Crack Branching Research Articles

Quasi-Static and Dynamic Crack Propagation by Phase Field Modeling: Comparison with Previous Results and Experimental Validation

In this paper, experimental tensile tests for pre-cracked high Carbon steel ‘C90’ specimens were performed for quasi-static and dynamic loading. High loading velocity affects the crack patterns by preventing deflection. On the other hand, an efficient numerical tool based on the phase field model was developed and validated to predict brittle fracture trajectories. A staggered numerical scheme was adopted to solve the displacement and damage fields separately. Implementation efficiency in initiating and propagating cracks, even from an undamaged microstructure, was proved. The effect of the critical fracture energy density Gc on the crack path was tested; with smaller Gc, the crack patterns become more complex. In addition, the impact of loading velocities was examined, and earlier and faster crack formation and greater crack branching is observed with higher impact velocity. In this study, bidimensional plane stress cases were treated. The phase field model with hybrid formulation was able to predict crack pattern and especially crack arrest and branching found in the literature. The developed model accurately determined the transition zone of the crack path topology that has been observed experimentally.

Modeling dynamic crack branching in unsaturated porous media through multi‐phase micro‐periporomechanics

AbstractDynamic crack branching in unsaturated porous media holds significant relevance in various fields, including geotechnical engineering, geosciences, and petroleum engineering. This article presents a numerical investigation into dynamic crack branching in unsaturated porous media using a recently developed coupled micro‐periporomechanics (PPM) paradigm. This paradigm extends the PPM model by incorporating the micro‐rotation of the solid skeleton. Within this framework, each material point is equipped with three degrees of freedom: displacement, micro‐rotation, and fluid pressure. Consistent with the Cosserat continuum theory, a length scale associated with the micro‐rotation of material points is inherently integrated into the model. This study encompasses several key aspects: (1) Validation of the coupled micro‐PPM paradigm for effectively modeling crack branching in deformable porous media, (2) Examination of the transition from a single branch to multiple branches in porous media under drained conditions, (3) Simulation of single crack branching in unsaturated porous media under dynamic loading conditions, and (4) Investigation of multiple crack branching in unsaturated porous media under dynamic loading conditions. The numerical results obtained in this study are systematically analyzed to elucidate the factors that influence crack branching in porous media subjected to dynamic loading. Furthermore, the comprehensive numerical findings underscore the efficacy and robustness of the coupled micro‐PPM paradigm in accurately modeling dynamic crack branching in variably saturated porous media.

Influencing mechanism of nanoscale He bubbles on the crack propagation in TiT1.75 under tension

This work investigates the influence of the pre-existing He bubble on the crack propagation in TiT1.75 with molecular dynamic simulations. Under high strain rate tension, TiT1.75 exhibits typical brittle fracture characteristics with low fracture toughness at the microscopic scale, and the crack propagation path approximately follows the (111) plane with normal stretching direction. However, the presence of He bubble may change the stress concentration near the crack tip, resulting in the bending and even branching of cracks. The position relationship between He bubbles and crack tips is discussed, and the variation of the tensile strength with the distance and the angle is revealed. The total length and pattern of crack propagation are also presented. It is found that the tensile strength approximately linearly decreases with the He bubble concentrations, and the self-expansion and coalescence of He bubbles will gradually dominate the fracture process.

Single-phase W2B5 ceramic enabled remarkable performance via spark plasma sintering-high-frequency (SPS-HF) process

The preparation of dense single-phase boride ceramics has always been a challenge. In this paper, single-phase W2B5 ceramic with excellent performance was successfully prepared using W2B5 powder and SPS-HF technology. Under the sintering condition of 1800 °C and 50 MPa, a nearly dense W2B5 ceramic material with excellent mechanical properties was obtained. The relative density of the as-sintered W2B5 ceramic achieved 96.72 % without any sintering additive. Additionally, the Vickers hardness, fracture toughness as well as bending strength were 30 GPa (9.8 N), 5.39 MPa·m1/2 and 522.7 MPa, respectively. The outstanding hardness and bending strength of W2B5 ceramic could be attributed to its monophase W2B5 structure and high densification degree. The primary fracture mode of W2B5 ceramic was transgranular fracture, and the toughening mechanisms included crack deflection, crack bridging, and crack branching.

