Periodic Cracks Research Articles

An analysis of the interaction between surface and basal crevasses in ice shelves

Abstract. The prescription of a simple and robust parameterization for calving is one of the most significant open problems in ice sheet modelling. One common approach to the modelling of crevasse propagation in calving in ice shelves is to view crevasse growth as an example of linear elastic fracture mechanics. Prior work has, however, focused on highly idealized crack geometries, with a single fracture incised into a parallel-sided slab of ice. In this paper, we study how fractures growing from opposite sides of such an ice slab interact with each other, focusing on different simple crack arrangements: we consider either perfectly aligned cracks or periodic arrays of laterally offset cracks. We visualize the dynamics of crack growth using simple tools from dynamical systems theory and find that aligned cracks tend to impede each other's growth due to the torques generated by normal stresses on the crack faces, while periodically offset cracks facilitate simultaneous growth of bottom and top cracks. For periodic cracks, the presence of multiple cracks on one side of the ice slab, however, also generates torques that slow crack growth, with widely spaced cracks favouring calving at lower extensional stresses than closely spaced cracks.

Weakened by an infinite system of transverse periodic cracks piezoelectric waveguide as a filter of electroacoustic waves

Abstract The problem of propagation of an electroactive unidirectional elastic shear wave signal in an infinite piezoelectric waveguide weakened by a periodic system of transverse cracks is considered. Wave formation is investigated in cases of different anisotropies of the piezoelectric material, under different electromechanical conditions on the waveguide surfaces. In contrast to the case of a homogeneous waveguide, the presence of a system of periodic cracks leads to the formation of Floquet waves with a periodic structure. Different anisotropies and asymmetric electromechanical conditions on the waveguide surface lead to different localization of wave energy over the thickness of the waveguide, as well as to the presence of different zones of acceptable frequencies. A comparative analysis of the influence of the presence of a periodic system of transverse cracks on the frequency transmittance of the waveguide is carried out.

Longitudinal Shear of a Composite Material in Which the Binder and Inclusions are Weakened by Cohesive Cracks

Background: An elastic medium is considered that is weakened by a doubly periodic system of round holes filled with washers made of a homogeneous elastic material and has cohesive cracks, the surface of which is uniformly covered with a cylindrical non-metallic film. The binder (medium) is weakened by two doubly periodic systems of rectilinear cohesive cracks, directed parallel to the abscissa and ordinate axes, and the length of the crack and their dimensions are not the same (different). General concepts are constructed that describe a class of problems with doubly periodic stress distribution outside circular holes and cohesive cracks under longitudinal shear. The analysis of the limit equilibrium of cracks within the framework of the end zone model is performed on the basis of a nonlocal failure criterion with a force condition for the advancement of the crack tip and a deformation condition for determining the advance of the edge of the end zone of the crack. In solving the problem, the main resolving equations are obtained in the form of infinite algebraic systems and three nonlinear singular integro-differential equations. The equations obtained in each approximation were solved by the Gaussian method with the choice of the main element for different order values depending on the radius of the holes. Calculations were carried out to determine the forces in the connections of the end zones and the ultimate loads causing crack growth. Objective: In the considered problem, the problem of longitudinal slip weakened by cracks parallel to the x axis in the filling medium with two pairs of two periodic cracks weakened by 2 periodic circular holes is considered. In the problem, the boundary problem along the contour of the circular holes is determined, and at the same time, the surface problem is established for the cracks parallel to the x and y axes. The solution of the problem is sought analytically, and taking into account the boundary condition, a system of linear algebraic equations for circular holes and 3 singular integral equations for cracks is obtained. Theoretical Framework: The problem is solved analytically, as the system of linear algebraic equations obtained for circular holes and the system of linear integral equations are jointly solved, and the stress intensity factor at the end of the cracks is determined. Method: The problem was solved using "Kolosova Muskhalashvili" functions and "Collondia's method of solving singular integral equations". Results and Discussion: The main essence of the considered issue is that the stress intensity factor at the end of the cracks is determined according to Fig. 1. Research Implications: For the first time, the stress intensity factor was calculated in composite materials with two pairs of biperiodic cracks of different lengths weakened by biperiodic round holes. Originality/Value: For the first time, the stress intensity coefficient was determined in composite materials with two periodic two pairs of cohesive cracks.

