Crack Velocity Research Articles

Interaction of propagating crack with microstructure in CGI: In situ tensile test and numerical simulation

Compacted graphite iron (CGI) is a double-phase material, in which complex graphite morphology greatly influences crack initiation and propagation. Despite its wide use and considerable past research on the fracture behaviour of CGI, the understanding of the interaction of propagating cracks with CGI's microstructure is still limited. In this study, a novel method is employed that integrates scanning electron microscopy (SEM) and an optical high-speed camera. This approach allows the clear visualisation of microstructures before and after fracture, as well as the calculation of crack-propagation rate during tensile tests. It is also revealed for the first time that in the case of graphite particles situated at a specific distance from the primary crack path, the initiation of secondary micro-cracks, near particles does not occur. A critical distance from the main crack path for crack initiation is analysed. Further, finite-element simulations are developed to study the effect of microstructure on the fracture behaviour of the tested microstructures. A Johnson-Cook (JC) damage model is calibrated and used in all simulations. The crack path and velocity of simulation results are in good agreement with the experimental data, demonstrating that the JC damage model can be used to predict the crack initiation and propagation of CGI. It is found that interface debonding and crack initiation always tend to appear near the tip of vermicular graphite. Thus, large vermicular graphite particles can affect negatively the toughness of CGI. Graphite particles situated farther from the primary crack significantly reduce the likelihood of crack initiation in that specific location. Furthermore, large nodular graphite particles absorb energy and generate secondary cracks, while small graphite particles have little effect on the crack-path direction. The newly discovered fracture mechanisms and simulation results provide new insights for the design and manufacture of metal-matrix composites (e.g., Al/SiC) with optimal mechanical properties.

Effects of multiple reflected P waves on crack-tip stress and crack propagation in directional fracturing blasting

Directional fracturing blasting is effective for rock engineering, but it is inevitably disturbed by multiple reflected waves from different directions in natural rock mass due to discontinuous boundaries. Reflected waves affect both crack-tip stress and crack propagation, hence affect the results of directional fracturing blasting. In this paper, with the aid of high-speed photography, an optical caustics method is used to study effects of multiple reflected P waves on a directional blast-induced crack in a polymethyl methacrylate (PMMA) plate, specifically on crack path, crack fracturing mode, crack-tip stress and crack velocity. Crack-tip stress field is indicated by the shape of caustics pattern. Before the loading of reflected P waves, the mode I directional crack driven by blast-induced gases propagates in a straight path; crack-tip stress field is K-dominated, and crack-tip caustics pattern is consistent with classical caustics theory. On the contrary, under the loading of reflected P waves, the directional crack changes to be mixed-mode I + II and propagates in a curved path; Crack-tip stress field is non-K-dominated due to transient stress superposition of reflected P waves, and crack-tip caustics pattern is consistent with modified caustics theory. Transient stress superposition is not obvious for reflected P waves with a longer reflection distance. The tension loading of reflected P waves plays a more important role than the compression loading, which increases crack-tip stress intensity factors and crack velocity. This study provides a comprehensive understanding of effects of multiple reflected P waves from different directions on directional fracturing blasting.

Size Selection of Crack Front Defects: Multiple Fracture-Plane Interactions and Intrinsic Length Scales.

Material failure is mediated by the propagation of cracks which, in realistic 3D materials, typically involves multiple coexisting fracture planes. Multiple fracture-plane interactions create poorly understood out-of-plane crack structures, such as step defects on tensile fracture surfaces. Steps form once a slowly moving, distorted crack front segments into disconnected overlapping fracture planes separated by a stabilizing distance h_{max}. Our experiments on numerous brittle hydrogels reveal that h_{max} varies linearly with both a nonlinear elastic length Γ(v)/μ and a dissipation length ξ. Here, Γ(v) is the measured crack velocity v-dependent fracture energy, and μ is the shear modulus. These intrinsic length scales point the way to a fundamental understanding of multiple-crack interactions in 3D that lead to the formation of stable out-of-plane fracture structures.