The influence of Co and SiC on the sintering, microstructure and tribological properties of (Ti1/3Zr1/3V1/3)B2 medium-entropy diboride-based ceramics

The (Ti1/3Zr1/3V1/3)B2(MEB) composite ceramics with various Co and SiC additions were prepared by spark plasma sintering technology at 1600 °C. The influence of Co and SiC on the microstructure and mechanical properties were studied. Reciprocating sliding wear experiments of boride ceramics sliding against GCr15 ceramic were also performed at 1 N, 5 N and 10 N (Temperature: 25 °C, frequency: 3 Hz, stroke: 1 mm). The result suggest that the sintering additives not only significantly reduces the sintering temperature of boride ceramic, but also refines the microstructure and improves its mechanical properties. The hardness and fracture toughness of MEB-20SiC–10Co ceramics are 27.76 GPa and 3.9 MPa m1/2, 30.6 % and 60 % higher than that of MEB, respectively. The increase in fracture toughness results from crack deflection and branching of the SiC particles. Tribological results indicates that MEB-20SiC–10Co also show the best tribological performance. The wear rate of MEB and MEB-20SiC–10Co at 10 N load are 2.17 × 10−6 mm3N−1m−1, 1.29 × 10−6 mm3N−1m−1, oxidative wear and adhesive wear are the main wear mechanisms. Analyzing of the wear tracks revealed a significant transfer of material from the counterpart to the tribo-interface. A friction film consisting mainly of titanium oxide and part of boron oxide was generated on the worn surface, which contributes to the improvement of tribological performance.

Tensile and Low‐Cycle Fatigue Behavior of Laser Powder Bed Fused Inconel 718 at Room and High Temperature

This study investigates the room‐ and high‐temperature (650 °C) tensile and low‐cycle‐fatigue behavior of Inconel 718 produced by laser powder bed fusion (PBF‐LB/M) with a four‐step heat treatment and compares the results to the conventional wrought material. The microstructure after heat treatment is characterized on different length scales. Compared to the wrought variant, the elastic and yield properties are comparable at both test temperatures while tensile strength, ductility, and strain hardening capacity are lower. The fatigue life of the PBF‐LB/M variant at room temperature is slightly lower than that of the wrought material, while at 650 °C, it is vice versa. The cyclic stress response for both material variants is characterized by cyclic softening, which is more pronounced at the higher test temperature. High strain amplitudes (≥0.7%) at room temperature and especially a high testing temperature result in the formation of multiple secondary cracks at the transitions of regions comprising predominantly elongated grain morphology and columns of stacked grains with ripple patterns in the PBF‐LB/M material. This observation and pronounced crack branching and deflection indicate that the cracks are controlled by sharp micromechanical gradients and local crystallite clusters.

Digital light processing‐based additive manufacturing of orientation‐controlled Al2O3 ceramics with improved damage tolerance

AbstractDigital light processing (DLP) provides a promising avenue for constructing ceramic parts with high precision and complex shapes, yet the inherent brittleness and strength‐toughness trade‐off hinder their wide applications. Here, according to DLP 3D printing, the textured alumina ceramic components with horizontally aligned textured microstructure were successfully created by adding anisotropically shaped platelets. As a critical process in the preparation of textured ceramics, the alumina platelets were aligned horizontally during printing by using the special shear fields and forming capabilities of DLP technology. The shrinkage, density, microstructure, mechanical performance, and damage‐tolerance behavior of alumina parts with different platelet concentrations were examined, and the toughening mechanisms were investigated. The strength and toughness of ceramics with 5 vol.% platelet addition are increased by 22% and 43%, respectively, as compared with those without platelets. The improved damage tolerance capabilities were primarily ascribed to the collaborative toughening mechanisms stimulated by the platelet addition, including crack branching, crack deflection, uncracked‐ligament bridging, and platelet pull‐out, which increased the crack tortuosity and consumed more fracture energy. The strategy opens up new opportunities to design complex 3D ceramic geometries with bio‐inspired layered or textured architectures, providing optimized damage tolerance.

