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Fracture Mechanics and Phase Field Approaches in Engineering Materials
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Fracture Mechanics and Phase Field Approaches in Engineering Materials

A special issue of Materials (ISSN 1996-1944). This special issue belongs to the section "Mechanics of Materials".

Deadline for manuscript submissions: closed (20 September 2023) | Viewed by 24364

Special Issue Editor

Prof. Francesco Freddi

E-Mail Website
Guest Editor
Department of Engineering and Architecture, University of Parma, 43124 Parma, Italy
Interests: fracture mechanics; phase field; variational fracture; cohesive interface; structural health monitoring

Special Issue Information

Dear Colleagues,

In recent years, developments in phase-field approaches toward fracture and damage mechanics in addition to the constant increase in computational resources have allowed for the simulation and prediction of complicated failure processes in materials that were previously inconceivable.

The present Special Issue aims to present a collection of new and recent methods for the description of fracture and damage phenomena at different scales and in different materials.

With the aim of presenting the recent developments in this matter, it is a pleasure to invite contributions to the Special Issue entitled “Fracture Mechanics and Phase-Field Approaches in Engineering Materials” of the open access MDPI journal Materials. Contributions in the form of research investigations and reviews of the state-of-the-art addressing major advancements and failings are within the scope of this Special Issue and will be greatly appreciated.

Specific topics of interest include:

  • Regularizations and approximations of crack discontinuities
  • Phase-field approaches to brittle, cohesive, and ductile fracture
  • Variational and multiscale models for fracture and damage
  • Non-local damage models in solids and structures
  • Fatigue failure
  • Fracture and damage in a multiphysics framework (e.g., coupling with plasticity, thermal and chemical effects, etc.)

Scientific contributions concerning theoretical, numerical, and experimental aspects are also welcome.

Prof. Francesco Freddi
Guest Editor

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. Materials 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 2600 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 mechanics
  • Phase field
  • Damage mechanics
  • Failure modes
  • Materials

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Published Papers (7 papers)

