Crack Propagation Velocity Research Articles

Fatigue behaviour against delamination under mixed-mode I/II and ADCB test of a carbon/epoxy composite material

Some composite morphologies are susceptible to loss of capacity due to the presence of interlaminar delaminations. The objective of this work is to experimentally evaluate the generation and propagation of these interlaminar cracks in a carbon-epoxy composite subjected to dynamic stress under mixed fracture mode I / II, using an ADCB type test methodology for this purpose. From a previous static characterization of the material the critical value of the energy release rate was obtained, from which the levels of the critical energy release rate to be applied in the fatigue tests were defined, the values ​​considered were: 45, 50, 55, 60, 65, 70 and 75% Gcr. In all the dynamic tests, an asymmetry coefficient of R = 0.1 was used. From these experimental data the fatigue initiation curves DGN (number of cycles necessary for the nucleation of a crack, for a given rate of energy release) were obtained, observing fatigue life limits of the order of 38% of Gcr . In addition, the crack propagation velocity curves da / dN-G were shown, which showed the trend of the Paris law. On the other hand, a fractographic analysis of the delaminated surfaces was carried out, showing the typical fracture typologies of both modes, I and II, both in the initiation and propagation of the crack, showing the presence of mixed mode I / II in the ADCB type assay.

Peridynamic simulation of dynamic fracture in functionally graded materials subjected to impact load

Dynamic crack propagation assessment in functionally graded materials (FGMs) with micro-cracks is accomplished using bond-based Peridynamics (PD). The dynamic fracture behaviour of various FGMs’ material models is studied in Kalthoff–Winkler experiment. Dynamic crack growth predictions and associated material damage of the specimen under dynamic loading conditions are considered. The effect of micro-cracks near macro-crack tips on the toughening mechanism is evaluated in terms of crack propagation velocities. Stochastically pre-located micro-cracks are modelled to obtain the toughening effect in the material. In addition, the velocities and time required for fracture are compared in different FGM cases. It is frankly found that if a crack propagates in the harder region of the specimen, velocities decrease and toughness increase in contrast to the softer region. Furthermore, micro-cracks around a macro-crack decelerate the crack propagation and enhance toughening mechanism in FGM body depending on gradation of material properties.

Crack propagation velocity and fracture toughness of hydroxyl-terminated polybutadiene propellants: Experiments and simulations

A critical part of failure analysis in solid rocket motors is understanding the fracture behavior of solid propellants. For single-edge notched tension (SENT) specimens of hydroxyl-terminated polybutadiene (HTPB) propellant, self-developed in-situ video imaging was employed to characterize the crack propagation and the crack-path morphology. Combining this in-situ video recording system with image digitization, then the crack propagation velocity can be obtained. Due to the viscoelastic properties of the propellant, the fracture properties were studied under different tensile rates (5-500 mm/min). A fracture mechanics method based on the J-integral was used to evaluate the fracture behavior of propellants, and a fracture criterion considering the burning rate of the propellant was proposed. Experimental research revealed that the HTPB propellant had a pronounced blunt crack tip during the fracture process. The plastic region in front of the crack tip where voids form and coalesce could cause crack propagation. The distribution of voids in front of the crack tip mainly determined the direction of crack propagation. The fracture characteristics of the HTPB propellant had evident rate dependence, and the J-integral changed significantly under different tensile rates. A simulation study was carried out in this paper. The 1/r singular elements were used to predict the J-integral of the SENT specimen during the tensile process. Two numerical simulation methods (XFEM: extended finite element method and CZM: cohesive zone model) were used to obtain crack propagation velocity and load–displacement curve. Furthermore, the simulation results were compared with experimental data.

Numerical fracture investigation of single-edge notched asphalt concrete beam based on random heterogeneous FEM model

A finite element simulation of a single-edge notched beam was performed to investigate the crack characteristics of asphalt concrete during the fracture process at different low temperatures. A novel algorithmic technique was proposed for random heterogeneous modeling considering the aggregate gradation and void of AC-13. The fracture constitutive parameter was calibrated using the Kalman filter algorithm combined with image recognition. Moreover, the reliability of the simulation was verified through a comparison with a physical test. The results indicate that as the temperature decreased, the crack path became more inclined to the vertical centerline at the mid-span, and the proportion of mode I fracture elements to the total sum of mixed mode I-II fracture elements along the crack path decreased. The equinoxes in the macro unfractured zone near the vertical centerline are approximately the demarcation points between the tensile and compressive stresses, and the tensile, shear, and compressive stresses fluctuate nonlinearly in the vertical direction. At the critical fracture state, the tensile stress distribution along the bottom of the beam appears ‘M’-shaped and exhibits multiple peaks owing to the existence of heterogeneous structures; the tensile stress reaches the maximum value at 30 ± 3 mm from the two sides to the vertical centerline. The velocity of crack propagation in the mastic increases as the temperature decreases. Cracks incubated inside the aggregate penetrate through the aggregate accompanied with the secondary fissures more rapidly than propagate in mastic. In addition, the connected microcracks appear wedge-shaped in the mastic and fan-shaped in the aggregate.

