Flat Crack Research Articles

Machine learning for nano-level defect detection in aligned random carbon nanotubes-reinforced electrically conductive nanocomposite

Machine learning allows fast nano-scale defect detection in polymer-impregnated aligned carbon nanotube (CNT) nanocomposites. Digital twins were populated by TEM-validated geometry; considered defects were flat cracks and close-to-spherical voids. Finite-element analysis of piezoresistive response was conducted by embedment of CNT network into matrix. Identification of a defect by change in CNT network piezoresistivity was challenged by: (1) randomness of CNTs’ shapes and placement, ML training happened on random realisations; (2) high strength of CNTs leading to the preservation of conductive paths along CNTs and changes only in conductivities of tunnelling contacts. “Artificial approximation“ was introduced to economise computer time multi-fold: ML was trained on cases with artificially degraded tunnelling conductivities within the defect. Three ML models: XGBoost, fully connected, and convolution neural networks were employed. All models managed the task for near-spherical voids, but performed poorly for flat cracks, due to the limited number of tunnelling contacts in crack volume. When trained on the mixed set of voids and cracks, both neural networks demonstrated the ability to learn the difference and detected even cracks, while XGBoost was not up to the challenge. By metrics, the convolutional neural network demonstrated the highest accuracy of predictions.

Ductile shear damage micromechanisms studied by correlative multiscale nanotomography and SEM/EBSD for a recrystallized aluminum alloy 2198 T8

The damage mechanisms of ductile fracture under shear loading of an aluminum alloy 2198T8R were studied using flat thin-sheet samples. One sample was loaded until 85% of the failure displacement and then unloaded, and another one was loaded up to failure. To overcome the inherent shortcomings of nanotomography concerning the investigation of flat samples, synchrotron nano-laminography was applied to the pre-loaded sample and provided structural information down to the nanometer scale, allowing ductile damage nucleation and evolution to be studied. The damage features, including flat cracks and intermetallic particle-related damage, were visualized in 3D from the highly-deformed shear band region. Using nano-laminography, no nano-voids were found. The damaged shear ligament was also observed after polishing via destructive correlative scanning electron microscope (SEM) and electron back-scatter diffraction (EBSD) which suggests that the detrimental flat cracks were both intergranular and transgranular. The flat cracks were related to highly-deformed bands. No nano-voids could be found using SEM analysis. Fractography on the second broken sample revealed that the flat cracks contained hardly observable nanometer-sized dimples. The final coalescence region was covered by sub-micrometer-sized dimples, inside which dispersoid particles were present. The fact that no nano-void was found for the pre-deformed sample implies that the nucleation, growth and coalescence of these sub-micrometer-sized voids occur at late stages of the loading history.

Optical properties and nanosecond laser damage characterization of liquid crystal polarization gratings

Liquid crystal polarization gratings (LCPGs) possess unique optical properties and therefore are widely used in laser systems. Therefore, developing our understanding of the laser damage resistance of LCPGs is critical for future high-intensity laser applications. In this study, the LCPGs (Λ = 8 μm) were fabricated from liquid crystal polymer (LCP) films with photo-alignment technology, which had a small-angle (∼7.51°) diffraction order with high diffraction efficiency (∼92 %) under chiral polarized incidence at 1064 nm. The diffraction efficiency and polarization of each diffraction order were determined by the polarization of the incident light. The damage characteristics of the LCPGs were investigated using a chiral polarized nanosecond laser at 1064 nm in a one-on-one test. The laser-induced damage thresholds (LIDTs) of left-handed circular polarization (LHCP) and right-handed circular polarization (RHCP) were 8.0 J/cm2 and 8.5 J/cm2, respectively. For comparison, the LIDTs of S-polarization and P-polarization were 7.8 J/cm2 and 8.4 J/cm2, respectively. All the damage occurred at the interface between the LCP layer and the substrate when the laser fluence was near the LIDT, and the damage morphology was observed with a scanning electron microscope (SEM), including flat pits, cracks, and bumps at the edge of the pits. The results indicate that the LIDTs and damage morphology of the LCPGs were insensitive to the polarization of the irradiation. The electrical effects of differently polarized irradiation on the LCPGs were simulated using the finite element method (FEM). The electric field distribution was symmetrical under irradiation by LHCP and RHCP lasers. However, the distribution of the electric field under different linearly polarized irradiation conditions were distinct. Based on these findings, we believe that the contribution of chiral polarized irradiation to the damage was consistent and that the LIDTs were similar. This study has important implications for the application and development of LCPGs in high-intensity laser systems.