Simulation of dynamic pulsing fracking in poroelastic media by a hydro-damage-mechanical coupled cohesive phase field model

This study develops a hydro-damage-mechanical fully coupled numerical method capable of modelling complex fluid-driven transient dynamic crack propagation in quasi-brittle poroelastic media. In this method, the fluid flow in both fractures and porous media is described by a fluid continuity equation with the modified Darcy-Poiseuille law based on the Biot's poroelastic theory. The fluid pressure and the inertial force of solids are coupled by governing equations of the mesh-insensitive phase-field regularized cohesive zone model that can simulate quasi-brittle multi-crack initiation, propagation, branching and merging without remeshing or crack tracking. The resultant displacement-pressure-damage coupled multiphysics system of equations is solved using an alternative minimization Newton-Raphson iterative algorithm with an implicit Newmark integration scheme within the finite element framework. The new method was first validated by a few 2D problems, including crack branching and deflecting in solids, fracking in a concrete cube, and consolidation and stress wave propagation in poroelastic media, subjected to various impulsive loadings. It was then applied to pressure pulsing fracking of a 40 m granite rock reservoir with extensive parametric studies of fluid viscosity and pulsing injection rate, mode and period. It was found that pulsing injection with higher fluid rates and lower fluid viscosities resulted in more developed crack patterns, and in particular, there existed an optimal pulsing injection period that could promote fracking under relatively low injection pressures. 3D horizontal well problems with multiple non-planar crack propagation and bifurcation were also successfully simulated to demonstrate the capacity and potential of the new method for engineering design and optimization of pressure pulsing fracking.

Toughening mechanism of B4C/TiB2 ceramic materials by in situ reaction via spark plasma sintering

AbstractTo enhance the fracture toughness of B4C ceramics, B4C/TiB2 ceramics with excellent performance were prepared by using TiO2 as the addition item and using spark plasma sintering to introduce TiB2 based on in situ reaction, which was compared with ceramics directly introduced with TiB2, the impacts of TiO2 content, temperature and holding time on B4C/TiB2 ceramics were studied, and the toughening mechanism of B4C/TiB2 ceramics in situ reaction was discussed. The results showed that compared with the ceramics directly introduced with TiB2, B4C/TiB2 ceramics with reinforcement phase TiB2 introduced through in‐situ reaction were easier to obtain higher relative density and better properties. Due to the existence of a discharge effect and the application of pulse current, B4C/TiB2 ceramics with excellent comprehensive properties can be prepared at lower temperatures and short time. When 15 vol% TiO2 was added, the temperature was 1750°C and the holding time was 10 min, the comprehensive properties were better, and their relative density, Vickers hardness, flexural strength, and fracture toughness were 98.5%, 27.72 GPa, 474 MPa, and 5.08 MPa·m1/2, respectively. Toughening mechanisms such as crack deflection, crack branching, and crack bridging improved the fracture toughness.

Formation of heterogeneous interfaces in the TiAl/Ti2AlNb layered composite and its effect on the fracture toughness

TiAl/Ti2AlNb intermetallic-intermetallic laminated (IIL) composites featuring brittle/ductile heterogeneous interfaces were fabricated through vacuum hot-pack rolling. The microstructures and the phase transformation behaviors of the interfaces of the IIL composites before and after annealing at 900 °C/6 h were investigated. The heterogeneous interfaces are composed of four distinct regions, individually I (βo+γ+α2), II (βo/B2+ω) (brittle part), III (O lath), and IV (equiaxed O) (ductile part) regions from TiAl to Ti2AlNb side. Notably, after annealing, an equiaxed O band approximately 50 μm wide was observed in region IV of the interface. In addition, a significant microhardness variation was observed between regions II and IV of the interface, where region II exhibited higher hardness compared to the TiAl alloy, and region IV displayed lower hardness than the Ti2AlNb alloy. The enhanced fracture toughness of the IIL composites, three times that of the TiAl base alloy, is attributed to the formation of the brittle/ductile heterogeneous interfaces and the layered design incorporating the Ti2AlNb alloy. The corresponding toughening mechanism was further discussed. The brittle II region plays a role in increasing crack branching, while the ductile IV region inhibits the propagation of microcracks and prevents the formation of main cracks. This work highlights the crucial role of the brittle/ductile heterogeneous interface in the toughening of laminated composites. Furthermore, the discovery of the O band provides novel insights into the design of TiAl/Ti2AlNb heterostructures.