Diamond machining of additively manufactured Ti6Al4V ELI: Newer mode of material removal challenging the current simulation tools

Single point diamond machining (SPDM) produces smooth machined surfaces that other production methods cannot match. While the mechanics of machining of cast alloys with SPDM is well-explored, the realm of SPDM for additively manufactured parts remains largely uncharted. This work reveals new insights into the surface generation process of an additively manufactured titanium alloy, specifically, a Ti6Al4V Extra Low Interstitials (ELI) alloy workpiece. Our examination of the chip morphology unveiled a distinct mode of chip removal, previously unrecorded in existing literature. During SPDM of additively made Ti6Al4V ELI workpiece, identification of numerous pores and discontinuities in the chips flowing on the tool rake face, indicating periodic intermittent cracking during the material's plastic flow was seen. To examine this phenomenon, a finite element analysis (FEA) model was developed. While the FEA model can well explain the machining mechanics and chip morphology of SPDM of cast Ti6Al4V ELI reported in the literature, it failed to describe the chip morphology that are obtained during machining of additively made workpiece in this work. This disparity underscores the need for innovative simulation approaches tailored for additively manufactured components. The experimental observations in this study highlight a unique form of chip formation in contrast to conventional Ti6Al4V alloy machining processes. At lower feeds, there was a presence of short, discontinuous chip formation with tearing at the outer periphery. Conversely, at higher feeds, a long, continuous ribbon-like chip formation was observed. In addition, some typical additive manufacturing defects appear on the machined surface and chips. Through optimisation of the SPDT parameters, a surface roughness (Ra) value of about 11.8 nm was achieved on additively manufactured Ti6Al4V ELI workpiece. This work provides a fresh perspective on the mechanics of SPDM for additively manufactured components, offering a stepping stone for subsequent studies.

A numerical investigation of thermal stress induced cracking pattern in the solidifying nuclear fuel droplet during MFCI

During Molten Fuel Coolant Interaction (MFCI) occurring in a Sodium-cooled Fast Reactor (SFR) following a severe accident, the corium jet breaks up into coarse droplets due to hydrodynamic instabilities and fine flaked debris are generated due to the thermal stress cracking occurring on the solidifying droplet. In particular mixed oxide core debris quenched by liquid sodium are more prone to thermal stress cracking because of the excellent heat transport properties of liquid sodium, which leads to a large temperature gradient across the crust of the ceramic fuel. In this paper, thermal stress initiated cracking of solid crust of the nuclear fuel droplet is studied using Fracture Bifurcation Theory (FBT) and Minimum Potential Energy Principle (MPEP). FBT is able to predict the minimum crack length needed for crack propagation or catastrophic failure depending on the computed KI values. On the other hand, MPEP can predict the periodic and hierarchical cracking pattern that can develop on the core debris. This helps in the prediction of number of cracks and the crack length that can develop on the solid crust. Parametric studies have been carried out by varying MOX droplet sizes, crust thickness and cooling conditions and calculating KI by semi-analytical means and comparing it with KIC. The analysis revealed that solidifying droplets with radius equal to or more than 2 mm are susceptible to thermal stress initiated crack growth and catastrophic breakage even if a few tens of micron size initial crack develops on its surface. Then a particular case of 2 mm radius core debris is considered and its cracking pattern is studied by applying MPEP. This optimal crack configuration is obtained by minimizing potential energy for a given range of crack length and spacing. The analysis has been carried out with ANSYS APDL code which calculates the strain energy for a given initial crack length and spacing. The 2D computational model is validated with a similar study carried out for Alumina disc quenched in water and the results are in good agreement. The minimum fine fragment size predicted by the analysis for mixed oxide debris is a flake like debris with equivalent radius of 41 µm when approximated to be a sphere. The particle size correlates well with the fine debris sizes reported in literature of MFCI experiments.

