Large Crack Propagation Research Articles

Crack propagation determined by energy release rate in cortical bone ultrasonic vibration assisted cutting

In orthopaedic surgery, bone cutting may occur serious mechanical damage due to large crack propagation, which impedes patient postoperative recovery. Ultrasonic vibration assisted cutting (UVAC) has emerged as a leading technique in bone cutting owing to its remarkable advantages, including minimal damage and cutting force. However, how to diminish its damage during bone UVAC remains challenging. Hence, this study established a sophisticated model to calculate the energy release rate for cortical bone UVAC and predicted the critical cutting depths of shear and fracture crack propagation. This superiority stems from the synergistic effects of periodic tool separation and the acoustic softening effect inherent in UVAC, which contribute to a lower average energy release rate and a subsequently reduced cutting force. Nevertheless, the high instantaneous energy release rate during UVAC can exceed the material's critical threshold for crack propagation, leading to the initiation of microcracks and thereby inducing material embrittlement behaviour. These insights shed light on the material removal mechanism of bone UVAC in medical orthopaedic surgery, thus enriching our understanding and potentially guiding further advancements in this field.

3D-printed bioinspired spicules: Strengthening and toughening via stereolithography

Recently, the replication of biological microstructures has garnered significant attention due to their superior flexural strength and toughness, coupled with lightweight structures. Among the most intriguing biological microstructures renowned for their flexural strength are those found in the Euplectella Aspergillum (EA) marine sponges. The remarkable strength of this sponge is attributed to its complex microstructure, which consists of concentric cylindrical layers known as spicules with organic interlayers. These features effectively impede large crack propagation, imparting extraordinary mechanical properties. However, there have been limited studies aimed at mimicking the spicule microstructure. In this study, structures inspired by spicules were designed and fabricated using the stereolithography (SLA) 3D printing technique. The mechanical properties of concentric cylindrical structures (CCSs) inspired by the spicule microstructure were evaluated, considering factors such as the wall thickness of the cylinders, the number of layers, and core diameter, all of which significantly affect the mechanical response. These results were compared with those obtained from solid rods used as solid samples. The findings indicated that CCSs with five layers or fewer exhibited a flexural strength close to or higher than that of solid rods. Particularly, samples with 4 and 5 cylindrical layers displayed architecture similar to natural spicules. Moreover, in all CCSs, the absorbed energy was at least 3–4 times higher than solid rods. Conversely, CCSs with a cylinder wall thickness of 0.65 mm exhibited a more brittle behavior under the 3-point bending test than those with 0.35 mm and 0.5 mm wall thicknesses. CCSs demonstrated greater resistance to failure, displaying different crack propagation patterns and shear stress distributions under the bending test compared to solid rods. These results underscore that replicating the structure of spicules and producing structures with concentric cylindrical layers can transform a brittle structure into a more flexible one, particularly in load-bearing applications.

Experimental study on mechanical and acoustic emission characteristics of sedimentary sandstone under different loading rates

In the field of rock engineering, complexity of stress environment is an important factor affecting its stability. Thus, in view of fracture mechanism of rock under different loading rates within the scope of quasi-static strain rate, four groups of uniaxial compression tests with different strain rates were carried out on sandstone specimens, and strength, deformation, failure modes and acoustic emission characteristics of specimens were compared and analyzed. Furthermore, the fracture mechanism was discussed from the perspective of fracture characteristics based on fractal dimension, crack propagation law inverted through acoustic emission b-value, and micro fracture morphology. The results showed that as the strain rate increased from 10 to 5 s−1 to 10−2 s−1, the fractal dimension of rock fragments increased, and the fractal dimension of rock fragments increased by 9.66%, 7.32%, and 3.77% successively for every 10 times increase in strain rate, which means that the equivalent size of fragments was getting smaller, and the fragmentation feature was becoming increasingly prominent. The crack propagation process based on acoustic emission b-value showed that with the increase of loading rate, the specimen entered the rapid crack propagation stage earlier, in order of 68%, 66%, 29%, and 22% of peak stress. Moreover, the microscopic fracture morphology showed that with the increase of loading rate, transgranular phenomenon was clear, and the fracture morphology changed from smooth to rough. That meant that the fracture of sandstone rock at high loading rates was mainly caused by the propagation of large cracks, which was different from the slow process of initiation, convergence and re-propagation of small cracks at low strain rates.

