Including Crack Propagation Research Articles

Mesh characteristic changes of spiral bevel gear pair with assembly errors during tooth crack propagation

Spiral bevel gears (SBGs) are often used because of their strong carrying capacity and lower vibration. However, this heightened load capacity can sometimes result in the development of tooth surface cracks. This study aims to simulate the three-dimensional propagation of cracks in SBGs under various assembly conditions and explore how the presence of cracks affects mesh characteristics. This paper investigates crack propagation in SBGs by applying principles of fracture mechanics. Employing a combination of finite element software ABAQUS and fracture mechanics software FRANC3D, the study conducts a three-dimensional analysis of crack propagation in SBGs. The study analyzes the impact of crack propagation on the lifespan and mesh characteristics of SBGs, including crack propagation morphology, transmission error, time-varying meshing stiffness (TVMS), gear life, and tooth surface force, under various assembly errors.

Investigation of the Influence of Non-uniform Strain zone on the Crack Propagation of PMMA Material Based on 2D-DIC

Hole defects can lead to non-uniform strain distribution under the impact load, thereby influencing crack propagation behavior. In this paper, 2D-DIC technology was employed to examine the effects of holes of varying sizes and loading rates on crack dynamics in PMMA materials, aiming to elucidate detailed knowledge into the characteristics of crack propagation under complex strain fields. Through DIC analyses, the dynamic evolution of strain fields around the crack tip and hole periphery could be precisely captured, enabling tracking of crack propagation behavior including crack propagation velocity, crack propagation path, and crack deflection angle. It is concluded that the non-uniform strain zones generated by holes exert both inhibitory and attracting effects on crack growth. The influence of non-uniform strain zones on crack propagation increases with the elevation of loading rate and hole size. However, as the loading rate increases, the kinetic energy of the crack itself also increases, necessitating sufficiently large hole sizes to effectively influence crack propagation. Overall, this study provides a detailed experimental explanation of the effects of holes on cracks, which will aid engineers in maximizing the positive impact of holes on material performance and their application in the design of microstructure materials.

Investigation on 2D SiCf/SiC composite scribing mechanism by single- and double-grit

To validate the proposed removal mechanism of 2D SiCf/SiC composite, single- and double-grit scribing experiments were conducted on the fiber woven surface (WS) and stacking surface (SS) along the 0°, 45°, and 90°. The results indicate that transverse fibers mainly undergo shear, tensile, and bending fractures. The removal modes of normal fibers are shear and bending fractures. The longitudinal fibers are damaged by tensile (cut-in side) and bending (cut-off side) fractures, accompanied by fiber peel-off. The removal forms of the matrix include crack propagation, ductile scratch, powdery removal, and brittle peel-off. The order of scribing force is FSS0 > FWS45 > FSS90 > FWS0. The maximum and minimum scribing force occur on SS0 and WS0, respectively, due to the powdery removal of matrix and fibers + matrix peel-off. The 2nd grit scribes the matrix layer and fiber tip in a very low depth to cause powdery and ductile removal, which exhibit the different material removal mechanism with the 1st grit. The scribing damage formed by 1st grit greatly reduces the force required by the 2nd grit for the same material removal volume. The coupling effect among grits in multi-grit scribing and grinding cannot be ignored.

Bond-Based Peridynamic Model for Tensile Deformation and Fracture of Polycarbonate and Polypropylene

Fracture mechanics has been a crucial aspect in the field of engineering science as technologies are rapidly growing nowadays. Various numerical methods have been developed to analyze fracture behaviour in different types of materials used in industries. Meanwhile, the application of polymers garners attention worldwide due to outstanding characteristics such as good strength, lightweight, and high temperature resistance, exemplified by polymers like polycarbonate (PC) and polypropylene (PP). Hence, failure aspects of such materials must be taken into consideration when conditions arise that may lead to failure, such as high-load impact, fatigue, and extreme temperatures. In this study, a bond-based Peridynamic model (PD) for the tensile behaviour, including fracture, of polymers has been developed. The PD model is constructed using the Centos software and encompasses both brittle and ductile fracture behaviours. Numerical results, including crack propagation, damage zone, and force-extension curves of notched specimens, are validated by comparison with experimental results of PC and PP. Through the validation process, PC specimens exhibit a difference percentage range for maximum load and rupture extension of 2.9% to 18.8% and 2.4% to 4.6%, respectively. PP specimens show a difference percentage range for maximum load and rupture extension of 31.2% to 43.5% and 0.9% to 30%, respectively. Consequently, the validation results indicate that the PD model for brittle specimens aligns more closely with experimental data compared to the PD model for ductile specimens.

