Crack Bifurcation Research Articles

Numerical simulation on effect of heterogeneity on mode I fracture characteristics of rock

Rock is more sensitive to tensile loading than compressive loading, since the tensile strength of rock is much lower than compressive strength. The fracture characteristics of rock in the tensile state are of great significance to the understanding of rock failure mechanisms. To this end, we have conducted numerical simulation researches on mode I cracking process of rock with varying homogeneity, using the Realistic Failure Process Analysis program. With the increase of homogeneity, cracks are concentrating to the ligament area with a decreasing number of crack bifurcations, and the main crack path is becoming smooth. Crack behaviors and mechanical properties are influenced significantly when the homogeneity index is in the range of 1.5 to 5. When the homogeneity index is greater than 30, they are not affected by rock homogeneity and the rock can be considered as essentially homogeneous. It is considered that the global and local strengths are affected by the distribution of rock mechanical properties at mesoscale, which influence the crack behaviors and mechanical characteristics.

Numerical investigation of blast-induced rock fragmentation

Optimum fragmentation of rocks during blasting is pivotal for the productivity of mining and civil engineering systems. Extensive studies on the ubiquitous fragmentation phenomena in nature and artificial processes have attested to the dominant control of the effective dimensionality and material brittleness on the size distribution of fragments. In this study, by further demonstrating that the impact of brittleness on fragmentation is physically inherent in the material dimension, we present new mechanistic insights into the blast-induced rock fragmentation via integrated analytical modelling, finite element simulation and image processing. A continuous-surface viscoplastic cap model was first calibrated step-by-step against rock behavior in different pressure and strain-rate regimes on various scales. Then, rock blasting was simulated under various bench dimensions and the fracture patterns were image-processed to provide quantitative insights into blast fragmentation. Our findings suggest that the fragments become smaller and rounder while their size distribution becomes more uniform as the rock dimensions decrease. We demonstrated that at smaller rock dimensions, the equivalent increase in energy density and suppression of pressure-induced ductility can conspire to assist crack bifurcation and thus create successively finer fragments towards the unbreakable limit. We also identified significant correlations between the fragment aspect ratio and its size and uniformity of distribution, highlighting the potential use of fragment shape as an indicator for evaluating blasting performance alongside conventional grading analysis.

Heterogeneous magnesium matrix nanocomposites with high bending strength and fracture toughness

Heterogeneous Mg matrix nanocomposites (Hetero-Mg-NCs) with different sizes/morphologies of soft phase were fabricated by planetary ball milling and subsequent hot-pressing sintering. The Hetero-Mg-NCs were subjected to non-notched and notched bending tests to investigate their bending behaviors. The results showed that high bending strength was successfully attained in the Hetero-Mg-NCs, especially the one with large soft phase exhibited a simultaneous improvement of bending strength and fracture toughness by 50% and 57.7%, respectively, compared with those of pure Mg. The fractography measurements revealed that the Hetero-Mg-NCs failed by a mixed-mode fracture. The abundant interfacial delamination cracks and micro-dimples were found in the Hetero-Mg-NC with large soft phase, indicating the enhancement of fracture toughness. By examining the crack propagation path, it was revealed that the Hetero-Mg-NC with large soft phase showed a longer zigzagging path, owing to the more profound crack tunneling, deflection and bifurcation phenomena. The results demonstrated that Mg–NCs with heterogeneous structure can simultaneously attain high strength and fracture toughness under bending loading.

Elaboration and mechanical properties of monolithic and multilayer mullite-alumina based composites devoted to ballistic applications

Both monolithic and multilayer mullite-alumina ceramic composites dedicated to ballistic applications were produced by uni-axial pressing and tape casting before being sintered at 1510 °C. The compositions combining andalusite and kaolin in addition to α-alumina exhibit the more promising mechanical properties, reaching the performances of pure ballistic alumina. However, for a given bulk density value, a significant improvement of the performances (Young's modulus and ballistic impedance) only by varying the composition of the monoliths is limited. The second approach reported in this work has consisted in the development of judicious multilayer materials based on the generation of internal residual stresses in thinner layers. Compared to the monolithic materials, the most efficient multilayer configurations exhibit a failure stress improved by +35% and a fracture energy increased by +60%. Indeed, the layers subjected to compressive stress promote a significant crack bifurcation during rupture.