A novel dealloying assisted machining method to improve the machinability of NiTi alloy as a typical high toughness difficult-to-machine material

High quality and high efficiency cutting process is of great significance to the components manufacturing related to machinability of workpiece materials. As a typical difficult-to-machine material induced mainly by high toughness, NiTi alloy faces challenges such as high cutting force and difficult chip breaking during the cutting process. To solve these problems, this paper presents a novel surface dealloying assisted machining method, i.e., the preparation of nanoporous structures on the workpiece surface with dealloying treatment, to improve the machinability of NiTi alloy. Based on high speed in-situ imaging of material removal process, the presence of dealloyed layer leads to a segmented flow mode instead of homogeneous severe plastic deformation without dealloying treatment. The change in material removal mode is beneficial to decrease the cutting force and energy and improve the machined surface quality. The embrittlement effect of dealloyed layer inhibits material plastic flow and promotes periodic crack nucleation and propagation. An analytical model is developed to characterize the brittle crack propagation, which provides theoretical basis for explaining embrittlement effect of dealloyed layer. This work verifies the feasibility and effectiveness of the proposed method to modify the machinability of NiTi alloy and provides new ideas for the development of manufacturing processes.

Prediction and demonstration of periodic tensile cracking in rate-dependent porous cement

Periodic tensile cracks are shown to occur when cylinder-shaped saturated cement specimens are subjected to rapid decompression, with the spacing between the cracks scaling as a power law of the decompression time. This behavior is predicted by theory, which is specified to this scenario based on prior work that was more general and applied to compaction bands. Specifically, the formation of the tensile cracks is shown to coincide with periodicity that naturally arises in the effective stress when the material follows a Terzaghi-type consolidation law, although in reverse for dilation and with material deformation described by a rate-dependent viscoplastic law. When strain rate is proportional to effective stress to a power that is greater than one, periodic regions of tensile effective stress arise through the poromechanical fluid–solid coupling. The theoretically-predicted exponent of the resulting power-law relationship between tensile cracks spacing and unloading time successfully brackets the experimental results, for which it is observed that the exponent is slightly stronger than a square-root relationship (0.28 to 0.67) at testing temperatures of 20 ℃ and 90 ℃. These results demonstrate that rapid-depressurization leads to periodic fracturing that could, on the one hand, be detrimental to the isolation provided by cement used to seal wellbores in the petroleum industry. On the other hand, the periodic tensile cracks could also be favorable to production if generated in low-permeability reservoir rocks such as shales that are targeted for petroleum production or granites that are targeted for geothermal energy.

Scratch behaviors of polyacrylate-based hard coatings on alternating multi-layered PMMA+PC substrates

In our previous work [1], the scratch behaviors of alternating multi-layered polymethyl methacrylate (PMMA)/polycarbonate (PC) laminates were studied. Generally, a hard coating layer must be introduced to the surface of PMMA + PC laminate to further enhance its hardness and scratch resistance. In this work, the same laminates used in our previous work were coated by a UV-cured polyacrylate hard layer, and the scratch behaviors and relating mechanisms of hard coating (HC) systems were investigated via both progressive normal load scratch test and pencil hardness test. Sliding counterfaces of two tests were stainless steel ball with a diameter of 1 mm and cylinder made of pencil core with a diameter of 2 mm, respectively. Length, width and thickness of test specimen were 150 mm, 33 mm and 1.6 mm, respectively. The effects of HC's thickness and substrate's hardness on scratch behaviors of HC systems were also included. In both scratch tests, experimental results demonstrated that scratch damages of HC systems were featured with dense periodic cracks. Finite element modeling (FEM) revealed that the formation of such crack types was attributed to the maximum principal stress perpendicular to crack propagation direction. Furthermore, it was found that the scratch resistances of HC systems were enhanced as thickness of HC or hardness of substrate increased, the mechanism behind which were found to be decreasing of the maximum principal stress and consequent delaying of crack formation as revealed through FEM.

Dynamic anti-plane response of circular inclusion in bi-material structure with interfacial periodic cracks due to the SH wave

This paper investigates the dynamic anti-plane response of the circular inclusion in the bi-material structure with interfacial periodic cracks due to the SH wave. In our analysis, we use the ‘conjunction’ technology and Green’s function method. The bi-material structure consists of two isotropic elastic right-angle domains consisting of a circular elastic inclusion and a series of periodic cracks at the bi-material interface. The periodic cracks are created to satisfy the free conditions of the stresses by using the interface ‘conjunction’ technology. The Green’s functions are also solved to obtain the displacement solutions of the out-place point source loaded on the vertical boundaries of the right-angle plane. The first Fredholm integral equations with unknown force systems are then established based on the continuity conditions at the bi-material interface. As an example, the distributions of the dynamic stress concentration factor (DSCF) around the circular inclusion are obtained and shown graphically. The numerical results indicate that compared with a single crack having periodic cracks strengthens the situation of the dynamic stress concentration around the inclusion.

