Micromechanical modeling of damage in elasto-plastic nanocomposites using unit cell representative volume element and cohesive zone model

Journal Pre-proof Micromechanical modeling of damage in elasto-plastic nanocomposites using unit cell representative volume element and cohesive zone model M.A. Eltaher, A. Wagih PII:

S0272-8842(20)30046-8

DOI:

https://doi.org/10.1016/j.ceramint.2020.01.046

Reference:

CERI 23978

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Ceramics International

Received Date: 30 October 2019 Revised Date:

31 December 2019

Accepted Date: 6 January 2020

Please cite this article as: M.A. Eltaher, A. Wagih, Micromechanical modeling of damage in elasto-plastic nanocomposites using unit cell representative volume element and cohesive zone model, Ceramics International (2020), doi: https://doi.org/10.1016/j.ceramint.2020.01.046. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

Micromechanical Modeling of Damage in Elasto-plastic Nanocomposites Using Unit Cell Representative Volume Element and Cohesive Zone Model M.A. Eltaher a,b* , A. Wagih b a

Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia b Faculty of Engineering, Mechanical Design and Production Department, Zagazig University, P.O. Box 44519, Zagazig, Egypt Email: [email protected] & [email protected] Tel:+966565518613

Abstract The article aims to investigate elasto-plastic nanocomposites damage behavior dependence on the interfacial bonding between metal and ceramic phase. To this end, a unit cell representative volume element and cohesive element model were developed numerically to simulate matrix and reinforcement phases and the bonding between them. Through experimental study, commercial pure Al and Al2O3 are used as raw materials to produce Al-5%Al2O3 nanocomposite by using high energy ball milling followed by cold compaction and sintering. The developed model with cohesive interface elements is validated and approximately it is identical with experimental results available in the literature and others done during this work for Al-5%Al2O3 nanocomposite. Numerical results show the validity of representative volume element with cohesive elements model to accurately simulate the stress-strain behavior of nanocomposites which highly reduce the computation cost of 3D models and binarization errors for simulating real microstructure. The results show that the interfacial bonding between ceramic and matrix phase has a large influence on the prediction of the stress-strain behavior which highlight that the assumption of considering fully bonded interface in the simulation of nanocomposites is inaccurate. The ultimate interface strength is the most critical parameter that affects the decohesion behavior between matrix and reinforcement nanoparticles which makes the bonding between these two phases a critical issue in production of nanocomposites. This highlights the immense demand of finding new methods to improve adhesion between reinforcement and matrix phases for production of nanocomposites with improved properties. Keywords: - Metal-Matrix Nanocoposites; Elasto-Plastic Damage Model; Exponential Cohesive Law;

High Energy Ball Milling; Finite Element Simulation.

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1. Introduction Today is the age of nanofabrication, nanoscience, and nanotechnology. So, new materials with superior mechanical, electrical, thermal and tribological properties are required for industrial applications such as: aerospace technology, automobiles, electronics, optics, chemistry, biomedical engineering, nuclear engineering, and micro/nano electromechanical systems (MEMS/NEMS) [1, 2]. Metal-matrix nanocomposite (MMNC), that has superior mechanical properties comparing to monolithic materials and conventional coarse-grained metal matrix composites, is one of promising materials that will be used in many of those applications. Mechanical processing is one of the effective techniques to the manufacture of MMNC materials, provides an opportunity to manufacture products with unique characteristics and homogenous distribution, which may be difficult to be produced by any other way. Through mechanical processing, a powder involving deformation, fracturing and cold welding of the particles during repeated collisions with a ball during high-energy milling is produced [3]. Prabhu et al. [4] and Poirier et al. [5] solved the reinforcement agglomeration issue in alumina/aluminum nanocomposites by using mechanical milling technique. Wagih [6,7] investigated mechanical properties and microstructure of Al–Mg/Al2O3 nanocomposite powder produced by mechanical ball milling technique. Cabeza et al. [8] studied morphology and microstructure properties of nano-sized TiC particle-reinforced 6005A aluminum alloy matrix composite manufactured by high energy ball milling. Wagih et al. [9] presented a system dynamic model to predict the optimum ball size, milling speed and milling time that achieve the best particle size reduction of metal-matrix nanocomposites. Abu-Oqail et al. [10] and Fathy et al. [11] produced copper matrix nanocomposites reinforced by ZrO2 particles by mechanical milling technique at different milling times and showed that the increasing in milling time will improve microhardness of nanocomposites. Guo et al. [12] investigated the influence of high B4C contents on the structural evolution of Al–B4C nanocomposite powders during high energy ball milling. Gasiorek et al. [13] developed a numerical model of the 2