Effect of microstructure on impact fracture mechanism of a high-strength Ti-5Al-7.5V-0.5Si-0.25Fe-0.2O alloy

The impact property of high-strength Ti-5Al-7.5V-0.5Si-0.25Fe-0.2O alloy (Ti575) with trimodal microstructure (TM) and lamellar microstructure (LM) were investigated by combining instrumented Charpy U-notch impact test with microstructure characterization. Impact load-displacement curves illustrated that the higher impact toughness of LM (47.8 J/cm2) than TM (38 J/cm2) were attributed to both intrinsic toughening during crack initiation and extrinsic toughening during crack propagation. In crack initiation stage of LM, electron back-scattered diffraction (EBSD) evidenced the nucleation of numerous {10–12} <–1011> tensile twins in coarsened lamellar α (αl) in vicinity of the crack notch. The high intrinsic toughness of LM was due to the dynamic microstructure refinement and facilitation of prismatic/pyramidal slip induced by twins during impact. For TM in contrast, smaller-sized primary α(αp) and αl suppressed the nucleation of twins, exacerbated stress concentration and reduced plastic deformation near the crack notch. In crack propagation stage, the kinking, shearing of αl, crack deflection at αl/β interfaces and secondary crack in αl colony borders contributed to a tortuous crack path and large energy dissipation in LM, whereas crack could bypass αp and cut through thin αl in TM easily, resulting in a flat crack path and poor extrinsic toughness of TM. In summary, this work provided a basic understanding of the impact fracture mechanism of Ti575 with different microstructures.

The elasticity-conductivity connection for materials with cracks of arbitrary shapes and orientation distributions

The cross-property connection between the effective elastic and conductive properties of a solid with cracks has been first given by Bristow (1960) for randomly oriented cracks, assuming that cracks have circular (penny) shapes. However, cracks in materials typically have “irregular” shapes and this factor, generally, has strong effect on the said properties (the strong stiffening effect produced by contacts between crack faces is an example). In addition, shapes of 3D cracks (for example, the statistics of the mentioned contacts) may be largely unknown. These factors make it difficult to estimate the effect of cracks on the elastic properties. We show that flat cracks of arbitrary shapes and orientation distributions produce similar effects on the elastic and conductive properties, so that changes of stiffnesses can be monitored by changes in electric conductivities. Extension to transversely isotropic materials is given. Possible extensions to non-flat crack shapes are discussed.

On an annular crack near an arbitrarily graded interface in FGMs

Annular cracks can be generated during the fabrication of materials and around the pre-existing defects. Previous works on the annular crack problems were most limited to homogenous materials. This paper extends the analysis and examines the axisymmetric problem of a flat mixed-mode annular crack near and parallel to an arbitrarily graded interface in functionally graded materials (FGMs). The crack is modelled as plane circular dislocation loop and an efficient solution for dislocation in FGMs is used to calculate the stress field at the crack plane. The three-parts mixed boundary value problem is solved by a series expansion method. Analytical solutions of the stress intensity factors are obtained. Compared with many other existing analytical treatments to the crack problems in FGMs with the assumption of special gradation, the present method can consider arbitrarily graded shear modulus and Poisson's ratio. It is shown that the present solution can reduce to existing solutions in literatures for annular crack in homogenous materials. Numerical study is conducted to investigate the fracture mechanics of annular crack in FGMs. A practical example of an annular crack in a real Epoxy-Glass FGM with measured data of material properties is also considered.

