Initial Crack Length Research Articles

A primary relationship between critical strain energy density and fracture toughness of mild steel

This paper presents a novel and simplified method for determining the initial fracture toughness of mild steel under the mode-I loading conditions. This method is proposed based on an established correlation between critical strain energy density and fracture toughness. A Digital Image Correlation (DIC)-based fracture toughness test is conducted on four different grades of mild steel to validate the proposed method. A comparative analysis of the results demonstrates a high level of agreement between the initial fracture toughness values obtained from the proposed method and the DIC-based tests, with a deviation of less than 5%. Furthermore, the test results show that the relationship between critical strain energy density and fracture toughness remains constant, regardless of the initial crack length ratio. The significance of this new method lies in its ability to obtain the fracture toughness from tensile tests only, offering a much-simplified approach for determining the initial fracture toughness of mild steel while maintaining an acceptable level of accuracy.

Analysis of mixed-mode Compact-Tension-Shear (CTS) specimens with slanted propagating cracks

Compact-Tension-Shear (CTS) specimen with its loading device has been widely used in mixed-mode I&II fatigue crack growth (FCG) experiments. To accurately describe the FCG behavior of materials, it is necessary to determine both the crack length and the parameters that represent crack driving force or crack front stress field in real-time. However, the relevant solutions are currently incomplete or insufficient. In this paper, for CTS specimen with slanted propagating crack, the variations of stress field parameters including stress intensity factors (SIFs) and T-stresses, as well as crack-mouth-opening-displacement (CMOD) compliance were investigated through finite element (FE) analysis. The results show that KI, KII and T11 are greatly influenced by the initial crack length ratio, the slanted propagating crack length ratio and the loading angle, but rarely by the specimen thickness among the considered range of geometries; T33 as an out-of-plane constraint parameter, however, is subject to the coupling effects of in-plane geometries, out-of-plane geometries and the mixed-mode loading. Moreover, it is shown that the measurement span has an effect on CMOD-compliance results for CTS specimens under mixed-mode loading, which is only negligible within the recommended range of D/W∈(0.02, 0.16]. Finally, the accuracy of the developed CMOD-compliance equations was validated through FCG experiments. The conclusions obtained in the current work will provide usable constraint-related crack front stress field parameter solutions for the analysis of FCG behavior in mixed fracture mode, and also give a reliable non-visual method for the determination of fatigue propagating crack length in CTS experiments.

Viscous healing of Vickers indentation–induced cracks in glass

AbstractViscous healing of cracks induced by the Vickers indentation in a soda lime magnesium silicate, a soda borosilicate, and a soda aluminosilicate glass (NAS) was studied by laser scanning microscopy. Plots of the crack length, width, and depth normalized to the initial crack length versus time over viscosity merge into single master curves of each of these quantities for each glass. Despite glass properties do not differ strikingly from each other, however, these master curves strongly differ among the glasses. This finding was attributed to a different interplay of various crack healing phenomena. Lateral cracks were found to be responsible for the bulging of the sample surface around the Vickers imprint, which in turn promotes radial crack widening as the main cause of healing delay. The most rapid healing of lateral cracks was observed in NAS in which bulging and crack widening were least pronounced.

An Analysis of Stress Distribution in a Spline Shaft Subjected to Cycilc Impulsive Load

In this paper the effect of engagement length, number of teeth, amount of applied load, wave propagation time, number of cycles, and initial crack length on the principal stress distribution, velocity of crack propagation, and cyclic crack growth rate in a spline coupling subjected to cyclic torsional impact have been investigated analytically and experimentally. It was found that the stresses induced due to cyclic impact loading are higher than the stresses induced due to impact loading with high percentage depends on the number of cycles and total loading time. Also increasing the engagement length and the number of teeth reduces the principal stresses (40%) and(25%) respectively for increasing the engagement length from (0.15 to 0.23) and the number of teeth from (8 to 10). while increasing the other parameters (amount of applied load, wave propagation time, number of cycles, and initial crack length) increase the principal stresses at the root of the tooth (37% when the applied load rises from (8 KN to 11KN) and (62% when the wavepropagation time rises from (0.5 to 1).

