Single Crack Research Articles

Effect of Thickness Eccentricity on the Stress Intensity Factors for a Pipe with a Single Internal Radial Crack under Internal Pressure

Effect of Thickness Eccentricity on the Stress Intensity Factors for a Pipe with a Single Internal Radial Crack under Internal Pressure

A generalized nonlinear three-dimensional failure criterion based on fracture mechanics

Based on fracture mechanics theory and wing crack model, a three-dimensional strength criterion for hard rock was developed in detail in this paper. Although the basic expression is derived from initiation and propagation of a single crack, it can be extended to microcrack cluster so as to reflect the macroscopic failure characteristic. Besides, it can be derived as Hoek–Brown criterion when the intermediate principal stress σ2 is equal to the minimum principal stress σ3. In addition, the opening direction of the microcrack cluster decreases with the increase of the intermediate principal stress coefficient, which could be described by an empirical function and verified by 10 kinds of hard rocks. Rock strength is influenced by the coupled effect of stress level and the opening direction of the microcrack clusters related to the stress level. As the effects of these two factors on the strength are opposite, the intermediate principal stress effect is induced.

Study on the electric resistance method in crack depth measurements

Obtaining geometric parameters, especially depth, and describing the morphological characteristics of cracks are of great significance to control engineering disasters and accidents caused by cracks. The electric resistance method is based on the principle of differences in electrical properties between cracks and soil, which could be used to measure the single crack depth at project sites. There exists an Rmin value corresponding to a specific electrode distance d value at each Rf-d value obtained by laboratory experiments. Furthermore, a two-dimensional finite element model of soil with a single crack is established to carry out numerical simulation analysis considering the crack width W, crack depth D and complex crack conditions. The results reveal dynamic variation rules of soil resistance after crack development, and for each Rf-d value, the electrode distance d value corresponding to the Rmin value is approximately equal to the crack depth D. In the range of the electric field, the offset and rotation of the crack have little effect, while the measurement results have a strong dependence on relocation movement. The regulation gives guidance to the inversion analysis of crack depth D at project sites and has been applied in crack depth measurements of an expansive soil slope. The electric resistance method as a proposed integrated approach is of great significance and brings new perspectives into the study of crack depth measurements for field applications.

Computer vision-based statistical crack quantification for concrete structures

This paper newly proposed a computer vision-based crack quantification algorithm using a statistical approach. Recently, high-resolution digital images have been effectively utilized for automated crack width and length evaluation on concrete structures. However, cracks are often difficult to accurately measure by randomly distributed and complex shapes. To overcome the technical limitation, a novel statistical crack quantification algorithm is proposed and experimentally validated through concrete structures in this paper. First, cracks on digital images are automatically detected using a deep semantic segmentation network. Then, multi-branched cracks are separated into single cracks through crack map generation. Each separated crack length and width is calculated by the Euclidean distance transform algorithm. Finally, crack width is presented as a representative value with a statistical confidence interval. The quantitative crack evaluation results for width and length were successfully compared with the actual field measurement values by average differences of 18.07% and − 26.28%, respectively.

Closed‐form solution of fluid flow in and around a crack disk embedded in a 3D porous medium

AbstractThis paper considers the fluid flow through a porous medium containing intersecting fractures and presents three main analytical findings, namely: (1) mass exchange between fractures and surrounding matrix at the fracture intersection; (2) fluid potential solution (pressure field) within the whole domain under the form of a single singular integral equation; and (3) closed‐form solutions of fluid flow in and around a crack disc under a far field pressure gradient. The crack is represented mathematically by a 2D smooth surface (i.e., zero thickness) within a 3D porous medium, while physically by a constant aperture. The fluid flow within the crack obeys Poisseuille's law, while Darcy's law is used to represent the fluid flow in the surrounding matrix. The general solution of pressure field for the general case of multiple intersecting cracks is firstly derived under a singular integral equation form. The mass exchange between the porous matrix and the crack, as well as the mass conservation at the intersection between cracks are the keys to obtaining this general solution. Then, the general solution is written for the case of a single crack. Rigorous derivation of the latter equation allows obtaining a closed‐form solution of flow through a single crack. Introducing this solution of flow into the general equation gives the pressure field around the crack. The solution derived in this paper for a crack disk with Poisseuille's flow is slightly different from the well‐known Eshelby's solution for the case of flattened inclusion in which the flow obeys Darcy's law.