Deep learning enables accurate soft tissue tendon deformation estimation in vivo via ultrasound imaging

Image-based deformation estimation is an important tool used in a variety of engineering problems, including crack propagation, fracture, and fatigue failure. These tools have been important in biomechanics research where measuring in vitro and in vivo tissue deformations are important for evaluating tissue health and disease progression. However, accurately measuring tissue deformation in vivo is particularly challenging due to limited image signal-to-noise ratio. Therefore, we created a novel deep-learning approach for measuring deformation from a sequence of images collected in vivo called StrainNet. Utilizing a training dataset that incorporates image artifacts, StrainNet was designed to maximize performance in challenging, in vivo settings. Artificially generated image sequences of human flexor tendons undergoing known deformations were used to compare benchmark StrainNet against two conventional image-based strain measurement techniques. StrainNet outperformed the traditional techniques by nearly 90%. High-frequency ultrasound imaging was then used to acquire images of the flexor tendons engaged during contraction. Only StrainNet was able to track tissue deformations under the in vivo test conditions. Findings revealed strong correlations between tendon deformation and applied forces, highlighting the potential for StrainNet to be a valuable tool for assessing rehabilitation strategies or disease progression. Additionally, by using real-world data to train our model, StrainNet was able to generalize and reveal important relationships between the effort exerted by the participant and tendon mechanics. Overall, StrainNet demonstrated the effectiveness of using deep learning for image-based strain analysis in vivo.

Blind prediction of curved fracture surfaces in gypsum samples under three-point bending using the Discontinuous Galerkin Cohesive Zone method

A computational framework based on a Discontinuous Galerkin (DG)/Cohesive Zone formulation is utilized to simulate the experiments of the Purdue Damage Mechanics Modeling Challenge. The inelastic response of the additively-manufactured gypsum material used in the experimental tests is modeled via a dilatational plasticity model. The constitutive and fracture model parameters are calibrated using the load–displacement curves corresponding to three-point bending tests initially provided by the Challenge organizers. The test samples contained initial notches especially designed to force specific types of mixed fracture modes. The calibrated computational modeling framework is used to blindly simulate the more complex configuration of the Challenge experiments. The numerical predictions of the load–displacement curve and the shape of the curved fracture surface are compared to the experimental data provided a posteriori. It is found that the computational method is able to quantitatively describe the fracture response of the material including crack propagation, plastic wake, and the curved geometry of the fracture surface that results from the evolving fracture mode mixity with significant fidelity.

A Novel Repair Technique of Pre-damaged T-Beams Failing in Shear Using Eco-Friendly Steel Fibre-Reinforced Geopolymer Concrete

Repair of reinforced concrete structures is required to preserve the adequate performance of these structures throughout their service life. One of the credible techniques is using fibrous concrete as a repair material. In this paper, the performance of steel fibre-reinforced geopolymer concrete (SFRGPC) in the repair of pre-damaged reinforced concrete T-beams (pre-loaded up to 50% of their shear capacity) failing in shear was investigated. Five T-beam series and a four-point loading test were adopted: one reference beam, three beams were repaired with different fibrous ratios of 1, 2, and 3%, and one was repaired with 2% steel fibre and additional U-steel stirrups. The key test results include crack propagation, crack width, initial stiffness, load deflection, peak loads, and strain associated with web stirrups. A clear enhancement was noticed in the performance of the repaired T-beams; their shear capacity was boosted by as much as 45% compared to the control beam. It was also deduced that the beam went from a brittle to a ductile failure mode at 3% SFRGPC and at 2% SFRGPC with U-stirrups. Finally, an analytical model prediction was proposed to predict the shear capacity of repaired T-beams with the SFRGPC. The model showed a satisfactory correlation with experimental results, with an average ratio of 0.995 and a standard deviation of 0.035.