Fatigue Crack Length Estimation and Prediction using Trans-fitting with Support Vector Regression

A method is described in this paper for crack propagation prediction using only the initial crack length of the target specimen. The proposed method consists of two parts, (1) crack length estimation using support vector regression (SVR) and (2) crack length prediction using a new trans-fitting method. Features based on the filtered wave signals were defined and a model was constructed using the SVR method to estimate the crack length. The hyper-parameters of the SVR model were selected based on a grid search algorithm. Prediction of the crack length was based on the previous crack length, which was estimated based on the wave signals. In this step, a newly proposed trans-fitting method was applied. The proposed trans-fitting method updated the selected candidate function to translocate the trend of crack propagation based on the training dataset. By translocating the trends to the estimated crack length of the target specimen, the crack propagation could be predicted. The proposed method was validated by comparison with given specimens. The results show that the proposed method can estimate and predict the crack length accurately.

Atomistic analyses of fracture in [formula omitted], [formula omitted] and lamellar [formula omitted] - [formula omitted] Ti single crystals

In this work, molecular dynamics simulations are employed to investigate crack growth behavior and related microstructural evolution in α-Ti, β-Ti, and lamellar-Ti single crystals under plane strain conditions. It is observed that the crack growth is independent of the initial crack length in α-Ti while it depends on the initial crack length in β-Ti and lamellar-Ti. The crack growth in β-Ti increases monotonically with an increase in initial crack length. However the crack growth in lamellar-Ti does not increase monotonically with respect to the initial crack length since the crack tip of different initial cracks may lie in α-phase, β-phase, or α−β interface in lamellar-Ti. Significant structural changes (α to β phase transformation) due to the applied deformation are not observed in α-Ti. For both β-Ti and lamellar-Ti, the β-phase is transformed into different variants of the α-phase. Dislocation density is the largest for lamellar-Ti followed by β-Ti and α-Ti. The critical strain energy release rate is the largest for β-Ti and it is lowest for α-Ti. The Gc for α-Ti decreases with an increase in initial crack length and does not appear to be much sensitive to the initial crack length. In the case of β-Ti and lamellar-Ti, Gc shows a strong dependence on the initial crack length and the variation of Gc relative to the initial crack length can be well described by an exponentially decaying function.

Multiscale Mechanics of Thermal Gradient Coupled Graphene Fracture: A Molecular Dynamics Study

The thermo-mechanical coupling mechanism of graphene fracture under thermal gradients possesses rich applications whereas is hard to study due to its coupled non-equilibrium nature. We employ non-equilibrium molecular dynamics to study the fracture of graphene by applying a fixed strain rate under different thermal gradients by employing different potential fields. It is found that for AIREBO and AIREBO-M, the fracture stresses do not strictly follow the positive correlations with the initial crack length. Strain-hardening effects are observed for “REBO-based” potential models of small initial defects, which is interpreted as blunting effect observed for porous graphene. The temperature gradients are observed to not show clear relations with the fracture stresses and crack propagation dynamics. Quantized fracture mechanics verifies our molecular dynamics calculations. We provide a unique perspective that the transverse bond forces share the loading to account for the nonlinear increase of fracture stress with shorter crack length. Anomalous kinetic energy transportation along crack tips is observed for “REBO-based” potential models, which we attribute to the high interatomic attractions in the potential models. The fractures are honored to be more “brittle-liked” carried out using machine learning interatomic potential (MLIP), yet incapable of simulating post fracture dynamical behaviors. The mechanical responses using MLIP are observed to be not related to temperature gradients. The temperature configuration of equilibration simulation employing the dropout uncertainty neural network potential with a dropout rate of 0.1 is reported to be the most accurate compared with the rest. This work is expected to inspire further investigation of non-equilibrium dynamics in graphene with practical applications in various engineering fields.

Insights into fracture behavior of Ni-based superalloy single crystals: An atomistic investigation

Comprehending the plastic deformation and failure mechanisms in Ni-based superalloys is vital to enhance their intrinsic ductility. In view of this, the present work intends to illustrate the complex deformation mechanisms ensued during tensile deformation of pre-cracked Ni-Ni3Al single crystals using atomistic simulations. Simulations of fracture, thermodynamic continuum treatments of crack initiation and detailed calculations of crack propagation toughness are performed synergistically to analyze the competition between dislocation emission and cleavage. This competition is evaluated under Mode-I loading for 18 different pre-cracked configurations (three different crack lengths, three phase orientations and two phases) in totality. Our results demonstrate that dislocation as well as twin plasticity eventuate and the competition between the two plastic modes depends on the crystallographic orientation of the abutting phases. Higher initial crack lengths can otherwise lead to cleavage like propagation in the material; however this does not imply inferior ductility of the system as long as the phase boundary lies in the path of advancing crack. Changes in configurations in terms of pre-cracked phase or initial crack lengths can engender appreciable differences in the elementary crack tip phenomena. The numerical computations of crack propagation toughness are compared favorably well with the available experiments in the literature. The calculated variations in overall toughness of the material are discussed and analyzed in light of the observed deformation landscapes.

