Crack Nucleation Process Research Articles

An interlaminar fatigue damage model based on property degradation of carbon fiber-reinforced polymer composites

Interface delamination is a significant damage mechanism in fiber-reinforced polymer (FRP) laminated composites caused by interlaminar normal and shear stresses. This is due to the low interlaminar properties including interface stiffness and strength that continuously degrade to cause fatigue crack nucleation and growth. In this respect, an interlaminar fatigue damage model is proposed to accurately address the reliability aspect of the FRP composite materials and structures. The model considers a damage process that consists of two stages: (1) fatigue damage evolution due to interlaminar properties degradation to the onset of crack nucleation. A cyclic cohesive zone model with a bilinear softening behavior is introduced along with the fatigue life model to capture the mean stress effect of the interface. This is followed by (2) the crack nucleation process leading to the physical separation/debonding of the interface material point, as governed by the cycle-dependent fracture energy dissipation. The mechanical prediction of the interlaminar fatigue damage process is illustrated through finite element simulation of a mixed-mode flexural test of a carbon fiber-reinforced polymer (CFRP) composite beam subjected to fatigue loading. The results indicate that the interlaminar normal and shear crack opening displacement increases exponentially with the larger number of load cycles. In addition, the high-stress gradient is limited to the interface crack front zone with the normal and shear stress peaks at 69.2 and 16.5 % of the respective interlaminar strength. Moreover, controlled interlaminar crack growth is initially foreseen at 7.0 × 10-6 mm/cycle, followed by an abrupt crack “jump” at 287,000 load cycles.

Understanding the Drying Process and Mud Cracking of Li-Ion Battery Electrodes through Synchrotron X-Ray Computed Tomography

The drying process of slurry cast Li-ion battery electrodes is a subject with significant impacts on the performance of the battery but where detailed understanding is lacking(1). Mud cracking, opening of cracks in the surface due to stress from the slurry shrinking as it dries, is the most dramatic phenomenon during the process. Cracks may be detrimental to electrode performance due to delamination, which makes sections of the electrode unusable, or generally poor electrode cohesion. However, cracks could provide channels for ion transport to deeper levels of the electrode, similar to templated electrodes (2) but without the extra manufacturing steps. Cracking is prominent in thick (3-5) or water processed electrodes (3), which are desirable for greater energy density and replacement of the toxic solvent N-methyl pyrrolidone (NMP), respectively. Thus, understanding mud cracking during drying can lead to more energy dense (thicker), greener (without toxic NMP), and better performing electrodes (fast charging).Li-ion electrodes are industrially produced by casting a slurry on a metal foil current collector by a slot die or doctor blade method in a roll-to-roll machine. In the case of the positive electrode this slurry typically contains active metal oxide (e.g. LiNiMnCoO2, LiNi0.6Mn0.2Co0.2O2) particles, polyvinylidene fluoride (PVDF) binder, and carbon black. Drying is composed of three stages illustrated in Fig. 1 a-d, with the binder, carbon black settling and migrating at random (1),(6, 7). Crack formation is thought to occur during the third stage when capillary forces cause stress in the drying slurry opening cracks as solvent menisci form between particles. However, the process of crack nucleation and their 3-dimensional growth has never been directly observed in-situ(1),(4). X-ray computed tomography (Fig. 1 f-j) is able to show the morphology of cracks in an electrode and can be used to characterize properties like delamination, crack volume, crack network connectedness or crack network tortuosity, which can be linked to electrode performance. However, to understand how these crack networks form requires observation of the time evolution of the cracks and the movement of active material particles near the cracks, which requires fast measurements. Here, we present synchrotron x-ray computed tomography of drying electrode which enable the fast measurements required and allows us to more fully explain mud cracking in drying electrodes, and the drying process in general.References Y. S. Zhang, N. E. Courtier, Z. Zhang, K. Liu, J. J. Bailey, A. M. Boyce, G. Richardson, P. R. Shearing, E. Kendrick and D. J. L. Brett, Advanced Energy Materials, 2102233 (2021). C. Huang, M. Dontigny, K. Zaghib and P. S. Grant, Journal of Materials Chemistry A, 7, 21421 (2019). Z. Du, K. M. Rollag, J. Li, S. J. An, M. Wood, Y. Sheng, P. P. Mukherjee, C. Daniel and D. L. Wood, Journal of Power Sources, 354, 200 (2017). B. Lu, C. Ning, D. Shi, Y. Zhao and J. Zhang, Chinese Physics B, 29, 026201 (2020). R. Sahore, D. L. Wood, A. Kukay, K. M. Grady, J. Li and I. Belharouak, ACS Sustainable Chemistry & Engineering, 8, 3162 (2020). S. Jaiser, L. Funk, M. Baunach, P. Scharfer and W. Schabel, Journal of Colloid and Interface Science, 494, 22 (2017). Y. S. Zhang, A. N. Pallipurath Radhakrishnan, J. B. Robinson, R. E. Owen, T. G. Tranter, E. Kendrick, P. R. Shearing and D. J. Brett, ACS Applied Materials & Interfaces, 13, 36605 (2021). Figure 1