Investigating the impact of thermal treatment on fracture toughness and sub-critical crack growth parameters under mode II loading

Studying subcritical crack growth is crucial to investigating the long-term behavior of rocks under applied loads and evaluating the long-term stability of underground and surface structures in rock masses. While considerable research has been done to determine subcritical crack growth parameters in mode I, Studies on subcritical crack growth under mode II loading are limited despite its important applications in rock engineering problems. The purpose of the study is to understand the thermal effect on the fracture behavior of hornfels rock, which were heated at 25 °C (without thermal treatment), 250 °C, 500 °C, and 750 °C, respectively. The subcritical crack growth parameters were determined using the constant stress rate test and one of the available fracture mechanics tests for mode II loading, namely, the four-point bending test. Experiments were conducted at three fixed displacement rates of 0.06 mm/min, 0.6 mm/min, and 6 mm/min, and three experiments were performed in each case to ensure repeatability. The results showed that the fracture toughness of hornfels samples increased with increasing temperature up to 250 °C and then decreased with increasing heat treatment temperature. The fracture toughness decreased drastically due to the thermal breakdown of the quartz crystal structure and the creation of wider intergranular fractures. The study indicated that for the hornfels samples, the subcritical parameter A decreased and beyond this temperature, parameter A began to increase while parameter n remained relatively constant as the temperature rose to 750 °C. The subcritical crack growth rate was calculated using the subcritical crack growth parameters and the stress intensity factor under mode II loading. For a certain value of the stress intensity factor KII, the highest subcritical crack velocity occurred at the temperature of 750 °C (5.76×10−7–2.47×10−1 m/s), and the lowest velocity of the subcritical crack occurred at the temperature of 250 °C (3.30×10−11–6.84×10−5 m/s). The impact of inert strength, calculated at the highest loading rate, on subcritical parameters across various temperatures was examined. The findings indicate that the subcritical crack growth parameter A is reliant on inert strength.

Acoustic Emission simulation: assessing the influence of AE source modeling and addressing the issue of dimensionality in the propagation medium

A thorough understanding of simulating Acoustic Emission (AE) requires the source modeling and propagation medium to be considered respectively. Crack initiation and propagation simulation as an AE source can be performed by the Successive Node Release (SNR) method and the Direct Node Release (DNR) method. Both are compared to show how the source model affects the AE signals. The SNR method is commonly used to simulate the crack initiation and propagation. It is necessary to consider the influence of the crack velocity profile on the crack initiation [1]. However, for the DNR method, all nodes are instantaneously released once the critical crack length is attained. Hence, it is not necessary to consider the velocity profile. Instead, it is sufficient to define the average crack velocity. However, the kinetic energy varies when employing different methods, leading to a variance in the source energy. We thus assess the suitable conditions to apply the DNR method to represent crack initiation and investigate the influence of the node release methods on the AE signals. Secondly, a comparative assessment of the Pencil-lead Break test on PMMA plates is conducted using both two-dimensional (2D) and three-dimensional (3D) finite element simulations. This analysis is valuable for understanding the deficiencies and constraints of the 2D simulation. However, there is a significant difference in the AE signals between 2D and 3D simulations, suggesting that the 2D simulation is unable to capture the AE information during wave propagation, in spite of its lower computational cost. Therefore, to obtain extensive and precise information from the PLB test, it is crucial to have an extensive understanding of the limits of the 2D simulation. This understanding should take into account factors such as the distance between the sensor and the source, as well as the descriptors chosen to characterize the AE.

Tensile strength and failure mechanism of rock–cement sample: Roles of curing temperature, nano-silica and rock type

Understanding the tensile strength and failure mechanism of rock–cement interfacial transition zone (ITZ) is of vital significance to the sealing integrity of cement sheath under downhole condition. Taking advantage of multiple techniques, i.e., digital image correlation (DIC), nano-indentation, XRD-Rietveld analysis, 29Si MAS solid NMR, and SEM-EDX, this study is devoted to investigating the impacts of curing temperature, rock type, and the addition of nano-silica (NS), on the tensile strength and failure mechanism of rock–cement sample. The experimental results show that both the curing temperature and the addition of NS leads to the formation of more C-S-H, which densifies the ITZ microstructure and responsible for high tensile strength of rock–cement samples; the tensile strengths of shale-cement samples are consistently higher than those of sandstone-cement sample; the crack velocities for rock–cement samples under three-point bending tests are approximately 1 mm/s, the crack velocities for rock–cement samples are slowed down when the NS is incorporated in cement paste, but they are independent on the rock type and curing temperature.