Evaluating Ice Load during Submarine Surfacing and Ice Breaking

At present, the calculation method of ice load on surface navigation ships has been very mature, but the calculation method of submarine ice load is very few. The reasonable evaluation of submarine ice load has become an urgent problem to be solved. In this paper, the mechanical characteristics of the submarine surfacing ice-breaking process are systematically analyzed. Based on the theory of plate and shell, the theoretical calculation models of ice-breaking resistance of the submarine command tower and hull are established, respectively, and the ice load calculation method of the command tower and the hull is obtained. Then, the submarine model SUBOFF is used to perform the numerical simulation of the submarine’s ice-breaking and surfacing process. The numerical result is compared with the ice-breaking resistance calculation model. The results show that the ice-breaking resistance calculation model proposed in this paper is consistent with the numerical simulation results, and the influence of parameters such as ice mechanical properties, the upper area of the command tower, and initial crack length on ice-breaking resistance is established. The calculation model in this paper can provide a theoretical reference for the optimization design of polar submarine structures.

Experimental study on Mode Ⅰ fracture characteristics of laminated flattened-bamboo lumber combined with VIC-3D system

According to ASTM E399, Mode I fracture tests were conducted on compact tension (CT) specimens of laminated flattened-bamboo lumber (LFBL) loaded parallel to grain, in combination with the optical measurement system VIC-3D (video image correlate, 3D) to observe the evolution of strains and crack propagation. In the test results, the average fracture toughness of the specimen gradually decreased as the ratio of initial crack length to specimen width increased, and after the ratio reached 0.45, the fracture toughness value tended to be stable; the fracture toughness tests could only be considered valid if the thickness of the specimen was greater than or equal to 25 mm. Compared to large-thickness specimens, small-thickness specimens had a lower degree of brittleness; microscopic failure modes were classified as ground-tissue cracking and fiber damage. During the test, the tension-strain field was always concentrated at the tip of the extending crack. When the cracks extended to equal length, the specimens were in the same state, indicating that crack extension followed a self-consistent pattern. Furthermore, the compliance calibration method was used to develop the equation for the function of crack length-compliance.

Specific application method for determining the strength and fracture toughness of metal materials

The elastic–plastic fracture of metal components with cracks is an interesting structural behavior because of the sizable crack-tip plastic zone and its strong interactions with the structural boundaries and load conditions. These complex interactions lead to constant elastic–plastic fracture phenomenon that does not exist normally. Currently, there are several restrictions, such as specific height, thickness, initial crack length, loading fixture, and loading method, on the test specimens to determine the fracture toughness of metal materials. Considering the plastic zone at the crack tip, it is proposed that the elastic–plastic fracture phenomenon of metals can be predicted entirely by two basic material properties, tensile yield strength and fracture toughness. A 40 mm wide plate is used to test ordinary carbon steel Q235B, low alloy carbon steel Q345B and aluminum alloy 6061 under tension. The initial cracks introduced through wire-cutting were 4, 8, 12, 16, 20, 24, and 28 mm in dimensions with the initial notch length to the width ratios of 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, and 0.7. Based on the elastic–plastic fracture model, the specific application method for determining the strength and fracture toughness of metal materials was realized, and the complete failure curves of three metal materials were determined.A cruciallinkbetween the structural behavior and material parameters of metal materials was established, which can predict the yield load of actual large-scale metal structures based on the elastic–plastic fracture model.

Crack safety analysis of coating with plastic behavior in surface-coated Zircaloy cladding

In this paper, consider the coupling of pressure, thermal flux and irradiation, the mechanical response of surface-coated Zircaloy cladding with different coating materials (Cr and Fe-Cr-Al), thickness and initial crack length has been investigated. The crack length and coating thickness determine whether the crack will propagate and whether the plastic zone will reach the interface of coating and cladding. The plastic zone size and energy release rate of different coating thickness are calculated in ABAQUS. Two failure modes of coating are determined, which are 1) the plastic zone reaches the interface of cladding and coating, 2) a crack channel connecting coolant and cladding formed in coating. According to the results, the second failure mode plays a decisive role in crack safety. Different crack lengths can be divided into three zones: safety zone, discussion zone and danger zone. Safe crack lengths under different conditions are calculated. Results show that the crack tolerance of Fe-Cr-Al is better than Cr and a relatively reasonable value should not exceed 40 μm. Meanwhile, the plastic behavior cannot be ignored in calculation. Conclusions in this paper have a positive impact on the actual engineering evaluation of structural safety. They can also provide reference for future experiments.