XFEM Analysis of Strain Rate Dependent Mechanical Properties of Additively Manufactured 17-4 Precipitation Hardening Stainless Steel

AbstractAdditively manufactured (AM) specimens of 17-4 precipitation hardening (PH) stainless steel (SS) corresponding to the three-point bend test, compact tension test, and single edge cracks were analyzed using the extended finite element method (XFEM) approach. A two-dimensional and three-dimensional elastic-plastic simulation were conducted using “abaqus 6.14” software based on the experimental results and validated with the simulation results. In XFEM, the partition of unity was used to model a crack in the standard finite element mesh. Based on simulation results, the present study compares the mechanical properties of AM 17-4 PH stainless steel samples with those of wrought 17-4 PH samples. Stress intensity factor and J integral were used to measure fracture toughness of the specimens. The change in fracture toughness with strain rate was evaluated by simulating two-dimensional compact tension specimens. The presence of defects such as pores resulting from entrapped gas, un-melted regions, and powder particles resulting from lack of fusion were the main reasons for lower elongation to failure of laser powder bed fusion (L-PBF) produced 17-4 PH SS reported in the literature.

Kalman Filter-Based Multitype Measurement Data Fusion for Stress Intensity Factor Evaluation in Marine Structures

Fracture is the main form of marine structural failure due to the action of waves and oceans. It is necessary to monitor the initiation and extension of cracks in a timely and accurate manner, and the stress intensity factor (SIF) is an important indicator for analysing the propagation of cracks. Based on existing research, this paper combines the calculation method of the SIF based on a single strain gauge (SSG) and maximum crack opening displacement (CMOD) and proposes a method based on the Kalman filter (KF). Numerical simulation and experimental verifications of this method have been carried out. The results show that the method can be used for a variety of configurations of precracked specimens. The KF-based method obtains more accurate results than the SSG-based and CMOD-based methods, and the relative error (RE) is not greater than 1.2%.

Micromechanics-based model of single crack propagation in Engineered cementitious composites (ECC)

Engineered Cementitious Composites (ECC) are composites exhibiting strain-hardening behavior accompanied by the formation of multiple cracks. A special feature of ECC is the ability to tune the material composition to meet the different needs of various structural components, which benefits from the special micromechanics-based design theory of ECC. However, these existing micromechanics-based design theories are specific to the case of direct tension and has not been fully discussed and developed for the case where the ECC is subjected to bending load. In this study, a micromechanics-based crack propagation model for ECC under bending load is developed to guide the design of flexural performance of ECC. The entire crack propagation process is simulated by considering the microstructure of ECC and the crack propagation criterion. For ECCs with different types of fiber, the simulated load-crack mouth opening displacement curves agree well with experimental results and the dispersion of the ECC specimens can be captured by imparting randomness to the model. Based on this model, parametric studies of several representative parameters are performed to illustrate the applicability of the model. The results indicate that the material has a higher ultimate flexural bearing capacity near a fiber aspect ratio of 448 for the given material property parameters; and the fiber/matrix bonding should not be excessively strong. Insights from this model can facilitate the design of ECC members with excellent bending properties through fiber tailoring and surface treatment.

A novel boundary tracing method without enrichment for modeling cracks and their propagation