guillotine cutting process of sheet aluminum bundles by using a FEM with a smoothed particle hydrodynamics approach. Micro/nano-mechanics models of composites are aimed to determine and evaluate effective properties of composite through models that incorporate the microstructural details [14]. One of these models is representative volume element, which applied to get the proper homogenized equations describing the mechanical deformation of the volume element. Hallberg [15] employed a finite strain elasto-viscoplastic constitutive model to evaluate the microstructure of commercial purity AA1050 aluminum during cold rolling. Aghdam et al. [16-18] presented a 3D FE micromechanical model to study effects of thermal residual stress, fiber coating and interface bonding on the transverse behavior of MMC under unidirectional, biaxial and shear loading. Mahmoodi et al. [19-20] developed a micromechanical model to study a damage of MMC subjected to off-axis and multi-axial loading. Saberi et al. [21] illustrated the role of nano-size SiC on lattice strain and grain size of Al/SiC nanocomposite. Rahimian et al. [22] and Reddy [23] investigated the effect of particle size and amount of alumina on microstructure and mechanical properties of Al matrix composite. Wagih [7] studied the effect of Mg addition on mechanical and thermoelectrical properties of Al−Al2O3 nanocomposite. Ma et al. [24] investigated a new mechanism namely as shear stress triggered fracture orientation, that is dominated in brittle shear fracturing. Wagih et al. [25] exploited 3D finite element (FE) model to predict microhardness and strengthening mechanisms of the nanocomposite. Bargmann et al. [26] and Bostanabad [27] presented a review on computational methods used in microstructure characterization and analysis of heterogeneous materials. Wagih and Shaat [28] illustrated the effects of microstructural changes, grain sub-division, stacking faults, and lattice strains on mechanical properties of commercial pure copper. Ahmadi et al. [29] investigated the mechanical properties of the polyethylene matrix reinforced by carbon nanotubes and carbon fibres by using a stochastic FE method and molecular dynamics (MD)

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simulations. Kazemi et al. [30] proposed robust inverse approach to identify the viscoelastic material properties under applied mechanical load. The elasto-plastic behaviors of nanocomposites is important for failure, strength, and damage evolutions. Bao et al. [31] studied theoretically the role of non-deformed particles in reinforcing ductile matrix materials against plastic flow. Qu et al. [32] and Shishvan and Asghari [33] applied strain-gradient plasticity theories to investigate the effect of particle size on uniaxial tension plastic behavior in composites. Zappalorto et al. [34] exploited a multiscale model to designate nanocomposite fracture toughness development by the plastic yielding. Hosseini-Toudeshky et al. [35] predicted micromechanical stress–strain behavior of dual phase steel by considering plasticity and grain boundaries debonding. Wang and Huang [36] presented comparative analytical micromechanics models to study elastoplastic behavior of long fibrous composites. Asiri et al. [37] presented FE model to simulate nanoindentation process on elastoplastic nanocomposites through loading and unloading. Elastoplastic damage initiates as debonding between matrix and reinforcement and ends by complete decohesion. These mechanisms can be studied analytically by cohesive zone model (CZM) that was proposed by Needleman [38-40] and Xu and Needleman [41, 42]. Camacho and Ortiz [43] exploited cohesive-law fracture model to simulate and investigate computationally damage in brittle materials. Zhang et al. [44] exploited the cohesive-zone model of interface and mesomechanics analysis to investigate interfacial adhesive strength for fiber-reinforced polymeric composites. Chandra et al. [45] and Elices et al. [46] discussed the applicability and limitations of CZM for metal-ceramics interfaces. Sun et al. [47] exploited elastoplastic with hardening and statistical damage model to predict the mechanical behavior of particle-reinforced metal matrix composites. Charles et al. [48] observed particle fracture of metal matrix composites reinforced with ceramics (zirconia and/or silica) by using plastic strain and CZM. Liu et al. [49] studied damage and cracks at the interface between CNTs and matrix by using bilinear CZM and FE. Dastgerdi et al. [50] 4