Phase-field modeling of drying-induced cracks: Choice of coupling and study of homogeneous and localized damage

Phase-field modeling has already proved to be a suitable framework to predict the initiation and propagation of drying cracks in variably saturated porous media. In this paper, we focus on some fundamental modeling aspects which have not yet been given sufficient attention. In the first part, different formulations for the total energy, characterized by different choices for the coupling between the damage and the poro-mechanical fields, are evaluated based on their ability to lead to qualitatively reasonable predictions for two benchmark cases of free and restrained desiccation. In the second part, for a selected energy formulation, we conduct the variational analysis of the quasi-static damage evolution. Hereby, we focus on restrained desiccation under a given capillary pressure distribution, resulting from the solution of Richards equation with either flux-driven or pressure-driven boundary conditions. Extending the analysis in Sicsic et al. (2014) to the present case, we show that the damage evolution follows first a fundamental branch without localization, and then bifurcates into another branch with damage localization, which leads to the initiation of periodic cracks. The analysis enables the computation of the drying crack spacing as a function of material and loading parameters.

Edge cracking of WEST tungsten actively cooled plasma facing components after plasma operation

The WEST tokamak operates with actively-cooled tungsten ITER-like divertor plasma facing units (PFUs) since 2018. Poloidally-distributed cracks along the leading edges of PFUs were observed after WEST plasma operations. Because cracks may have an impact on the PFUs lifetime, mechanisms related to the cracks initiation and propagation are still under investigation. Previous numerical simulations lead to assess the location of the privileged initiation of the first crack on the PFU and the rationale for its initiation (disruption events causing brittle crack). In this paper, the goal is to identify, the most likely mechanism involved in the PFU damage process during transient. For this, in the first part of this paper, the observed crack topologies (depth and width of cracks) are described based on the recent post-mortem analysis in WEST. Then numerical simulations assuming initial crack(s) at the leading edge lead to assess the evolution of the stress mechanical field and explains the cracking mechanisms. Results of the simulations assuming several initials cracks (primary, secondary) highlight the leading edge periodic cracking under successive disruptions up to a threshold which corresponds to a minimum distance between two cracks and no further cracks are generated. The cracking threshold length has been assessed between 0.4 mm and 0.8 mm which is fully consistent with the WEST post-mortem observations. Finally, the leading edge crack initiation domain is specified as function of the thermal quench disruption impact factor and the component misalignment.

A deeper generative adversarial network for grooved cement concrete pavement crack detection

Periodic grooved cement concrete pavement crack detection is of great importance for pavement condition monitoring and maintenance. The current state-of-the-art (SOTA) detection solutions highly depend on datasets. However, due to the limited access to crack images, more efficient methods are urgently needed to advance the detection of cracking on grooved cement concrete pavement. This study proposes an improved deeper Wasserstein generative adversarial network with gradient penalty (WGAN-GP) to generate datasets of pavement images with a size of 512 × 512 pixels 2. Poisson bleeding is adopted to create the synthesized grooved cement concrete pavement crack images based on the generated crack images and groove images. The robustness of the proposed improved deeper WGAN-GP model is validated by Faster R-CNN, YOLOv3, and YOLOv4 models trained on original crack images and generated crack images for region-level detection. U-Net and W-segnet are used to achieve pixel-level crack detection to evaluate the effectiveness of proposed model. Results show that the improved deeper WGAN-GP could generate more realistic transverse, longitudinal and oblique crack images. In addition, the Poisson bleeding algorithm contributes to synthesizing grooved cement concrete pavement crack images. Moreover, it is observed that YOLOv3 trained by the augmented dataset could achieve a mean average precision (MAP) of 81.98%, 6% MAP higher than the non-augmented dataset. U-Net and W-segnet benefit from augmented dataset with a better pixel-level segmentation result. Based on the results, it can be concluded that the improved deeper WAGN-GP image generation method can provide a straightforward way to fill the data shortage gap of grooved cement concrete pavement cracks, thus increasing the problem-solving capability of the SOTA crack detection models.

