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Applied Sciences
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Fracture Mechanics – Theory, Modeling and Applications
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Fracture Mechanics – Theory, Modeling and Applications

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Mechanical Engineering".

Deadline for manuscript submissions: closed (17 February 2021) | Viewed by 37220

Special Issue Editors

Dr. Esteban Rougier

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Guest Editor
Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
Interests: combined finite–discrete element simulations; finite element modeling; high strain rate processes; material modeling; fracture and fragmentation processes; shock wave propagation in solids and fluids
Special Issues, Collections and Topics in MDPI journals
Dr. Abigail Hunter

E-Mail Website
Guest Editor
Computational Physics Division, Los Alamos National Laboratory, USA
Interests: fracture and fragmentation processes; brittle materials; reduced-order models; multiscale modeling; constitutive models; mesoscale models; crack interaction and propagation; impact loading; shock physics; phase-field models
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The field of fracture mechanics developed during the throes of World War II and since then it has been a very active area of research. This is a very energetic and vibrant field because fracture processes are relevant for a vast range of engineering applications spanning different temporal and length scales. Depending on the application, material fracture and fragmentation may be either a desirable feature (for example, for the purpose of hydraulic fracturing operations), or something that is to be avoided at all costs (for example, in key components of mechanical systems). In some other instances, fractures are already present and must be accommodated for through novel design (for example, in the case of earthquake ruptures occurring in the Earth’s crust). Because of this wide spectra of motivation, there is a continuous need for the fracture mechanics research community to gain more insight on how fractures are created, evolve, and interact with themselves and with material microstructures. In addition, there are still many remaining questions about how fracture propagation, growth, and interaction impact overall material behavior, and how to develop accurate models to predict this behavior.

This Special Issue focuses on gathering the latest advances on the theoretical, numerical, and application-based fronts for the study of fracture initiation, propagation, arrest, interaction, and fragmentation in engineering materials in general, including but not limited to ceramics, geo-materials, granular materials, and metals. Original contributions from engineers, mechanical materials scientists, computer scientists, physicists, chemists, and mathematicians are encouraged. Both experimental and theoretical papers are welcome.

Dr. Esteban Rougier
Dr. Abigail Hunter
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Applied Sciences is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Fracture
  • Fragmentation
  • Ductile fracture
  • Brittle fracture
  • Fatigue fracture
  • Dynamic Fracture
  • Inter- and Trans-granular Fracture
  • Stress corrosion cracking
  • Delamination
  • Creep crack growth

Published Papers (12 papers)

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Editorial

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4 pages, 173 KiB  
Editorial
Fracture Mechanics—Theory, Modeling and Applications
by Esteban Rougier and Abigail Hunter
Appl. Sci. 2021, 11(16), 7371; https://doi.org/10.3390/app11167371 - 11 Aug 2021
Viewed by 1953
Abstract
The field of fracture mechanics was developed during the throes of World War II, and since then, it has been a very active area of research [...] Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)