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

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

Evaluation of crack initiation load of silica glass surfaces formed during subcritical crack growth

AbstractThe crack initiation load of freshly fractured surfaces for silica glass was evaluated with ball indentation. The fracture surfaces were formed during subcritical crack growth in the regions I, II, and III of the stress intensity factor (KI)—crack velocity (V) curve. From the KI–V curve, we linked the obtained fracture surfaces with the ones in the regions I, II, and III. It was found that the crack‐forming probability was the lowest for the fracture surface formed in the region III of the KI–V curve. In order to understand the controlling factors of the crack formation, some properties which are topography, relative nonbridging oxygens (NBO), hydrogen concentrations, and Si–O three‐ or four‐membered ring structures, of the fracture surfaces were measured by atomic force microscopy, X‐ray photoelectron spectroscopy, dynamic secondary ion mass spectroscopy, and Raman spectroscopy, respectively. No distinct difference in NBO and hydrogen concentrations nor the ring structures were found among the fracture surfaces formed in different regions in the KI–V curve. The peak‐to‐valley height of the fracture surface, however, decreased with increasing crack velocity. It is concluded that the roughness or topography of the freshly fractured surface is one of the controlling factors which reduce the intrinsic strength of silica glass.

On the importance of the cracking process description for dynamic crack initiation simulation

A dynamic implementation of the coupled criterion under quasi-static loading, based only on the mean velocity during crack initiation, is proposed. It relies on a simultaneous node release method. It consists of computing the dynamic incremental energy release rate by simultaneously opening a crack of a finite length during a given time increment rather than progressively opening smaller crack increments following a velocity profile as in the progressive node release method. Both methods result in significantly different kinetic energy variations as a function of the crack length, and thus different incremental energy release rates for large enough crack velocities, for which the kinetic energy magnitude is similar to the elastic strain energy magnitude. Both simultaneous node release method and progressive node release method can however be equivalently used for small enough crack velocities since similar incremental energy release rates are obtained with both methods. Inverse identification of fracture properties based on dynamic crack initiation at a hole in Brazilian disk specimens yields critical energy release rates in the same order of magnitude as the one obtained based on dynamic crack propagation modeling.

Quenched disorder and instability control dynamic fracture in three dimensions

Materials failure in 3D still poses basic challenges. We study 3D brittle crack dynamics using a phase-field approach, where Gaussian quenched disorder in the fracture energy is incorporated. Disorder is characterized by a correlation length R and strength σ. We find that the mean crack velocity v is bounded by a limiting velocity, which is smaller than the homogeneous material’s prediction and decreases with σ. It emerges from a dynamic renormalization of the fracture energy with increasing crack driving force G, resembling a critical point, due to an interplay between a 2D branching instability and disorder. At small G, the probability of localized branching on a scale R is super-exponentially small. With increasing G, this probability quickly increases, leading to misty fracture surfaces, yet the associated extra dissipation remains small. As G is further increased, branching-related lengthscales become dynamic and persistently increase, leading to hackle-like structures and a macroscopic contribution to the fracture surface. The latter dynamically renormalizes the actual fracture energy until, eventually, any increase in G is balanced by extra fracture surface, with no accompanying increase in v. Finally, branching width reaches the system’s thickness such that 2D symmetry is statistically restored. Our findings are consistent with a broad range of experimental observations.