Fracture mechanism of rock around a tunnel-shaped cavity with interconnected cracks under blasting stress waves

The existence of cracks in the surrounding rock significantly affects tunnel stability under dynamic disturbances. To study the fracture mechanism of tunnels in fractured rock masses under blasting stress waves, a new specimen, i.e., the specimen with a tunnel-shaped cavity and interconnected cracks (TCIC), was proposed in this paper. Using these specimens, blasting tests were conducted. The crack propagation data were monitored by crack propagation gauges (CPGs) and strain gauges (SGs). The Riedel-Hiermaier-Thoma (RHT) model was used to perform equal-scale numerical simulations on TCIC specimens. The stress distribution and fracture modes around the tunnel in a fractured rock mass under blasting stress waves were characterised. The results show that the interconnected cracks have an important influence on the dynamic response of the tunnel under blasting stress waves. The stress distribution around the tunnel remarkably changes due to the existence of the interconnected cracks, resulting in the initiation and propagation of these cracks, but there is no fracture on the tunnel boundary. The dynamic crack propagation behaviours are influenced by the incident direction of the blasting stress wave. The crack propagation velocity in the front blasting side of the tunnel is higher than that in the back blasting side. The research results are significant to the analysis of tunnel stability and the support design.

Influence of circular hole defect on dynamic crack propagation behavior under impact loads

Cavities and crack defects usually coexist in deep earth rock mass structures, which together affect the structural safety and stability of rock masses. In order to study the effect of circular cavity on crack propagation behavior in rock mass under dynamic loads, circular opening specimens with straight crack cavity (COSSCC) specimen were proposed in this study, and a large-scale drop hammer impact device was applied to conduct impact tests. Crack propagation gauges were implemented to measure fracture mechanics parameters, such as dynamic crack initiation time and crack propagation velocity. Then a modified finite difference code Autodyn was applied to carry out the numerical simulation analysis of crack propagation path and stress field around the circular hole. The traditional finite element code Abaqus was also used to calculate the dynamic initiation toughness and dynamic propagation toughness. The results indicate that: (1) when the inclination θ of the circle hole is less than 10°, the crack propagation path deflects and passes through the surface of the circle hole; when the inclination θ of circle hole is 20° and 30°, the crack propagation paths deflects in the direction of the hole but does not pass through the circular hole, indicating that the circular hole has obvious guiding effect on crack propagation; when the inclination θ of circle hole is 40° and 50°, crack propagation path does not deflect, and the guiding effect of the circular hole is obvious weaken. (2) When the crack propagation path reaches the vicinity of the circular hole, the tensile stress zone at the crack tip coincides with the tensile stress zone at the edge of the circular hole. At this time, the crack propagation speed increases significantly, and the dynamic fracture toughness of the crack decreases significantly. (3) The deflection direction of the crack is basically the same as the direction of the maximum circumferential stress at the crack tip. (4) The dynamic fracture toughness of the crack is always smaller than the crack initiation toughness, and the dynamic fracture toughness of the crack has a linear relationship with the dynamic crack growth rate. The larger the dynamic crack growth rate, the smaller the dynamic fracture toughness of the crack.

Experimental and Numerical Analysis of Mode I Fracture Process of Rock by Semi-Circular Bend Specimen

The semi-circular bend (SCB) specimen is widely used to measure fracture toughness of brittle materials such as rock. In this work, the stress field, fracture process zone (FPZ), and crack propagation velocity of SCB specimen are analyzed during the fracture process of rock specimens. The FPZ of specimen is obtained by experimental and numerical methods under a three-point bend test. The stress concentration zones of specimen present a heart shape at peak load points. FPZ forms before macro fracture occurs. The macro fracture form inside FPZ in a post-peak region of a load–displacement curve. The crack propagation process of specimen include two stages, namely the rapid crack initial development stage, and the final crack splitting stage. The maximum crack propagation velocity of specimen is about 267 m/s, and the average crack propagation velocity is about 111 m/s.