Research

Jump to: Editorial

16 pages, 29447 KiB  
Article
The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta
by Jie Chen, Darby J. Luscher and Saryu J. Fensin
Appl. Sci. 2021, 11(8), 3378; https://doi.org/10.3390/app11083378 - 09 Apr 2021
Cited by 7 | Viewed by 2097
Abstract
A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to [...] Read more.
A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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14 pages, 1518 KiB  
Article
Assimilation of Dynamic Combined Finite Discrete Element Methods Using the Ensemble Kalman Filter
by Humberto C. Godinez and Esteban Rougier
Appl. Sci. 2021, 11(7), 2898; https://doi.org/10.3390/app11072898 - 24 Mar 2021
Cited by 1 | Viewed by 1487
Abstract
Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). [...] Read more.
Simulation of fracture initiation, propagation, and arrest is a problem of interest for many applications in the scientific community. There are a number of numerical methods used for this purpose, and among the most widely accepted is the combined finite-discrete element method (FDEM). To model fracture with FDEM, material behavior is described by specifying a combination of elastic properties, strengths (in the normal and tangential directions), and energy dissipated in failure modes I and II, which are modeled by incorporating a parameterized softening curve defining a post-peak stress-displacement relationship unique to each material. In this work, we implement a data assimilation method to estimate key model parameter values with the objective of improving the calibration processes for FDEM fracture simulations. Specifically, we implement the ensemble Kalman filter assimilation method to the Hybrid Optimization Software Suite (HOSS), a FDEM-based code which was developed for the simulation of fracture and fragmentation behavior. We present a set of assimilation experiments to match the numerical results obtained for a Split Hopkinson Pressure Bar (SHPB) model with experimental observations for granite. We achieved this by calibrating a subset of model parameters. The results show a steady convergence of the assimilated parameter values towards observed time/stress curves from the SHPB observations. In particular, both tensile and shear strengths seem to be converging faster than the other parameters considered. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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19 pages, 5561 KiB  
Article
Benchmarking Numerical Methods for Impact and Cratering Applications
by Wendy K. Caldwell, Bryan Euser, Catherine S. Plesko, Carene Larmat, Zhou Lei, Earl E. Knight, Esteban Rougier and Abigail Hunter
Appl. Sci. 2021, 11(6), 2504; https://doi.org/10.3390/app11062504 - 11 Mar 2021
Cited by 8 | Viewed by 2099
Abstract
Large scale computational models are important for studying impact cratering events that are prevalent both on Earth and, more broadly, in this solar system. To address these problems, models must reliably account for both large length scales (e.g., kilometers) and relatively long time [...] Read more.
Large scale computational models are important for studying impact cratering events that are prevalent both on Earth and, more broadly, in this solar system. To address these problems, models must reliably account for both large length scales (e.g., kilometers) and relatively long time scales (hundreds of seconds). This work benchmarks two such approaches, a more traditional hydrodynamics approach and a finite-discrete element method (FDEM), for impact cratering applications. Both 2D and 3D results are discussed for two different impact velocities, 5 km/s and 20 km/s, striking normal to the target and, for 3D simulations, 45° from vertical. In addition, comparisons to previously published data are presented. Finally, differences in how these methods model damage are discussed. Ultimately, both approaches show successful modeling of several different impact scenarios. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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16 pages, 3774 KiB  
Article
Impact Fracture and Fragmentation of Glass via the 3D Combined Finite-Discrete Element Method
by Zhou Lei, Esteban Rougier, Earl E. Knight, Mengyan Zang and Antonio Munjiza
Appl. Sci. 2021, 11(6), 2484; https://doi.org/10.3390/app11062484 - 10 Mar 2021
Cited by 18 | Viewed by 6187
Abstract
A driving technical concern for the automobile industry is their assurance that developed windshield products meet Federal safety standards. Besides conducting innumerable glass breakage experiments, product developers also have the option of utilizing numerical approaches that can provide further insight into glass impact [...] Read more.