Enhanced printability and strength of unweldable AA2024-based nanocomposites fabricated by laser powder bed fusion via nano-TiC-induced grain refinement

The formation of undesirable coarse columnar grains and periodic hot cracks has been a long-standing issue in the additive manufacturing (AM) of unweldable high-strength aluminum alloys and their nanocomposites. Herein, the LPBF-printability of AA2024-based nanocomposites is improved by TiC-induced in-situ reinforcement and nanoparticle-enabled grain refinement during laser powder bed fusion (LPBF). The TiC-triggered in-situ reaction during LPBF overcomes the poisoning of the TiC grain refiner that occurs during conventional solidification. It not only results in fine equiaxed grains with a minimum average size of ∼1.6 μm but also suppresses hot crack formation. Powerful L12-Al3Ti nucleants are incorporated in-situ into AA2024 through TiC nanoparticle addition during LPBF, promoting the heterogeneous nucleation of α-Al. Moreover, the growth restriction effect induced by residual TiC nanoparticles and lamellar Al4C3 nanoparticles through pinning behavior along grain boundaries also contributes to grain refinement. Furthermore, these particles serve as effective reinforcement particles as well as grain refiners. The as-built AA2024-based nanocomposites tailored by nano-TiC show a maximum ultimate tensile strength (UTS) of ∼388 MPa, a yield strength (YS) of ∼332 MPa and an elongation (El) of ∼10.2%. After T6 heat treatment, the nanocomposites exhibit an outstanding UTS of ∼507 MPa, a YS of ∼456 MPa and an El of ∼6.6%. This nano-TiC-induced microstructural control method provides new insights into successful AM of hot-crack-sensitive high-strength aluminum alloys and their composites.

Dynamic stress intensity factor for periodic interfacial cracks in a bi-material half space disturbed by SH waves

The dynamic anti-plane properties of mode III interfacial collinear periodic cracks in a bi-material half space are investigated by the complex function and Green’s function methods. The responses of a rectangular domain under the action of an out-plane point source are solved, i.e. the required Green’s function is found. Periodic cracks at the interface are constructed by using the “cutting” method. Using the continuity conditions at the bi-material interface, the Fredholm integral equations of the first kind including the out-of-plane force system are established by the interface “conjunction” technique. Analytical expressions for the dynamic stress intensity factors (DSIFs) at crack tips are derived. Numerical analyses of DSIFs are conducted, and results discussed in depth.

Anisotropic Microparticles through Periodic Autofragmentation of Amphiphilic Triblock Copolymer Microfibers

Fracture formation due to drying is a common process in a range of systems, from mud cracks to thin polymeric films. Design and control of the fracturing process can be used as a tool for directing the fractures into predefined paths, leading to patterning and controlled fragmentation. In this work, we report the spontaneous periodic fragmentation of polymeric microfibers upon drying. The microfibers are fabricated via electrospinning of amphiphilic triblock copolymers over a glass substrate, and throughout their drying, highly periodic and sharp transverse cracking occurs along the fiber, resulting in the production of anisotropic microparticles (MPs) with a remarkably narrow size distribution. The average length of the MPs depends on the fiber’s diameter; hence, by tuning the diameter of the fibers, size control over the MPs is achieved. X-ray scattering measurements reveal the formation of a lamellar arrangement of the copolymers along the fiber, providing a molecular insight into the formation of sharp transverse fractures. Adjusting the lipophilicity of the two terminal hydrophobic dendritic blocks of the triblock copolymers allows tuning the solubility of the obtained MPs in water and the release rate of hydrophobic cargo, opening a new route for the fabrication of anisotropic MPs for controlled release applications.

Laser Powder Bed Fusion Additive Manufacturing of Fe3Al-1.5Ta Iron Aluminide with Strengthening Laves Phase