The delamination performance of composite laminates with bionic high toughness regions

Inspired by the composite structure of soft and hard phases found inbiological materials, this paper prepares the CF/PPS woven composite laminates with bionic high toughness regions to improve the delamination resistance. The optimal bionic high toughness regions can increase the flexural strength by 75% compared to Baseline. These bionic regions improve the delamination resistance via two mechanisms. i) The paths of crack change from interlaminar to intralaminar because of crack deflection, branching, and convergence. ii) The singular concentrations of interlaminar stress are improved by producing tiny cracks. Finally, the damage mode is investigated in details. It shows that the pure mode II failure is transformed into a mixture of mode I and mode II failures. The cracks are more likely to transition from interlaminar to intralaminar when the distribution of bionic regions is more dispersed. As a result of these regions, the catastrophic delamination failure is improved effectively.

Assessing fracture toughness of vintage and modern X65 pipeline steels under in situ electrochemical hydrogen charging using advanced testing methodology

The susceptibility of pipeline steels to hydrogen embrittlement, which can significantly impair mechanical performance, especially fracture toughness, is a critical issue in infrastructure integrity. This study evaluates the fracture toughness of modern and vintage API X65 steels under cathodic polarization (CP) conditions, employing methods such as rising displacement testing, stepwise rising constant load testing, and constant load testing. Tearing crack growth was detected at crack tip opening displacements (CTODs) of 0.032 to 0.055 mm while subsequent crack arrest under constant force loading was observed with CTOD thresholds of 0.148 mm and 0.255 mm for modern and vintage X65, respectively. Electron channelling contrast imaging demonstrated that arrested cracks in both steels exhibited reduced plasticity and a higher propensity for crack branching compared to propagating cracks. These findings highlight the need for tailored strategies to mitigate the effects of hydrogen embrittlement in pipeline materials and underscore the differences in damage tolerance between steel generations.

Meshfree simulation of dynamic brittle and quasi-brittle fracture using a local damage model based on lattice particle method

In this paper, the particle size-dependent issue of Lattice Particle Method (LPM) for simulating dynamic brittle and quasi-brittle fracture is addressed by coupling LPM with a local damage model based on fracture energy. The proposed model is simple and more robust than the Stress Intensity Factor (SIF)-based approach as it can model mixed-mode fracture with multiple cracks without any application-dependent tuning parameter. Numerical procedures for estimating the dissipative energy and the crack tip velocity for LPM simulation are also proposed. A series of benchmark problems involving dynamic fracture and crack branching are simulated using the proposed model. Good agreements are found against existing experimental observation and solutions from other numerical methods. Although a Cartesian-like (structured) lattice configuration is employed in the current LPM method, physically meaningful and accurate crack patterns can still be captured without any special numerical treatment.

A new type of high flexural strength micro-nano-composite ceramic tool material Ti(C,N)/WC/ZrO2 for integrated micro milling cutter

Ti(C,N) composites are widely applied in various advanced manufacturing industries. However, the intrinsic brittleness and relatively high metal content for Ti(C,N) composites significantly limit their further applications, especially in high-temperature and high-speed machining conditions. Herein, a new type of high flexural strength micro-nano-composite ceramic tool material Ti(C,N)/WC/ZrO2 for integrated micro milling cutter which will be used to mill difficult-to-machine material such as titanium alloy was proposed and developed successfully by hot press sintering technique under vacuum. The Ti(C,N) composites with low metal phase strengthened by nano-3Y-ZrO2 and micro-WC particles, the effect of compositions and sintering parameters on the mechanical properties and microstructure of the composite ceramic materials were systematically investigated. The results demonstrated that the Ti(C,N) composites with low metal phase containing 15 wt% nano-3Y-ZrO2 and 15 wt% micro-WC, sintered at 32 MPa and 1500 °C for 45 min had the optimal mechanical properties under vacuum and the flexural strength, Vicker's hardness, fracture toughness and relative density were 1501 ± 86 MPa, 19.97 ± 0.43GPa, 7.25 ± 0.76 MPa.m1/2 and 99.55%, respectively. Meanwhile, the superior mechanical properties of the Ti(C,N) composites with low metal binder phase could be achieved when sintered at higher temperatures and longer holding times compared to conventional cerments. Moreover, the toughening and strengthening mechanisms for Ti(C,N) composites with low metal phase are the synergistic effects of crack bridging, crack branching, crack deflection, pinning effect, particle pull-out, intragranular microstructure, transgranular and intergranular fracture. These toughening and strengthening mechanisms and the solid solution effects generated by the joint action of oxides and carbides could remarkably improve the properties for the Ti(C,N) composites. In this study, a novel insight on developing high-property Ti(C,N) composites was proposed, and it will make a significant contribution to material synthesis and design, application for cutting tools and composite ceramics investigations.