Fracture toughness and microstructure damage behavior of thin Al–Cu alloy fabricated by wire-arc directed energy deposition

This study aimed to investigate the factors influencing the fracture toughness of thin Al–Cu alloy fabricated using Arc-Direct Energy Deposition (Arc-DED). By adjusting process parameters, samples with different microstructure characteristics were obtained, including an air-cooled (AC) deposit with a high proportion of equiaxed grains, a water-cooled (WC) deposit with a high proportion of columnar grains, and a post-heat-treated air-cooled deposit (T6) with numerous nano-sized precipitates. The conditional fracture toughness (KQ)/crack tip opening displacement (CTOD) values for the AC, WC, and T6 samples were 11.7 MPa m1/2/23.27 μm,11.4 MPa m1/2/22.70 μm, and 17.6 MPa m1/2/22.39 μm, respectively. The fracture toughness of the T6 sample was 50.4% and 54.4% higher than that of the AC and WC samples, respectively. The heterogeneity of the equiaxed/columnar microstructure affected the distribution of brittle θ-Al2Cu phases and pores, thereby influencing crack behavior. While columnar grains exhibited a stronger capacity for accumulating geometrically necessary dislocations (GNDs) and coordinating deformation compared to equiaxed grains, cracks were more likely to propagate along grain boundaries when the loading direction was parallel to the growth direction of columnar grains. Consequently, flat crack paths were observed in columnar grains, while equiaxed grains displayed tortuous paths. Furthermore, the precipitation of nano-sized θ'-Al2Cu phases contributed to improved fracture toughness. By integrating microstructure characterization, fractographic observation, analysis of uneven grain deformation behavior, and examination of GNDs distribution near crack paths, the study revealed microscopic damage characteristics, fracture behavior, and toughening mechanisms.

On the role of hydrogen in the stress corrosion cracking behavior of Q345R steel in HF vapor environment

The stress corrosion cracking (SCC) behavior of Q345R steel in hydrofluoric acid (HF) vapor environment was investigated. It is shown that Q345R has a high susceptibility to SCC in HF vapor environment, which is negatively correlated with the strain rate. Several different crack morphologies and cracking factors are verified: flat cracks in ferrite are associated with anodic dissolution triggered by micro-galvanic corrosion, and porous cracks at the pearlite and pearlite-ferrite interfaces are mainly influenced by hydrogen. The results of hydrogen charging tests show that pre-charging has little effect on the hydrogen embrittlement of Q345R steel, while in-situ charging leads to severe brittle fracture of the material, because hydrogen interacts with large number of moving dislocations generated by in-situ stretching process and penetrates more readily into the material. The synergistic relationship between hydrogen and dislocation motion is found to be the main mechanism for the transition from ductile to brittle fracture.

Failure mechanism and heat treatment effect of 3D-printed bio-inspired helicoidal CF/PEEK composites

The bio-inspired helicoidal structure has displayed a unique combination of lightweight, high strength, and high impact resistance. This study presents an experimental and numerical investigation of the failure mechanism and heat treatment effect of 3D-printed helicoidal composites by adopting a helicoidal laminate stacking configuration found in the dactyl club in Homarus americanus. The helicoidal specimens were additively manufactured with short carbon fiber reinforced Polyether ether ketone (PEEK) composites and their mechanical performance was characterized through quasi-static three-point bending. The results showed that the flexural strength, flexural modulus, and absorbed energy of the helicoidal composites with the twisted crack pattern were 6.9%, 23.9%, and 5.9% higher than those of the quasi-isotropic composites with the flat crack pattern. Stress analysis was then carried out to investigate the underlying failure mechanism of helicoidal materials. The stress component of σ33 and σ13 in helicoidal specimens showed a milder distribution than that of quasi-isotropic specimens, which plays a major role in the resulting fracture-resistant behavior. Further results showed that the helicoidal specimens under heat treatment of 250 °C over 6 h achieved 24.9% and 20.9% enhancement in flexural strength and modulus. The cracking surface area was increased with extensive translaminar twisted cracks observed with a scanning electron microscope. Experiment results show that heat treatment can exert a significant influence on the crack path of the CF/PEEK helicoidal specimens. Meanwhile, the increased degree of crystallization and crosslinking at the interface could inhibit the initiation of delamination failure.