Numerical solution for the interior electric displacement of the moving DBY‐PS model for semi‐permeable cracked piezoelectric material

AbstractIn this study, we analysed a moving crack at the interface of an infinitely long piezoelectric bilayer using the Dugdale–Barenblatt yield (DBY) model and the polarisation saturation (PS) model. To model the moving crack problem, a Yoffe‐type crack moves at a constant subsonic speed on the interface of an infinitely long piezoelectric bilayer. The crack faces are assumed to be semi‐permeable, and at the boundary of the bilayer, in‐plane electrical and out‐of‐plane mechanical stresses are applied. Due to the application of electro‐mechanical loads, cracks propagate, mechanical yielding zones and electric saturation zones are developed. To arrest the crack from further propagation, mechanical yield stress and saturation electric displacement are applied at the developed zones. To address this problem analytically and numerically, the mixed boundary value problem is transformed into a set of coupled Fredholm integral equations (FIEs) of the second kind using the Fourier transform and the Copson method. The closed‐form analytical expressions for the length of the electrical saturation zone (ESZ), whether longer, shorter or equal to the mechanical yielding zone (MYZ), show dependence on external electro‐mechanical loads under semi‐permeable crack conditions. The algorithm to solve the electric crack condition parameter (ECCP) has been defined using numerical discretization and the bisection method. Illustrative examples demonstrate the proposed technique's effectiveness and suitability for Yoffe‐type moving cracks. The numerical results show the convergence of the ECCP. Furthermore, the numerical results show how mechanical and electrical zone lengths and energy release rate (ERR) are affected by electrical and mechanical loads, strip thickness and crack velocity. In addition, the size of the mechanical yielding zone is consistently promoted by electrical load, while the promotion or prevention of the electrical saturation zone by mechanical load depends on the relative sizes of the nonlinear zones.

Mechanisms governing crack speed in peridynamic model

Peridynamic, an innovative solid mechanics method in continuum theory, offers unique advantages for discontinuity modeling such as fracture simulation. This study addressed a puzzling phenomenon observed in peridynamic dynamic fracture modeling, where the predicted normalized limiting crack velocity remained nearly constant across different material parameters input. Delving into the mechanism influencing predicted crack velocity in peridynamic model, we systematically explored the impacts of stiffness distribution of the nonlocal region around the crack tip, through numerical simulations and theoretical analyses. Additionally, the implicit wave velocity degradation in the damage zone of the peridynamic model was uncovered. A prediction formula for the limiting crack velocity was then derived based on these analyses. Furthermore, the wave velocity degradation scheme and the proposed prediction model were validated through numerical instances, involving convergence studies and material density degradation investigation. This work contributes to a further understanding of the peridynamic model and provides new insights for crack velocity prediction in dynamic fracture scenarios.

Hydride orientation near pressure tube-end fitting rolled joints

The connection between Zr–2.5%Nb pressure tubes and modified martensitic stainless steel-403 end fittings in Pressurized Heavy Water Reactors (PHWRs) at the rolled joint is a critical site marked by enhanced hydrogen diffusion and elevated tensile residual stresses. The application of circumferential stress above a threshold leads to the formation of radial hydrides. Formation of radial hydride leads to a drastic reduction in fracture toughness and increase in Delayed Hydride Cracking (DHC) velocity. A comprehensive understanding of residual stress, hydride orientation and radial hydride fraction in this region is essential for the assessment of pressure tube structural integrity. In this study, we employ 3D nonlinear finite element analysis to estimate the residual stresses near rolled joints for both 220 MWe and 700 MWe pressure tubes. Additionally, we pioneer an experimental investigation into hydride orientation near roll joints through internal pressurization of hydrided pressure tube and end fitting assemblies. The study delves into the influence of residual stresses due to rolling process on hydride orientation and radial hydride fraction, providing crucial insights for the evaluation of the structural integrity of pressure tubes.

Analytical modeling and simulations of dynamic mode-III fracture in pre-stressed dry sandy elastic continuum

A mathematical model has been developed to investigate the SIF (stress intensity factor) and COD (crack opening displacement) for the propagation of mode-III fracture influenced by propagating SH-wave in a pre-stressed dry sandy elastic continuum. The Wiener-Hopf mathematical method along with the Fourier integral transform (FIT) technique have been successively implemented to obtain the solution of the boundary value problem associated with the mathematical model. Furthermore, the closed form solutions of SIF and COD for non-static and static conditions of mode-III fracture have been obtained, and are found to be in well agreement with the existing results present in the literature. The sound effects of various affecting parameters viz. horizontal and vertical (compressive/tensile) pre-stresses, crack depth, and crack velocity on SIF and COD have been explored. In order to delineate the influences of these aforementioned parameters on SIF and COD graphically, numerical simulation has been accomplished.