An innovative quasi-bond approach to bridge continuity, anisotropic damage and macroscopic fracture of solids and structures

Spontaneous formation and evolution of discontinuities in solid media still poses one of the significant challenges in solid mechanics and computational mechanics. To facilitate numerical modeling, a new model called herein ‘quasi-bond’ model is proposed, which redefines the form of local interaction between material particles. Unlike traditional discrete methods that require direct connections between material particles, in this quasi-bond method, only one end of each bond is actually connected to a material particle, rendering great flexibility in describing bond distribution and anisotropic damage by bond breakage. Homogenization of solid body can be performed by an integral over quasi-bonds, while the process of crack nucleation, propagation and coalescence to form fracture is simulated through bond breakage. Especially, the relationship between material elastic constants and bond stiffness parameter is established in both two- and three-dimensional contexts. Furthermore, a smoothed strain-based fracture description is proposed with the ability of eliminating particle density/distribution dependence problems. Finally, several benchmark tests are conducted to demonstrate the efficiency and accuracy of the proposed approach in solving elasticity and fracture problems.

Research on low‐cycle fatigue behavior of Ni‐based single crystal superalloy with shaped film cooling holes at high temperature

AbstractFilm cooling holes (FCHs) geometric structure significantly affects low‐cycle fatigue (LCF) of the single crystal turbine blade. This study investigates the LCF behavior of Ni‐based single crystal plate specimens with two different structure FCHs, including elliptical and fan‐shaped FCHs, by high temperature fatigue tests and crystal plasticity simulation. The results show that the LCF life of the fan‐shaped FCHs is shorter than those of the elliptical FCHs. The fracture characteristics and microstructure evolution of different structure FCHs are dissimilar. Oxidation affects the fatigue crack nucleation process at the FCH edge. The resolved shear stress (RSS) around fan‐shaped FCHs is greater than elliptical FCHs under one cyclic stress, and the area with larger RSS is consistent with fatigue crack nucleation position. The early LCF failure is mainly attributed to the high temperature oxidation of the local slip deformation induced by RSS concentration around the FCHs.

Simulation of fluid driven crack propagation along metal/elastomer interface - Application to the numerical analysis of the rubber cord adhesion inflation test

The Rubber Cord Adhesion Inflation Test (RCAIT) has been proposed as an alternative technique to more standard pull out protocols such as H, T or pull out tests for characterizing the adhesion between cord/cable reinforcement and rubber. During this test, a fluid is injected in between a wire and a rubber cylindrical envelope to provoke the interface separation once a critical pressure is reached. A simple energy balance analysis is used to evaluate the critical strain energy release rate, GC, which drives the crack propagation from measurable quantities. However, some assumptions should be assessed to ensure reliable GC evaluation. Then, a predictive finite elements simulation of the RCAIT is proposed to simulate the fluid driven crack nucleation and propagation process along the rubber cord interface. These results are compared with the ones obtained from the RCAIT simplified analysis.

