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Senapati S, Banerjee A, Rajesh R. Role of composition in fracture behavior of two-phase solids. Phys Rev E 2023; 107:055002. [PMID: 37329015 DOI: 10.1103/physreve.107.055002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2022] [Accepted: 04/11/2023] [Indexed: 06/18/2023]
Abstract
In a two-phase solid, we examine the growth of a preexisting macroscopic crack based on simulations of a random spring network model. We find that the enhancement in toughness, as well as strength, is strongly dependent on the ratio of elastic moduli as well as on the relative proportion of the phases. We find that the mechanism that leads to enhancement in toughness is not the same as that for enhancement in strength; however, the overall enhancement is similar in mode I and mixed-mode loading. Based on the crack paths, and the spread of the fracture process zone, we identify the type of fracture to transition from nucleation type, for close to single-phase compositions, whether hard or soft, to avalanche type for more mixed compositions. We also show that the associated avalanche distributions exhibit power-law statistics with different exponents for each phase. The significance of variations in the avalanche exponents with the relative proportion of phases and possible connections to the fracture types are discussed in detail.
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Affiliation(s)
- Subrat Senapati
- Department of Applied Mechanics, IIT Madras, Chennai 600036, India
| | | | - R Rajesh
- Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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Kumar D, Banerjee A, Rajesh R. Interplay between disorder and hardening during tensile fracture of a quasi-brittle solid. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2021.0934] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
We examine the specific role of the interplay between hardening and disorder characteristics of a representative quasi-brittle material on its failure mechanisms using a random spring network model. The model incorporates quasi-brittleness in its spring constants and disorder in the failure strain threshold and is shown to be effective in simulating the experimentally observed tensile and fracture behaviour of a quasi-brittle epoxy resin-based polymer. It is shown that rapid localization of deformation and associated damage growth occurs for a weakly hardening solid while for a linear elastic material, damage nucleates at multiple independent sites, and there is significant growth of damage, independent of other nucleating sites, prior to maximum load. The failure mechanism is shown to crossover from an avalanche-dominated fracture for a linear elastic material to nucleation-dominated fracture for a weakly hardening material.
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Affiliation(s)
- Deepak Kumar
- Department of Applied Mechanics, IIT Madras, Chennai 600036, India
| | | | - R. Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Tharamani, Chennai 600113, India
- Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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Kumar A, Ghosh R. A review on experimental and numerical investigations of cortical bone fracture. Proc Inst Mech Eng H 2022; 236:297-319. [DOI: 10.1177/09544119211070347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
This paper comprehensively reviews the various experimental and numerical techniques, which were considered to determine the fracture characteristics of the cortical bone. This study also provides some recommendations along with the critical review, which would be beneficial for future research of fracture analysis of cortical bone. Cortical bone fractures due to sports activities, climbing, running, and engagement in transport or industrial accidents. Individuals having different diseases are also at high risk of cortical bone fracture. It has been observed that osteon orientation influences cortical bone fracture toughness and fracture mechanisms. Apart from this, recent studies indicate that fracture parameters of cortical bone also depend on many factors such as age, sex, temperature, osteoporosis, orientation, location, loading condition, strain rate, and storage facility, etc. The cortical bone regains its fracture toughness due to various toughening mechanisms. Owing to these factors, several experimental, clinical, and numerical investigations have been carried out to determine the fracture parameters of the cortical bone. Cortical bone is the dense outer surface of the bone and contributes to 80%–82% of the skeleton mass. Cortical bone experiences load far exceeding body weight due to muscle contraction and the dynamics of motion. It is very important to know the fracture pattern, direction of fracture, location of the fracture, and toughening mechanism of cortical bone. A basic understanding of the different factors that affect the fracture parameters and fracture mechanisms of the cortical bone is necessary to prevent the failure and fracture of cortical bone. This review has summarized the advancement considered in the various experimental techniques and numerical methods to get complete information about the fracture mechanisms of cortical bone.
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Affiliation(s)
- Ajay Kumar
- School of Engineering, Indian Institute of Technology Mandi (IIT Mandi), Kamand, Mandi 175005, Himachal Pradesh, India
| | - Rajesh Ghosh
- School of Engineering, Indian Institute of Technology Mandi (IIT Mandi), Kamand, Mandi 175005, Himachal Pradesh, India
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Kumar GA, Rambabu Y, Guntu RK, Sivaram K, Reddy MS, Rao CS, Venkatramu V, Kumar VR, Sriman Narayana Iyengar NC. Zr xCa 30-xP 70 thermoluminescent bio glass, structure and elasticity. J Mech Behav Biomed Mater 2021; 119:104517. [PMID: 33872922 DOI: 10.1016/j.jmbbm.2021.104517] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2020] [Revised: 04/04/2021] [Accepted: 04/05/2021] [Indexed: 11/25/2022]
Abstract
Phosphate glasses of calcium oxide have been well proved materials for various bio bones and dental implants. However, still there is a lot of scope and demand to produce efficient elastic bio implants and resource. In view of this, ZrxCa30-xP70 phosphate materials are prepared by using melt quenching method. Bio, physical, thermoluminescence and elastic techniques are used to characterize the samples. Additionally, simulated body fluid was prepared and it is used especially for bio techniques. Further, the glasses are taken for different dose (~0, 10, 20 & 50 kGy) of gamma irradiation around half an hour. And again similar techniques are used to characterize the samples. All the findings from bio, physical, thermoluminescence and elastic characterization results are analysed and took for better comparison with previous studies to develop various bio bone (or) bio dental resource. Structural reports suggests that the ZrxCa30-xP70 materials were glassy before immersion in SBF solution and immersed (~720 h) samples are showing partial ceramic nature. The weight loss and pH reports suggests them for alternative bio resource as a bio bones and dental implants. Observed thermal stability, microhardness and elastic modulus evaluations of ZrxCa30-xP70 materials in required standards are also additional advantage. Furthermore, thermoluminiscence (TL) under different γ-irradiation doses is reported for glasses with and without immersing in a simulated body fluid. The glasses lose TL intensity when immersed in simulated body fluid for nearly 720 h. This is useful to modulate bio-behaviour in terms of hydroxyapatite layer growth on the glass surface.