Automatic batch recognition of rock deformation areas based on image segmentation methods

Image recording and analysis is an important but time-consuming method for understanding the rock mechanics mechanism. In this paper, a method for automatic batch identification of rock deformation areas is proposed. We crop the original image to remove irrelevant background. And we use adaptive threshold segmentation, region growth segmentation and global threshold segmentation and combine the characteristics of the image to identify the rock deformation area. Finally, we use image morphology processing to make the recognition result more accurate. For validation, 359 images of the rock samples of the uniaxial compression test were quickly identified. The identification time was approximately 5′56.83′. The average relative error of the method in the X and Y directions is 10.88% and 8.60%, respectively. In addition, using the identification results and the stress-strain curve, it was found that the water content and initial crack length of rock increase, and the compressive strength decreases; the effect of the initial fracture inclination on the compressive strength of the rock is not obvious.

Experimental and numerical study of delamination phenomenon in sandwich structures with hybrid corrugated core in the mode II of crack growth

The present study experimentally evaluates delamination of hybrid corrugated-core sandwich structures in the mode II of failure under flexural loading. Three sandwich structures with different cores, including core with no reinforcement, trapezoidal reinforcement, and triangular reinforcement, were fabricated. The strain energy release rate (G) of each specimen was then measured in the mode II of crack growth. The R-curves of the specimens were also extracted using experimental data, and by photographing the crack growth. Furthermore, the effects of the initial crack length on the R-curve were measured. In the last phase of this study, the specimens were numerically modeled using the finite element method (FEM). The delamination of the core and face sheets was modeled using the cohesive zone method (CZM), and the load–displacement curves of the specimens were extracted and compared to those of experimental data.

Fracture model for predicting tensile strength and fracture toughness of concrete under different loading rates

For the sake of safety evaluation of concrete structures under dynamic loading conditions, the rate dependences of concrete fracture parameters are necessary to be elucidated rationally first. Therefore, the aim of this study is to develop a fracture model for determining the size-independent tensile strength (ft), the fracture toughness (KIC) and the fracture energy (GF) under different loading rates. The fracture mechanism was analyzed comprehensively using three-point bending tests on concrete beams with varied depths (h) and ratios of the initial crack length to the beam depth (a0/h). As the loading rate increases, the number of fractured coarse aggregates is increased, and the shape of the load–displacement curve around the maximum fracture load (Fmax) becomes sharper. Subsequently, a fracture model was proposed to predict the size-independent parameters ft, KIC and GF by incorporating the average aggregate size (davg) and a discrete coefficient (β) to indicate material heterogeneity and discontinuity, respectively. The critical effective crack length (Δac) was discretized and quantified as davg multiplied by β. Closed-form solutions of ft, KIC and GF were obtained using Fmax based on the boundary effect model. ft, KIC and GF can be explicitly predicted after determining Fmax from the fracture tests, and were generally irrelevant to h and a0/h under individual loading rates, indicating their size-independence. The scatters in the ft, KIC and GF values were determined using a statistical analysis. The rate dependences of the fracture parameters were clarified quantitatively through elucidating the variations in ft, KIC and GF with respect to the loading rate. Moreover, the predicted fracture parameters based on the proposed model were insensitive to the possible variations of davg and β. This study brings a new insight into the fracture behaviors of concrete under different loading rates and provides scientific guidance for the disaster prevention of concrete structures.

Characterization of Ductile Crack Propagation by Fractal Energy Dissipation Rate

Because of its geometry dependence and loss of physical meaning, the incremental crack resistance curve cannot characterize ductile fractures with large crack extensions and plastic deformations. Therefore, the energy dissipation rate R is employed to overcome these deficiencies, even though specimen size effects still exist. In the study, considering the fractal crack path and concomitant plastic dissipation in the fractal domain, a scale-invariant energy dissipation rate, γp*, is proposed in the context of renormalization group theory. Some experiments in the literature have validated this approach. The fitted fractal energy dissipation rate is independent of the specimen size and initial crack length; moreover, as the specimen size increases, progressive fractality vanishing is found consistently with geometrical multifractality.