Trans-layer and inter-layer fracture behavior of extrusion-based 3D printed concrete under three-point bending

This paper presents a systematic study on the effect of layer-by-layer printing process on the fracture behavior of hardened extrusion-based 3D printed concrete (3DPC). Based on three-point bending tests on center-notched beams, the fracture response of printed specimens with two fracture patterns including crack propagation across layers (trans-layer fracture) and crack propagation along layers (inter-layer fracture) was compared with that of cast specimens. The fracture mechanism of 3DPC was explored using the fracture parameters and fracture process zone (FPZ) characteristics. Experimental phenomena can be explained by the additional interlaminar cracking in FPZ of concrete introduced by the layer-by-layer stacking process. It could produce a toughening effect if cracks propagate through layers, as it is beneficial to reduce stress concentration and improve deformability. In the printing process design of 3DPC, such feature can be rationally utilized to transform the process-induced weak interfaces from inherent defects to toughening means.

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

The classical theory of continuum mechanics is formulated using partial differential equations (PDEs) that fail to describe structural discontinuities, such as cracks. This limitation motivated the development of peridynamics, reformulating the classical PDEs into integral-differential equations. In this theory, each material point interacts with its neighbours inside a characteristic length-scale through bond-interaction forces. However, while peridynamics can simulate complex multi-physics phenomena, its integration in the study of mechanical systems is still limited. This work presents a methodology that incorporates a peridynamics formulation into a planar multibody dynamics (MBD) formulation to allow the integration of flexible structures described by peridynamics into mechanical systems. A flexible body is described by a collection of point masses, in analogy with the meshless collocation scheme commonly used for peridynamics discretisations. Each point mass interacts with other point masses through nonlinear forces governed by a bond-based peridynamics (BBPD) formulation. The virtual bodies methodology enables the definition of kinematic joints connecting the flexible body with the neighbouring bodies. The implementation of the methodology proposed is illustrated using various mechanisms with different levels of complexity. Notched plates subjected to different loading conditions are compared with the results presented in the literature of the peridynamics field. The deformations of a flexible slider-crank mechanism compare well with the results obtained using a classical flexible MBD formulation. Additionally, three scenarios involving a rotating pendulum illustrate how the methodology proposed allows simulating impact scenarios. The results demonstrate how this methodology is capable to successfully simulate highly nonlinear phenomena, including crack propagation, in a multibody framework.

Characterization and mechanism of petaling failure under high-velocity impact using plastic state-based peridynamics

Petaling failure is one of the most prevalent modes for tubular members exposed to high-velocity impacts. Capturing progressive damage in real-time is crucial for elucidating the trigger mechanism and damage evolution. In this study, a three-dimensional plastic ordinary state-based peridynamics (POSB-PD) was developed to predict the material discontinuity of high-grade X80 steel pipelines under high-velocity impacts. Characteristics of the petaling mode were analyzed quantitatively using cluster analysis and statistical description. The impact processes of petaling formation, including crack propagation, stress triaxiality, bond stretch, and damage number, were systematically discussed. Penetration mechanisms of petaling formation were revealed based on bond breakage and cumulative damage. Intrinsic relationships between mesoscopic defects and macroscopic fractures were established, considering various fracture parameters. A simplified model of energy release rate was established to evaluate the critical fracture condition. These results provided insights into revealing the penetration mechanisms and establishing macro-micro failure linkages for ductile failures in metal structures.

Peridynamic elastic waves in two-dimensional unbounded domains: Construction of nonlocal Dirichlet-type absorbing boundary conditions