Advanced aluminides strengthened with incoherent Laves phase precipitates are promising lightweight and creep-resistant alternatives for high-alloy steels and superalloys for high-temperature critical components up to 750 °C service temperature. A significant issue with manufacturing these aluminides with conventional casting is the strong coarsening tendency of the Laves phase precipitates at elevated temperatures, leading to a significant strength reduction. In this context, the short lifetime of the melt pool in additive manufacturing and its fast solidification and cooling rates promise to consolidate these aluminides with homogeneously distributed fine Laves phase particles without coarsening. The main scientific objective of this work is to exploit the unique characteristics of the laser powder bed fusion (L-PBF) additive manufacturing (AM) process to print dense and crack-free bulk Fe3Al-1.5Ta samples containing uniformly distributed (Fe, Al)2Ta Laves phase precipitates. The Fe-25Al-2Ta (at.%) alloy was selected for this work since its creep resistance at 650 °C surpasses the one of the P92 martensitic–ferritic steel (one of the most creep-resistant alloys developed for steam turbine applications). Fundamentals on process–microstructure relationships governing the L-PBF-fabricated builds are provided by a detailed microstructural characterization using X-ray diffractometer (XRD) and ultra-high-resolution scanning electron microscopy (SEM) equipped with energy-dispersive X-ray spectroscopy (EDX) and high-resolution electron backscatter diffraction (EBSD) detectors. Orientation imaging microscopy (OIM) and grain reference orientation deviation (GROD) maps were applied to measure texture and visualize substructures within the grains. The mechanism of voids formation, morphology, and volume fraction as a function of the input energy density was identified. The melting and solidification dynamics led to microstructures with large columnar grains, porosity, and periodic cracks during the printing process. Processing samples at the building temperatures below the brittle-to-ductile transition temperature, BDTT (750 °C), often caused severe macrocracking and delamination. Crack-free samples with densities higher than 99%, some approaching 99.5%, were fabricated from pre-alloyed gas-atomized powders with a combination of high laser power (250–300 W), slow-to-medium scanning speed (500–1000 mm/s), and 800 °C build plate preheating using a 67° rotation scanning strategy. The morphology of the pores in the volume of the samples indicated a relatively sharp transition from spherical geometry for scanning speeds up to 1000 mm/s to crack-like pores for higher values. The ultra-fast cooling during the L-PBF process suppressed D03 Fe3Al-ordering. The Fe3Al-1.5Ta builds were characterized by B2 FeAl-type order clusters dispersed within a disordered A2 α-(Fe, Al) matrix. Additionally, the (Fe, Al)2Ta Laves phase (C14–P63/mmc) was predominantly formed at the matrix phase grain boundaries and frequently dispersed within the grains. The quantitative EDX analysis of the matrix gave 77.6–77.9 at.% Fe, 21.4–21.7 at.% Al, and 0.6–0.8 at.% Ta, while the composition of the Laves phase was 66.3–67.8 at.% Fe, 8.7–9.8 at.% Al, and 22.4–24.9 at.% Ta, indicating that the Laves phase is considerably enriched in Ta with respect to the matrix. The L-PBF-fabricated alloys were characterized by coarse, columnar grains which grow epitaxially from the substrate, were several m in width, and extended across several layers along the building direction. The grains exhibited a relatively strong microtexture close to <0 0 1> with respect to the building direction. The L-PBF builds showed a bulk hardness value comparable to the as-cast and spark plasma-sintered counterparts. A negligible variation of the hardness across the build height was observed. Within the framework of this study, we demonstrated that the porosity and cracking issues could be resolved mainly by controlling the process parameters and preheating the build platform above the BDTT. Nevertheless, alloy modifications and/or post-manufacturing processing are required for microstructure refinement.

Analysis of nonlinear energy evolution in fractured limestone under uniaxial compression

The development of dissolution underground results in the appearance of holes of different shapes in limestone, which affect its deformation and failure characteristics. Generally, the deformation and failure of the rock mass are accompanied by energy dissipation and release. To investigate the nonlinear energy evolution mechanism, a series of uniaxial compression and acoustic emission (AE) tests were conducted on limestone with holes of different shapes. Subsequently, based on the theory of nonlinear dynamics and rock micro-energy evolution, a nonlinear energy self-promotion-inhibition model and a nonlinear energy evolution law for limestone were proposed. The nonlinear energy self-promotion- inhibition model suggested an energy mechanism that could inhabit energy development, particularly when a critical failure occurred. In addition, the crack closure and propagation nonlinear behavior characteristics were investigated via a UCS test. Experimental results showed that energy promotion and inhibition occurred during loading, where the effect of the former was greater than that of the latter. Additionally, the energy promotion and inhibition effects of limestone with a “mushroom-shaped hole” were more significant than those of intact and other limestones. The “base” of limestone with a “dumbbell-shaped hole” reduced the stress concentration of the samples. Based on the nonlinear characteristics of the average growth rate of elastic strain energy density and the stress-time curve, the evolution of limestone with holes of different shapes under uniaxial compression can be categorized into five main stages, which can be further classified into seven substages based on the AE characteristics. Moreover, three threshold stress indicators, i.e., initial equilibrium stress, periodic crack growth stress, and chaotic initial stress, for describing the closure and propagation of microcracks were proposed. The results of this study reveal the nonlinear energy evolution mechanism of limestone with holes of different shapes and provide a basis for further research on the meso-evolution of rock mass.