Large deformation and crack propagation analyses of hydrogel by peridynamics

In this paper, the large tensile deformation and Mode-I crack propagation of hydrogel are effectively simulated by the bond-associated (BA) non-ordinary state-based (NOSB) peridynamics (PD). Based on the nonlocal theory and meshless characteristic, the fracture involving large deformation of hydrogel is solved with simple implementations. In the analysis, the Gent model is first introduced into NOSB PD as the constitutive model to describe the stress-stretch response of hydrogel under a large tensile stretch. The bond-associated scheme is applied to overcome zero-energy modes and numerical oscillation in conventional NOSB PD. Effective stretch criterion is applied to capture the crack propagation. With the explicit dynamic solver, the tensile deformation of a hydrogel sheet with a hole and the crack propagation process of a hydrogel sheet with a pre-notch under pure shear are analyzed. The predicted stress-stretch responses are in good agreement with the experimental observations, which demonstrates the effectiveness and efficiency of the developed PD approach for predicting large deformation and crack propagation of hydrogel.

Simulations of complex crack paths using a robust and cost-efficient continuous–discontinuous approach

Prediction of complex crack propagation is necessary to guarantee performance in service of critical parts of transport vehicles despite the presence of a crack. In cases where linear fracture mechanics assumptions are not valid, e.g. for ductile rupture, this prediction may require continuous–discontinuous strategies to insert a strong discontinuity (i.e. a crack) into a continuous model based on a scalar variable related to material degradation. These strategies still face difficult challenges regarding robustness and cost-efficiency, in particular for 3D problems. To overcome these challenges, it is useful to consider the different ingredients that constitute a continuous–discontinuous strategy and try to optimize each of them. With this perspective, this work addresses the simulation of crack initiation and propagation in ductile metals and proposes new contributions to some rarely addressed points: (i) a simple geometrical approach to initiate realistic crack shapes in 3D meshes, (ii) a new 3D insertion criterion to minimize the number of transfer operations, (iii) a pragmatic remeshing procedure to refine only Active Process Zones, and (iv) an equilibrium recovery method meant to improve the convergence rate after the insertion of a discontinuity.The effectiveness of these new ingredients is demonstrated in 2D axisymmetric, 2D plane strain, and 3D cases in the case of test specimens used to characterize ductile failure in metals. This includes axisymmetric specimens exhibiting cup-cone fracture, plane strain specimens with slant fracture, and pre-cracked CT-like specimens with crack blunting and large crack propagation.

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

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

Effect of annealing treatment on the mechanical properties of spiked-shell aerographite particles

The spiked-shell microparticles of aerographite exhibit excellent flexibility owing to their unique shell structures consisting of radially aligned hollow carbon nanorods. However, their flexibility is likely transitory, and fatigue damages related to imperfections in the crystallinity of their graphitic layers are observed upon cyclic deformation. In this study, aerographite microparticles were heat treated to examine the effects of annealing on their crystallinity and mechanical behaviors. Experimental results showed that the crystallinity of the particles was improved by annealing above 1600 °C; however, excess annealing at 2000 °C caused severe changes in the shell morphology, leading to a lack of flexibility. Single-particle-level compressive test results showed that the particles annealed at 1600 °C performed significantly better in terms of mechanical behaviors by reducing the probability of fracture due to large crack propagation. These particles also exhibited excellent flexibilities in their stress–strain relationships even after 100-times cycle tests. These findings suggest that annealing treatment at 1600 °C is an effective option to improve the mechanical properties of aerographite particles.