Statistical continuum damage healing mechanics (SCDHM)

Damage healing mechanics has been under tremendous development during the past decade in which many constitutive models for different classes of materials have been proposed in the literature. However, to bridge the gap between the physics of healing and the theoretical framework, the statistical nature of the damage healing mechanics must be considered. The statistical nature of the crack nucleation and propagation processes is well-known, and the healing mechanisms follow similar probabilistic processes. In general, the healing process consists of two steps: (I) sealing, in which the free crack surfaces are brought in contact with the help of external forces, and then, (ii) healing, which may include a variety of techniques including the flow of molten polymers or liquid healing agents into the crack free surface areas and solidifying. Both sealing and healing processes can be considered within statistical mechanics to include multiple uncertainties involved in the healing process. This work proposes a framework to integrate statistical mechanics into the continuum of damage healing mechanics. The proposed statistical damage healing mechanics may help designers and scientists to perform more realistic simulations for components under complex damage and healing cycles. The key outputs of the proposed statistical framework are (I) healing method choice, and (II) healing parameter optimization.

Multi-dimensional non-uniform deformation and failure of siltstone determined using acoustic, 3D-digital image correlation, and computed tomography

Uniaxial compression tests monitored using linear variable differential transformers (LVDTs), digital image correlation (DIC), computed tomography (CT), acoustic emission (AE), and ultrasonic velocity were utilized to study the multi-dimensional non-uniform deformation and failure characteristics of siltstone. Under one-dimensional (1D) conditions, the characteristic stress of the siltstone was determined by the AE counts, ultrasonic velocity, and volumetric strain measured by the extensometer. Under two-dimensional (2D) conditions, zonal disintegration was observed on the apparent fracture of the siltstone specimen. The crack nucleation process, stress release characteristics, and crack type were analyzed in the “broken area,” “penetrating crack area,” and “non-penetrating crack area” under different characteristic stress states. Subsequently, the evolution of the non-uniformity coefficient of the 2D strain field with the 1D characteristic stress was established. Under three-dimensional (3D) conditions, the fracture size of the siltstone was divided according to the equivalent length of fracture volume, and the spatial distributions of macro-, meso-, and microfractures were analyzed. The siltstone 3D zonal disintegration phenomenon was further quantitatively described by calculating the fractal dimensions of fractures in different radius ranges. Finally, the AE source localization method was improved by modifying the wave velocity. The transformation of the primary and secondary bearing areas in different stress stages was revealed based on the spatio-temporal evolution of the AE sources with different energy levels.

A Probabilistic Model for Forging Flaw Crack Nucleation Processes for Heavy Duty Gas Turbine Rotor Operations

Abstract We present a probabilistic model for quantifying the number of load cycles for nucleation of forging flaws—for a 3.5NiCrMoV high strength low alloy rotor steel—into a crack under gas turbine operating conditions. The model correlates low cycle fatigue data, ultrasonic testing indication data, flaw morphology, and type with the nucleation process. This paper is the third of a series of publications presenting this modeling approach progressively. It focuses on the effect of temperature variation on the nucleation life of forging flaws. We quantified the number of cycles to crack nucleation was for specimens that included forging flaws at elevated temperatures. Flaws of different sizes and shapes are effectively described at respective temperature and stress levels by either an ellipsoidal finite element model or an analytical area-based model. A local probabilistic low-cycle fatigue model analyzes the resulting stress distributions accounting for statistical size effects. Via Maximum Likelihood Estimation of these probabilistic low cycle fatigue results, a probabilistic model for crack nucleation of forging flaws is obtained. This proposed probabilistic model is based on experimental data for realistic heavy duty gas turbine rotor temperature and stress conditions. It can be utilized in the energy sector for component life time quantification. Our suggested approach can support component assessment under flexible gas turbines operation conditions driven by increased availability of intermittent renewable energy sources.

Fabricating Ti–22Al–25Nb intermetallic with ductility higher than 25% by advanced printing technique: Point-forging and laser-deposition

