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Linear and Non-linear Mechanical Behavior of Brittle Materials

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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 10571

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Prof. Dr. Giovanni Bruno

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Guest Editor

Bundesanstalt für Materialforschung und –prüfung (BAM), Berlin, Germany
Interests: neutron diffraction; residual stress; mechanical properties of materials; additive manufacturing; porous ceramics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Brittle materials include a wide range of material classes: From polymers to metals, through classic glass, ceramics, and composites. They all share a supposed linear elastic behavior but are often found to display non-linear features: stress–strain relationships, high temperature dilation, etc.

After the success of the first of a series (Brittle Materials under Mechanical Extremes), in this Special Issue, I want to encourage contributions describing and explaining the non-linear mechanical behavior of brittle materials, whether due to microcracking, interaction among constituent phases, or microstructural features.

As in the previous Special Issue, advanced characterization techniques, numerical and analytical models, as well unconventional experiments should be reported. The idea is not to create an exhaustive compilation of unexpected behaviors but to spark a debate about the origin of (non-linear) mechanical behavior of brittle materials.

The description and understanding of the mechanical behavior of brittle materials under operational (sometimes unconventional) loads, such as mechanical and temperature cycling (including cryogenic), electric fields, and corrosion environments represents one focus of the Special Issue. The discussion of analogies and differences between different materials, such as polymers and concrete, or metals and ceramics, represents another focus of the issue (the comparison between plasticity and microcracking would well depict such kind of discussions). Modeling and rationalization of peculiar behaviors of brittle materials will be a further focus of the issue.

All should be corroborated by advanced microstructural studies (microscopy, 3D imaging, etc.), leading to the identification of microstructure–property relationships.

In spite of their apparently simple mechanical behavior, brittle materials still show knowledge gaps. This issue should contribute to fill them.

Prof. Dr. Giovanni Bruno
Guest Editor

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Keywords

ceramics
concrete
composites
glass
anelasticity
viscoelasticity
microcracking
electric/thermal properties
uniaxial/biaxial/triaxial testing
high-temperature
micromechanical modeling
FEM
in situ testing

Published Papers (6 papers)

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Research

16 pages, 6899 KiB

Open AccessArticle

Compaction Behavior and Damage Constitutive Model for Porous Cement Mortar under Uniaxial Cyclic Loads

by De-Hang Liu, Yue Qin, Li Zhuo, Jian-Feng Liu, Zhao-Qiang Zheng, Jian-Liang Pei and Huai-Zhong Liu

Materials 2022, 15(23), 8302; https://0-doi-org.brum.beds.ac.uk/10.3390/ma15238302 - 22 Nov 2022

Viewed by 1016

Abstract

The void compression stage causes porous cement mortar to present special mechanical properties. In order to study the compaction behavior and the damage evolution of the porous material, cement mortar specimens with an average porosity of 26.8% were created and cyclic uniaxial compression tests were carried out. The irreversible strain accumulated in the tests was obtained by cyclic loading and unloading. As the secant modulus of the porous cement mortar increases with stress in the pre-peak deformation stage, its damage variable is defined according to the accumulated irreversible strain instead of modulus degradation. The strain-based damage indicator fitted with the damage evolution law is characterized by linear accumulation at the beginning and has an acceleration rate of about 0.3 in the pre-peak deformation stage, and the damage value converges to 1 at failure. Based on the Weibull distribution, a constitutive damage model of porous cement mortar is improved by considering both the damage evolution during the plastic deformation stage and the mechanical behavior in the compaction stage. The theoretical envelope curves obtained by the constitutive model are in good agreement with the experimental envelope curves of cyclic uniaxial compression in the compaction and pre-peak stages, and the average absolute error is about 0.54 MPa in the entire pre-peak stage, so the proposed damage constitutive model can characterize the damage-induced mechanical properties of porous cement mortar in the compaction and pre-peak stages. Full article

(This article belongs to the Special Issue Linear and Non-linear Mechanical Behavior of Brittle Materials)

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16 pages, 78622 KiB

Open AccessArticle

Influence of the Composition on the Compressive Behaviour of a Semi-Metallic Brake-Pad Material

by Itziar Serrano-Munoz, Vincent Magnier, Florent Brunel and Philippe Dufrenoy

Materials 2022, 15(22), 7911; https://0-doi-org.brum.beds.ac.uk/10.3390/ma15227911 - 09 Nov 2022