Experimental investigation of overload effects on fatigue crack growth behaviour of 7050‐T7451 aluminium alloy

AbstractFatigue damage and fracture of metals are the major failure modes of mechanical structures. Studying the fatigue crack growth (FCG) behaviour under overload effects can better explain the loading interactions and develop more accurate FCG prediction models. This research innovatively designed and established the experimental system that is suitable for FCG test under variable amplitude loading (VAL). Systematically, FCG experiments were carried out by introducing single tensile overload, single compressive overload and tensile/compressive sequential overload in constant amplitude loading (CAL). The effects of overload ratio, stress intensity factor (SIF) range ∆K and tensile/compressive overload sequence on the FCG behaviour of 7050‐T7451 aluminium alloy were comparatively analysed. The retardation or acceleration effects on the macro FCG and the micro crack deflection, crack bifurcation and particle falling effects of different overloads as well as their interactions were revealed.

Bifurcation criterion and the origin of limit crack velocity in dynamic brittle fracture

By employing a variational phase field model, we investigated the dynamic brittle fracture of poly (methyl methacrylate) (PMMA) through computer simulation. Without the explicit fracture criterion, current simulations not only successfully reproduced the crucial experimental observations on crack propagation, such as crack patterns, velocity evolutions and limit crack velocity but also discovered some new features not reported in the experimental study yet. Through quantifying the energy flux into the crack tip and fracture energy, we observed that the crack bifurcation of PMMA always occurs with the energy flux into the crack tip exceeding a critical value and proposed that crack bifurcation obeys an energy criterion. Based on this criterion, the long-standing challenge of limit crack velocity in experiments is successfully predicted by continuum theory, which unveils that crack bifurcation sets the upper limit for crack velocity. Combining the crack bifurcation criterion and continuum theory provides a rational explanation for complex path selection of cracks.

The characteristics of high speed crack propagation at ultra high loading rate

It is important to understand the characteristics of high speed crack in brittle materials under ultra high loading rate forming through impact loading condition, which is important for understanding the impact damage evolution of ceramics and solid explosives. In this paper, a lattice spring model, which can accurately show the mechanical properties of brittle materials, is used to study the evolution law and mechanism of crack path and crack velocity in brittle materials under ultra high loading rate. This model uses the quantitative parameter mapping method proposed by Gusev to solve the spring stiffness coefficient of the model accurately, and the fracture criterion of the model based on the energy balance principle of Griffith is set up. Simulations show that the path of high speed crack behave the evolution process of a single crack and then micro-branching crack and bifurcation crack finally under the influence of ultra high loading rate. The crack propagation distance between the beginning and the bifurcation decreases with the increase of the loading rate; the crack bifurcation is not immediately after the crack initiation, but as the crack propagation speed reaches the critical value, the expansion path produces more secondary cracks, and then the crack is bifurcated. With the increase of loading rate, the average velocity of cracks gradually increases in three stages, but it shows a different variation after reaching the stable value. In the single crack stage, the steady average velocity is 0.584 times the Rayleigh wave velocity (CR), and there exists only a very small velocity oscillation; the steady value of the average crack velocity corresponding to the differential fork phase is 0.5 times the Rayleigh wave velocity, accompanied by a certain oscillation; The average speed of the stable crack corresponding to the bifurcation stage is much higher than the value of the first two stages, and it can reach 0.638 times the Rayleigh wave speed. It is also accompanied by obvious speed oscillation. The study of the propagation of cracks under different loading rates can predict the internal crack growth rate, propagation direction, and extension distance of brittle materials such as ceramics and rocks.

Crack Behavior and Crystallographic Feature for TMCP690 Steel under Fatigue Loading

For a new type of thermomechanical controlled process steel, when stress intensity factor was about 32 MPa m1/2, several slip bands with different orientations occurred in cyclic plastic zone. Some slip bands had strong interaction with dominant crack, which led to crack bifurcation and aggregation. After that, electron back-scattered diffraction technique was employed to evaluate the cyclic plasticity effect on crystallographic features of kernel average misorientation (KAM), strain distribution and fraction of different categories of grains for fatigue loading sample in crack tip zone. Before fatigue loading, KAM distribution map revealed relatively homogeneous plastic deformation and few grains displayed distortion based on strain distribution map. After fatigue loading, KAM showed higher cyclic plasticity in the middle, and lower value on both sides. Strain network structure formed. Meanwhile, when fatigue loading was executed, proportion of recrystallized grains had a little variation from 3.15 to 5.58%. Ratio of substructured grains increased to 19.63%, and deformed grains reduced to 74.79%.