On the influence of secondary branches on crack propagation in rolling contact fatigue

Gear and bearing failures are most often caused by rolling contact fatigue (RCF). Understanding the growth of a main surface-initiated crack into the depth of the piece, as well as the growth of subsurface-initiated branches towards the surface is necessary, in order to improve fatigue life prediction and reduce fatigue damage repair or component replacements before catastrophic failure. The purpose of this work is to analyze, based on 3D finite element simulations, the initiation and mode I growth of secondary branches in a case hardened gear, their influence on the main crack growth in mode II, and the competition between mode I and mode II crack growth. The residual stress field issued by the case hardening is taken into account and its role is analyzed. The reasons why branch cracks develop only from the upper main crack face and why only those initiated when the main crack is still shallow can reach the surface, inducing spalling are explained.

Stress corrosion cracking of leaded brass used in oil temperature sensor of vehicle

In today’s modern age, many kinds of sensors are used in cars. Sensors used in automobiles monitor the performance of the entire vehicle. They are used to control and process oil, temperature, emission level, coolant level, etc. In vehicle engine, oil is pumped under high-pressure throughout the engine system to lubricate the engine parts that are in constant friction. By doing so, it also transfers away heat from these engine parts. As the oil travels around the motor, large amount of heat keeps being absorbed and transferred. It eventually reaches engine sump where it is cooled using a coolant, and then again recirculated through the engine. In this process, overheating of this oil can greatly affect its viscosity and reduce its efficiency, eventually causing performance issue of the engine. To prevent overheating, temperature oil sensors are used, that continuously send data to the Electronic Control Unit (ECU) then subsequently ECU adjusts and regulates the fuel quantity and ignition timing. Oil Temperature Sensors (OTS) usually consists of three parts: brass body, thermistor unit and a coupler unit. For continuous temperature monitoring, the brass body is continuously in contact with the engine oil that are based on sulphates and ammoniate, under high pressure and elevated temperature. In present study, we observed leakage failure in the brass body of OTS and conducted root cause failure analysis. The basic objective of failure analysis is to identify the overall damage mode like: mechanical overload, environmental degradation / corrosion, fatigue etc. and its type and root-cause leading to the failure and its understanding help to mitigate similar failures in near future. In the present work, the failed / cracked brass body material was analyzed by using Scanning Electron Microscopy attached with Energy Dispersive Spectroscopy for identifying mechanisms of corrosion failures in OTS brass body components is highlighted. Failure analysis of cracked brass body showed the Stress Corrosion Cracking (SCC) failure which is further confirmed by multiple crack branching and Intergranular (IG) fracture.

Effects of kinetic energy and firearm-to-target distance on fracture behavior in flat bones.

This research implements a fractographic approach to investigate the relationships between kinetic energy, firearm-to-target distance, and various aspects of fracture behavior in gunshot trauma. Gunshot experiments were performed on pig scapulae (n = 30) using three firearms generating different muzzle (initial) kinetic energies, including a 0.32 pistol (103 J), 0.40 pistol (492 J), and 0.308 rifle (2275 J). Specimens were shot from two distances: 10 cm (n = 15) and 110 cm (n = 15). Features evaluated in fractographic analysis such as cone cracks, radiating cracks, crack branching points, and circumferential cracks could be easily identified and measured in flat bones and allowed for statistical comparison of crack propagation behavior under different impact conditions. Higher-energy bullets produced more radiating cracks, more crack branching points, and longer fracture lengths than lower-energy bullets. Distance had no significant effect on fracture morphology at the distances tested. That quantitative measures of crack propagation varied with energy affirms that kinetic energy transfer is important in determining the nature and extent of fracture in gunshot wounds and suggests it may be possible to infer relatively high- versus relatively low-energy transfer using these features. Ranges obtained with the three firearms exhibited considerable overlap, however, indicating that other variables such as bullet caliber, mass, and construction influence the efficiency of energy transfer from bullet to bone. Therefore, fracture morphology cannot be used to identify a specific firearm or to directly reconstruct the muzzle (initial) kinetic energy in forensic cases.