A dynamic tensile Tear test methodology to characterise dynamic fracture behaviour of modern High-Grade pipeline steels

Propagating fractures are a considerable risk for high-pressure pipelines transporting natural gas and other resources to various industries. To ensure structural integrity over several decades, the pipe material is subjected to an extensive fracture analysis. Determination of the fracture resistance is a crucial part in safe pipeline design. In this study, a Dynamic Tensile Tear Test (DT3) is investigated in order to address the issues related to the Charpy V-Notch (CVN) and the Drop Weight Tear Test (DWTT). In contrast to current lab-scale tests, the DT3 method applies a dynamic tensile load instead of an impact to fracture a specimen. Consequently, the DT3 test resembles the actual loading conditions of in-service pipelines. Experiments were conducted at room temperature using high-speed camera imaging. An analysis was made of the dynamic crack propagation in a X70 grade pipeline steel. A long fracture ligament of 172 mm allowed to capture a large steady-state crack propagation section of approximately 135 mm. Both phenomena of crack tip flipping (CTF) and the formation of arrowhead markings (AHMs) were observed on the fracture surface. Scanning Electron Microscope (SEM) images revealed a complex ductile–brittle fracture morphology. The experiments were complemented by a numerical analysis using finite element modelling. Ductile crack propagation was simulated using the Modified Bai-Wierzbicki (MBW) damage model. A good correlation between the numerical predictions and experimental data was obtained.

Generalized coordinate smoothed particle hydrodynamics with an overset method in total Lagrangian formulation

AbstractThis study proposes a generalized coordinate smoothed particle hydrodynamics (GCSPH) method coupled with an overset method using the total Lagrangian formulation for solving large deformation and crack propagation problems. In GCSPH, the physical space is decomposed into multiple domains, each of which is mapped to a generalized space to avoid coordinate singularities as well as to flexibly change the spatial resolution. The SPH particles are then non‐uniformly distributed in the physical space (e.g., typically in a boundary‐conforming manner) and defined uniformly in each generalized space, similar to the standard SPH. The SPH particles in the generalized and physical spaces are numerically related by coordinate transformation matrices. The use of non‐uniform particle distributions decreases the total number of particles, thus significantly reducing the simulation cost. Three numerical cases: three‐dimensional brittle crack propagation, Taylor impact, and plugging failure, are presented to validate the proposed method. The numerical results are sufficiently accurate compared with the standard total Lagrangian SPH. Furthermore, these results also show the benefits of GCSPH, which not only effectively reduces the computational cost but also eliminates the effects of particle arrangement. These advantages allow GCSPH to perform high‐resolution three‐dimensional problems, which are otherwise costly to perform with the standard SPH.

Epoxy resin/graphene nanoplatelets composites applied to galvanized steel with outstanding microwave absorber performance

Abstract The necessity of new electromagnetic interference shielding materials has expanded scientific research, especially with regard to microwave frequency range (X-band). In this context, polymer-based composites with nanoparticles – such as graphene – are promising electromagnetic interference shielding materials. In this work, epoxy resin/graphene nanoplatelets (NPG) composites with 0.10, 0.25 and 0.5% w/w were developed and applied to galvanized steel substrates. Dynamic-mechanical tests showed that the addition of NGPs increased the resin rigidity due to molecular restrictions of the organic chains imposed by the NPG. With the increase of the NPG concentration to 0.50%, the impact strength and the adhesion of the composites significantly decreased due to the formation and propagation of large cracks, followed by delamination. The epoxy resin sample containing 0.25% NPG presented the best microwave absorber performance with an increase of 48% in the attenuated energy and 80% in the reflection loss, respectively. Moreover, this sample extended the microwave absorption range to 10 GHz.