A driving technical concern for the automobile industry is their assurance that developed windshield products meet Federal safety standards. Besides conducting innumerable glass breakage experiments, product developers also have the option of utilizing numerical approaches that can provide further insight into glass impact breakage, fracture, and fragmentation. The combined finite-discrete element method (FDEM) is one such tool and was used in this study to investigate 3D impact glass fracture processes. To enable this analysis, a generalized traction-separation model, which defines the constitutive relationship between the traction and separation in FDEM cohesive zone models, was introduced. The mechanical responses of a laminated glass and a glass plate under impact were then analyzed. For laminated glass, an impact fracture process was investigated and results were compared against corresponding experiments. Correspondingly, two glass plate impact fracture patterns, i.e., concentric fractures and radial fractures, were simulated. The results show that for both cases, FDEM simulated fracture processes and fracture patterns are in good agreement with the experimental observations. The work demonstrates that FDEM is an effective tool for modeling of fracture and fragmentation in glass. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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14 pages, 21035 KiB  
Article
Failure in Confined Brazilian Tests on Sandstone
by Tyler Hagengruber, Mahmoud Reda Taha, Esteban Rougier, Earl E. Knight and John C. Stormont
Appl. Sci. 2021, 11(5), 2285; https://doi.org/10.3390/app11052285 - 04 Mar 2021
Cited by 6 | Viewed by 2005
Abstract
Strength of rocks in the confined tension region, where the minimum principal stress is tensile, has only infrequently been measured and is not well understood. Quasi-static confined Brazilian tests under a range of confining stresses (2.76 to 27.58 MPa) where used to determine [...] Read more.
Strength of rocks in the confined tension region, where the minimum principal stress is tensile, has only infrequently been measured and is not well understood. Quasi-static confined Brazilian tests under a range of confining stresses (2.76 to 27.58 MPa) where used to determine the strength of sandstone in the confined tension region. The test results indicate that the strength in the confined tension region was a strong function of the intermediate principal stress: increasing the intermediate principal stress significantly increased the strength of the sandstone. The strength data were well fit by the Mogi–Coulomb criterion, which accounts for the intermediate principal stress. Unconfined Brazilian strength data were not well fit to the Mogi–Coulomb criterion derived from the confined Brazilian test data, consistent with a transition from tensile to shear processes dominating failure with increasing confining pressure. Observations of post-failure fracture surfaces reveal more indication of shear processes with increasing confining pressure. Numerical simulations from combined finite-discrete element method are compared to the experimental results and reflect similar conditions for failure compared to the experimental tests in the confined tension region. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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16 pages, 10957 KiB  
Article
Stress and Fatigue Analysis of Picking Device Gears for a 2.6 kW Automatic Pepper Transplanter
by Md Nafiul Islam, Md Zafar Iqbal, Milon Chowdhury, Mohammod Ali, Kiraga Shafik, Md Shaha Nur Kabir, Dae-Hyun Lee and Sun-Ok Chung
Appl. Sci. 2021, 11(5), 2241; https://doi.org/10.3390/app11052241 - 03 Mar 2021
Cited by 7 | Viewed by 2579
Abstract
A seedling picking device is an essential component for an automatic transplanter to automatically convey the seedling to the dibbling part. It is necessary to find the appropriate material and dimensions for the picking device gears to avoid mechanical damage and increase their [...] Read more.
A seedling picking device is an essential component for an automatic transplanter to automatically convey the seedling to the dibbling part. It is necessary to find the appropriate material and dimensions for the picking device gears to avoid mechanical damage and increase their durability. Therefore, the objectives of this research were to analyze the stress of a picking device gear mechanism in order to select suitable materials and dimensions, and to predict the fatigue life by considering the damage level. The picking device gear shaft divided the input power into two categories, i.e., crank and cam gear sets. Finite element analysis simulation and American Gear Manufacturers Association standard stress analysis theory tests were conducted on both of the crank and cam gear sets for different materials and dimensions. A test bench was fabricated to collect the load (torque) data at different gear operating speeds. The torque data were analyzed using the load duration distribution method to observe the cyclic load patterns. The Palmgren–Miner cumulative damage rule was used to determine the damage level of the picking mechanism gears with respect to the operating speed. The desired lifespan of the transplanter was 255 h to meet the real field service life requirement. Predicted fatigue life range of the picking mechanism gears was recorded as from 436.65 to 4635.97 h, making it higher (by approximately 2 to 18 times) than the lifespan of the transplanter. According to the analyses, the “Steel Composite Material 420H carbon steel” material with a 5 mm face width gear was suitable to operate the picking device for a 10-year transplanter service life. The analysis of stress and fatigue presented in this study will guide the design of picking device gears with effective material properties to maintain the recommended service life of the pepper transplanter. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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11 pages, 10516 KiB  