PF-LD is an advanced printing technique which introduces point-forging (PF) into the process of conventional laser-deposition (LD). Ti–22Al–25Nb intermetallic fabricated by PF-LD technique presented the excellent combination of room-temperature ultimate tensile strength (UTS: 1050.1–1169.3 MPa) and elongation after failure (EL: 20.8%–25.7%). An elaborately designed controlled trial by simultaneous use of LD and PF-LD techniques was employed to investigate the effect of PF on LD microstructural evolution. The results pointed out that the occurrence of static recrystallization (SRX) was the essential reason for the ultra-high mechanical properties. Both mechanisms of continuous-SRX (CSRX) and discontinuous-SRX (DSRX) played an important role in grain refinement. By in-situ forging and subsequent re-heating, the coarse columnar grains were first broken into fine equiaxed grains through progressive subgrain rotation. After two-pass PF-LD, the solidification texture <100>//DD disappeared while no obvious recrystallization texture was found. In subsequent PF-LD process, micron-scale CSRX grains were developed within original equiaxed grains through repeated polygonization and progressive subgrain rotation while DSRX grains appeared along grain boundaries driven by the differential dislocation density. We elucidated the excellent mechanical properties by detailed microstructural analysis. The results revealed that the finer equiaxed grains and the reasonable phase composition (O + BCC) greatly retarded the process of crack nucleation and propagation resulting in the typical micro-void accumulation ductile fracture while both high-density dislocations and finer recrystallized grains were beneficial to strength enhancement.

A computational algorithm for random particle breakage

Random breakage can be defined as the breakage patterns independent from the stressing environment and the nature of the broken particle. However, the relevant literature studies give contrary evidence against random breakage of particles. A simple way to detect random breakage is to evaluate the fragment (progeny) size distributions. Such distributions are estimated analytically or through numerical models. The latter models generally treat random breakage as a geometric statistical problem with prior assumptions on particle/flaw geometry and external stressing environment, which may violate the randomness of the breakage process. This study presents a random-breakage algorithm that does not require such assumptions. The simulated progeny size distributions were compared with the experimental size distributions by impact loading (drop-weight) tests. Random breakage events should yield number-weighted size distributions that is fitted well to the lognormal distribution function. Also, a mass-weighted (sieve) size distribution function is presented for random breakage. Nevertheless, the results refute the random breakage of clinker and other brittle particles after impact loading. Instead, the sieve size distribution of fragments may evolve due to crack branching/merging and Poissonian crack nucleation processes.

Crack nucleation and propagation in the phase-field cohesive zone model with application to Hertzian indentation fracture

Hertzian indentation fracture (Hertz, 1896) is an intriguing problem with no pre-defects. Recent studies indicated that those popular phase-field models for brittle fracture might be restrictive in dealing with this problem — crack nucleation can be considered only for the failure strength within a rather limited range. In this work, this problem is analyzed by the phase-field cohesive zonde model (PF-CZM), focusing on the whole failure process of crack nucleation and propagation. Analytical and numerical results show that for any realistic failure strength, the ‘spontaneous’ crack nucleation in an initially defect-free surface, the subsequent small but rapid vertical extension and finally the stable cone-shaped crack propagation, etc., can all be qualitatively and quantitatively captured by the PF-CZM with no modification. This competence is credited to treating the failure strength and the fracture energy (toughness) as two independent material properties. Accordingly, the phase-field length scale is a numerical parameter of no further constraint, which can be made as small as possible such that the convergence to the Barenblatt (1959) cohesive zone model is guaranteed even for short cracks. Moreover, the seamless incorporation of the strength-based crack nucleation criterion and the energy-based crack propagation criterion endows the PF-CZM with the capability of tackling crack nucleation and propagation in pristine solids.

Crack nucleation at forging flaws studied by non-local peridynamics simulations

We present a computational study and framework that allows us to study and understand the crack nucleation process from forging flaws. Forging flaws may be present in large steel rotor components commonly used for rotating power generation equipment including gas turbines, electrical generators, and steam turbines. The service life of these components is often limited by crack nucleation and subsequent growth from such forging flaws, which frequently exhibit themselves as non-metallic oxide inclusions. The fatigue crack growth process can be described by established engineering fracture mechanics methods. However, the initial crack nucleation process from a forging flaw is challenging for traditional engineering methods to quantify as it depends on the details of the flaw, including flaw morphology. We adopt the peridynamics method to describe and study this crack nucleation process. For a specific industrial gas turbine rotor steel, we present how we integrate and fit commonly known base material property data such as elastic properties, yield strength, and S-N curves, as well as fatigue crack growth data into a peridynamic model. The obtained model is then utilized in a series of high-performance two-dimensional peridynamic simulations to study the crack nucleation process from forging flaws for ambient and elevated temperatures in a rectangular simulation cell specimen. The simulations reveal an initial local nucleation at multiple small oxide inclusions followed by micro-crack propagation, arrest, coalescence, and eventual emergence of a dominant micro-crack that governs the crack nucleation process. The dependence on temperature and density of oxide inclusions of both the details of the microscopic processes and cycles to crack nucleation is also observed. The results are compared with fatigue experiments performed with specimens containing forging flaws of the same rotor steel.