A phase‐field model for brittle fracture of anisotropic materials

SummaryIn the present work, a phase field damage model is developed to address the numerical simulation of brittle fracture. This model successfully captures some important aspects of crack propagation, including crack branching and bifurcation. In addition, the proposed phase field model has been developed in the general framework of anisotropic elasticity. It can thus be used for the simulation of brittle fracture in polycrystalline materials, for which crack propagation is impacted by crystallographic orientation because of the anisotropic character of stiffness properties.

Improved fracture toughness and multiple toughening mechanisms of NdPO4/NdYbZr2O7 composites

The low fracture toughness of NdYbZr2O7 limits its application as a novel thermal barrier coating (TBC) material. In the present work, NdPO4 was selected to toughen NdYbZr2O7 and the NdPO4/NdYbZr2O7 composites were synthesized by solid-state reaction sintering. Microstructures, fracture toughness and associated toughening mechanisms of the composites were investigated. The fracture toughness of the composite with 20 mol% NdPO4 was ~1.6 MPa m1/2, nearly 25% higher than that of NdYbZr2O7 ceramic. With the addition of NdPO4, the fracture mode transformed from intragranular fracture to a mixed mode of transgranular fracture and intergranular fracture. Besides, several crack propagation paths such as crack bridging, deflection and bifurcation were observed in the NdPO4 grains, indicative of enhanced fracture toughness. Compressive stress in the NdYbZr2O7 matrix, weak NdPO4/NdYbZr2O7 interface and tensile stress in the layered NdPO4 second phase are responsible for the improvement of fracture toughness.

The generation of non-ordinary state-based peridynamics by the weak form of the peridynamic method

A weak form of the peridynamic (PD) method derived from the classical Galerkin framework by substituting the traditional derivatives into the PD differential operators is proposed. The attractive features of the proposed weak form of PD method include the following: (1) a higher-order approximation than the non-ordinary state-based peridynamic (NOSB-PD) in the strain construction; (2) the NOSB-PD is demonstrated as a special case of the weak form of the PD method; (3) as an extension of the NOSB-PD, the zero-energy mode oscillations in the weak form of the PD can be significantly reduced by introducing higher-order PD derivatives. In addition, a series of numerical tests are conducted. The results show the following: (1) the three proposed stabilization items containing higher-order PD derivatives have a better accuracy and stability than the traditional items of the NOSB-PD. In particular, the stress point stabilization item is preferred since it has the highest accuracy and efficiency and does not introduce any additional parameters; (2) the weak form of PD method is very suitable in dealing with the crack propagation and bifurcation problems.

Interlaminar to intralaminar mode I and II crack bifurcation due to aligned carbon nanotube reinforcement of aerospace-grade advanced composites

Aerospace-grade unidirectional carbon microfiber reinforced epoxy prepreg composite laminates were reinforced in the relatively weak interlaminar regions with high densities (>10 billion nanofibers per cm2) of uniformly-distributed vertically aligned carbon nanotubes (A-CNTs), creating a hierarchical architecture termed “nanostitch”. Such nanostitched laminates have been shown to increase laminate in-plane and interlaminar shear strengths. Here, the Mode I and Mode II fracture behavior and associated toughening mechanisms are investigated experimentally by performing double cantilever beam and end-notched flexure tests, respectively, of unidirectional 0° laminates following the ASTM Standards. Investigation of the crack surfaces via microscopy and micro-computed tomography (μCT) show that in both Mode I and II, the interlaminar crack bifurcates into the intralaminar region from the interlaminar precrack, and then propagates within the intralaminar region parallel to the nanostitched interlaminar region as an “intralaminar delamination” in steady state. This before unobserved phenomenon is attributed to the A-CNTs adding interlaminar toughness to a level that causes the interlaminar crack to bifurcate into the less tough intralaminar region. Microscopy and μCT analyses reveal that the A-CNTs do not increase the interlaminar thickness, and drive the crack into the intralaminar region within 1–2 mm of crack initiation in both Mode I and II, with the distance of the “intralaminar delamination” crack from the interlaminar region (at the laminate centerline) being greater in Mode II than in Mode I (~30 μm vs. ~15 μm, respectively). Finite element simulation of the crack bifurcation in Mode I predicts a minimum of 10% increase in interlaminar toughness due to the A-CNTs to propagate the crack in the intralaminar region in steady state, as observed experimentally. This unique crack behavior in advanced composites provides new insights into the magnitude and effects of reinforcement induced by A-CNTs that influence the macroscopic fracture and failure behavior of laminates, and suggests new opportunities for toughening laminates.