A novel direct numerical modeling method for preexisting cracks and their propagation is developed based on the integral-generalized finite difference (IGFD) method which has an excellent performance in accuracy, flexibility, and convenience in dealing with boundary conditions. “Direct modeling” means discontinuities and their propagation are directly treated as boundaries of subdomains. The standard IGFD method for continuity problems is adopted in regions far from discontinuities, while modifications are required around the discontinuities. Some special treatments such as paired nodes and birth–death algorithms are employed to characterize the existing cracks and track the crack growth path. These techniques together constitute the extended IGFD (xIGFD) method realizing the application of IGFD method in discontinuity problems. Three specific technologies, xIGFD-A, xIGFD-B, and xIGFD-C are proposed to treat the growing nodes along the discontinuities. The xIGFD-A needs to number the newly generated nodes and add degrees of freedom for propagating cracks, which would change the dimensions of the global matrices, while the xIGFD-B and the xIGFD-C do not. The successful applications of this proposed xIGFD method as well as the comparisons with existing numerical methods in a series of examples involving quasi-static propagation of a single crack and cross cracks have fully proved its effectiveness and superiority. The proposed method neither needs enriched basis functions based on prior knowledge nor requires re-meshing operations, which shows the unity and conciseness of the discretization scheme for continuity and discontinuity problems. Therefore, it has application potential in more complex practical problems like hydraulic fracturing and fatigue cracks.

Fracture of brittle material with two 3D parallel internal cracks under thermal stress: Experimental and numerical analysis

Many defects such as cracks are often present inside brittle solids, and most of the cracks do not appear in a single form. The fracture and failure of brittle solids are basically caused by the interaction and expansion of multiple cracks. Most of the traditional studies on this topic have focused on surface or penetration crack interaction under tensile and compressive loads, while there have been very few studies on the expansion characteristics and interaction of parallel internal cracks under temperature loading. This study applies the 3D internal laser-engraved crack (3D-ILC) method to fabricate parallel internal cracks inside the 3D cube. Physical tests and numerical simulations of parallel internal cracks of different sizes and single crack propagation under temperature fields are carried out, and the propagation characteristics of internal cracks and the interaction between parallel internal cracks of unequal size under temperature loading are investigated. The study results show that the big crack will inhibit and shield the expansion of the small crack. In addition, there are typical “anti-binary tree” mode III features on both sides of the parallel large crack and single large and small crack propagation surface, which are classified as mixed I-II-III crack, while the parallel small cracks are mode I-II. Compared with the quasi-static crack growth criterion, the simulation results of the subcritical crack growth criterion are more in line with the physical test results, and there is a subcritical growth phenomenon in the parallel crack propagation under the temperature load. The results provide experimental and theoretical references for the study of 3D bi-parallel cracks interaction of different sizes and the fracture of mode I-II-III crack under the temperature field.

Study on deterioration, cracking mechanism and treatment measures of plain concrete lining with cold joints in high-speed railroad tunnel

Cracks in lining will lead to derivative diseases even seriously threaten the safety of high-speed trains. Construction-induced defects and external environmental changes are the main causes of lining cracks. From a typical high-speed railroad tunnel with a large number of lining cracks in China, construction cold joints are the main cause of its lining cracks. Based on the current research, both microscopic model and macroscopic model of concrete with cold joints were established to verify the applicability of the macroscopic model to simulate concrete elements with cold joints. Besides, finite element models with single and multiple cold joints were constructed to analyze the bearing performance and cracking mechanism of lining with cold joints. Finally, measures were proposed for the lining cracks caused by the expansion of cold joints. The results showed that: Using macroscopic model to simulate concrete elements with cold joints is reasonable. The tension area with cold joints has the most obvious deterioration, which is consistent with the cracking characteristics of field lining. Therefore, it is necessary to detect the cold joint defects in tensile area and where the pouring intervals exceed the initial setting time. The cracking of lining with single cold joints can be divided into two patterns, the back-side tension misalignment model and the inner-side tension misalignment model. While the cracking model with multiple cold joints can be regarded as a combination of single cold joint cracking models. The stress distribution and performance deterioration of lining with multiple cold joints is more complicated than that of single cold joints, more researches can be carried out by the method of this study.