Cited by 1 | Viewed by 1084

Abstract

The contact interface between the rotation and static part of a friction brake is central to the optimal functioning of the brake system due to the occurrence of heat dissipation, mechanical interaction and thermal exchanges. Generally, braking performances are evaluated by the energetic efficiency and wear rates of the contact surface. However, the compressive behaviour of the contact materials has also a significant contribution to the overall performances. In this work, the meso- and microscopic compressive behaviour of a sintered semi-metallic brake-pad material is investigated mainly via compression testing coupled with Digital Image Correlation (DIC) technique, as well as optical and scanning electron microscopy (SEM) analysis. The composition of a reference material (RM) is simplified to a selection of nine components, as opposed to up to thirty components typically used in commercial brake-pad materials. The retained components are considered as the most crucial for safe-operating performances. At the studied stress levels, the RM material is flexible (E = 5330 MPa), deformable (E

_{z z - p l a s t i c}

= −0.21%), and exhibits hysteresis loops. Subsequently, the contribution to the mechanical response of each individual component is investigated by producing the so-called dissociated materials, where the number of components is, at a time, further reduced. It is observed that the macroscopic behaviour is mainly controlled by the content (i.e., size distribution, shape and nature) of graphite particles, and that the hysteresis is only related to one of the two types of graphite used (G2 particles). Moreover, RM containing 13 wt% of G2 particles embedded in a relatively soft matrix (10.86 GPa) is able to increase the hysteresis (by 35%) when compared to the dissociated material containing 20 wt% of G2 particles which is embedded in a stiffer matrix (E = 106 GPa). Full article

(This article belongs to the Special Issue Linear and Non-linear Mechanical Behavior of Brittle Materials)

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27 pages, 123357 KiB

Open AccessArticle

Experimental Investigation on Dynamic Tensile Behaviors of Engineered Cementitious Composites Reinforced with Steel Grid and Fibers

by Liang Li, Hongwei Wang, Jun Wu, Shutao Li and Wenjie Wu

Materials 2021, 14(22), 7042; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14227042 - 20 Nov 2021

Cited by 5 | Viewed by 1352

Abstract

Engineered cementitious composites (ECC) used as runway pavement material may suffer different strain rate loads such as aircraft taxiing, earthquakes, crash impacts, or blasts. In this paper, the dynamic tensile behaviors of the steel grid-polyvinyl alcohol (PVA) fiber and KEVLAR fiber-reinforced ECC were investigated by dynamic tensile tests at medium strain rates. The mixture was designed with different volume fractions of fibers and layer numbers of steel grids to explore the reinforcement effectiveness on the dynamic performance of the ECC. The volume fractions of these two types of fibers were 0%, 0.5%, 1%, 1.5%, and 2% of the ECC matrix, respectively. The layer numbers of the steel grid were 0, 1, and 2. The dynamic tensile behaviors of the PVA fiber and the KEVLAR fiber-reinforced ECC were also compared. The experimental results indicate that under dynamic tensile loads, the PVA-ECC reveals a ductile and multi-cracking failure behavior, and the KEVLAR-ECC displays a brittle failure behavior. The addition of the PVA fiber and the KEVLAR fiber can improve the tensile peak stress of the ECC matrix. For the specimens A0.5, A1, A1.5, and A2.0, the peak stress increases by 84.3%, 149.4%, 209.6%, and 237.3%, respectively, compared to the matrix specimen. For the specimens K0.5, K1, K1.5, and K2, the peak stress increases by about 72.3%, 147.0%, 195.2%, and 263.9%, respectively, compared to the matrix specimen. The optimum fiber volume content is 1.5% for the PVA-ECC and the KEVLAR-ECC. The KEVLAR-ECC can supply a higher tensile strength than the PVA-ECC, but the PVA-ECC reveals more prominent deformation capacity and energy dissipation performance than the KEVLAR-ECC. Embedding steel grid can improve the tensile peak stress and the energy dissipation of the ECC matrix. For the strain rate of 10⁻³ s⁻¹, the peak stress of the A0.5S1 and A0.5S2 specimens increases by about 49.1% and 105.7% compared to the A0.5 specimen, and the peak stress of the K0.5S1 and K0.5S2 specimens increases by about 61.5% and 95.8%, respectively, compared to the K0.5 specimen. Full article