The focus of this paper is on application of peridynamics (PD) to propagation of elastic waves in unbounded domains. We construct absorbing boundary conditions (ABCs) derived from a semi-analytical solution of the PD governing equation at the exterior region. This solution is made up of a finite series of plane waves, as fundamental solutions (modes), which satisfy the PD dispersion relations. The modes are adjusted to transmit the energy from the interior region (near field) to the exterior region (far field). The corresponding unknown coefficients of the series are found in terms of the displacement field at a layer of points adjacent to the absorbing boundary. This is accomplished through a collocation procedure at subregions (clouds) around each absorbing point. The proposed ABCs offer appealing advantages, which facilitate their application to PD. They are of Dirichlet-type, hence their implementation is relatively simple as no derivatives of the field variables are required. They are constructed in the time and space domains and thus application of Fourier and Laplace transforms, cumbersome for nonlocal models, is not required. At the discrete level, the modes satisfy the same numerical dispersion relations of the near field, which makes the far-field solution compatible with that of the near field. We scrutinize the performance of the proposed ABCs through several examples. Our investigation shows that the proposed ABCs perform stably in time with an appropriate level of accuracy even in problems characterized by highly-dispersive propagating waves, including crack propagation in semi-unbounded brittle solids.

Mechanical behavior and constitutive model of frozen soil subjected to cyclic impact loading

During the construction and service of projects in cold regions, frozen soil generally experiences strong dynamic loads, such as high-speed collisions and impact tunneling. Notably, during the mining of frozen soil in cold regions, the soil suffers from multiple impact loads owing to the drilling and blasting. To ensure project safety, the deformation and failure of frozen soil near the excavation face under load must be controlled using passive support technology. Thus, the cyclic dynamic response and constitutive model of frozen soil under a one-dimensional strain state must be studied for the safe implementation of projects in cold regions. Cyclic impact is the main driving force for defect development, which can induce multiple types of damage, such as sliding friction and instability propagation of microcracks, non-reversible plastic failure, ice phase transition, and weak interval of structure formation. Frequent impact loading is accompanied by the permeation and reflection of stress waves and the dissipation and propagation of energy, ultimately leading to a decline in the bearing performance of frozen soil, which exhibits dynamic fatigue characteristics. Based on the split Hopkinson pressure bar equipment, this study analyzed the strength deformation characteristics and toughness evolution law of frozen soil under cyclic impact loading and clarified the influence mechanism of damage, the coupling effect between defects, and the connection between wave impedance and the number of cycles. In the process of constructing the constitutive model, first, the slip friction of microcracks was considered based on the meso-mechanical theory. The macro-mesoscale transition and Drucker-Prager yield criteria were combined to construct a mesoscopic constitutive model of frozen soil under passive confining pressure. Subsequently, combined with the irreversible law of energy dissipation, the degradation behavior of frozen soil under cyclic impact loading was characterized by a specific energy absorption value. Furthermore, according to the boundary characteristics and loading conditions, the evolution mode and interaction mechanism of stress-induced defects at the mesoscale were analyzed, including crack propagation, plastic deformation, and progressive thermal damage. A coupling law of multistep damage was constructed based on the wing-shaped crack growth model, cavity collapse model, and relationship between temperature rise and phase transformation. Finally, a thermal–mechanical coupling cyclic mesoscopic model of frozen soil under a one-dimensional strain state was established. The rationality of the model was verified by predicting the strength and deformation behavior of frozen soil over a wide pressure range.

Fatigue testing of cold forging tools using elastomer compression

Cold forging is an ecological production technology for high-strength metal parts. Tool fatigue is the most significant constraint preventing the enhancement of process limits towards complex part geometries. To better analyse tool fatigue, a test method for dies under high inner pressure is researched. The load usually transmitted by the workpiece is applied by compression of elastomers. Results show that the test is able to accurately model the fatigue behaviour of forging tools including crack propagation and the influence of prestressing systems. Compared to conventional fatigue tests, the analysis of different reinforcements and tool geometries is enabled.

Hydraulic fracturing analysis in fluid-saturated porous medium.

This paper addresses fluid-driven crack propagation in a porous medium. Cohesive interface elements are employed to model the behaviour of the crack. To simulate hydraulic fracturing, a fluid pressure degree of freedom is introduced inside the crack, separate from the fluid degrees of freedom in the bulk. Powell-Sabin B-splines, which are based on triangles, are employed to describe the geometry of the domain and to interpolate the field variables: displacements and interstitial fluid pressure. Due to their -continuity, the stress and pressure gradient are smooth throughout the whole domain, enabling a direct assessment of the fracture criterion at the crack tip and ensuring local mass conservation. Due to the use of triangles, crack insertion and remeshing are straightforward and can be done directly in the physical domain. During remeshing a mapping of the state vector (displacement and interstitial fluid pressure) is required. For this, a new methodology is exploited based on a least-square fit with the energy balance and mass conservation as constraints. The accuracy to model free crack propagation is demonstrated by two numerical examples, including crack propagation in a plate with twonotches.