A Rock Material Micro-Strength Calibration Model for Bonded Models in Particle Flow Code

Distinct Element Method (DEM) can accurately simulate the large deformation and crack propagation phenomenon of soft rocks. When employing the DEM method via Particle Flow Code, an initial issue is to calibrate the parameters utilized in the model. Typically, trial and error are used to achieve calibration; however, a lack of accuracy and time and effort requirements highly threaten its application. Based on the Parallel Bonded Model (PBM), we researched the bond’s failure criterion in this study. Then, the influence of micro parameters (tension strength σ c and cohesion strength c ) on the rocks’ macro strength and failure mechanisms are studied. Two different test groups were considered by changing the two parameters (1): remains constant (2): σ c remains constant. The results illustrated that rock macro strength is positively correlated with its inferior PBM strength parameters. The macro strength will gradually stabilize at an upper boundary equal to 3.3c or 3.3σ c . With the increasing of c, the rock failure mechanisms vary from block fragmentation to shear failure. In general, the macro strength depends on the coupling effect of c and σ c expressed with an exponential relationship. Through this relationship, only two steps are enough to calibrate the two micro-strength parameters. This research proposed a new way to calibrate PBM micro-strength parameters and provided insight into building the correlation between other micromechanical parameters in the DEM.

GeoMFree[formula omitted]: A package of meshfree local Radial Point Interpolation Method (RPIM) for geomechanics

Mesh-based numerical methods such as the Finite Element Method (FEM) and Finite Difference Method (FDM) are widely used in various fields of science and engineering. However, the shortcomings of mesh-based methods are becoming increasingly obvious mainly due to the distorted or broken elements when analyzing the problems of large deformation or crack propagation. To overcome the above problems, meshfree methods such as the Meshless Local Petrov–Galerkin (MLPG) and Radial Point Interpolation Method (RPIM) were proposed, which can eliminate or partially eliminate the difficulties triggered by mesh-dependence. In geotechnics, the numerical modeling of deformations and failures of soil and rock masses is one of the most important approaches to understand and prevent geohazards, such as landslides and ground subsidence. In this paper, a local RPIM-based meshfree software package GeoMFree3D is specifically developed for analyzing the deformations and failures of soil and rock masses. To enhance the computing capability of GeoMFree3D, (1) effective memory storage strategies are adopted to solve the memory requirement bottleneck; and (2) parallel computing strategies are utilized and heterogeneously implemented on multi-core CPU and many-core GPU to improve the computational efficiency. To demonstrate the performance of GeoMFree3D, three simple verification examples and one application case are presented in this paper. The verification examples indicate that the computational accuracy and efficiency of the package GeoMFree3D is acceptable. Furthermore, the application case indicates that GeoMFree3D is capable of analyzing the displacements of complex rock slopes. GeoMFree3D is currently under intensive development, plans for future work on the development of GeoMFree3D are also introduced.

Crack initiation and propagation in small-scale yielding using a nonlocal GTN model

This study aims at investigating a non-local Gurson-Tvergaard-Needleman (GTN) ductile damage model at finite strains within the framework of small-scale yielding. This model solves the problems of spurious strain localization and volumetric locking. The model is applied to simulate large crack propagation under small-scale yielding and plane-strain mode I conditions. A new method to extract crack length from the porosity field is introduced. Besides, purely numerical parameters are introduced to help convergence. An adequate range is exhibited for each of them so that their impact on the J−Δa crack growth resistance curves remains negligible. A parametric study is performed for several values of the material properties in order to estimate their influence on the crack growth resistance. It is found that the relation between the non-local intrinsic length implicitly introduced by the hardening gradient terms and the width of the damage/strain localization band is quasi-linear; crack tip blunting, crack initiation and large crack propagation can be well captured with the modified GTN model; the numerical formulation is robust; wide ranges for material plasticity and damage parameters can be used in a reliable way so that toughness at crack initiation as well as ductile tearing behavior can be thoroughly studied.