characterized reinforcement/matrix interface and debonding behaviors by using cohesive finite element model. Ben et al. [51] focused on the applicability of CZM in studying the interface debonding of large structures with functionally graded interphase that used in MEMS structures. Elkhateeb and Shin [52] exploited MD simulation and CZM to predict the crack propagation along the interface of Ti6Al4V/TiC in Titanium metal matrix composites under Mode-I and II loadings and at different temperatures. Jiang et al. [53] developed MD and CZM to simulate the interfacial behavior between graphene coating and aluminum substrate. Heidarhaei et al. [54] studied analytically the interfacial debonding in graphene-reinforced polymer nanocomposites by using CZM. Based on Isogeometric analysis, Phung-Van et al. [55] simulated buckling of functional graded (FG) nanoplates by using Mori–Tanaka schemes and rule of mixtures. Thanh et al. [56] presented size-dependent e ects on thermal buckling and post-buckling behaviors of FG micro-plates with porosities. Phung-Van [57] captured the size effects on the static and vibration behaviors of porous FG nanoplates based on nonlocal elasticity. Thanh et al. [58] exploited modified couple stress theory to study static and free vibration behaviors of FG carbon nanotube reinforced composite nanoplates. Thanh et al. [59, 60] illustrated the size-dependent phenomenon on bending and buckling behaviors of composite laminate microplate modeled by modified couple stress theory and higher order shear deformation. Thanh et al. [61] presented a nonlinear numerical model to capture the small-scale effects on the geometrically nonlinear behaviors of FG carbon nanotube reinforced composite microplate. Khatir et al. [62] proposed a technique based on Artifcial Neural Network combined with Particle Swarm Optimization to quantify a damage in laminated composite plates using Cornwell indicator. From literature and authors’ best knowledge, it is the first time to inspect damage in elastoplastic nanocomposites experimentally and computationally by using unit cell representative volume element (UCRVE) and cohesive zone model. Metal-matrix nanocomposite of Al-Al2O3 are 5

manufactured using high energy ball milling. Microstructure of nanocomposite is investigated by using SEM, EDX and XRD. Elasto-plastic isotropic strain hardening, and exponential cohesive law are proposed and implement by FE to simulate the deformation behavior of the metal matrix and the decohesion between metal matrix and reinforcement nanocomposite. The proposed model is validated with experimental results available in the literature and others done during this work for Al-Al2O3 nanocomposites. 2. Material and experiment Commercial pure Al (average particle size of 10 µm) and Al2O3 (average particle size of 2 µm) were used to produce Al-5%Al2O3 nanocomposite. High energy ball milling technique was performed to achieve homogeneous distribution of Al2O3 particles in Al matrix and to reduce the average particle size of Al and Al2O3. High energy ball milling was applied using a Fritsch planetary ball-milling machine with four containers each of 1 L volume. Hardened steel balls of 10 mm diameter and ball to powder ration of 10:1 was used. To avoid stacking of Al particle due to its high tendency for cold welding, 3 wt% Stearic acid was added to the mixture as process control agent. The rotating speed was kept at 250 rpm and the total weight of powder in each container is 25 g. The milling process was applied for 15 h with a stop of 3 min after each 1 h milling to avoid over heating of the powder and the loss of milling energy as thermal energy [8, 9]. Cold compaction at pressure 600 MPa followed by sintering in hydrogen for 5 h at 450ºC were applied to consolidate the prepared nanocomposites. Sintering was applied in a laboratory furnace with 1 ºC thermo-regulation. The heating and cooling rates were 2 ºC/min and 10 ºC/min, respectively. The mechanical properties of the prepared nanocomposites were obtained using tensile tests following a standard ASTM E8/E8M-11 test [63]. To meet the quasi-static test condition, the crosshead speed was adopted at 2 mm/min. Three specimens were tested for each set of materials. Fig.1 shows experimental test setup and sample dimensions.

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The microstructure of the prepared powders and consolidated samples were examined using SEM (model Quanta 250 FEG attached with EDX unit). The average particle size of Al2O3 after sintering was approximated using several SEM micrographs of the consolidated samples. X-Ray Diffraction (XRD) with 2-theta ranging from 20º to 70º (step size 0.02º) was used to check the composition of the prepared samples.