Study of mechanical characteristics and damage mechanism of sandstone under long-term immersion

The microscopic pore structure of sandstone gradually changes under long-term immersion, resulting in dynamic changes in the mechanical and damage properties of sandstone, which brings challenges to maintain the long-term stability of underground engineering. In this paper, the evolution of pore structure and mechanical behavior of sandstones at different immersion times (0d, 3d, 30d, 90d, 180d and 360d) is studied. A series of physico-chemical experiments and uniaxial compression tests (with simultaneous acquisition of acoustic emission (AE) signals) are conducted to explore the weakening mechanism and failure mode of sandstones during long-term immersion. The results show that long-term immersion has a significant effect on the pore structure and mechanical behavior of sandstones. Various physical parameters indicate that the change in the pore structure of a sandstone with increasing immersion time can be divided into two stages, namely the swelling stage of clay minerals (saturation process) and the corrosion stage of potassium feldspar (long-term immersion process). The variation of pH value and K+ concentration in soaking solution can provide a basis for the division of pore structure stages. From the perspective of mechanical behavior, the uniaxial compressive strength (UCS) and cumulative AE counts of a sandstone decrease by 83% and 96.8% respectively after 360 d of immersion, with enhanced plastic characteristics. The macroscopic failure mode of a sandstone changes from combination of shear and tensile crack surfaces to a single shear crack surface. Based on the results of physico-chemical experiments and mechanical tests, it can be assumed that microcracks in long-term immersion sandstones are more prone to develop along weakened cementation surfaces. Under the effect of stress, corrosion pores formed by potassium feldspar provide space for the rotation and movement of quartz grains, making it more prone to shear slip. The study results enhance our understanding of weakening mechanisms at long-term immersion and provide a basis for assessing the long-term stability of underground engineering.

Why does an elastomer layer confined between two rigid blocks grow numerous cavities?

For a thin layer of elastomer sandwiched between two rigid blocks, when the blocks are pulled, numerous cavities grow in the elastomer like cracks. Why does the elastomer grow numerous small cracks instead of a single large crack? Here we answer this question by analyzing an idealized model, in which the elastomer is an incompressible neoHookean material and contains a penny-shaped crack. To simulate one representative crack among many, the model is axisymmetric with zero radial displacement at the edge. When the rigid blocks are pulled by a pair of forces, a hydrostatic tension develops in the elastomer. At a critical hydrostatic tension, a small crack deforms substantially, as predicted by an elastic instability, resulting in an unbounded energy release rate. Consequently, the small crack initiates its growth, regardless of the toughness of the elastomer. As the crack grows, the energy release rate decreases, so that the crack arrests. Meanwhile, the rigid blocks constrain deformation of the elastomer far away from the crack, where hydrostatic tension remains high, allowing other cracks to grow. For an elastomer of thickness H, shear modulus μ, and toughness Gc, the crack radius and spacing decrease as the normalized toughness Gc/(μH) increases. Therefore, a tough elastomer of small modulus and thickness will grow numerous small cracks when confined by two rigid blocks and pulled beyond a critical force.

Prediction of multiple fatigue crack growth based on modified Paris model with particle filtering framework

This paper presents a novel method based on modified Paris model with particle filtering (PF) framework to prognosis fatigue multi-cracks in metal structures. Since conventional Paris model is only applicable for the single crack, modified Paris model is proposed by introducing the mutual interaction between multiple cracks into stress intensity factor (SIF) expression and utilized to portray multiple fatigue crack growth process. To accurately monitor multi-cracks lengths, Lamb waves are periodically acquired during the fatigue growth of multiple cracks and fed into a deep autoencoder (DAE) network to automatically track response signals variations. Online monitoring model of multi-cracks lengths is then constructed by fitting the mapping relationship between the deep damage feature extracted by the bottleneck layer of DAE network and crack length. PF framework is further adopted to strategically fusing the prediction results of modified Paris model and real-time measurements of online monitoring model to reduce the uncertainties of material parameters and obtain more reliable prognosis results of multi-cracks lengths. The proposed method is demonstrated on center-hole metal specimens with two fatigue cracks. Experimental results show that the proposed method can accurately prognosis two fatigue cracks lengths, in which modified Paris model could more accurately describe multiple fatigue crack growth than conventional Paris model, and online monitoring model based on deep damage feature could more accurately track the fatigue crack length than artificial damage feature.