Verification of a fracture model for fiber reinforced concrete beams in bending

Modeling fiber-reinforced concrete at failure by fracture is a challenging task because we need insight into the post-peak behaviour of the model after failure, including crack propagation. In this paper, we present the basic properties of the fiber-reinforced concrete model and its ability to capture the phenomena in three-point bending tests. In this work, we deal with a proof of concept - the verification of the model. The verification of the code includes the selection of the optimal solution algorithm and the selection of the appropriate solution from possible pairs of solutions. Verification of the calculation includes the influence of the number of layers used in the discretisation and, in particular, the influence of the shape of the piecewise defined force–displacement curves of the layers. Only the first stage of verification was performed, i.e. qualitative comparison of the model and experimental results and the influence of the shape of the force–displacement curves. One of the most desirable features of the model is its suitability for subsequent inverse analysis and parameter determination.

High cycle fatigue performance, crack growth and failure mechanisms of an ultrafine-grained Nb+Ti stabilized, low-C microalloyed steel processed by multiphase controlled rolling and forging

An effort has been made to examine the high cycle fatigue (HCF) properties including crack propagation characteristics and related fracture mechanisms of submicron-grained (SG) Nb + Ti stabilized low C steel processed through advanced multiphase-controlled rolling (MCR) and multiaxial forging (MAF). The HCF and other mechanical properties have been correlated with microstructural features characterized by light optical (LOM), transmission electron (TEM) and scanning electron microscopy (SEM), aided with electron backscatter diffraction (EBSD). TEM analysis near the fracture zones of the fatigue tested samples and corresponding fractographic analysis corroborated well in explaining the improved fatigue life of the SG steel. The fatigue strength was found to have a linear relationship with the tensile strength in both types of processed samples. The fatigue strength of the forged specimens was estimated to be nearly twice than that of the untreated annealed steel, demonstrating significantly different fracture characteristics. Intergranular fracture is found to be dominant in the rolled/forged specimens, in comparison to the transgranular fracture observed in the as-received steel. Such variances in fatigue strength and fracture characteristics have been endorsed to their microstructural constituents. Superior combinations of yield strength (YS), tensile strength (UTS), elongation (% El.) and high cycle fatigue strength (σf) (YS = 1027 MPa, %El. = 8.3%, σf = 355 MPa) were obtained in multiphase-controlled 15-cycle multiaxially forged (MAFed) specimens (processed in intercritical α+γ phase regime). An enhancement of the fatigue strength can be ascribed to the formation of evenly dispersed nano-sized fragmented cementite (Fe3C) particles (~35 nm size) present in the SG ferritic matrix (average ~280 nm size). The fine dislocation substructures/cells together with the nano-sized Fe3C particles could efficiently block the initiation and propagation of cracks thereby enhancing the fatigue endurance limit of the steel. Superior mechanical properties together with high fatigue resistance in the SG material render the present steels highly beneficial for high-strength structural applications.

Numerical simulation of crack paths in asphalt mixture using ordinary state-based peridynamics

Cracking creates major distress in asphalt pavements. Because of mathematical complications, existing simulation efforts are incapable of simulating the crack branching and crack coalescence in asphalt mixtures. To overcome this deficiency, this paper developed a two-dimensional (2D) ordinary state-based peridynamics (OSB-PD) method to simulate the entire crack propagation phase, which includes crack propagation, crack branching and crack coalescence. The 2D asphalt mixture digital image was acquired via the X-ray computed tomography method. The Prony series coefficients of the fine aggregate mixture (FAM) were obtained from the dynamic modulus test. The fracture energy of the FAM was determined from the semicircular bending (SCB) test. The measured mixture properties were then input into the 2D OSB-PD numerical method to simulate the crack paths under the SCB test and the three-point bending (TPB) test conditions. The simulated crack paths matched well with those observed from the experiments (at 5% level of significance), thus validating the accuracy of the proposed 2D numerical simulation method. The validated method was finally implemented into the simulation of the crack paths in the laboratory-used asphalt mixture and subjected to compressive loading. The simulation results indicated that the diagonal crack exists when the crack propagates in an asphalt mixture. The diagonal crack then continues to branch and coalesce through the following possible paths until the failure of the asphalt mixture: (a) penetrating through the aggregate; (b) branching along the surface of aggregate in different directions; and (c) coalescing with each other.

