Crack Propagation Process Research Articles

Molecular dynamics simulation of intergranular fracture in austenitic steel containing precipitation

Molecular dynamics simulation is applied to study the crack propagation in austenitic steel containing precipitation. Based on the experimental results, models containing precipitation with two shapes and three volume fractions are constructed. The interactions of the crack with precipitation, dislocation, twin and stacking faults are investigated. It demonstrates that the crack propagation process is strongly related to the temperature and the characteristic parameter of the precipitation. However, the microstructure evolution and dislocation emission are more affected by the temperature. At the same temperature, the initial emission position of the dislocation is changed due to the variation of the precipitation shape. It also indicates that the peak dislocation density is weakly correlated with the single characteristic parameter of the precipitation. Combined with the variation of the crack propagation rate and the peak dislocation density with temperature, it illustrates a negative relationship between these two results.

Continuous–discontinuous element method for simulating three‐dimensional reinforced concrete structures

AbstractReinforced concrete structures experience crack propagation, bond‐slip, and accompanied stress redistributions when subjected to high loading levels, as a typical continuous–discontinuous process. This work proposes a numerical system composed of discrete blocks, springs, and one‐dimensional bolt elements within the continuous–discontinuous element method (CDEM) framework. This hybrid finite‐discrete element method is enhanced by explicit integration. By simulating the pull‐out tests, the mechanical interactions between bars and concrete are determined. Numerical studies demonstrate the effectiveness of the proposed method in capturing the process of multiple crack propagation and bond‐slip in three‐dimensional reinforced concrete structures, such as columns and beams.

Computational modeling of cracking in cortical bone microstructure using the mesh fragmentation technique

The cortical bone is a hierarchical composite material that, at the microscale, is segmented in an interstitial matrix, cement line, osteons, and Haversian canals. The cracking of the structure at this scale directly influences the macro behavior, and, in this context, the cement line has a protagonist role. In this sense, this work aims to simulate the crack initiation and propagation processes via cortical bone microstructure modeling with a two-dimensional mesh fragmentation technique that captures the mechanical relevance of its constituents. In this approach, high aspect ratio elements are inserted between the regular constant strain triangle finite elements to define potential crack paths a priori. The crack behavior is described using a composed damage model with two scalar damage variables, which is integrated by an implicit-explicit (Impl-Ex) scheme to avoid convergence problems usually found in numerical simulations involving multiple cracks. The approach’s capability of modeling the failure process in cortical bone microstructure is investigated by simulating four conceptual problems and one example based on a digital image of an experimental test. The results obtained in terms of crack pattern and failure mechanisms agree with those described in the literature, demonstrating that the numerical tool is promising to simulate the complex failure mechanisms in cortical bone, considering the properties of its distinct phases.

An adaptive finite element method for coupled fretting wear and fatigue crack propagation simulation

Fretting wear and fatigue crack propagation often occur at the same time in the service of mechanically connected structures. In order to analyze the effect of fretting wear on the process of fatigue crack propagation, a finite element simulation method for fatigue crack propagation considering fretting wear is proposed. In this method, the Archard model is used to predict the wear process, and the conventional Paris equation is modified based on the wear rate. In order to improve the accuracy of crack propagation prediction, a crack-tip super singular element (CSSE) is used to calculate the singular stress field and fracture control parameters of the crack tip. An adaptive meshing technique that automatically adjusts the mesh density according to the simulation process is designed to ensure the computational efficiency of the algorithm and the accuracy of the numerical results. The smoothing technique used in wear simulation can alleviate the influence of contact stress fluctuation on wear profile prediction. The usage of the new simulation method is introduced through benchmark examples. It is proved that the numerical results of crack propagation obtained by the adaptive finite element method (FEM) have high precision, good convergence and high computational efficiency. It is found that wear reduces the crack growth rate compared with the simulation results without considering wear. This method has a promising application in the coupling analysis of fretting wear and fatigue crack propagation of mechanically connected structures.