V-notch crack toughness of PMMA by strain gages and its comparison with caustics results under impact loading

Strain gages and dynamic caustics were used in this experiment to measure the V-notch crack initiation toughness and propagation toughness of polymethyl methacrylate (PMMA) specimens. Furthermore, a method of pasting strain gages on V-notch PMMA specimens for three-point bending test was proposed. The specimens were divided into five groups according to the opening angle (ω), and each group corresponded to two pasting methods: acute-angle pasting method and obtuse-angle pasting method. The results of notch stress intensity factors (NSIFs) obtained by strain gage measurement were consistent with the results calculated using the dynamic caustics method. The concept of the dimensionless notch stress intensity factor (DNSIF) was introduced for a better analysis of the effect of opening angles on cracking. The experimental results revealed that the initiation of V-notch crack in the specimens were inhibited more when ω was larger than 90° than for small opening angles. Under this condition, the specimens displayed higher cracking initiation toughness. Furthermore, the time required for crack initiation was longer, and the cracking was instantaneous. An analysis of the vicinity of the V-notch crack tip showed that with the increase in ω, the stress component decreased, and the rate of decrease became higher. This also explains the phenomenon wherein the specimens transformed from being easy to crack to not being so as ω increased. The experimental results showed that the crack propagation velocity and propagation toughness were also affected by the opening angle of the V-notch crack.

Effect of thermal treatment on the fracture toughness and subcritical crack growth of granite in double-torsion test

An understanding of the fracture behavior and subcritical crack propagation of hard rock under different temperatures is necessary for the design and stability of nuclear waste disposal projects. The aim of this study was to understand the thermal effect on the fracture behavior of granite, which had been heated at 25 (untreated), 100, 200, 400, and 600 °C, respectively. A series of uniaxial compressive tests and double-torsion tests were performed on granite specimens. The three-dimensional digital image correlation technique was used to investigate the strain evolution and fracture pattern in granite specimens during subcritical crack propagation. According to the results, the uniaxial compression strength, Young’s modulus and fracture toughness of the granite specimens increased and then decreased with an increase in treatment temperature. These parameters dropped sharply as the treatment temperature exceeded 400 °C, mainly because of the thermally-induced destruction of the quartz crystal structure and a generation of wider intergranular fractures. A comparison of the subcritical crack length by theoretical calculations and experimental observations from digital image correlation showed that the two values were consistent. At a treatment temperature of 400 °C and 600 °C, the velocity of the subcritical crack propagation was accelerated, so the length of the subcritical crack during the relaxation test was 4.14 times and 5.25 times that at 25 °C, respectively. The subcritical crack growth and fracture process of the double-torsion tests were visible by the three-dimensional digital image correlation system. A subcritical crack growth index (n) can be used to characterize the susceptibility of the subcritical crack propagation in rock relaxation tests, which helps to evaluate the long-term stability of nuclear waste disposal projects.

Strain gauge experimental study on mode I rock fracture characteristics under impact loading

Based on the analysis of the strain field of the dynamic crack tip under impact loading, a specific acute (obtuse) angle multi-point strain gauge method is proposed to study the mode I rock crack dynamic fracture. Compared with the dynamic caustics method, the feasibility of the strain gauge method for calculating the crack propagation velocity and dynamic stress intensity factor (SIF) is verified. The rock specimen mode I crack dynamic fracture behaviour under impact loading was studied by the strain gauge method and assisted by high-speed photography and scanning electron microscopy. The results showed that the mode I crack propagation behaviour calculated by two strain gauge methods under impact loading was close to the caustics experimental results. Compared with the dynamic caustics method, the multi-point strain gauge method could roughly record the crack propagation behaviour of rock under impact loading, which provides an experimental basis for studying non-transparent impact fracture. The rock section mainly experienced tensile stress failure under impact loading, manifested as mode I cracking, and the granite specimen fracture damage occurred in white spot micro-crack propagation. Under impact loading, cracks in both polymethyl methacrylate (PMMA) and granite specimens propagated stably in the middle stage of propagation, the average granite specimen crack propagation velocity was 647.9 m/s, and the average SIF value of was 5.37 MN/m3/2, which were higher than the PMMA specimen experimental results.