SPH-FEM simulation of concrete breaking process due to impact of high-speed water jet

The process of concrete breaking by a high-speed water jet was simulated in this study based on the coupled method of smoothed particle hydrodynamics and the finite element method. The Riedel–Hiermaier–Thoma constitutive model was adopted to describe the mechanical characteristics of the concrete material. Various impact velocities (250–800 m/s) and jet diameters (1.0–3.0 mm) were simulated to investigate the effect of incident parameters on the dynamic responses and damage behaviors of the concrete material. The simulation results were also verified by water-jet impact experiments. The results show that the model can reproduce the nonlinear behaviors of concrete due to the impact of the water jet, including crack propagation, large deformation of the crushing crater, and penetration. For the constant jet diameter, a critical velocity of water-jet flow is identified. Lateral cracks can be generated inside concrete when the impact velocity exceeds the critical velocity, which can enhance the water-jet capability significantly to damage the concrete. The evolution process of the concrete crushing crater is also obtained. The initial shape of the crushing crater is “ω-shaped” and then gradually transforms into “V-shaped” until being penetrated by the water jet. The section shape of the concrete crushing hole is trapezoidal after penetration. For impact velocity v ranging from 250 to 500 m/s, the size of the concrete crushing hole increases with the increase in v, and the section shape tends to be rectangular. If v exceeds 500 m/s, the size and section shape no longer change significantly. It was also found that the greater the diameter of the water jet, the more the sensitivity of crushing hole size on water-jet velocity.

Back-analysis of Donghekou landslide using improved DDA considering joint roughness degradation

Currently, the dynamic behavior of high-speed long-runout landslides triggered by earthquakes remains unclear due to the complexity of such phenomena. Degradation in the shear strength of rock masses is considered a primary factor contributing to the high velocities and long runout distances of these landslides. In this study, the strength degradation induced by changes in rock joint morphology is analyzed considering a numerical model of the Donghekou landslide, by using discontinuous deformation analysis (DDA). First, an exponential joint roughness degradation function (i.e., JRCm) that depends on displacement is incorporated with the nonlinear Barton–Bandis (B–B) shear strength criterion, and this modified B–B criterion is combined with the DDA. Moreover, a virtual joint is introduced in the DDA to model the propagation of cracks in intact rock masses, in order to simulate the dynamic phenomenon of earthquake-induced landslides. Subsequently, this improved DDA (IDDA) is validated via simulations of a shear test and a sliding block over an inclined plane. Finally, the IDDA is employed to simulate the Donghekou landslide, which was induced by the 2008 Wenchuan earthquake in China. Furthermore, the entire dynamic process of the landslide, including crack propagation, instability, initiation, and motion, is depicted. The simulated deposit patterns obtained via the IDDA are in good agreement with the results of field investigations. The simulation results also prove that the IDDA can reflect key movement behaviors of Donghekou landslide and that the degradation of rock joints significantly influences the long runout distance and high velocity of sliding mass.

Layered model of crack growth in concrete beams in bending

Fracture properties of various types of concrete, like plain or fiber reinforced concrete are determined in 3-point bending experiments resulting in a force-displacement diagram. Standard properties of concrete are then determined using technical norms. However, post-peak behavior of concrete, including crack propagation, cannot be described using standard properties. Authors are developing nonlinear, stochastically based material model for concrete to describe post-peak concrete behavior together with crack propagation. One of the most desirable properties of the model is its suitability for later in-verse analysis and parameter determination. Model is based on moment – curvature (m-κ) relation and layered approach to discretization. In this work, we are presenting the basic properties of the model and its ability to capture the phenomena of interest (proof of concept).