3. Numerical model and validation A 2D Unit-Cell RVE (UCRVE) was used to simulate the response of elasto-plastic MMNC. Based on the current experimental results and the author’s previous investigations [6-7, 10-11], it is noted that after sufficient milling time, the reinforcement particles take approximately spherical shape. Following this observation and Bao et al. [31] recommendation, a unit cell with quarter of the reinforcement particle and the surrounding matrix was simulated suing UCRVE as shown in Fig. 2, which representing a cylindrical matrix containing a single spherical reinforcement particle. A free finite element mesh of biquadratic elements with reduce integration was used to achieve an acceptable accuracy in the decohesion interface between reinforcement and matrix [45]. Three different FE meshes were considered, 4200, 5700 and 8750 elements, varying from coarse to fine mesh to investigate the mesh sensitivity of the presented model. A very fine mesh was applied at the interface between matrix and reinforcement as shown in Fig. 2. The boundary conditions applied to the model are illustrated in Fig. 2. Axisymmetry boundary condition was applied to the side in the left of the figure, symmetry boundary condition was applied to the lower side in the figure and coupling of all the nodes in the right side was applied to constrain these nodes to move equally in xdirection. All nodes in the upper side were coupled to move equally in y-direction. The simulation was performed under displacement control like that occur in the real experimental test. The displacement was applied on the upper side in various steps which is mandatory to control the convergence of nonlinear elasto-plastic simulations. 7

The matrix material is defined as elasto-plastic material, which can be modeled by isotropic strain hardening model. The constitutive equation for the matrix material was defined as: = where

and

matrix,

and

. ,

,

<

≥

(1)

are the uniaxial stress and strain, respectively.

is the Youngs modulus of the

are the yield stress and yield strain, respectively and

is the strain hardening

exponent defining the post yielding response of the material. The four material parameters, ,

,

and

were obtained by fitting the experimental tensile stress-strain curve of the matrix

material and fed to the FE model. A comparison between tensile test of pure Al metal and isotropic strain hardening model, Eq (1), is presented in Fig. 3. As shown, the experimental results are approximately identical with proposed model. So, the isotropic strain hardening model is considered to simulate the behavior of matrix material by using FE simulation. A fifth parameter should be fed to the FE model is the Poisson’s ratio of the matric material,

, which can be measured

experimentally. Since the reinforcement material is always ceramic phases, it is defined using linear elastic material model considering its elastic modulus ( ) and Poisson’s ratio ( ). Cohesive zone model [38-42] was used to define the decohesion interface between matrix and reinforcement. In this proposed model, the failure process zone is expressed as zero-thickness surface composed of two conceding cohesive surfaces. So, each element at the interface is defined by conceding nodes at the same coordinate. The decohesion between these elements is controlled by the separation across the cohesive interface. Sometimes, the cohesive model is named as “tractionseparation law” or “cohesive law” because the separation between the two interfaces is resisted by the cohesive traction. When this interface subjected to external stress, the two surfaces of the interface separates according to the pre-defined cohesive law. Several forms of cohesive law are presented in the literature including bi-linear, tri-linear, multi-linear and exponential [16, 42, 44, and 8

65]. In this work, the exponential cohesive law, that suggested by Charles et al. [48] and Dastgerdi at al. [50], is exploited through FE Simulation. This model can be represented as: ∅( ) = e

̅ 1 − (1 + ∆ )

in which ∅( ) is the surface potential, (

!∆" !∆$#

%

(2)

is the cohesive strength. ∆ = ''''" and ∆( = '''# , where &

&

&"

&#

and

are the normal and tangential separation. ̅ is the normal separation of the interface when the

maximum normal traction is reached at shear traction is reached at

(

=

√, * (. ,

(

= 0 and *( is the shear separation when the maximum

Through simulation procedure, for simplicity and the lake of

information, the normal and tangential separation are assumed to be equal. To validate and predict the global stress-strain constitutive relation of produced nanocomposites, the presented UCRVE model with cohesive interface elements is compared with available experimental results of Al-15% SiC presented by Lloyd [64]. The properties of the matrix and reinforcement materials are illustrated in Table 1. The SiC average particle diameter is 7.5 µm. The cohesive interface properties considered in the simulations are:

= 430 MPa and

=

(

= 79 nm, [32].