Article
Investigation of the Destruction Process of Potash Ore with a Single Cutter Using Promising Cross Cutting Pattern
by Dmitriy Shishlyannikov and Ivan Zvonarev
Appl. Sci. 2021, 11(1), 464; https://doi.org/10.3390/app11010464 - 05 Jan 2021
Cited by 9 | Viewed by 4564
Abstract
The creation of modern machines and improvement of existing designs of rock cutting bodies of combines is constrained by the lack of experimental studies of the process of separation of successive elementary cleavages during the potash ore cutting with cutters of winning machines. [...] Read more.
The creation of modern machines and improvement of existing designs of rock cutting bodies of combines is constrained by the lack of experimental studies of the process of separation of successive elementary cleavages during the potash ore cutting with cutters of winning machines. The potential of the cross cutting pattern of potash ore is shown, since the formation of zones of localization of weakening and induced fractures on the surface of layer-by-layer cutting face determines the separation of the elementary cleavages with stable geometric parameters. The verification of the conclusions obtained theoretically was carried out during laboratory tastings on a specially designed bench. The research procedure provided for comparative tests of the potash block ore cutting, staggered and cross cuttings. It has been proven that the use of the cross pattern for set cutting parameters makes it possible to reduce the specific energy costs of the cutting of potash mass, to reduce the average load on the cutter, to reduce the root-mean-square deviation, and to reduce the number of fractions that are hard to enrich in the crushing products, compared to the traditional staggered cutting pattern. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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22 pages, 1600 KiB  
Article
Damage and Failure in a Statistical Crack Model
by L.G. Margolin
Appl. Sci. 2020, 10(23), 8700; https://doi.org/10.3390/app10238700 - 04 Dec 2020
Cited by 2 | Viewed by 1405
Abstract
In this paper I will take a close look at a statistical crack model (SCM) as is used in engineering computer codes to simulate fracture at high strain rates. My general goal is to understand the macroscopic behavior effected by the microphysical processes [...] Read more.
In this paper I will take a close look at a statistical crack model (SCM) as is used in engineering computer codes to simulate fracture at high strain rates. My general goal is to understand the macroscopic behavior effected by the microphysical processes incorporated into an SCM. More specifically, I will assess the importance of including local interactions between cracks into the growth laws of an SCM. My strategy will be to construct a numerical laboratory that represents a single computational cell containing a realization of a statistical distribution of cracks. The cracks will evolve by the microphysical models of the SCM, leading to quantifiable damage and failure of the computational cell. I will use the numerical data generated by randomly generated ensembles of the fracture process to establish scaling laws that will modify and simplify the implementation of the SCM into large scale engineering codes. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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22 pages, 7313 KiB  
Article
Three-Dimensional Combined Finite-Discrete Element Modeling of Shear Fracture Process in Direct Shearing of Rough Concrete–Rock Joints
by Gyeongjo Min, Daisuke Fukuda, Sewook Oh, Gyeonggyu Kim, Younghun Ko, Hongyuan Liu, Moonkyung Chung and Sangho Cho
Appl. Sci. 2020, 10(22), 8033; https://doi.org/10.3390/app10228033 - 12 Nov 2020
Cited by 12 | Viewed by 3001
Abstract
A three-dimensional combined finite-discrete element element method (FDEM), parallelized by a general-purpose graphic-processing-unit (GPGPU), was applied to identify the fracture process of rough concrete–rock joints under direct shearing. The development process of shear resistance under the complex interaction between the rough concrete–rock joint [...] Read more.