Resistance of fatigue crack propagation induced by large α colony in a Ti‐Al‐V‐Mo‐Zr alloy

AbstractFor Ti alloys used in oil drilling pipe, the fatigue crack propagation (FCP) resistance is one of the key properties for petroleum industrial applications. In this work, the fatigue crack propagation behaviors of bimodal, equiaxed, lamellar, and Widmanstatten microstructures have been systematically investigated and characterized by SEM and EBSD. The results show that the Widmanstatten microstructure containing α colonies has higher yield strength (877 MPa), moderate elongation (9.3%), and better FCP resistance compared to other specimens. During the process of crack propagation, the large α colonies can effectively deflect the cracks and induce secondary cracks, which significantly impedes the main crack propagation. Additionally, tensile twinning can occasionally occur within the large α colony along the crack, improving the plasticity of the crack tip and resulting in a decrease in fatigue crack propagation rate (FCPR).

Mechanics of inner core debonding of composite sandwich beam with CFRP hexagonal honeycomb

The inner core debonding of composite sandwich beams with carbon fiber reinforced polymer (CFRP) hexagonal honeycomb core is investigated theoretically and experimentally. Based on the principle of minimum potential energy, a theoretical model is established to reveal the core debonding mechanism with Timoshenko’s beam theory and Extended High-Order Sandwich Panel Theory (EHSAPT) for composite face sheets and CFRP hexagonal honeycomb core, respectively. The theoretical approach of core debonding simulation is based on the framework of the cohesive zone model (CZM). By constructing the constitutive relation of the core interface as the discontinuous stress and displacement boundary conditions, the vertical core debonding can be simulated overcoming the singularity of equilibrium equations. The crack propagation process is decomposed into three stages with the consideration of the double crack propagation mechanism. In experiments, the regular and reinforced hexagonal honeycomb sandwich beams are designed and fabricated, and the quantification of the defect degree of the core bonding interface is achieved by equivalent energy release rate obtained from the homogenized hexagonal honeycomb. The double cantilever beam (DCB) experiments are performed to determine the equivalent energy release rate and reveal the core debonding mechanism of CFRP hexagonal honeycomb sandwich beams. Comparing the load–displacement curves and debonding deformation patterns indicates that the established theoretical model can effectively predict the core debonding mechanical response. Finally, parametric analysis is carried out to discuss the impact of structural dimension parameters, defect location and defect degree on the debonding modes of CFRP hexagonal honeycomb sandwich beams.

Dynamic evolution of crack fractal of polypropylene fiber reinforced geopolymer during flexural process

Crack mouth opening displacement (CMOD) is the most widely used parameter to evaluate the crack width changing process in concrete fracture research. However, it is difficult to accurately and comprehensively describe the multi-crack cracking characteristics of high-toughness concrete with only crack width. This paper investigates the dynamic evolution of the fractal dimension (FD) of surface cracks on polypropylene fiber-reinforced geopolymer (PFRG) during flexural process. The box counting method was used to calculate the FD of cracks in the segmentation images that were generated by deep learning. Crack FD at the peak load and the fracture failure load could be used as indicators of deflection hardening behavior, with threshold values of 0.83 and 0.86, respectively. Crack development can be divided into four stages based on load, FD, CMOD, and energy capacity with time: elastic segment, internal crack development segment, surface crack extension segment, and crack destabilization segment. FD shows an obvious exponential increase in the surface crack extension segment and crack destabilization segment, and the changing trend is basically parallel with the load in the surface crack extension segment. The FD of peak load and fracture failure load showed a trend of increasing and then decreasing as the fiber factor was increased. The FD value peaks at 585 when W/B = 0.35 and at 252 when W/B = 0.38. To achieve the best stress diffusion and crack propagation process and achieve the toughening objective, it is necessary to reasonably match the fiber factor and matrix strength.