Lode-dependent second porosity in porous plasticity for shear-dominated loadings

Ductile fracture of metallic alloys in shear-dominated loadings is usually modeled either with uncoupled failure criteria or with porous plasticity. In the first approach, criteria depending on the third invariant of the stress tensor: the Lode variable, have been developed. In porous plasticity, a second porosity was added to the GTN yield criterion. In this work, the two approaches are combined with a very simple equation for the second porosity evolution depending on the Lode variable. The new model involves two material parameters. They determine the intensity of the Lode effect and could be calibrated with several specimen geometries in which the Lode variable ranges from zero to some intermediate value (positive or negative). Finite element calculations of a notched KAHN specimen are performed with the Rousselier porous plasticity model (polycrystalline version). The model without the Lode effect first includes the Coulomb-Rousselier-Luo failure model at the slip system scale for ductile damage in shear, in agreement with the experimental load-notch opening displacement curve of an aluminum alloy sheet and with observations of the fracture mechanisms at the micro-scale. Then the Lode effect is also included. The damage mechanisms involved in the different resulting cracks are discussed: flat tensile crack in the notch plane, shear lips on the two specimen surfaces and slant crack, in relation with the local Lode variable. The load-displacement curve softening depends on the model parameters.

Role of δ-ferrite in fatigue crack growth of AISI 316 austenitic stainless steel

FF sample (nearly free of δ-ferrite) and CF sample (containing ∼4% δ-ferrite) were prepared from the AISI 316 austenitic stainless steel plate to elucidate the role of δ-ferrite in the fatigue crack growth under the solution treated and accelerated aged conditions. It is found that the fatigue crack growth resistance of the CF sample is higher than the FF sample under the solution treated condition. However, a significant deterioration of the fatigue crack growth resistance is observed in the CF sample while little variation is found in the FF sample after accelerated aging treatment at 750 °C for 10 h. In the solution treated condition, deflected crack growth path is present when the main crack encounters the δ-ferrite in the CF sample due to the differences in the fatigue responses between austenite and δ-ferrite. The measured growth rate of the deflected crack is significantly slower than that of the flat crack of the same length. After the accelerated aging treatment, microcracks are produced at the M23C6/δ interface due to the strain incompatibility between M23C6 and retained δ-ferrite when the decomposed δ-ferrite is subject to plastic deformation in the crack tip plastic zone. The preexisting microcracks in the front of crack tip provide a viable path for crack propagation, resulting in the relatively flat crack path.

A two characteristic length nonlocal GTN model: Application to cup–cone and slant fracture

Ductile failure prediction is essential to avoid loss of structural integrity or to control crack propagation during forming processes. One of the main difficulties is the prediction of complex crack paths. This study proposes a nonlocal extension of a local Gurson–Tvergaard–Needleman (GTN) ductile damage model at finite strains able to capture cup–cone or slant fracture. The proposed model is based on an implicit gradient formulation which enables to solve the problem of spurious strain and damage localization. The model integrates two different material characteristic lengths, which are used to separately regularize damage by void growth and damage by damage nucleation. After parameter fitting using data for a line pipe steel, conditions to obtain converged solutions are studied, which can be used to select the mesh size in the localization band. With the appropriate mesh design, it was possible to study the effect of the characteristic lengths on the formation of cup–cone fracture and slant fracture. It is observed that, for a given specimen size, larger characteristic lengths favor flat crack advance. Similarly, for given material lengths, size effects can be predicted with small specimens being more prone to flat fracture. This paves the way to a more direct determination of material lengths by using homothetic specimens so as to obtain different crack paths.

3D in situ study of damage during a ‘shear to tension’ load path change in an aluminium alloy

A load path change (LPC) from shear to tension has been studied for a recrystallized 2198 T8 aluminium alloy sheet material by three-dimensional (3D) X-ray imaging combined with image correlation and interpreted by complementary 3D finite element (FE) simulations. A cross-shaped specimen was designed for the non-proportional loading and multiscale study. The effect of the LPC on the formability and related strain localisation, damage and failure was investigated and damage mechanisms could be clearly identified. The macroscopic tension stretch to fracture, measured by an optical extensometer during the shear to tension test, was reduced by about 20% compared to the proportional tension test. Damage, measured by in situ laminography imaging at μm-scale resolution, has interestingly already been found under shear, and was quantified as surface void fraction during the LPC. Strain was measured inside the material and at the mesoscale by 2D digital image correlation (DIC) on projected volume data, using the (natural) intermetallic particle contrast present in the 3D laminographic data. An accumulated equivalent strain definition, suited for the description of non-proportional loading, has been applied to the DIC data and FE simulations, indicating good agreement between both. On the microscopic scale, damage was seen to nucleate under shear load in the form of flat cracks, of similar width as the grain size, and in the form of cracks inside intermetallic particles. This damage subsequently grew and coalesced during tensile loading which in turn led to final fracture.