Prediction of ductile crack growth in a narrow gap Inconel dissimilar weld

Predicting the behavior of large ductile crack propagation in a pipe is a major concern for many industries, especially in the nuclear industry. Leaning on the STYLE project, a European experimental program, tests are predicted using the local approach model of Gurson.The mock-up presents a narrow gap INCONEL (nickel base alloy) dissimilar metal weld joining a low alloy ferritic steel pipe and a 316L type stainless austenitic steel pipe. It was performed in the frame of the STYLE project funded by the European Commission (EC) (2010–2013). During the four points bending test on the mockup, the behavior of the crack growth was highly unexpected, and could not be deeply analyzed. The initial crack, located at the interface between the weld and the ferritic Heat-Affected Zone (HAZ), grew in the weld and deviated from it to finally reach the austenitic HAZ. A local approach modeling in order to explain the crack behavior has thus been performed, using the Gurson-Tvergaard-Needlemann (GTN) model.The characterization of the materials composing the weld was made through the STYLE project. Then, GTN parameters are identified using experimental results from the laboratory tests. The behavior of Compact Tension (CT) specimens and the pipe are then numerically predicted using finite element simulations. It is shown that the GTN model is able to catch the mechanical differences between the CT specimens and the pipe, providing a good prediction of the crack propagation during the four points bending test performed for the STYLE project.

Temperature induced structure degradation of yttria-stabilized zirconia thermal barrier coatings

The structural aspects of yttria-stabilized zirconia (YSZ) thermal barrier coatings grown on a polycrystalline alumina substrate have been studied as a function of annealing time at 1250 °C with the use of electron microscopy, X-ray diffraction, and Raman spectroscopy. Upon the high temperature exposure, the feathery morphology of the columnar grains of the as-deposited coatings smoothens out with the concurrent development of surface undulations and grain coarsening. It is shown that the grain coarsening results in significant voiding along the merged grain boundaries and inside YSZ grains. The nucleation and growth of the high density of voids is related to the clustering of vacancies supplied from the merged gaps between columnar grains and subgrains within the columnar grains. The continued development of the voids leads to the formation and propagation of large cracks within the columnar grains, which weakens the overall mechanical integrity of the coating.

High frequency in situ fatigue response of Ni-base superalloy René-N5 microcrystals

A novel in situ scanning electron microscope (SEM), high frequency fatigue testing methodology is developed using a combination of laser milling, focused ion beam fabrication and nanoindentation. This methodology is used to investigate crack initiation, propagation, fracture, fatigue life, and the mechanical response of microcantilever samples of a Ni-based superalloy (René-N5) under different cyclic strain amplitudes. The crack initiation and propagation in the microcantilever is monitored by observing changes in the beam's dynamic stiffness and continuous SEM imaging. The dynamic stiffness response of the micro-beams exhibits a transition from softening to hardening at a critical strain amplitude of 7×10−3. Theoretical analysis indicates that this transition corresponds to the stress required to shear γ′ precipitates. SEM imaging reveals the evolution of significant extrusions, intrusions, and slip traces during cyclic loading above this critical strain amplitude. Below this strain amplitude, very little surface roughening is observed. In addition, the measured dynamic stiffness is observed to exhibit two regimes of decrease after crack initiation. These two regimes correspond to short and large crack propagation. Finally, an overall increase in fatigue life is observed when comparing to bulk scale experiments on nickel-base superalloys. It is proposed that this is an inherent size effect in the small-volume, single crystal specimens tested.

The transition from micro- to macrocrack growth in compacted graphite iron subjected to thermo-mechanical fatigue

The complete fatigue process involving the growth of microstructurally small fatigue cracks prior to macrocrack initiation and the subsequent large crack propagation in notched compacted graphite iron, EN-GJV-400, specimens subjected to thermo-mechanical fatigue has been investigated. It is shown that microcracks are initiated at graphite tips within an extended volume at the notch which eventually leads to an abrupt microcrack coalescence event. As a macrocrack is generated in this way, the crack growth switches to conventional characteristics which is assessed in terms of elasto-plastic fracture mechanics parameters. Consequently, two important implications regarding lifetime assessment are identified; possible underestimation due to (i) how the stress is evaluated in view of the spacial distribution of microcracking and (ii) the crack retardation effect associated with the crack growth transition.