Effect of caliber rolling reduction ratios on the microstructure and mechanical properties of 45 medium carbon steel

Tempered medium carbon steel with poor low-temperature toughness always limits its practical applications, while temper forming process can realize the strengthening-toughening aim by changing the microstructure. In this work, a grade 45 medium carbon steel was deformed with different rolling reduction ratios of 28%, 52%, 78%, and 82% by caliber rolling at the temperature of 500oC, respectively. The texture intensity, high angle boundaries density, and elongated fibrous grains are gradually increased, as well as the tensile strength, fracture elongation, and low-temperature impact toughness are also improved with the increase of caliber rolling reduction ratio, and strengthening-toughening aim of 45-grade steel has been realized at high caliber rolling reduction ratio. Fibrous grains, <110>//RD texture, grain boundaries type, and carbides bimodal distribution resulted in the formation of crack bifurcation and delamination cracks during the tensile testing and impact testing, which can obviously decrease the ductile-brittle transition temperature and improve the low-temperature impact toughness. The caliber rolled 45 steel at the rolling reduction ratio of 82% obtains superior mechanical properties with the tensile strength of 964MPa, uniform elongation of 0.18, and low-temperature impact toughness of 176J at −40oC, which can effectively extend the practical low-temperature service range of 45-grade steel.

Numerical Simulation Research on Crack Bifurcation Mechanism of Bidirectional Cumulative Tensile Blasting

Shaped energy blasting has been widely used in the field of geotechnical engineering because of its good orientation and high energy utilization. However, the bifurcation of cracks in the direction of energy accumulation seriously affects the precracking effect in the direction of energy accumulation. In order to study the influence of the shaped energy angle on the crack propagation and bifurcation in the direction of energy accumulation, this paper used theoretical analysis and numerical simulation to study the influence of the energy angle on the crack propagation law in the energy‐concentration direction. It was found that the energy release rate in the direction of energy accumulation after blasting was the main determinant of crack propagation and bifurcation in the direction of energy accumulation, and it decreased with the increase of the shaped energy angle. When the energy release rate in the direction of energy absorption exceeded a certain critical value, the stress intensity factor K at the crack tip would be affected by the impact load more than the bifurcation toughness KB, resulting in bifurcation of the crack in the direction of the energy. The SPH method was used to simulate and analyze the energy blasting of four different shaped energy angles. The results show that as the shaped energy angle increases when the shaped energy angle is greater than or equal to 35°, the cracks in the direction of energy accumulation after blasting are bifurcated, two cracks at the crack tip. When the shaped energy angle is less than 24°, only one horizontal crack is generated in the direction of shaped energy, which is in good agreement with the theoretical analysis. The research in this paper will provide a certain research basis for the design of the blasting device and the optimization of the blasting effect.

Crack propagation in 3PB specimen made from welded joint

Crack propagation in 3PB specimen has been investigated experimentally by using Digital Image Correlation (DIC) technique. For this purpose, specimens were taken from butt welded plates, made of P460NL1 micro-alloyed steel. Fatigue pre-crack of 3PB specimens was introduced in the weld metal. Specimens were then statically loaded and analyzed using digital image correlation software ARAMIS to assess strain fields and crack propagation paths. Bifurcation of cracks was noticed as the main characteristics of crack prop-agation in the analyzed case.