Mapping deformation and dissipation during fracture of soft viscoelastic solid

Energy dissipation around a propagating crack is the primary mechanism for the enhanced fracture toughness in viscoelastic solids. Such dissipation is spatially non-uniform and is highly coupled to the crack propagation process due to the history-dependent nature of viscoelasticity. We present an experimental approach to map the dissipation field during crack propagation in soft viscoelastic solid. Specifically, we track randomly distributed tracer particles to measure the evolving deformation field. The measured deformation field is then put into a nonlinear constitutive model to determine the dissipation field. Our methodology was used to investigate the deformation and dissipation fields around a propagating crack in a Polyampholyte (PA) hydrogel. The deformation field measurements allowed us to assess whether the commonly assumed translational invariance in viscoelastic fracture theories holds true in practical experiments. Furthermore, by combining the obtained deformation fields with a nonlinear viscoelastic model, we captured the complete history of the dissipation field during crack propagation. We found that dissipation occurred even at material points that are a few millimeters away from the crack tip. The mapped dissipation field also enabled the separate determination of the intrinsic and dissipative components of fracture toughness for the viscoelastic hydrogel.

Damage of a post-tensioned concrete bridge – Unwanted cracks of the girders

The cracking of a post-tensioned T-beam superstructure, which was built using the incremental launching method, is analyzed in the paper. The problem is studied in detail, as specific damage was observed in the form of longitudinal cracks, especially in the mid-height zone of the girder at the interface of two assembly sections. The paper is a case study. A detailed inspection is done and non-destructive testing results of the girders are briefly discussed. The attention is especially focused on advanced and comprehensive numerical simulations of the bridge mechanical behavior. Linear and nonlinear static calculations are performed employing the Finite Element Method at global and local levels of precision, enabling deep insight into the bridge response during all the stages of bridge construction and after it is opened to traffic. The crack propagation process in local analyses is described by the application of the Concrete Damage Plasticity law, the parameters of which were carefully chosen. The predicted damage patterns closely resemble those observed at the site. The results reveal, that the girder damage process was initiated when centric prestressing was applied, because vertical reinforcement of the assembly section front-end surface was not designed. However, the damage did not compromise the safety of the bridge. Finally, the repair methods employed are described and also a discussion is presented on how to prevent the occurrence of such cracking.

Effect of Er2O3/MgO ratio on mechanical and thermal properties of Si3N4 ceramics

AbstractSi3N4 ceramics with high mechanical properties and thermal conductivity, exhibiting fine and bimodal microstructure, were prepared by adjusting the Er2O3/MgO ratio and hot‐pressing sintering at 1800°C for 4 h. The microstructure, grain distribution, lattice oxygen content, mechanical properties, and crack propagation process of the sintered bulk samples were systematically investigated. It was found that a low Er2O3/MgO ratio contributed to the densification of Si3N4 ceramics, whereas a high Er2O3/MgO ratio favored the grain growth of Si3N4 ceramics. In this research, the grain size distribution and average diameters as well as their impact on mechanical properties were examined. When the ratio of Er2O3/MgO was 3:1, Si3N4 had a larger average diameter and higher thermal conductivity, but the mechanical properties were somewhat reduced. When the ratio of Er2O3/MgO was 2:2, the sample displayed enhanced mechanical performance, which can be explained by the formation of a bimodal structure. The research indicates that it is feasible to control the microstructure and optimize the mechanical properties of Si3N4 ceramics by tailoring the sintering additives.

An experimental study of Lode angle impact on the rock failure procession based on acoustic emission

The laws of acoustic emission (AE) before and during rock failure are different under different stress states. In this article, a new multi-functional true triaxial geophysical (TTG) apparatus was applied to analyze the AE law of sandstone under different stress paths. The results show that (1) with the increase of Lode angle, the tensile fractures in the sandstone increase initially, followed by a decrease. The number of AE decreases initially, followed by an increase, while the average energy of AE signal increases initially, followed by a decrease. (2) During the loading process, the IB values of rock can be divided into wave type, band type and mixed type, which represent crack propagation process driven by external force, self-driving and mixed driving. It can provide a basis for early warning of underground engineering construction disasters. (3) The variation characteristics of RA and AF in rock failure process show the corresponding relationship with IB value. The RA value corresponding to the IB value of band, wave and distribution type distribution mainly concentrated around 0.05, 0.03 and widely distributed, respectively. According to the value of RA, the types of cracks show different characteristics under different driving forces. (4) With the increase of Lode angle, the failure types of rocks change from single oblique fracture (− 30°) to double-X-type fracture (10°), and finally changes to single-X-type fracture when Lode angle is 30°. The fracture angle of rock decreases initially, followed by an increase with the increase of Lode angle. Therefore, it is important to explore the AE law of rock failure process under different stress states for the early warning of underground engineering construction disasters, and can provide a guidance for the application of human underground space.