Thermal conductivity of crack-containing media: A numerical study

The present study aims to evaluate the effective thermal conduction behavior of crack-containing media through micromechanical modeling. Numerical analyses were performed using the finite element method, first using periodic arrays of elliptical pores and then reducing the elliptical minor axis to reach the crack limit. This parametric approach was seen to be able to capture the effect of discontinuity across the crack face in a straightforward manner. The overall thermal conductivity of the model structures, encompassing a range of crack densities and spatial distributions, was investigated. It was found that, for cracks with mixed orientations, the effective thermal conductivity is insensitive to the actual crack alignment and can be uniquely represented by the crack density. The mixed-orientation periodic crack configurations are also representative of random sizes, orientations, and spatial distributions of cracks, thus exhibiting a high degree of generality. The modeling analyses can also be used to determine simple empirical expressions for two- and three-dimensional media containing random cracks.

Scattering of SH waves in a bi-material half space with a circular hole and periodic type III interfacial cracks

The dynamic anti-plane response of a bi-material half space including a circular hole and periodic interfacial cracks is investigated. An analytical model is established for periodic type III cracks that adopt the idea of “conjunction” modeling. The definite integral equations suitable for modeling the existence of multiple interfacial cracks are derived that satisfy the continuity conditions at the interface. Numerical calculations are carried out to find the dynamic stress concentration factor (DSCF), whose results indicate that the number of interfacial cracks has a significant effect on the dynamic stress concentration around the hole edge, especially for low-frequency incident SH waves.

The Irradiance-Based Growth of Surface Structures Induced by Nanosecond Laser Pulses on Si and Ge and Their Correlation With Plasma Ion Kinetic Energies and Densities

Abstract The laser irradiance-based surface structural growth on Si and Ge has been correlated first time with plasma parameters. The better control over plasma parameters makes manufacturing of various sized and shaped surface structures on the semiconducting materials. The effect of laser irradiances on surface morphology of Si and Ge has been explored. For this purpose, Nd: YAG laser (532 nm, 6 ns, 10 Hz) has been employed as an irradiation source at the various laser irradiances ranging from 4 to 7.1 GW/cm2 under the vacuum condition. Surface modifications of laser-ablated Si and Ge were analyzed by performing scanning electron microscope (SEM) analysis. It has been revealed that laser irradiance plays a significant role in the growth of the micro- and nanostructures on the laser-irradiated target surfaces. The surface morphology of laser-ablated Si and Ge exhibited the formation of various structures such as laser-induced periodic surface structures (LIPSS), cracks, spikes, ridges, and cones. Density and size of these structures have been found to be strongly dependent upon the laser irradiances. SEM analysis exhibits the cones formation at central ablated region of both Si and Ge. These cones become more distinct and pronounced with increasing the laser irradiance due to more energy deposition with Gaussian profile distribution at the central region. Microspikes were observed at boundaries of laser-ablated Si. Whereas, in case of Ge-ablated boundaries, wave-like ridges have been observed, which are then converted into globules at higher laser irradiances up to 7 GWcm−2. LIPSSs were seen at outer boundaries of laser-ablated Ge, whose periodicity varies with the laser irradiances. Faraday cup has been employed in order to probe the kinetic energy and density of laser-induced Si and Ge plasma ions at the similar values of laser irradiances. A correlation at similar values of laser irradiances has been established between the evaluated plasma ion parameters (kinetic energy and density of plasma ions) and observed structures for both materials. This correlation reveals the dependence of kinetic energy and density of plasma ions on the corresponding surface modification of both laser-ablated Si and Ge, as well as enables us for the better understanding of the laser-induced plasma to be used as ion source in various fields ion implantation, surface structuring, and material modification. The results of ion energies are explained by the generation of ambipolar field or self-generated electric field (SGEF) in the expanding plasma due to the charge separation and double-layer structure. The values of SGEF have also been evaluated at different laser irradiances.