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Affiliation(s)
- G Anil Kumar
- Department of Physics, Sreenidhi Institute of Science and Technology, JNT University, Hyderabad, 501301, India
| | - Y Rambabu
- Department of Physics, Sreenidhi Institute of Science and Technology, JNT University, Hyderabad, 501301, India
| | - Ravi Kumar Guntu
- Department of Physics, Sreenidhi Institute of Science and Technology, JNT University, Hyderabad, 501301, India.
| | - K Sivaram
- Department of Physics, DMSSVH College of Engineering, Machilipatnam, 521 001, JNT University, Kakinada, Andhra Pradesh, India
| | - M Sreenath Reddy
- Department of Physics, Osmania University, Hyderabad, 500 007, Telangana, India
| | - Ch Srinivasa Rao
- Department of Physics, Andhra Loyola College, Krishna University, Vijayawada, 520 008, Andhra Pradesh, India
| | - V Venkatramu
- Department of Physics, DR.MRAR PG Center, Krishna University, Nuzvid, 521 201, Andhra Pradesh, India
| | - V Ravi Kumar
- Department of Physics, Acharya Nagarjuna University, Guntur, 522 510, Andhra Pradesh, India
| | - N Ch Sriman Narayana Iyengar
- Department of Information Technology, Sreenidhi Institute of Science and Technology, JNT University, Hyderabad, 501301, India
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Parihar RPS, Mani DV, Banerjee A, Rajesh R. Role of spatial patterns in fracture of disordered multiphase materials. Phys Rev E 2020; 102:053002. [PMID: 33327211 DOI: 10.1103/physreve.102.053002] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/12/2020] [Accepted: 11/03/2020] [Indexed: 11/07/2022]
Abstract
Multiphase materials, such as composite materials, exhibit multiple competing failure mechanisms during the growth of a macroscopic defect. For the simulation of the overall fracture process in such materials, we develop a two-phase spring network model that accounts for the architecture between the different components as well as the respective disorders in their failure characteristics. In the specific case of a plain weave architecture, we show that any offset between the layers reduces the delocalization of the stresses at the crack tip and thereby substantially lowers the strength and fracture toughness of the overall laminate. The avalanche statistics of the broken springs do not show a distinguishable dependence on the offsets between layers. The power-law exponents are found to be much smaller than that of disordered spring network models in the absence of a crack. A discussion is developed on the possibility of the avalanche statistics being those near breakdown.
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Affiliation(s)
| | - Dhiwakar V Mani
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai-600036, India
| | - Anuradha Banerjee
- Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai-600036, India
| | - R Rajesh
- The Institute of Mathematical Sciences, C.I.T. Campus, Taramani, Chennai-600113, India.,Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai-400094, India
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Mayya A, Banerjee A, Rajesh R. Role of porosity and matrix behavior on compressive fracture of Haversian bone using random spring network model. J Mech Behav Biomed Mater 2018; 83:108-119. [PMID: 29698930 DOI: 10.1016/j.jmbbm.2018.04.013] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2018] [Revised: 03/18/2018] [Accepted: 04/13/2018] [Indexed: 10/17/2022]
Abstract
Haversian remodeling is known to result in improved resistance to compressive fracture in healthy cortical bone. Here, we examine the individual roles of the mean porosity, structure of the network of pores and remodeled bone matrix properties in the fracture behavior of Haversian bone. The detailed structure of porosity network is obtained both pre- and post-testing of dry cubical bone samples using micro-Computed Tomography. Based on the periodicity in the features of porosity along tangential direction, we develop a two dimensional porosity-based random spring network model for Haversian bone. The model is shown to capture well the macroscopic response and reproduce the avalanche statistics similar to recently reported experiments on porcine bone. The predictions suggest that at the millimeter scale, the remodeled bone matrix of Haversian bone is less stiff but tougher than that of plexiform/primary bone.
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Affiliation(s)
- Ashwij Mayya
- Department of Applied Mechanics, IIT-Madras, Chennai 600036, India
| | | | - R Rajesh
- The Institute of Mathematical Sciences, Tharamani, Chennai 600113, India; Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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