In order to highlight the effect of considering cohesive interface elements for decohesion between matrix and reinforcement, the simulation was repeated by considering full bond between matrix and reinforcement. Fig. 4 shows the stress-strain response of Al-15% SiC composites, experimental results, Lloyd [64], prediction of UCRVE model with fully bonded interface (without considering cohesive interface elements) and prediction of the presented UCRVE model with cohesive interface elements. As shown in the figure, the model with fully bonded interface over estimates the stressstrain relation. The over estimation indicates that the assumption of fully bonded interface between matrix and reinforcement particles is misleading assumption. However, it is noticed that, the proposed UCRVE cohesive interface model is approximately identical with experimental data obtained by Lloyd [64]. It is observed that, cohesive interface and the fully bonded models have the

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same elastic response. However, when the decohesion starts at the interface between SiC and Al, the predicted stress is reduced than the fully bonded due to the dissipation of the energy in the decohesion of the interface elements achieving better correlation with the experimental results. 4. Results and discussion This section is divided to two subsections. The first one is concerned by fabrication of nanocomposite by using high energy ball milling process and investigated the microstructure and mapping of manufactured of Al-5% Al2O3 nanocomposite. The second subsection is devoted to UCRVE with cohesive interface model to simulate the response of elasto-plastic Al-5%Al2O3 metal matrix nanocomposites. 4.1 Microstructure analysis of nanocomposite SEM micrographs of Al-5% Al2O3 nanocomposite powders after ball milling is shown in Fig 5. The figure shows reduction of Al average particle size in Al-5%Al2O3 nanocomposite powders than pure Al powders. This is due to the presence of Al2O3 nanoparticles during high-energy ball milling. During collision of ball in high-energy ball milling process, Al2O3 nanoparticles are entrapped between Al ductile particles which reduce its plastic deformation ability and increase the tendency of particles to fracture than plastic deformation [7, 11, 37]. Fig. 5 (b) illustrates the presence of Al2O3 nanoparticles stacked over the surface Al particles that confirms the explained mechanism. The figure also demonstrates the reduction of Al2O3 nanoparticle size to less than 500 nm (see Fig.5 (b)) because of the kinetic energy absorbed by particles during high energy ball milling which results in fracture of Al and Al2O3 nanoparticles. This observation proves that, during high-energy ball milling process, not only the ductile matrix particles are fractured but also the hard-ceramic particles are fractured as well. XRD analysis of Al and Al-Al2O3 nanocomposite powders after ball milling is presented in Fig. 6. The figure shows the presence of two phases only Al and Al2O3 which indicates the validity of the 10

manufacturing process of nanocomposites. It noted that, there is no contaminants are produced through the process. The crystallite size of Al-5%Al2O3 nanocomposite after milling is reduced to 72 ± 12 compared to 115 nm for pure Al. This observation indicates Al grain refinement during milling process due to plastic deformation of Al particles during milling which cause and increase of crystal defects such as point defects and dislocations [16]. The microstructure of Al-5%Al2O3 nanocomposites after consolidation is shown in Fig. 7. EDX analysis for two different positions in the sample are shown in Fig.7 (c) and (d) confirming that the white particles are Al2O3 while the other part of the sample is the matrix, Al. The SEM micrographs in Fig. 7 (a) and (b) shows that Al2O3 particles has almost spherical shape. It is observed that submicron particles and nanoparticles can be observed (see Fig.7 (a)) which reflect reduction of Al2O3 particles during milling process. The majority of Al2O3 particles have an average size of 800 nm particle diameter achieving 60 % Al2O3 particle size reduction due to milling. Based on these observations, using Al2O3 particles in micro size as a start material for the preparation of Al-Al2O3 nanocomposite has an advantage of elimination of particle agglomerations rather than using nanoparticles. Additionally, due to the high energy of milling process, the fractured Al2O3 particles are reduced in size and distributed homogenously through Al matrix. A key parameter controlling the structural and mechanical properties of nanocomposites is the homogeneity of the reinforcement phase in the matrix. Fig. 8 shows the mapping analysis of Al5%Al2O3 nanocomposites. The figure proves the excellent distribution of Al2O3 nanoparticles in Al that reflects the validity of high energy ball milling for reducing Al2O3 particle to nanosized and achieving uniform dispersion of Al2O3 nanoparticles inside Al matrix. 4.2 UCRVE model simulation Since the Al2O3 nanoparticles has approximately spherical shape in the manufactured composites, the presented UCRVE model is applied to simulate the tensile response of these composites as

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shown in Fig. 9. This figure shows a single particle of Al2O3 with its surrounded Al matrix and the simulated unit cell.