Modeling dynamic cracks initiation and propagation with the local to global approach

AbstractThe recently proposed local to global (L2G) method shows an excellent ability of modeling complex arbitrary cracking problem with high efficiency and robustness. Here, we extend the L2G to model dynamic cracks initiation and propagation, in which additional nodes are dynamically introduced to capture displacement discontinuities induced by cracks' propagation, but displacements/accelerations of additional nodes are obtained by solving local nonlinear problems of cracked elements associated with a crack. This unique operation removes the divergence risks caused by adding nodes, and improves the numerical efficiency by decreasing iteration times of the global problem. Crack branching problem is also taken into consideration in current work. Numerical examples for dynamic cracks propagation are provided to demonstrate the effectiveness and robustness of the proposed method.

Embrittlement Fracture Behavior and Mechanical Properties in Heat-Affected Zone of Welded Maraging Steel.

In welded maraging steels, mechanical properties, particularly ductility and toughness, are often compromised in the heat-affected zone (HAZ). This study focuses on 300-grade maraging steel bars, solution annealed at 1123 K for 1.5 h (5.4 ks) and welded using gas tungsten arc welding, followed by a post-weld heat treatment at 753 K for 13.33 h (48 ks). In situ observations during three-point bending tests on HAZ samples featuring coarsened prior austenite grain sizes were conducted to examine damage behavior and the crack path near the crack tip. The main crack initiated at the peak applied load during the bending test and, upon further loading, exhibited significant deflection and extension accompanied by numerous microcracks and localized crack branching. Distinctive damage features, such as transgranular cracking across block regions, intense intergranular cracking along packet boundaries with a pronounced shear component, and crowding of microcracks ahead of the crack tip, were observed in the HAZ sample during the in situ test. The interaction between the main crack tip and microcracks and its influence on the local crack propagation driving force was discussed using fracture mechanics. Experimental results, including tensile fracture surface observations and in situ images, along with analysis of the stress anti-shielding effect by microcracks, suggest that the HAZ sample exhibits embrittlement fracture behavior with lower ductility and toughness compared to the base metal sample.

Dynamic strength and full-field cracking behaviours of pre-cracked rocks under impact loads

The impact loads have a significant influence on the dynamic strength and cracking behaviours of pre-cracked rocks, which plays a key role in the stability and safety of rock engineering. In this study, impact tests were performed by using a split Hopkinson pressure bar (SHPB) in conjunction with the high-speed photography technique. The dynamic strength of pre-cracked rocks under different strain rates and flaw angles was analysed, and the full-field cracking behaviours were elucidated by the evolution of strain localization zones based on the digital image correlation (DIC) analysis. By means of discrete element method (DEM), the impact tests were numerically reproduced to study the strength enhancement and the cracking processes. The results illustrate that the increase in the strain rate and flaw angle would lead to the increasing dynamic strength, the change of tensile and shear crack number is consistent with the strength variation, implying that the microcracking processes has a significant influence on the rate dependency of dynamic strength. As for the cracking behaviours, the strain localization zones would form around the flaw, and the crack branching phenomenon could be witnessed in dynamic tests. Furthermore, the complexity of cracking patterns becomes larger with the increasing strain rate, while the samples with the large flaw angle are difficult to generate strain localization zones and macroscopic cracks. By using a DIC-based method to analyse the crack initiation mechanisms, three types of stress-induced cracks were identified, i.e., mode I, II, and mixed mode I/II cracks. Among these cracks, the mode II cracks are the dominate type of cracks. Based on the mathematical analysis of Griffith model, the combined action of the tangential stress distribution and sliding deformation might be the reason for the crack initiation, and the rate-dependent strength might be induced by the increase of the maximum tangential stress regarding external stress.