crack arrester systems, which is used to prevent the growth of fatigue cracks. However, the stop hole is not expected to prevent high-speed crack propagation. Because the mechanical condition of fast crack propagation behavior near the stopping hole is not cleared, the criterion of the stop for brittle fracture is not established. In this study, authors focus re-propagation start (restart) condition of crack from the stop hole. To discuss the restart condition of high-speed crack propagation, experiment observation and finite element analysis result are compared. In the numerical simulation, dynamic crack propagation simulations are carried out, using the moving finite elememt method based on Delaunay automatic triangulation. The various parameters are calculated from the numerical results.

Study for High-speed Crack Propagation Phenomena under Static Multi Loading System

Study for High-speed Crack Propagation Phenomena under Static Multi Loading System

A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials

Numerical investigations are conducted to simulate high-speed crack propagation in pre-strained PMMA plates. In the simulations, the dynamic material separation is explicitly modeled by cohesive elements incorporating an initially rigid, linear-decaying cohesive law. Initial attempts using a rate-independent cohesive law failed to reproduce available experimental results as numerical crack velocities consistently overestimate experimental observations. As proof of concept, a phenomenological rate-dependent cohesive law, which bases itself on the physics of microcracking, is introduced to modulate the cohesive law with the macroscopic crack velocity. We then generalize this phenomenological approach by establishing a rate-dependent cohesive law, which relates the traction to the effective displacement and rate of change of effective displacement. It is shown that this new model produces numerical results in good agreement with experimental data. The analysis demonstrates that the simulation of high-speed crack propagation in brittle structures necessitates the use of rate-dependent cohesive models, which account for the complicated rate-process of dynamic fracture at the propagating crack tip.

Flutter of crack tips

Abstract Flutter of a crack tip occurs when the relatively flexible tip collides with density fluctuations in a solid. The crack velocity must exceed a critical value. The crack tip behaves like a self-excited oscillator. Its fundamental frequency can be estimated using Friedel's dislocation model of a crack. Surface energy, γ, provides the restoring force for displacements, x of the leading dislocation line. The force constant is, −4γx/b, where b is the Burgers displacement. The oscillator frequency is then about: (v L/b)/π where v L is the velocity of longitudinal acoustic waves. Thus it is proposed that self-excited oscillations of crack tips cause the hackle markings on fracture surfaces after high speed crack propagation.

Propagating semi-infinite crack in fluid-saturated porous medium of finite height

Derived in this work are the Mode I stress intensity factor results for a constant velocity semi-infinite crack moving in a fluid-saturated porous medium with finite height. Two limiting cases are discussed; they correspond to a low and high speed crack propagation. To be expected is that the crack front stress intensification would increase as the medium height is reduced in relation to the segment length in which mechanical pressure is applied. Moreover, the stress intensity factor for the high speed crack is larger than the low speed crack, the magnification of which depends on the material. Dissatisfaction of the crack surface and tip boundary condition is found in the present solution which calls possibly for the additional consideration of a local boundary layer as discussed by other authors.

High speed crack propagation in bi-phase materials: an experimental study

We have studied experimentally the high speed propagation of a crack perpendicular to an interface between materials with different mechanical properties. The tests presented in this paper were restricted to the case of a two-dimensional model, without debonding of the interfacial region. Cracks started at a notch machined in the first low modulus phase of the bi-phase single edge notch samples. Our investigations were focussed on the relation between the crack velocity in each phase and the mechanical state of the specimen. The results demonstrate a direct dependence of the crack velocity on the elastic energy stored in the specimen at the moment of crack initiation. For a given experimental situation, we show that the velocity of the crack in each phase and the occurrence of crack arrest can be predicted knowing the relative positions of the two curves crack speed vs. elastic energy for the two constituents of the “bimaterial”. For example, this permits the determination of the critical level of stored elastic energy which is necessary to obtain an acceleration of the crack at the interface, without arrest.

Influence of isotropic strain hardening on plane strain dynamic growth in elastic-plastic materials

In this paper, dynamic crack growth in an elastic-plastic material is analysed under mode I, plane strain, small-scale yielding conditions using a finite element procedure. The material is assumed to obey J 2 incremental theory of plasticity with isotropic strain hardening which is of the power-law type under uniaxial tension. The influence of material inertia and strain hardening on the stress and deformation fields near the crack tip is investigated. The results demonstrate that strain hardening tends to oppose the role of inertia in decreasing plastic strains and stresses near the crack tip. The length scale near the crack tip over which inertia effects are dominant also diminishes with increase in strain hardening. A ductile crack growth criterion based on the attainment of a critical crack tip opening displacement is used to obtain the dependence of the theoretical dynamic fracture toughness on crack speed. It is found that the resistance offered by the elastic-plastic material to high speed crack propagation may be considerably reduced when it possesses some strain hardening.