Effect of bond coat topography on the fracture mechanics and lifetime of air-plasma sprayed thermal barrier coatings

A modified four-point bending test was conducted on air-plasma sprayed (APS) thermal barrier coatings (TBC) to investigate the impact of bond coat (BC) topography tortuosity on the TBC fracture mechanics. The degree of BC tortuosity was quantified by the novel total thresholded summit area surface descriptor (Ssth) and was found to influence the crack path configuration, critical energy release rate (Gc) and crack propagation velocity (νprop). Specimens with higher BC interface tortuosity and more compliant TBC microstructures displayed a reduced strain energy release rates (Gc ≤ 79.90 J. m−2) and crack propagation velocities (vprop ≤ 0.90 mm. s−1). Delamination was primarily governed by the degree of inter-splat cohesion and intra-splat segmentation, although the topography-induced inter-splat tortuosity still had a relevant impact on fracture mechanics. The correlation observed between these results and the lifetime of analogous thermally cycled specimens tested herein suggests that the BC interface can affect the effectiveness of the microstructural stress relaxation mechanisms and by extension the TBC durability.

Derivation of crack propagation velocity formula for investigation dynamic problems

The following thesis will illustrate derivations of crack propagation’s formula for investigating brittle and elastic bodies. This work will look at the static and dynamic cases for crack initiation and propagation. Some approaches will be outlined in this work, which are the technics widely used in the field of mechanics for investigating the crack propagation and initiation related problems. At the end of the work crack propagation velocity formula will be derived.

Study on dynamic fracture behaviour and fracture toughness in rock-mortar interface under impact load

The stability of grouting reinforced rock structures under impact loading mainly depends on the interface strength between rock and mortar. In this paper, a Bi-material Single Cleavage Triangle (BSCT) specimen was employed in a split Hopkinson pressure bar experiment to investigate the dynamic fracture of the rock-mortar interface under impact loading. The interfacial roughness of the specimen was considered in the experiment as well as the loading rates effect. The crack extension velocity in the interface was obtained by the Crack Propagation Gauge (CPG). The stress wave propagation behavior and failure mechanism in the interface were analyzed by the AUTODYN software. Notably, the Complex Stress Intensity Factors (CSIF) were calculated by using the experimental–numerical method. The results show that interfacial roughness and loading rate have a great effect on interfacial fracture behaviour. Compared with the granite-mortar specimen, the stress wave propagation velocity in the sandstone part and mortar part are very close, making it hard to find shear failure in the sandstone-mortar interface. The interfacial crack propagation velocity of the sandstone-mortar specimen may outpace the Rayleigh wave in the intact sandstone. The complicated relationship amongst the loading rates, interfacial roughness, and parameter K1 of the CSIF has been unveiled elaborately in the present paper.

Dynamic cracking simulation by the nonlocal macro‐meso‐scale damage model for isotropic materials

AbstractThe newly proposed nonlocal macro‐meso‐scale damage (NMMD) model is extended to dynamic cracking simulation. For this purpose, the framework of continuum damage mechanics and damage constitutive model are firstly described. The NMMD, where the meso‐scale damage is determined according to the deformation of material bond and then the macroscopic topologic damage is endowed with the weighted averaging over the meso‐scale damage in the influence domain of the material point, is then elaborated and incorporated into the framework. Specifically, the criterion of meso‐scale damage is renormalized. The numerical algorithms including the spatial discretization by the finite element methods and the time integration methods by an explicit scheme are outlined. Several examples are studied in detail, showing the effectiveness of the proposed method. In particular, due to the nonlocal property, there is no spatial mesh size sensitivity. Owing to the scale renormalization of the meso‐scale damage, the results are insensitive to the influence radius in some examples. The dynamic cracking, including the crack propagation velocity, the damage dissipation rate, and the connection to the dynamic crack branching, is discussed in detail based on the computed results.

A multi-state progressive cohesive law for the prediction of unstable propagation and arrest of Mode-I delamination cracks in composite laminates

In this paper, a finite element simulation study was performed on the dynamic crack propagation and arrest in double cantilever beam (DCB) specimens with interleaves. The expressions of crack initiation toughness, propagation toughness, arrest toughness, and kinetic energy during unstable crack propagation were theoretically derived based on the energy balance principle. The dynamic fracture toughness parameters were calibrated based on the DCB test results. For the simulations, a multi-state progressive cohesive law (MP-CL) suitable for quasi-static analysis was proposed, and the MP-CL parameters were introduced into the finite element model using the USDFLD subroutine in the ABAQUS software. The unstable crack stick–slip propagation behavior of the DCB specimens was successfully simulated, revealing the complex mechanical characteristics, such as the load–displacement response, kinetic and fracture energy, and crack propagation velocity, during unstable crack propagation. The simulation results were quite consistent with the experimental results, validating the correctness and effectiveness of the proposed model.