Strength, crack resistance and optical losses of heat-treated silica fibers coated with non-ferrous metal

Metallic coatings currently provide the highest performance for silica fibers. The purpose of the present works predict of crack resistance, in determining the hardness and strength of uncoated and copper-coated optical fibers, as well as in the study of changes in strength parameters and optical losses after thermal effects on the studied optical fibers. The hardness and crack resistance values of silica fibers are measured by indentation. Crack resistance K1c is calculated using a semi-empirical Niihara relationship that relates the indentation size, radial crack length, and crack resistance. It was found that copper coating of silica fibers increases crack resistance 4 times, probably due to the affect of compressive stresses. The tensile strength of the fibers is determined by axial tension and two-point bending methods at a constant loading rate. Using a scanning electron microscopy, the initial crack length is calculated and the size of the characteristic defect is determined.

Closed-form solution for predicting tensile strength and fracture toughness of ultra-high-performance concrete

As a popular cementitious material in civil engineering in recent years, ultra-high-performance concrete (UHPC) has been used in harsh working conditions for its superior mechanical properties and durability. However, cracking in UHPC is a significant threat to its durability. Thus, studying the fracture properties of UHPC for rational design of crack resistance is important. The aim of this study was to develop closed-form solutions of the size-independent tensile strength (ft) and fracture toughness (KIC) of UHPC. Three-point-bending tests were performed on 80 UHPC beams with different depths and initial crack lengths; the fracture behaviour was comprehensively analysed and a predictive model was proposed to determine ft and KIC. A characteristic microstructure parameter (Cch) and two discrete coefficients (β and C) were introduced to indicate material heterogeneity and discontinuity, respectively. Cch was determined as the average fibre spacing in this study. These coefficients also quantified the critical effective crack propagation length at the maximum fracture load (Fmax) and the characteristic crack length defined by the bulk toughness and strength properties. A linear relationship of Fmax with respect to ft and KIC was established; the size-independent ft and KIC were obtained after determining Fmax from three-point-bending tests. The effects of Cch, β, and C on the predicted ft and KIC values were analysed. Although both ft and KIC exhibited certain differences as Cch, β and C were simultaneously varied, the results were within the upper and lower limits of the ft and KIC values predicted by statistical analysis.

Acoustic Emission Source Characterisation during Fatigue Crack Growth in Al 2024-T3 Specimens.

While acoustic emission (AE) testing can be used as a valuable technique in structural health monitoring and non-destructive testing, little research has been conducted to establish its sources, particularly in 2024-T3 aluminium alloys. The major contribution of this work is that it provides a method to obtain a better linear relationship of count rate with crack growth rate based on waveform. This paper aims to characterise AE sources by synchronising the AE waveforms with load levels and then to propose possible dominant frequency ranges. The AE waveforms during fatigue crack growth in edge-notched 2024-T3 aluminium specimens, from an initial crack length of 10 mm to 70 mm, were collected at two different load ratios R = 0.125 and 0.5. At the same time, the crack growth rate was determined using thermal imaging and associated control software. The AE waveforms obtained were processed using the fast Fourier transform. It was shown that a significantly higher AE count rate was recorded at R = 0.125 compared to R = 0.5 when the maximum load was kept the same. This means that the R-ratio would affect the total amount of AE activities collected. It was also found that the dominant frequency range of the AE waveforms directly related to crack growth was 152-487 kHz, and the ranges due to crack closure were likely to be 310 kHz-316 kHz and 500-700 kHz. Based on the proposed frequency ranges, waveform selection was conducted and a better linear relationship between count rate and crack growth rate was observed. This study provides a better understanding of the AE sources and waveforms for future structural health monitoring applications.

Quantitative fatigue limit prediction of mechanically long crack under mixed modes based on fracture mechanics and fatigue mechanism

To predict the fatigue limit with a mechanically long crack under mixed modes based on the fracture mechanics, fatigue tests were conducted with an inclined notch. As a result, damage accumulation (DA) mode of fatigue crack propagation was found to occur from the crack tip. The DA mode is caused by the formation and coalescence of micro-voids. Therefore, the method of modifying the initial crack length by considering the DA mode crack propagation length has shown potential application in fatigue limit prediction. Moreover, a classification method of DA and normal modes is proposed.