Mechanical and fracture characteristics in center cracked circular discs of coal specimens with different sizes: An experimental investigation

The propagation of cracks on a small scale can result in dynamic disasters, such as rock bursts induced by large-scale fractures in coal seams. To gain insights into the mechanism of fracture-induced disasters in deep coal seams, this study investigates the micro-process and size effect of crack propagation in coal specimens featuring different sizes of center-crack circular discs (CCCD). We conducted Brazilian splitting tests on coal samples with varying dimensions and employed acoustic emission (AE) and digital image correlation (DIC) techniques to quantitatively describe the crack propagation process. Additionally, coal specimens of different diameters were compared for the size effect characteristics of different fracture parameters during the tensile failure process. The results show that as the specimen size increases, quasi-brittle failure characteristics become pronounced, tensile strength gradually decreases and stabilizes, while fracture toughness and fracture process zone length gradually increase and tend to stabilize. The macroscopic cracks in the coal specimens generally extend from the centre of the specimen to both ends along the precracks. Large energy events are mainly concentrated at the lower end of the precracks. As coal specimen size increases, the number of AE events decreases, while the proportion of large energy events gradually increases, and the critical crack opening quantity exhibits a linear increase with specimen size. By conducting the fracture size effect experiment on coal specimens, we extend the relevant mechanical parameters from laboratory-scale tests to field engineering scales. This provides fundamental parameters for the analysis of large-scale fracture process of in-situ coal based on fracture mechanics.

A coupled hydro-thermo-mechanical model based on TLF-SPH for simulating crack propagation in fractured rock mass

In this paper, a hydro-thermo-mechanical coupling model based on the smoothed particle hydrodynamics with total Lagrangian formula (HTM-TLF-SPH) is proposed to simulate the crack propagation and instability process of fractured rock mass. TLF-SPH uses the Lagrangian kernel approximation, that is, the kernel function and its gradient need only be calculated once in the initial configuration, which is much more efficient than the smoothed particle hydrodynamics (SPH) based on the Euler kernel approximation. In TLF-SPH, particles interact with each other through virtual link, and the crack propagation path of rock mass is tracked dynamically by capturing the fracture of virtual link. Firstly, the accuracy and robustness of the HTM-TLF-SPH coupling model are verified by a reference example of drilling cold shock, and the simulation results agree well with the analytical solutions. Then, the crack propagation law of surrounding rock and the evolution characteristics of physical fields (displacement, seepage and temperature fields) after excavation and unloading of deep roadway under the coupling condition of hydro-thermo-mechanical are investigated. In addition, the seepage and heat transfer processes of the surrounding rock of Daqiang coal mine under different coupling conditions are successfully simulated. Meanwhile, the effect of the boundary water pressure difference on the temperature and seepage fields under the hydro-thermal coupling condition is quantitatively analyzed.

Research on ultrasonic bone cutting mechanism based on extended finite element method.

The research on the crack propagation mechanism of bone has important research significance and clinical medical value for the selection of cutting parameters and the development of new surgical tools. In this paper, an extended finite element method (X-FEM) model of ultrasonic bone cutting considering microstructure was developed to further study the ultrasonic bone cutting mechanism and to quantitatively analyze the effects of cutting direction, ultrasonic parameters, and cutting parameters on the mechanism of ultrasonic bone cutting crack propagation. The results show that ultrasonic bone cutting is essentially a controlled crack propagation process, in which brittle crack and fatigue crack are the main crack propagation mechanisms. In order to improve the efficiency of ultrasonic bone cutting, large amplitude and high-frequency ultrasonic vibration are preferred. Compared with the other two cutting directions, the crack propagation deflection angle in the transverse cutting direction is the largest, resulting in the worst cutting surface. Therefore, in the path planning of orthopedic surgical robots, the transverse cutting direction should be avoided as much as possible. Frequency only has a significant effect on the crack propagation rate and has a positive correlation. There is a positive correlation between the deflection angle, propagation length, propagation rate, and amplitude, which provides the possibility to control the direction and length of crack propagation by controlling the amplitude of ultrasonic. The feed speed is much lower than the ultrasonic vibration speed, which makes the influence of ultrasonic vibration speed on the crack propagation characteristics dominant. The X-FEM model of ultrasonic bone cutting provides an effective method for selecting reasonable machining parameters of orthopedic robot and optimize the design of ultrasonic osteotome.