Water effect on subcritical crack growth and fracture behavior of marble

Understanding the fracture properties and subcritical crack growth of rocks in aqueous environments is significant for the effective assessment of the long-term stability of the masonry buildings, cultural heritage structures, and art sculptures. We use double torsion techniques to systematically investigate the subcritical crack growth behavior of marble under air, fluid, saturated and saturated + fluid test conditions. In the fluid condition and the saturated + fluid condition, the load reductions during the relaxation test are larger than other conditions, reaching 12.81% and 12.26%, respectively. There is a water-weakening effect on both the subcritical crack growth index (SCI) and KIC, but the water weakening sensitivity in KIC is lower than that of SCI. Compared to the air condition, the SCI values of the marble decreased by 43.69% under the fluid condition, 17.64% under the saturated condition, and 38.09 % under the saturated + fluid condition, respectively. The introduction of water during the relaxation test results in an immediate increase in the crack velocity and the major principal strain of the specimen, as evidenced by the appearance of the Ⅳ region on the KI-V curve. Scanning electron microscope images show that the most triangular pits and dissolution pits are present in the marble under fluid and saturated + fluid conditions, leading to a more pronounced deterioration of the mechanical properties. The test results highlight the significant impact of water on subcritical crack growth in marble. In particular, during rainfall, both dry and saturated marble masonry buildings are more prone to cracking due to the introduction of water.

Crack propagation and damage evolution of metallic cylindrical shells under internal explosive loading

This paper investigates the three-dimensional crack propagation and damage evolution process of metallic column shells under internal explosive loading. The calibration of four typical failure parameters for 40CrMnSiB steel was conducted through experiments and subsequently applied to simulations. The numerical simulation results employing the four failure criteria were compared with the differences and similarities observed in freeze-recovery tests and ultra-high-speed tests. This analysis addressed the critical issue of determining failure criteria for the fracture of a metal shell under internal explosive loads. Building upon this foundation, the damage parameter Dc, linked to the cumulative crack density, was defined based on the evolution characteristics of a substantial number of cracks. The relationship between the damage parameter and crack velocity over time was established, and the influence of the internal central pressure on the damage parameter and crack velocity was investigated. Variations in the fracture modes were found under different failure criteria, with the principal strain failure criterion proving to be the most effective for simulating 3D crack propagation in a pure shear fracture mode. Through statistical analysis of the shell penetration fracture radius data, it was determined that the fracture radius remained essentially constant during the crack evolution process and could be considered a constant. The propagation velocity of axial cracks ranged between 5300 m/s and 12600 m/s, surpassing the Rayleigh wave velocity of the shell material and decreasing linearly with time. The increase in shell damage exhibited an initial rapid phase, followed by deceleration, demonstrating accelerated damage during the propagation stage of the blast wave and decelerated damage after the arrival of the rarefaction wave. This study provides an effective approach for investigating crack propagation and damage evolution. The derived crack propagation and damage evolution law serves as a valuable reference for the development of crack velocity theory and the construction of shell damage evolution modes.

Microcantilever investigation of slow crack growth and crack healing in aluminium oxide