A three-dimensional combined finite-discrete element element method (FDEM), parallelized by a general-purpose graphic-processing-unit (GPGPU), was applied to identify the fracture process of rough concrete–rock joints under direct shearing. The development process of shear resistance under the complex interaction between the rough concrete–rock joint surfaces, i.e., asperity dilatation, sliding, and degradation, was numerically simulated in terms of various asperity roughness under constant normal confinement. It was found that joint roughness significantly affects the development of overall joint shear resistance. The main mechanism for the joint shear resistance was identified as asperity sliding in the case of smoother joint roughness and asperity degradation in the case of rougher joint asperity. Moreover, it was established that the bulk internal friction angle increased with asperity angle increments in the Mohr–Coulomb criterion, and these results follow Patton’s theoretical model. Finally, the friction coefficient in FDEM appears to be an important parameter for simulating the direct shear test because the friction coefficient affects the bulk shear strength as well as the bulk internal friction angle. In addition, the friction coefficient of the rock–concrete joints contributes to the variation of the internal friction angle at the smooth joint than the rough joint. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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17 pages, 22202 KiB  
Article
Evaluation on Rock Tensile Failure of the Brazilian Discs under Different Loading Configurations by Digital Image Correlation
by Diyuan Li, Bang Li, Zhenyu Han and Quanqi Zhu
Appl. Sci. 2020, 10(16), 5513; https://doi.org/10.3390/app10165513 - 10 Aug 2020
Cited by 24 | Viewed by 4755
Abstract
The fracture behavior of the disc specimens in the Brazilian test is closely related to the reliability and accuracy of the experimental results. To comprehensively investigate the effect of various loading methods and rock material types on the failure mechanism of the Brazilian [...] Read more.
The fracture behavior of the disc specimens in the Brazilian test is closely related to the reliability and accuracy of the experimental results. To comprehensively investigate the effect of various loading methods and rock material types on the failure mechanism of the Brazilian discs, five different rock types tested with three typical loading methods were employed in this work. The digital image correlation (DIC) method was applied to record and analyze the strain and displacement field of the specimens during the loading process. Experimental results indicate that the peak load and deformation characteristics of the Brazilian discs are strongly affected by the loading types. The Brazilian test with the Chinese standard is evidently not suitable for measuring the tensile strength of rocks, and the other two testing methods may lead to an invalid failure mode for rock materials with high stiffness and tensile to compressive strength ratio. Furthermore, it revealed that the maximum equivalent stress point of a disc specimen is co-controlled by the material stiffness and its tensile–compression ratio. The present work shows that it is necessary to select a suitable loading configuration for each rock type in the Brazilian test. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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16 pages, 9505 KiB  
Article
A Study on Shock Absorption Characteristics of Honeycomb-Inserted Bollards
by Sangwon Seon, Kyungwuk Kim, Cheonho Bae and Won Yi
Appl. Sci. 2020, 10(9), 3014; https://doi.org/10.3390/app10093014 - 26 Apr 2020
Cited by 3 | Viewed by 3257
Abstract
Lack of shock absorption capability of conventional steel bollards causes significant vehicle damage and, consequently, high repair costs. This research studies a solution to reduce vehicle damage by inserting polylactic acid (PLA) honeycomb structures. A honeycomb-inserted bollard was designed based on numerical simulations [...] Read more.
Lack of shock absorption capability of conventional steel bollards causes significant vehicle damage and, consequently, high repair costs. This research studies a solution to reduce vehicle damage by inserting polylactic acid (PLA) honeycomb structures. A honeycomb-inserted bollard was designed based on numerical simulations using LS-DYNA, which yielded the bollard designed for actual vehicle-bollard collision experiments. Simulation efforts were focused on calculating the acceleration characteristics when a vehicle collides with steel and honeycomb-inserted bollards. Compared to the simulated steel bollards, 20 MPa yield-strength honeycomb-inserted bollard showed 0.017 s delay in the maximum acceleration occurrence time, reduction of the maximum acceleration of 37.4% of that of steel bollards, and a 13.1% reduction in the B-pillar maximum acceleration. Actual vehicle-bollard collision experiments, with a gyro-sensor installed at the test vehicle front bumper frame, also proved improved shock absorption characteristics of the honeycomb-inserted bollards. An experiment with honeycomb-inserted bollard showed a 0.783 s delay in the maximum acceleration occurrence time, a significant delay when compared to steel bollards. The maximum acceleration measured by the gyro-sensor was 0.35 × 103 m/s2 when the simulation predicted it to be 0.388 × 103 m/s2, proving the similarity in the simulations and experiments. Thus, this study of shock absorption characteristics promised reduced damage to vehicles and lower repair cost. Full article
(This article belongs to the Special Issue Fracture Mechanics – Theory, Modeling and Applications)
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