Uniaxial tensile properties of multi-scale fiber reinforced rubberized concrete after exposure to elevated temperatures

With the rapid development of transportation and population growth, there is a surge hike in demand for automobile tires. Waste rubber disposal has become a big environmental concern worldwide due to the non-biodegradability of waste rubber. Based on the previous literature, waste rubber has great potential to make green concrete. However, the mechanical behavior of concrete, especially the tensile strength after being heated, will be reduced by adding waste crumb rubber. To improve the residual tensile behavior of rubberized concrete, steel fibers, PVA fibers (or PE fibers), and CaCO3 whiskers were added to make green concrete with better fire resistance. This study investigated the influences of the crumb rubber and multi-scale fibers on the failure mode, first cracking strength and strain, ultimate strength and strain, and the stress-strain relationships of MSFRRC subjected to elevated temperatures (up to 800 °C). In addition, the damage evolution of rubberized concrete under uniaxial tension was studied by the acoustic emission (AE) technique. Results show that specimens without fibers exhibited a single straight crack and a brittle failure. Adding crumb rubber could not improve the brittleness of concrete and eliminate explosive spalling. However, the brittleness of rubberized concrete could be improved and a multi-cracking behavior could be achieved by incorporating multi-scale fibers. Meanwhile, the ultimate strength decreased significantly when the crumb rubber volume replacement ratio increased from 0% to 30% since the increase in the porosity of the concrete specimen. The incorporation of multi-scale fibers could mitigate the strength loss and contribute to the first cracking strength, ultimate strength, and strain-hardening capability. The tensile strength of MSFRRC was enhanced by 54.4%–64.3% and the ultimate strain increased by 26.9–50.4 times. Nevertheless, the strain-hardening capability was eliminated owing to the weakened interfacial bond between the steel fiber and the matrix and the decomposition of PVA fibers when the temperature reached 400 °C. In addition, the large and medium capillary pores were reduced due to the additives of multi-scale fibers and the content of mesopores increased. Furthermore, the empirical formulas to predict the residual uniaxial tensile stress-strain relationship of MSFRRC considering parameters of crumb rubber, multi-scale fibers, and elevated temperatures were proposed based on the test results.

Quantitative analysis of steel fibers on UHPFRC uniaxial tensile behavior using X-CT and UTT

Steel fiber is usually used to improve ultra-high-performance fiber-reinforced concrete (UHPFRC) tensile properties and remedy its brittle failure. X-ray CT scanning (X-CT) was used to observe the orientation and distribution of steel fibers inside UHPFRC. It revealed that the steel fiber inside UHPFRC distribution angle is not equal probability, and the probability is higher along the pouring direction in uniaxial tensile specimen mold. The uniaxial tensile tests (UTT) of 19 UHPFRC specimens with different fiber volume fractions and aspect ratios were performed to analyze the steel fiber on the tensile response and tension failure patterns of UHPFRC. Test results indicated that with an increase in the volume fraction or aspect ratio of steel fiber, the first-cracking strength, tensile strength and peak tensile strain of UHPFRC increase; while they have different growth rates. In addition, with the increase of volume fraction and aspect ratio, the failure patterns of UHPFRC tension specimens gradually changed from brittle failure with single crack to ductile failure with multiple cracks. The stress superposition compositions of tensile strength were different under different failure patterns. Combining mechanical analysis and numerical statistical analysis, prediction equations of the tensile strength of strain softening UHPFRC and pseudo-strain hardening UHPFRC considering the effect steel fiber parameters were respectively proposed. Through the mesoscopic equivalent model analysis of UHPFRC uniaxial tensile specimens, the functional relationships between the effect of steel fiber parameters on the first-cracking strength and peak tensile strain were analyzed, and then their prediction equations were proposed, combined with numerical statistical analysis. The calculation accuracy of the series of prediction equations proposed in this paper were verified by the collected literature data. Meanwhile, comparing the prediction equations proposed in this paper with the existing equations in the literature, the equations proposed in this paper were better.