Slow crack growth (SCG) plays an important role in the fracture of ceramics and glasses. A full understanding of the long term reliability of ceramic components therefore requires knowledge not only of fracture toughness (Kc) but also characteristics of SCG such as the threshold stress intensity factor (K0) of individual microstructural features. Previous investigations have been limited by the small scale of the microstructure and low crack growth rates involved. Here, the stress intensity factors for crack propagation Kp in sapphire were measured continuously under stable crack growth using chevron-notched microcantilevers, in air and in vacuum. Kp in vacuum was considered close to the fracture toughness Kc, with a value of 2.8 ± 0.1 MPa m1/2 for the a-plane of sapphire. Kp in air at 54 % relative humidity was reduced substantially by moisture-assisted SCG to around 1.7 MPa m1/2 and, with crack velocities of ∼20 nm/s, was considered to be close to K0. Cyclic loading in vacuum enabled quantitative measurements to be made during repeated crack growth and healing for the first time. Cracks healed up along their full length when unloaded but exhibited severe degradation of toughness on reloading. The toughness fell from 2.8 MPa m1/2 on the a-plane of pristine sapphire to 1.6 MPa m1/2 after one healing cycle and to successively lower values after further cycles. This technique offers a powerful method of investigating SCG and crack healing at the microstructural scale in different environments, with greater accuracy and on shorter timescales than can be achieved in macroscopic tests.

Improved high-temperature resistance of limestone calcined clay cement (LC3) paste with biochar: Multiscale evaluation and mechanistic analysis

In this research, the effects of biochar on the evolutions of the LC3's residual compressive strength, cracking, and ultrasonic pulse velocity were investigated after being heated to 300, 550, and 900 °C. The novelty of this study lies in the dual effect of adapting to climate change while optimizing high temperature resistance by encapsulating biochar in LC3. Moreover, an experimental design that applies multiple analytical methods and macro-micro mutual verification. The compositional changes in the hydration products and interface microstructure were analyzed in detail. The results showed that biochar increased the residual compressive strengths and curbed the crack's development. Especially at 900 °C, 1% and 2% of biochar increased its strength by 14.86% and 27.55%, respectively. These improvements may be closely related to the porous structure of biochar. The results of this study provide a valuable reference for the high temperature resistance of LC3 and help to deepen its understanding.

Fracture behavior in blasting under different static stresses and high stress unloading

AbstractIn this paper, the effects of static stresses on the blast‐induced crack in polymethyl methacrylate specimens with an empty hole were investigated by caustic system. The propagation behavior and re‐initiation process of blast‐induced crack under initial static stress and high stress unloading were investigated. The results show that when the direction of the empty hole is perpendicular to the static stress, the static stress reduces the length of the main crack. However, when the static stress is very high, the length of main cracks does not decrease. In addition, the static stress reduces the crack velocity and dynamic stress intensity factor (DSIF) and suppresses the increase of DSIFs and crack velocity due to reflected wave. The crack arrested under high stress unloading propagates again in the later stage. Moreover, the duration of high stress unloading lasts approximately 1 ms.

Poroviscoelastic relaxations and rate-dependent adhesion in gelatin.

Hydrogels, polymeric networks swollen with water, exhibit time/rate-dependent adhesion due to their poroviscoleastic constitution. In this study, we conducted probe-tack experiments on gelatin and investigated the influence of dwelling times and unloading rates on pull-off forces and work of adhesion. We utilized in situ contact imaging to monitor separation kinematics and interfacial crack velocities. We found that the crack velocities scaled nonlinearly with the unloading rate, in a power law with an exponent of 0.8 and were independent of dwelling time. At maximum unloading rates corresponding to subsonic interfacial crack speeds, we observed an order of magnitude enhancement in the apparent work of adhesion. The enhancement of adhesion and the crack velocities were related by a power law with an exponent of 0.39. The maximum vertical extension during unloading, a measure of crack opening, exhibited linear correlation with the enhancement of adhesion. Both correlations were in line with the rate-dependent work of fracture modeled for viscoelastic solids (e.g., Persson and Brener model). We explored the links between dwelling times corresponding to varying degrees of poroelastic diffusion and the adhesion. We found 40% additional enhancement in adhesion at the highest unloading rate. This enhancement is due to the unbalanced osmotic pressure, also known as the suction effect. The influence of dwelling times on adhesion was negligible for the interfacial cracks propagating slower than the diffusive time scales. These results identify viscoelastic relaxations as the dominant mechanism governing the rate-dependent enhancement of adhesion, and hence pave the way for tuning rate-dependent adhesion in soft multiphasic materials.