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16 pages, 4978 KiB  
Article
Effects of Pore–Crack Relative Location on Crack Propagation in Porous Granite Based on the Phase-Field Regularized Cohesion Model
by Shiyi Zhang and Qiang Shen
Materials 2023, 16(23), 7474; https://doi.org/10.3390/ma16237474 - 1 Dec 2023
Viewed by 1239
Abstract
This study employs the phase-field regularized cohesion model (PF-CZM) to simulate crack propagation and damage behavior in porous granite. The impact of the pore radius (r), initial crack–pore distance (D), and pore–crack angle (θ) on crack propagation is investigated. The simulation findings reveal [...] Read more.
This study employs the phase-field regularized cohesion model (PF-CZM) to simulate crack propagation and damage behavior in porous granite. The impact of the pore radius (r), initial crack–pore distance (D), and pore–crack angle (θ) on crack propagation is investigated. The simulation findings reveal that, with a fixed deflection angle and initial crack–pore distance, larger pores are more likely to induce crack extension under identical loading conditions. Moreover, with r and θ remaining constant, the crack extension can be divided into two stages: from its initiation to the lower edge of the pore and then from the lower edge to the upper boundary of the model. Multiple combinations of different D/r ratios and pore radii are derived by varying the values of D and r. These results demonstrate that with a constant r, cracks tend to deflect towards the pore closer to the initial crack. Conversely, when D remains constant, cracks will preferentially deflect toward pores with a larger r. In summary, the numerical simulation of rock pores and initial cracks, based on the PF-CZM, exhibits remarkable predictive capabilities and holds significant potential in advancing rock fracture analyses. Full article
(This article belongs to the Special Issue Fracture Mechanics and Phase Field Approaches in Engineering Materials)
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21 pages, 4694 KiB  
Article
Stress Triaxiality in Anisotropic Metal Sheets—Definition and Experimental Acquisition for Numerical Damage Prediction
by Felix Rickhey and Seokmoo Hong
Materials 2022, 15(11), 3738; https://doi.org/10.3390/ma15113738 - 24 May 2022
Cited by 11 | Viewed by 3525
Abstract
Governing void growth, stress triaxiality (η) is a crucial parameter in ductile damage prediction. η is defined as the ratio of mean stress to equivalent stress and represents loading conditions. Attempts at introducing material anisotropy in ductile damage models have started [...] Read more.
Governing void growth, stress triaxiality (η) is a crucial parameter in ductile damage prediction. η is defined as the ratio of mean stress to equivalent stress and represents loading conditions. Attempts at introducing material anisotropy in ductile damage models have started only recently, rendering necessary in-depth investigation into the role of η here. η is commonly derived via finite elemnt (FE) simulation. An alternative is presented here: based on analytical expressions, η is obtained directly from the strains in the critical zone. For anisotropic materials, η associated with a specimen varies with yield criterion and material (anisotropy). To investigate the meaning of triaxiality for anisotropic materials, metal sheets made of dual phase steel DP780, and zirconium alloy Zirlo are chosen. Analytical expressions for η are derived for three popular yield criteria: von Mises, Hill48 and Barlat89. Tensile tests are performed with uniaxial tension, notch, and shear specimens, and the local principal strains, measured via digital image correlation (DIC), are converted to h. The uniaxial tension case reveals that only the anisotropic yield criteria can predict the expected η = 1/3. The ramifications associated with anisotropy become apparent for notched specimens, where η differences are highest; for shear specimens, the yield criterion and material-dependence is relatively moderate. This necessitates η and, consequently, the triaxiality failure diagram (TFD) being accompanied by the underlying yield criterion and anisotropy parameters. As the TFD becomes difficult to interpret, it seems more advantageous to provide pairs of principal strain ratio β and failure strain. Suggestions for deriving representative β and η are made. Full article
(This article belongs to the Special Issue Fracture Mechanics and Phase Field Approaches in Engineering Materials)
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28 pages, 4594 KiB  
Article
Phase Field Models for Thermal Fracturing and Their Variational Structures
by Sayahdin Alfat, Masato Kimura and Alifian Mahardhika Maulana
Materials 2022, 15(7), 2571; https://doi.org/10.3390/ma15072571 - 31 Mar 2022
Cited by 3 | Viewed by 1787 | Correction
Abstract
It is often observed that thermal stress enhances crack propagation in materials, and, conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot and study its energy dissipation property. [...] Read more.
It is often observed that thermal stress enhances crack propagation in materials, and, conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot and study its energy dissipation property. The Biot thermoelasticity model takes into account the following effects. Thermal expansion and contraction are caused by temperature changes, and, conversely, temperatures decrease in expanding areas but increase in contracting areas. In addition, we examine its thermomechanical properties through several numerical examples and observe that the stress near a singular point is enhanced by the thermoelastic effect. In the second part, we propose two crack propagation models under thermal stress by coupling a phase field model for crack propagation and the Biot thermoelasticity model and show their variational structures. In our numerical experiments, we investigate how thermal coupling affects the crack speed and shape. In particular, we observe that the lowest temperature appears near the crack tip, and the crack propagation is accelerated by the enhanced thermal stress. Full article
(This article belongs to the Special Issue Fracture Mechanics and Phase Field Approaches in Engineering Materials)
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14 pages, 4407 KiB  