A new digital image correlation method for discontinuous measurement in fracture analysis

The Digital Image Correlation (DIC) method is commonly used in fracture analysis, but it has limitations in measuring discontinuities, which is crucial in fracture analysis. To address this issue, this paper proposes the Adaptive Discontinuous Digital Image Correlation (AD-DIC) method, which is explicitly designed to measure discontinuous displacement fields effectively and accurately in fracture analysis. The AD-DIC method both overcomes the limitations of previous methods by incorporating an adaptive subset tracking technique, which adaptively adjusts the binarization threshold, and improves the traditional Reliability Guided-Digital Image Correlation algorithm to reconstruct the displacement field near cracks. According to high-precision discontinuous displacement fields measured by AD-DIC method, we can accurately identify cracks, measure crack opening, and calculate inclination angles. To validate the effectiveness of the AD-DIC method, theoretical images of type I and mixed-mode I/II cracks are analyzed, as well as four actual experiments. The results show that the AD-DIC method achieves a high level of accuracy in calculating crack opening, with an error of less than 0.1 pixels. The actual experiments presented in this study demonstrate the wide-ranging applications of the AD-DIC method in fracture analysis, including identifying cracks that are difficult to detect with the naked eye, measuring crack opening and inclination angle, and tracking crack propagation processes over time. This study provides an effective tool for brittle fracture analysis, and the relevant algorithms can serve as a reference for discontinuous measurement.

Failure behaviors of EB-PVD thermal barrier coatings under isothermal oxidation and thermal cycling conditions

The thermal growth oxide (TGO) layer formed by oxidation of the bond coat (BC) layer is an important factor affecting the durability of thermal barrier coatings (TBCs). In this study, a series of isothermal oxidation and thermal cycling experiments were performed on samples containing TBCs at different temperatures. The initiation, propagation and connection process of cracks in the cross-section of the samples were studied, and the oxidation failure mechanism of the samples was analyzed. The results demonstrate that the diffusion of the Al element in NiCoCrAlYHf coating to the top coat (TC) layer promotes the formation and rapid thickening of TGO at TC/BC interface. With the consumption of Al, two sublayers of mixed oxide layer and Al2O3 layer are gradually formed in the TGO layer. The TC/TGO interface is the main initiation location of interface crack. In addition, the types and initiation locations of cracks caused by isothermal oxidation are different from those caused by thermal cycling. Under isothermal oxidation, the TC layer near the TC/TGO interface and the TC/TGO interface are prone to induce horizontal cracks, which finally lead to the delamination and spalling of TBCs. Under the thermal cycling, vertical cracks occur in the TC layer, extend towards the TC/TGO interface, and merge with the interface cracks, eventually resulting in the delamination failure of the TBCs.

Failure analysis of the end surface of the burner nozzle made of UMCo50 material in long-term high temperature oxygen-enriched sulfur-chlorine environment

As the core device of coal water slurry gasification technology, the failure of the burner nozzle will bring serious technical and safety problems. The purpose of this paper is to determine the mechanism of burner failure based on the characteristics of corrosion products and cracks. The results showed that the Cr2O3 oxide film on the surface of UMCo50 was damaged under the effect of mechanical erosion, high temperature and stress, and the corrosive elements S and Cl in the combustion chamber made it further cracked and peeled off. Therefore, the matrix was corroded and cracks occurred. During the crack propagation process, more M23C6 carbides were precipitated at the grain boundary, it caused Cr-depleted at the grain boundary, which reduced the corrosion resistance of the matrix near the grain boundary. The exfoliation of carbides distributed along the grain boundary also accelerated crack propagation. Through XPS and XRD analysis, it was found that the main corrosion products on the crack surface of the failed parts were: Cr2O3, CoCr2O4, CoO, Fe2O3, FeS. According to the causes of failure analysis, the corresponding improvement measures are put forward.