Experimental Investigation of Obliquely Incident Blast Wave Effect on Deflection of Running Cracks

Abstract Dynamic caustics in conjunction with high-speed photography were used in experiments to investigate the interaction of obliquely incident blast stress waves with running cracks. The dynamic photoelastic experiment method was used to supplement and improve the effects of different blast stress wave properties on the running crack. This indicated that the crack-tip mode II stress field affected the crack deflection direction. When the moving crack-tip mode II stress intensity factor KII was positive, the crack deflected clockwise. When the stress intensity factor KII was negative, the crack deflected in the counterclockwise direction. The incident direction of the blast stress wave affected the deflection of the crack. When the direction of the blast stress wave was the same as the direction of the moving crack propagation, the moving crack deflected away from the blast wave source. When the blast stress wave propagation direction was opposite to the crack propagation direction, the crack deflected toward the blast wave source. During the interaction of an obliquely incident blast stress wave with a moving crack, the P wave caused the deflection of the crack. The tails of the P wave and S wave interacted with the kinked crack to increase the mode I stress intensity factor KI and the crack propagation velocity.

Experimental and numerical study on the fracture characteristics of concrete under uniaxial compression

Since concrete infrastructure may lose its expected physical and functional properties over time, accurate inspection and assessment of such infrastructure systems is necessary to ensure safety and serviceability and prevent unsafe working conditions and the occurrence of hazards. In this paper, an experimental investigation was conducted on several concrete specimens under uniaxial compression to fully explore the fracture process and mechanical characteristics of concrete materials under compressive loading conditions. More specifically, a high-resolution industrial camera and a real-time geophysical acquisition system were employed to capture the fracture process and the microseismic (MS) and electromagnetic emission (EME) signals simultaneously. Based on digital image processing, a robust crack extraction algorithm was proposed for automatically identifying cracks on a concrete surface at the pixel level, and then two novel crack features were introduced to depict the dynamic crack propagation process quantitatively. Then, the correlation between MS, EME, stress drop and dynamic crack evolution characteristics was analyzed. The results indicate that: (1) the MS and EME signals of the concrete specimens have good consistency in the time domain, especially in the fully fractured stage; (2) the crack area, to a certain extent, can reflect the stress drop of a concrete specimen under the compression fracture process; (3) the crack propagation velocity parallel to the loading axis (along the vertical direction) is faster than that the perpendicular one to the loading axis (along the horizontal direction); and (4) the crack area, stress, MS signal, and EME signal reach their peak values nearly simultaneously. Finally, a novel mesh-free numerical model based on peridynamic (PD) theory was established to simulate the fracture process, and the displacement fields were presented to further reveal the failure mechanism of concrete under compressive loading.

An Experimental Research on Crack Propagation Regularity During Fracture Grouting

A new grouting model test device has been developed to model the fracture grouting process and improve understanding of the crack propagation regularity during grouting. It was concluded that the propagation process of crack is not one-time formed but undergoes the sequential mode of “expansion, stagnation, re-expansion, re-stagnation” after fracture initiation. The smaller the grouting pressure is, the longer the stagnation time is, and the smaller the crack propagation velocity is. The crack width increases rapidly when the crack tip stagnates or the expansion speed is small. Research results can help achieve better grouting aims and realize grouting safety in practice

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.

Development of a Model of Crack Propagation in Multilayer Hard Coatings under Conditions of Stochastic Force Impact.

The article deals with the problems of cracking in the structure of multilayered coatings under the conditions of stochastic loading process. A mathematical model has been proposed in order to predict the crack propagation velocity in the coating while taking the influence of interlayer interfaces into account. A technique for calculating the probability density distribution of the coating fracture (failure rate) has been developed. The probability of a change in the crack growth direction is compared with the experimental data that were obtained as a result of the studies focused on the pattern of cracking in the Zr,Nb-(Zr,Nb)N-(Zr,Nb,Al)N and Ti-TiN-(Ti,Cr,Al)N coatings under the conditions of the real stochastic loading of cutting tools during the turning. The influence of the crystalline structure of the coating on the cracking pattern has been studied. The investigation has found the significant effect of the crystalline structure of the coating layers on the cracking pattern.