Application of High Temporal and Spatial Resolution Image Measurement on Crack Bifurcation

Application of High Temporal and Spatial Resolution Image Measurement on Crack Bifurcation

How variability in interfacial properties results in tougher bonded composite joints by triggering bridging

Toughening strategies are needed to design high performance secondary bonded joints. Although adhesively bonded joints present a promising solution for cost-saving assembly, they are however among the most vulnerable parts in composite structures. Due to the inherent heterogeneity of composite substrates and the infeasibility of ideal surface pretreatments, the bonding properties of composite joints feature a spatial variability that can result in a wide variety of debonding phenomenology, such as crack tip transfer, crack bifurcation or ligament bridging. In the present work, we apply a cohesive zone model with spatially stochastic interfacial properties to model the physical behaviors that take place during debonding of an adhesively bonded composite joint. The joint distribution of the two essential bonding properties, namely, the critical separating stress σm and the strain energy release rate Gc, follows a bivariate lognormal probability distribution. The proposed model captures the mechanisms of crack-tip transfer and the failure of bridging adhesive ligaments between the composite adherends, as well as the associated toughening of joints. We find that the extrinsic dissipation attributed to extra debonding areas and plastic-damage mechanisms of ligaments may be one of the primary causes for the thickness effect of bondline on the fracture toughness, commonly observed for adhesively bonded joints. Through a parametric study, we discuss the effect of variability in interfacial properties on the enhancement of toughness of bonded composite joints. The outcomes of this work may provide insights into the fundamental failure mechanisms of secondary bonded composite joints.

Numerical investigation of impact breakage mechanisms of two spherical particles

Recently developed peridynamic (PD) simulations, allowing spontaneous crack nucleation and propagation, have been conducted to investigate the dynamic breakage behavior of impact spherical particles as a function of impact speeds. With the increase of impact speed, the Hertzian cracks, primary meridian cracks, secondary meridian cracks, circumferential cracks, and crack bifurcations are observed. The crack propagation speeds can reach 62% Rayleigh wave speed at impact speed of 20 m/s. Then with the further increase of impact speed, crack bifurcation is observed due to dynamic path instability, leading to the catastrophic failure of impact spheres. The evolution of damage ratio, defined as the ratio of broken bonds to total initial bonds in PD model, agrees with previous results using discrete element method (DEM), validating the current model. Furthermore, the comparison between computed and theoretic contact force is performed along with experimental measurements. The research provides additional insights into breakage mechanisms of particles.

A Comparative Study of Dynamic Fracture of Soda-Lime Glass Using Photoelasticity, Digital Image Correlation and Digital Gradient Sensing Techniques

The dynamic fracture of high-stiffness and low-toughness materials such as soda-lime glass (SLG) typically involves crack initiation and growth prior to branching, underlying mechanics of which is not yet fully understood. Investigation of this issue using full-field optical techniques face numerous spatio-temporal challenges since crack speeds in these materials reach 1500 m/s or more and are accompanied by highly localized deformations. However, often it is tacitly assumed that most optical methods are equally capable of studying this challenging problem and it turns out not to be true. To this end, three prevalent optical techniques - transmission photoelasticity, 2D Digital Image Correlation (DIC) and transmission Digital Gradient Sensing (DGS) - are implemented concurrently to visualize crack-tip fields and quantify fracture characteristics associated with crack initiation, crack growth and macroscopic crack bifurcation in SLG plates subjected to nominally identical loading in three separate experiments. Each method is implemented in conjunction with ultrahigh-speed (1 Mfps) photography, flash/pulse illumination, and a modified-Hopkinson pressure bar for impact loading of specimens. The feasibility of measuring fracture parameters and imposed force histories along with the pros and cons of each approach for this material system are examined.

Biaxial fatigue crack propagation behavior of ultrahigh molecular weight polyethylene reinforced by carbon nanofibers and hydroxyapatite.

Ultrahigh molecular weight polyethylene (UHMWPE) artificial joint has remained the preferred polymer component in total joint replacement surgery. However, more and more concerns have been raised about the failure of UHMWPE components due to the initiation and propagation of cracks at the notches with fixed functions. For this reason, biaxial fatigue crack growth (FCG) experiments of UHMWPE reinforced by carbon nanofibers (CNF) and hydroxyapatite (HA) were carried out using elastic-plastic fracture mechanics theory. The FCG resistance of UHMWPE, UHMWPE/CNF, and UHMWPE/HA was compared, and the effects of stress ratio (R) value and phase difference on FCG rate were investigated. At the same time, the influence of loading path was considered, and the corresponding crack path was analyzed. Results suggest that UHMWPE/CNF has better FCG resistance and the FCG rate increases with the increase of R value and the existence of 180° phase difference. In addition, crack bifurcation behavior is not observed under nonproportional loading conditions. The findings in this study will provide experimental validation and data support for better clinical application of UHMWPE-modified materials.