(This article belongs to the Special Issue Linear and Non-linear Mechanical Behavior of Brittle Materials)

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19 pages, 6360 KiB

Open AccessArticle

Rheological Model to Describe the Cyclic Load-Bearing Behaviour of Strain-Hardening Cement-Based Composites (SHCC)

by Dominik Junger, Steffen Müller and Viktor Mechtcherine

Materials 2021, 14(21), 6444; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14216444 - 27 Oct 2021

Cited by 1 | Viewed by 1553

Abstract

The mechanical behaviour of strain-hardening cement-based composites (SHCC) under monotonic tensile loading has been the subject of research for many years. The recent research on the SHCC’s performance under cyclic loading has enabled the identification of a wide variety of damage phenomena different to those observed under monotonic loading. The article at hand first summarises the experimental evidence of such phenomena in the context of the material performance observed. On this basis, the mechanisms behind these phenomena are discussed and explained using rheological modelling. Full article

(This article belongs to the Special Issue Linear and Non-linear Mechanical Behavior of Brittle Materials)

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15 pages, 6775 KiB

Open AccessArticle

Growth Ring Orientation Effects in Transverse Softwood Fracture

by Parinaz Belalpour Dastjerdi and Eric N. Landis

Materials 2021, 14(19), 5755; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14195755 - 02 Oct 2021

Cited by 2 | Viewed by 1694

Abstract

In this study, the fracture mechanics of eastern spruce were characterized in relation to end-grain orientation. Compact tension-type specimens with small pre-formed cracks were prepared such that grain angle varied relative to the load axis. Specimens were loaded under crack mouth opening displacement (CMOD) control as to maintain stable crack growth. Specimen fracture was characterized using both R-curve and bulk fracture energy approaches. The results showed that under a RT grain orientation, as well as grain deviations up to about 40

^{\circ}

, cracks will follow a path of least resistance in an earlywood region. As the grain angle exceeds 40

^{\circ}

, the crack will initially move macroscopically in the direction of maximum strain energy release rate, which extends in the direction of the pre-crack, but locally meanders through earlywood and latewood regions before settling once again in an earlywood region. At 45

^{\circ}

, however, the macroscopic crack takes a turn and follows a straight radial path. The results further show that RT fracture is macroscopically stable, while TR fracture is unstable. None of the end-grain fracture orientations showed rising R-curve behavior, suggesting that there is not a traditional fracture process zone in this orientation. Full article

(This article belongs to the Special Issue Linear and Non-linear Mechanical Behavior of Brittle Materials)

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19 pages, 8314 KiB

Open AccessArticle

Calibration of Drucker–Prager Cap Constitutive Model for Ceramic Powder Compaction through Inverse Analysis

by Vladimir Buljak, Severine Baivier-Romero and Achraf Kallel

Materials 2021, 14(14), 4044; https://0-doi-org.brum.beds.ac.uk/10.3390/ma14144044 - 20 Jul 2021

Cited by 15 | Viewed by 2938

Abstract

Phenomenological plasticity models that relate relative density to plastic strain are frequently used to simulate ceramic powder compaction. With respect to the form implemented in finite element codes, they need to be modified in order to define governing parameters as functions of relative densities. Such a modification increases the number of constitutive parameters and makes their calibration a demanding task that involves a large number of experiments. The novel calibration procedure investigated in this paper is based on inverse analysis methodology, centered on the minimization of a discrepancy function that quantifies the difference between experimentally measured and numerically computed quantities. In order to capture the influence of sought parameters on measured quantities, three different geometries of die and punches are proposed, resulting from a sensitivity analysis performed using numerical simulations of the test. The formulated calibration protocol requires only data that can be collected during the compaction test and, thus, involves a relatively smaller number of experiments. The developed procedure is tested on an alumina powder mixture, used for refractory products, by making a reference to the modified Drucker–Prager Cap model. The assessed parameters are compared to reference values, obtained through more laborious destructive tests performed on green bodies, and are further used to simulate the compaction test with arbitrary geometries. Both comparisons evidenced excellent agreement. Full article

(This article belongs to the Special Issue Linear and Non-linear Mechanical Behavior of Brittle Materials)

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