Numerical Simulation of the Diffusion of Fissure Slurry at High Temperature

Deep-buried tunnel at high-ground temperature is prone to the sudden surge of water when crossing the water-rich formation, resulting in casualties and economic losses. Slurry injection is a common and effective method of governance for addressing this issue. However, there has been little research into pulping at high-ground temperature, with most of the existing research focusing on room temperature conditions. We studied two kinds of slurry commonly used in grouting, cement slurry and cement-sodium silicate slurry. Indoor testing was used in this paper to clarify the effect of temperature on slurry viscosity, and numerical simulation was used to study slurry diffusion in flat cracks at different temperatures. The results showed that in a hydrostatic environment, the spread rate of slurry was independent of temperature and type of slurry. For the same kind of slurry, the higher the temperature, the greater the maximum slurry pressure. The higher the temperature in a flow environment, the faster the slurry diffusion. As the temperature rised, the grouting pressure required for crack sealing decreased at first then rises. In a flow environment, the sealing effect of cement-sodium silicate slurry was superior to that of cement slurry.

Characterization of externally solidified crystals in a high-pressure die-cast AlSi10MnMg alloy and their effect on porosities and mechanical properties

The characterization of externally solidified crystals (ESCs) and porosities in a high-pressure die-cast AlSi10MnMg alloy was investigated using optical microscope (OM) and computed tomography (CT) with particular attention on the effect of shot speeds on the ESCs and fracture behavior. Results showed that ESCs tended to agglomerate at the center region and changed from fine globular grains into large size dendrites from surface to center. The formation of the ESCs is found to be coarser as the "slow shot speed" in the first stage of high-pressure die casting (HPDC) or the "fast shot speed" in the second stage of HPDC is reduced, consequently, the corresponding ESC area fraction increased. From the fractured morphology, the plate specimen with a higher ESC content exhibited a rough fracture and a large volume fraction of shrinkage porosities was discovered beneath the fracture surface especially when a lower fast shot speed was applied. In in-situ tensile test, the large size shrinkage porosity served as a crack source and it further expanded in an inter-granular mode along ESC boundaries/other porosities (which caused a tortuous crack route) or in a trans-granular mode across the ESC grains/fine (α-Al) II grains (which caused a flat crack route). In addition, the gas porosities in the specimen promoted the crack propagation as a crack concentration area and experienced almost no deformation during the tensile process.

On the key role of crack surface area on the lifetime of arbitrarily shaped flat cracks

Accurate fatigue lifetime prediction is a central element in many industries. Often, a damage tolerant approach is used to ensure that some given imperfections are safe. In this context, these lifetime predictions are frequently made using simplified crack geometries leading to costly conservatism. In particular for a closed crack front, a circular or elliptical crack enclosing the real defect is generally used leading to an underestimation of the real lifetime. Using an iterative perturbation method to simulate the fatigue growth of many tensile complexly shaped cracks, we show that in the absence of any additional complexity, (i) the front quickly becomes circular; (ii) its evolution with the number of loading cycles can be obtained analytically using a circular crack of same area as the original distorted defect. In practice, it means that replacing a complex crack front shape with this simple, analytically solvable configuration is an effective way to improve predictions and that it is not useful to invoke more complex shapes such as elliptical cracks. These take-home messages are illustrated by an example from the aviation industry.

Microstructural sensitivity and deformation micro-mechanisms of a bimodal metastable β titanium Ti–7Mo–3Nb–3Cr–3Al alloy