The Study on Fatigue Crack Growth Rate of 4130X Material under Different Hydrogen Corrosion Conditions.

In this paper, the fatigue crack growth rates of typical pressure vessel material 4130X under different corrosion conditions are investigated, and the effects of corrosion modes and loading frequency on the fatigue crack growth rate of 4130X are discussed. The results show that under the same loading conditions, the pre-corroded crack propagation rate is increased by 1.26 times compared with the uncorroded specimens. The plastic deformation mechanism of the crack tip in air is dominated by phase transformation but the hydrogen introduced by pre-corrosion causes a small number of dislocations at the crack tip. The crack growth rate obtained by corrosion fatigue is four times that of the uncorroded specimen, and the fracture surface shows a strong corrosion effect. The molecular dynamics simulation shows that the hydrogen atoms accumulated at the crack tip make the plastic deformation mechanism dominated by dislocation in the crack propagation process, and the coupling interaction between low frequency and the corrosion environment aggravates the hydrogen embrittlement of the crack tip. In the air condition, the loading frequency has no obvious effect on the crack growth rate: when the frequency decreases from 100 Hz to 0.01 Hz and other conditions remain unchanged, the fatigue crack growth rate increases by 1.5 times. The parameter n in the Paris expression is mainly influenced by frequency. The molecular dynamics simulation shows that low frequency promotes crack tip propagation.

Interaction of cracks with grain boundaries in iron bicrystals

Molecular dynamic modelling of seed cracks evolution in iron bicrystals with inclined grain boundaries under uniaxial expansion was carried out. The process of seed crack evolution can be divided into four stages. At the first stage, in the interval of elastic deformations, the seed crack is stationary, and the stresses increase linearly, reaching a maximum value of ~7.0 GPa. At the same time, the atomic volume and stresses at the crack tip before its opening grow significantly faster than the average for the sample. At the second stage, the crack begins to spread into the grain volume. The process of crack propagation leads to an abrupt stress release due to relaxation processes in the areas adjacent to the crack banks and the emission of defects from the crack tip. After reaching the grain boundary, the crack stops and blunts. At the third stage, the crack remains in the grain boundary, and the sample stresses experience significant oscillations, which is caused by the emission of various defects both from the grain boundary and from other interfaces. The emission of defects from the crack tip can cause local migration of the grain boundary, which is formation of a bend on the initially flat surface of the grain boundary. When defects cease to be emitted from the crack tip, the voltage and atomic volume in this region increase rapidly. At the fourth stage, the crack begins to spread into the second grain. It was found that a boundary with a large grain misorientation angle is a more effective barrier restraining crack propagation. Initiation of the seed crack propagation in material is always preceded by an abrupt increase in atomic volume and stresses at the crack tip.

Phase-field modeling of anisotropic crack propagation based on higher-order nonlocal operator theory

This paper presents a novel higher-order nonlocal operator theory for the phase-field modeling of brittle fracture in anisotropic materials. Incorporating higher order nonlocal operators can enhance the accuracy of the phase-field model by effectively capturing long-range interactions that hold significance in numerous materials. The reproducing kernel particle method is employed to derive a nonlocal differential operator to enhance computational stability and accuracy. Moreover, the proposed method eliminates the need for direct computation of derivatives of the modified kernel function, which avoids the calculation of moment matrix derivatives and improves computational efficiency. The phase-field modeling of polycrystalline materials, considering the anisotropic fracture resistance of each grain, is implemented using this numerical framework. The present method is able to capture different scenarios intergranular and transgranular crack propagation patterns in polycrystalline materials. The proposed method involves a detailed representation of the complex process of crack initiation and propagation in 2D and 3D models of polycrystalline materials.