A Probabilistic Model for Forging Flaw Crack Nucleation Processes

Abstract A probabilistic model for quantifying the number of load cycles for nucleation of forging flaws into a crack has been developed. The model correlates low cycle fatigue (LCF) data, ultrasonic testing (UT) indication data, flaw morphology and type with the nucleation process. The nucleation model is based on a probabilistic LCF model applied to finite element analyses (FEA) of flaw geometries. The model includes statistical size and notch effects. In order to calibrate the model, we conducted experiments involving specimens that include forging flaws. The specimens were machined out from heavy duty steel rotor disks for the energy sector. The large disks, including ultrasonic indications on the millimeter scale, were cut into smaller segments in order to efficiently machine specimens including manufacturing related forging flaws. We conducted cyclic loading experiments at a variety of temperatures and high stresses in order to capture realistic engine operating conditions for flaws as they occur in service. This newly developed model can be incorporated into an existing probabilistic fracture mechanics framework and enables a reliable risk quantification allowing to support customer needs for more flexible operational profiles due to the emergence of renewable energy sources.

Crack nucleation from non-metallic inclusions in aluminum alloys described by peridynamics simulations

Conventional engineering methods oftentimes have challenges in the quantification of crack nucleation processes from manufacturing defects that are relevant for engineering component lifing. We present peridynamic simulation framework for the description of the crack nucleation process from cluster of non-metallic inclusions in aluminum alloys. Our non-local simulation framework characterizes crack nucleation process as multiple micro-crack nucleation events from individual inclusions, and eventually one micro-crack dominates. We define individual stages of the crack nucleation process, i.e., nucleation, micro-crack, technical, and crack initiation, that allow a quantification and meta model development of both the individual stages and the entire crack nucleation process.

Effects of infilling materials on mechanical behaviors and cracking process of pre-cracked rock: Insights from a hybrid continuum-discontinuum method

The process of crack nucleation, initiation and propagation are of great significance in rock engineering such as hydrofracturing, underground excavation and gas or petroleum industry. In this study, the fracturing process of rock models with filled-flaws are mimicked by the hybrid continuum-discontinuum method. The effects both on mechanical response and cracking behaviors induced by the frictional properties including cohesion and friction coefficients of infilling materials are investigated. The results indicated that the minimum crack initiation stress of infilled flawed specimens lie in the inclination angle of 45–75° with different cohesions. When the friction angle changes, the minimum crack initiation stress appears when the inclination angle is in the range of 15–60°. The inclination angles are in accordance with that value when the normalized stress intensity factor of K1 acquired by changing cohesion and friction angle reaches maximum in the sliding crack model. Besides, with the increasing of cohesion and friction angle, the transition from wing crack to secondary crack appeared. The crack initiation sequence and pattern are comparable with the laboratory test.

Remarks on dynamic cohesive fracture under static pre-stress — with a comparison to finite fracture mechanics

The role of inertia effects during crack formation under non-singular static pre-stress is investigated by utilizing a linear softening cohesive zone model. In case of a 1D tensile bar, the closed-form solution shows that during the finite time of decohesion about one third of the released strain energy is converted into kinetic energy. In case of crack initiation from a circular hole in a 2D plate under remote tension or compression, results from dynamic finite element analyses utilizing the same cohesive zone model are compared with predictions from finite fracture mechanics which assumes the spontaneous formation of a finite crack increment. While both methods capture the overall critical load for crack initiation at the hole well, the highly transient process of crack nucleation (not accounted for by finite fracture mechanics) is resolved by the numerical cohesive zone model analyses and displays a complex dependence on the hole radius.