The bimodal microstructure of a metastable β Ti–7Mo–3Nb–3Cr–3Al (Ti-7333) alloy was successfully tuned through various thermomechanical processing steps, to achieve strength and ductility combinations, in the range between 903 and 1443 MPa and 2.9 % and 17 %, respectively. The influence of the microstructural variables on the deformation micro-mechanisms and fracture mechanisms were further elucidated by the assistance of TEM and fractographic analysis. The results indicate that the strength of bimodal Ti-7333 is mainly governed by secondary αS precipitation through the introduction of a high density of α/β interfaces that effectively block dislocation transmission, whereas ductility is tuned through the control of the primary αP, rod-like αr and retained β phases. Moreover, ductility can be extremely deteriorated if the formation of a continuous grain boundary αCGB phase is not prevented. Plastic deformation of bimodal Ti-7333 is dominated by dislocation slip and tangling, whereas the microstructural sensitivity that accelerated at high strength level is originated from the deformation incompatibility between the fine acicular αS and parent β. In addition, the {10–11}<-1012>α micro-twinning of equiaxed αP phases also contributes to improved ductility and coordinates deformation to an extent. The fractographic analysis revealed either fracture by microvoid coalescence or a mixture of intergranular fracture and microvoid coalescence, depending on thermomechanical condition. The mixed fracture mode results in a relatively flat crack propagation path and reduced ductility; whereas a tortuous crack propagation is obtained when the alloy solely undergoes fracture by microvoid coalescence.

Indirect boundary element method for modelling 2‐D poroelastic wave diffraction by cavities and cracks in half space

AbstractAn indirect boundary element method (IBEM) is developed to solve two‐dimensional (2‐D) wave diffraction by cavities and cracks in a fluid‐saturated poroelastic half space. The dynamic Green's functions of forces and fluid source in a poroelastic full‐space, rather than their half‐space counterparts, are utilized, because of their closed‐form expressions. The diffracted wave field is constructed by distributing forces and sources in fictitious densities over the boundaries, based on the single‐layer potential theory. The densities are determined by matching the approximate solution with the boundary conditions. The nonuniqueness of integral equation caused by the degenerated geometry of a crack is treated by a zoned approach. The numerical accuracy and stability of the IBEM are verified by comparing with available results in the literature. Problems of wave scattering by cavity and flat crack in saturated half plane are solved. The displacement amplification effect on the free surface is investigated. The numerical solutions show that the response is strongly dependent on factors such as wave frequency, incident angle, the length and depth of the crack, and material properties.

Grinding characteristics of CVD diamond grits in single grit grinding of SiC ceramics

Single crystalline diamond (SCD) grits are usually made by a high-pressure and high-temperature (HPHT) method and exhibit cuboctahedral shapes and smooth surfaces. In this paper, we synthesized new kinds of SCD grits and nanocrystalline diamond (NCD) grits by a chemical vapor deposition (CVD) method and explored their grinding performance by single grit grinding of SiC ceramics. Grinding by HPHT grits was also conducted for comparison. The CVD-SCD grits exhibit cuboctahedral shapes, but surfaces are covered by protruded twin crystals of several microns, while the NCD grits are spherical agglomerations of nano-grains. We demonstrated that these morphological features have profound influences on material removal behavior. Results show that the wear of NCD grits is dominated by wear flat and intergranular cracks. The worn NCD grits can exert intense rubbing and ploughing effects on the workpiece. In contrast, the wear of CVD-SCD grits is dominated by fracture of the protruded twin crystals. It is proved that the twins on the grit surface are effective cutting edges to remove the material in a micro scale and thus lead to the formation of fine grinding striations and smaller cracking pits, but this process has little influence on specific grinding energy. Besides, grits with rough twins, especially on the flank face, tend to exhibit lower grinding force ratios and thus better sharpness. Moreover, for grits with smooth rake faces, there exists an explicit critical undeformed chip thickness value around 0.4–0.6 μm, above which the material removal mechanism changes from ductile to brittle rapidly. However, for grits with rough twins on rake faces, this transition process becomes vague.

Low-Temperature Micro-Fracture Toughness Testing of Grain Boundaries in Steel

Temper embrittlement in high-strength steel occurs due to the segregation of impurity elements along prior austenite (γ) grain boundaries, resulting in a decrease in intergranular strength. However, the grain boundary properties have not yet been experimentally investigated. In this study, we developed a micro testing method to selectively process micro-cantilever specimens based on a specific prior γ-grain boundary to measure the grain boundary fracture toughness. Fracture toughness tests using micro-cantilever specimens with side grooves and notch were carried out at 183 K and brittle fracture behavior was successfully obtained. The fracture surface showed almost flat and brittle crack propagation along the prior γ-grain boundary. The derived fracture toughness value, KQ, is lower than that from previous values. By employing this method for the evaluation of intergranular fractures in steel, we believe that we can evaluate more intrinsic prior γ-grain boundary properties compared with conventional methods.