Study on the Hydraulic Fracturing of the Inter-Salt Shale Oil Reservoir with Multi-Interfaces

Hydraulic fracture morphology and propagation mode are difficult to predict in layers of the various lithological strata, which seriously affects exploitation efficiency. This paper studies the fundamental mechanical and microscopic properties of the two main interfaces in inter-salt shale reservoirs. On this basis, cement-salt combination samples with composite interfaces are prepared, and hydraulic fracturing tests are carried out under different fluid velocities, viscosity, and stress conditions. The result shows that the shale bedding and salt-shale interface are the main geological interfaces of the inter-salt shale reservoir. The former is filled with salt, and the average tensile strength is 0.42 MPa, c = 1.473 MPa, and φ = 19.00°. The latter is well cemented, and the interface strength is greater than that of shale bedding, with c = 2.373MPa and φ = 26.15°. There are three basic fracture modes for the samples with compound interfaces. Low-viscosity fracturing fluid and high-viscosity fracturing fluid tend to open the internal bedding interface and produce a single longitudinal crack, respectively, so properly selecting the viscosity and displacement is necessary. Excessive geostress differences will aggravate the strain incompatibility of the interface between different rock properties, which makes the interfaces open easily. The pump pressure curves’ morphological characters are different with different failure modes.

Fracturing failure simulations of rock discs with pre-existing cracks by numerical manifold method

Diametral compression of disc-like specimens with pre-existing cracks is widely used in the study of rock fracturing failures. In the present study, a unified numerical method, namely, numerical manifold method (NMM), is further enhanced for better simulations of rock cracking by effectively considering the friction on the new crack surfaces. Simulations of disc and semi-disc specimens with a single pre-existing crack of different inclinations prove that the improved NMM can reproduce the crack development path which agrees better with the theoretical and experimental results. Thereafter, disc specimens with vertically or horizontally distributed parallel pre-existing cracks of different numbers and distances are simulated, respectively. The derived fracturing failure patterns of the discs match the corresponding results by other numerical methods or physical experiments well. The NMM simulations also indicate that the increase of the pre-existing crack number will reduce the strength of the disc, but the number of the vertically distributed pre-existing cracks shows a much more obvious influence. Meanwhile, the increase of the pre-existing crack distance will increase the strength of the disc with horizontally distributed pre-existing cracks, while the pre-existing crack distance shows a nonmonotonic influence on the disc strength for discs with vertically distributed cracks.

Predicting mechanical fields near cracks using a progressive transformer diffusion model and exploration of generalization capacity

We report a deep learning method to predict high-resolution stress fields from material microstructures, using a novel class of progressive attention-based transformer diffusion models. We train the model with a small dataset of pairs of input microstructures and resulting atomic-level Von Mises stress fields obtained from molecular dynamics (MD) simulations, and show excellent capacity to accurately predict results. We conduct a series of computational experiments to explore generalizability of the model and show that while the model was trained on a small dataset that featured samples of multiple cracks, the model can accurately predict distinct fracture scenarios such as single cracks, or crack-like defects with very different shapes. A comparison with MD simulations provides excellent comparison to the ground truth results in all cases. The results indicate that exciting opportunities that lie ahead in using progressive transformer diffusion models in the physical sciences, to produce high-fidelity and high-resolution field images.Graphical abstract

Electrochemically induced fracture in LLZO: How the interplay between flaw density and electrostatic potential affects operability

Fracture and short circuit in the Li7La3Zr2O12 (LLZO) solid electrolyte are two key issues that prevent its adoption in battery cells. In this paper, we utilize phase-field simulations that couple electrochemistry and fracture to evaluate the maximum electric potential that LLZO electrolytes can support as a function of crack density. In the case of a single crack, we find that the applied potential at the onset of crack propagation exhibits inverse square root scaling with respect to crack length, analogous to classical fracture mechanics. We further find that the short-circuit potential scales linearly with crack length. In the realistic case where the solid electrolyte contains multiple cracks, we reveal that failure fits the Weibull model. The failure distributions shift to favor failure at lower overpotentials as areal crack density increases. Furthermore, when flawless interfacial buffers are placed between the applied potential and the bulk of the electrolyte, failure is mitigated. When constant currents are applied, current focuses in near-surface flaws, leading to crack propagation and short circuit. We find that buffered samples sustain larger currents without reaching unstable overpotentials and without failing. Our findings suggest several mitigation strategies for improving the ability of LLZO to support larger currents and improve operability.