Strength-induced peridynamic modeling and simulation of fractures in brittle materials

This paper presents a hybrid peridynamics and classical continuum mechanics modeling approach for brittle fracture, in which peridynamics is activated according to a strength criterion. The proposed approach represents a new way of simulating the fracture process, including elastic deformation and crack nucleation and propagation. Classical continuum mechanics and peridynamics are coupled into a closed equation system, and an adaptive algorithm is developed to solve it. The algorithm initially employs classical continuum mechanics throughout the entire structure to describe its mechanical response. Once the stress state of a point reaches the strength of the material, peridynamics is adaptively activated in the vicinity of that point to further describe the crack nucleation and propagation processes. Two-dimensional numerical examples illustrate that successful fracture simulations of complex structure can be achieved by this approach.

Crack nucleation in the adhesive wear of an elastic-plastic half-space

The detachment of material in an adhesive wear process is driven by a fracture mechanism which is controlled by a critical length-scale. Previous efforts in multi-asperity wear modeling have applied this microscopic process to rough elastic contact. However, experimental data shows that the assumption of purely elastic deformation at rough contact interfaces is unrealistic, and that asperities in contact must deform plastically to accommodate the large contact stresses. We therefore investigate the consequences of plastic deformation on the macro-scale wear response using novel elastoplastic contact simulations. The crack nucleation process at a rough contact interface is analyzed in a comparative study with a classical J2 plasticity approach and a saturation plasticity model. We show that plastic residual deformations in the J2 model heighten the surface tensile stresses, leading to a higher crack nucleation likelihood for contacts. This effect is shown to be stronger when the material is more ductile. We also show that elastic interactions between contacts can increase the likelihood of individual contacts nucleating cracks, irrespective of the contact constitutive model. This is supported by a statistical approach we develop based on a Greenwood–Williamson model modified to take into account the elastic interactions between contacts and the shear strength of the contact junction.

Modeling the fretting fatigue endurance from partial to gross slip: The effect of debris layer

Abstract Fretting Fatigue (FF) appears as a key damaging process in many industrial assemblies subjected to vibrations. In this study, the “U-shape” experimental fretting fatigue endurance evolution of a 35NiCrMo16 steel cylinder/plane contact versus the applied displacement amplitudes is simulated using a complete finite element modeling. This method takes into account the crack nucleation process, the crack propagation phenomenon but also surface wear as well as the evolution of the “third body” debris layer entrapped within the interface. This dynamic simulation of the fretting fatigue endurance from partial to gross slip condition confirms that surface wear effects can be neglected under partial slip but must be taken into account including the debris layer effect, in order to predict the fretting fatigue endurance under gross slip conditions. An original “DSN“ fretting fatigue chart strategy allowing a global description of the fretting fatigue damage (wear, crack nucleation and failure) as a function of the displacement amplitude, fatigue stress and loading cycles is introduced and discussed.

Atomistic mechanisms of crack nucleation and propagation in amorphous silica

This paper presents an atomistic understanding of the nanoscale processes that govern crack nucleation and propagation in amorphous silica using a combination of theoretical calculations and molecular dynamics simulations with the ReaxFF potential. We show that both crack nucleation and propagation are governed by chainlike nanoscale virial stress-fibers formed by an intricate mixture of Si and O atoms. The stress-fibers are of a few nanometers in length, aligned parallel to the loading direction, and spatially localized at the evolving crack front at the nucleating site or a propagating crack tip. They form and break continuously during the crack nucleation and propagation process and are responsible for localizing stress at the crack nucleation site or propagating crack front. As soon as the stress-fibers reach a critical density the material starts nucleating cracks or leads to the propagation of initial crack. Additionally, the virial stress fields in the domain is highly heterogeneous and species-dependent---and the O and Si atoms play fundamentally distinct roles throughout the deformation process. With increased loading, heterogeneity in virial stress for the Si atoms goes up, whereas for the O atoms it goes down. Furthermore, from the virial and Hardy estimates of atomic stress, it is found that the stress field emanating from the crack tip decays as $1/r$. Also, presence of holes or pores within the interaction distance of a crack tip intensifies the stress state of the stress-fibers near the crack front leading to an improved effective toughness compared to the situation where the pore is far from the crack tip. Nucleation and propagation of cracks are strictly mediated by a complex admixture of localized bond rupture processes across a set of interacting stress-fibers. The details of the atomistic process regulating the underlying mechanisms are undetectable from the macroscopic stress-strain data.