Article
Determination and Verification of GISSMO Fracture Properties of Bolts Used in Radioactive Waste Transport Containers
by Bonjoon Gu, Jongmin Lim and Seokmoo Hong
Materials 2022, 15(5), 1893; https://doi.org/10.3390/ma15051893 - 3 Mar 2022
Cited by 2 | Viewed by 2001
Abstract
Transport containers for radioactive materials should withstand drop tests according to the regulations. In order to prevent a loss or dispersal of the internal radioactive materials in the drop tests, a tightening of the lid of the transport container should be maintained. The [...] Read more.
Transport containers for radioactive materials should withstand drop tests according to the regulations. In order to prevent a loss or dispersal of the internal radioactive materials in the drop tests, a tightening of the lid of the transport container should be maintained. The opening of the lid, due to the drop impact, might cause the dispersion of internal contents or a loss of shielding performance. Thus, it is crucial to predict damage to the fastening bolt and its fracture. In this study, the damage parameters of the fastening bolt were acquired, and its fracture was predicted using the generalized incremental stress state-dependent damage model (GISSMO), a phenomenological damage model. Since the dedicated transport container is large and heavy, various jigs that can simulate the fall of the container were designed, and the accuracy of fracture prediction was verified. Digital image correlation (DIC) was introduced for the accurate measurement of the displacement, and load–displacement data for tensile, shear, and combined loads were successfully acquired. Finally, the load–displacement curve of the finite element analysis (FEA) with GISSMO until the point of the bolt fracture was compared with the curve obtained from the experiment, where a good agreement was observed. Full article
(This article belongs to the Special Issue Fracture Mechanics and Phase Field Approaches in Engineering Materials)
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19 pages, 2087 KiB  
Article
A Unified Abaqus Implementation of the Phase Field Fracture Method Using Only a User Material Subroutine
by Yousef Navidtehrani, Covadonga Betegón and Emilio Martínez-Pañeda
Materials 2021, 14(8), 1913; https://doi.org/10.3390/ma14081913 - 11 Apr 2021
Cited by 74 | Viewed by 10680
Abstract
We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance equation and heat transfer, which [...] Read more.
We present a simple and robust implementation of the phase field fracture method in Abaqus. Unlike previous works, only a user material (UMAT) subroutine is used. This is achieved by exploiting the analogy between the phase field balance equation and heat transfer, which avoids the need for a user element mesh and enables taking advantage of Abaqus’ in-built features. A unified theoretical framework and its implementation are presented, suitable for any arbitrary choice of crack density function and fracture driving force. Specifically, the framework is exemplified with the so-called AT1, AT2 and phase field-cohesive zone models (PF-CZM). Both staggered and monolithic solution schemes are handled. We demonstrate the potential and robustness of this new implementation by addressing several paradigmatic 2D and 3D boundary value problems. The numerical examples show how the current implementation can be used to reproduce numerical and experimental results from the literature, and efficiently capture advanced features such as complex crack trajectories, crack nucleation from arbitrary sites and contact problems. The code developed is made freely available. Full article
(This article belongs to the Special Issue Fracture Mechanics and Phase Field Approaches in Engineering Materials)
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20 pages, 4049 KiB  
Article
Phase Field Simulation of Laminated Glass Beam
by Francesco Freddi and Lorenzo Mingazzi
Materials 2020, 13(14), 3218; https://doi.org/10.3390/ma13143218 - 20 Jul 2020
Cited by 11 | Viewed by 2823
Abstract
The complex failure mechanisms of glass laminates under in-plane loading conditions is modelled within the framework of phase-field strategy. Laminated glass is widely used for structural purposes due to its safe post-glass-breakage response. In fact, the combination of several glass plies bonded together [...] Read more.
The complex failure mechanisms of glass laminates under in-plane loading conditions is modelled within the framework of phase-field strategy. Laminated glass is widely used for structural purposes due to its safe post-glass-breakage response. In fact, the combination of several glass plies bonded together with polymeric interlayers allows overcoming the brittleness of the glass and to reach a pseudo-ductile response. Moreover, the post-breakage behaviour of the laminate is strictly correlated by the mechanical properties of the constituents. Ruptures may appear as cracks within the layers or delamination of the bonding interface. The global response of a glass laminate, validated against experimental results taken from the literature, is carried out by investigating a simplified layup of two glass plies connected by cohesive interfaces through an interlayer. Delamination of the adhesive interface is described, and crack patterns within the materials are fully described. Finally, the proposed approach put the basis for future comparisons with results of experimental campaign and real-life applications. Full article
(This article belongs to the Special Issue Fracture Mechanics and Phase Field Approaches in Engineering Materials)
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1 pages, 190 KiB  
Correction
Correction: Alfat et al. Phase Field Models for Thermal Fracturing and Their Variational Structures. Materials 2022, 15, 2571
by Sayahdin Alfat, Masato Kimura and Alifian Mahardhika Maulana
Materials 2022, 15(10), 3623; https://doi.org/10.3390/ma15103623 - 19 May 2022
Viewed by 1019
Abstract
The authors were not aware of typographical errors made in the writing phase, and, hence, wish to make the following corrections to the original paper [...] Full article
(This article belongs to the Special Issue Fracture Mechanics and Phase Field Approaches in Engineering Materials)
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