Mechanical-probabilistic evaluation of size effect of fatigue life using data obtained from single smooth specimen: An example using Fe-30Mn-4Si-2Al seismic damper alloy

Abstract A recently developed high Mn austenitic steel damper was found to show an excellent low-cycle fatigue resistance, irrespective of specimen size. To explain the robustness against specimen size, this study proposes a probabilistic prediction method for the effect of specimen size on fatigue life. In the present study, a Fe-30Mn-4Si-2Al model austenitic alloy that shows a superior low-cycle fatigue property was used as a case study. The prediction method is based on the measurement results of the rate of fatigue subcrack propagations, which are separated into two parts: small and large fatigue crack propagations. An important aspect of the prediction is the scatter characteristics of the small and large fatigue crack propagations; the former showed a large scatter in the propagation rate data, while the latter did not show large scatter data. Based on the scatter, two characteristic crack lengths were introduced in the probabilistic analyses: a) a boundary, l 0 , for small and large fatigue crack propagations, and b) a critical fatigue crack length for fracture, l f . Moreover, the effect of specimen size on the small fatigue crack propagation scatter was estimated using a Poisson distribution. The effect of specimen size on the large fatigue crack propagation part was estimated by an exponential approximation of the relationship between fatigue crack length and number of cycles after the l 0 . In addition, the boundary condition between the fatigue crack propagation and the fracture was determined using the critical fatigue crack length for fracture obtained from a fractograph. According to our prediction model, the small fatigue crack propagation lives decreased with an increase in the specimen size, and the large crack propagation lives increased with an increase in the specimen size.

A [formula omitted]-integral-based arc-length solver for brittle and ductile crack propagation in finite deformation-finite strain hyperelastic solids with an application to graphene kirigami

Arc-length methods based on Newton–Raphson (NR) iterative numerical solvers are indispensable in non-linear mechanics to trace the equilibrium curves of systems with snap-back or snap-through behaviours. An example is a crack propagating in a rubber-like solid, which can generate extremely sharp snap-backs when the elastic energy is released.A standard arc-length solver satisfies the arc-length constraint which only limits the increment in displacements and in load level to a fixed amount. Thus, it cannot guarantee the satisfaction of the energy balance in the rate form. This work proposes an arc-length based on the J-integral, and assumes the Griffith balance as a constraint equation.Firstly, a fracture criterion (critical load and direction of crack increment) is formulated, consistent with the thermodynamic principle of maximum dissipation: a crack propagates in the direction of the maximum strain energy release rate. For this purpose, this paper provides an explicit and simple expression of the J-integral for varying angles. This fracture criterion does not require the computation of mixed mode Stress Intensity Factors, or asymptotic solutions or derivatives of the tangent stiffness matrix. By doing so, it is shown that the proposed method easily reconciles with the theory of Configurational Forces.Secondly, because of the explicit expression of J provided in this paper, it is easy to linearize the discretized equations of motions consistently.The method proves able to handle very sudden snap-backs occurring under large strains, and both brittle and ductile crack propagation. A particular example of such behaviour is kirigami (paper-cuts) structures made of graphene. The proposed arc-length can capture, for these structures, the transitions from brittle to ductile crack propagation for the same crack patterns, but different pre-crack lengths.

A Runge–Kutta–Chebyshev SPH algorithm for elastodynamics

A stable and accurate Smoothed Particle Hydrodynamics (SPH) method is proposed for solving elastodynamics in solid mechanics. The SPH method is mesh-free, and it promises to overcome most of disadvantages of the traditional finite element techniques. The absence of a mesh makes the SPH method very attractive for those problems involving large deformations, moving boundaries and crack propagation. However, the conventional SPH method still has significant limitations that prevent its acceptance among researchers and engineers, namely the stability and computational costs. In approximating unsteady problems using the SPH method, attention should be given to the choice of time integration schemes as accuracy and efficiency of the SPH solution may be limited by the timesteps used in the simulation. This study presents an attempt to reconstruct an unconditionally stable SPH method for elastodynamics. To achieve this objective we implement an explicit Runge–Kutta Chebyshev scheme with extended stages in the SPH method. This time stepping scheme adds in a natural way a stabilizing stage to the conventional Runge–Kutta method using the Chebyshev polynomials. Numerical results are shown for several test problems in elastodynamics. For the considered elastic regimes, the obtained results demonstrate the ability of our new algorithm to better maintain the shape of the solution in the presence of shocks.