Fig. 10 shows the tensile stress-strain curves for both Al and Al-5%Al2O3 nanocomposites experimentally and numerically by FE model including cohesive interface model with the following parameters:

= 310 MPa and

=

(

= 40 nm.

To the author’s knowledge, there is no available experimental data on the determination of cohesive strength and separation for the interface between Al matrix and Al2O3 nanoparticle. Therefore, these parameters are determined to best fit the experimental results since the experimental results and numerical simulation on this kind of materials are rare as will be discussed later on. The figure shows good agreement between experimental and numerical results. As shown, the figure illustrates that the ultimate tensile stress is improved to 250.7 MPa compared 206.2 MPa for Al. This improvement due to the presence of Al2O3 nanoparticles which share the applied load with the matrix. Additionally, the presence of Al2O3 nanoparticles contain the plastic flow of Al grains during tensile test. Fig. 11 presents the equivalent plastic strain distribution in Al-5%Al2O3 nanocomposite considering full bonded interface and cohesive zone interface between Al and Al2O3. As shown in the Fig. 11(a) for fully bonded interface, the concentration of plastic strain occurs in the matrix and far from the Al2O3 particle which is not the real case. In such a test, it is evident that the damage initiates as a decohesion between Al2O3 nanoparticles and Al matrix due to the week bonding between them [50]. But in case of cohesive zone interface as shown in Fig. 11(b), plastic strains are concentrated at the interface and the surrounding area in the matrix at which the initiation of crack occurs. The initiation of decohesion between Al2O3 and Al occurs at the regions with high strains. Therefore, the shear strain concentration could give an indication on the decohesion initiation by simulations.

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Fig. 12 shows the shear strain distribution and hydrostatic pressure concentrations in Al-5%Al2O3 nanocomposite considering fully bonded and CZM interface. The maximum shear strain is observed at the interface in both models (see Fig. 12(a)) due to the properties mismatch between Al2O3 nanoparticles and Al matrix. This observation confirms the hypothesis of damage initiation at the interface between matrix and reinforced nanoparticles. As shown in the figure, considering CZM change the shear strain distribution in the sample due to the separation at the interface which allow strain distribution in the sample. The maximum hydrostatic pressure occurs at the region where the maximum shear strain is localized which confirm the initiation of crack at this region. The CZM normal separation of the interface is illustrated in Fig. 13. The figure shows that the maximum normal separation occurs at the region of the maximum shear strain (see Fig. 12). The mechanical properties of the global composite are affected by several microstructural parameters including the dispersion of reinforcement particles in the matrix [6, 9, 11, 2, the grain size and orientation [21, 25, 28] and the interface mechanical properties [32 50]. In the current study, Al2O3 nanoparticles are uniformly and well dispersed in Al matrix as shown in Fig. 9 and the grain size is almost the same for milled Al and Al-5%Al2O3 nanocomposite. Therefore, the current analysis will be focused on studying the influence of interface properties on decohesion initiation using the presented UCRVE model with cohesive elements. Three key parameters govern the cohesive elements in the used model: the cohesive strength, (,

and normal and tangential separations,

and

respectively. A detailed review on the available cohesive zone models available in the literature

[38-43, 65-67] is presented by Chandra et al. [48]. They concluded that for metal-ceramic interface, the cohesive strength varies from MPa to GPa with an increase of three orders in magnitude and the normal separation varies from nanometers to micrometers. Since, there is no available experimental results on the determination of cohesive strength and separation for the interface between Al matrix and Al2O3 nanoparticle, Fig. 14 shows the effect changing the cohesive strength on the decohesion between Al2O3 nanoparticle and Al matrix 13

considering four different values of cohesive strength varying from MPa to GPa as: 200, 310, 800, 1500 MPa while maintaining the normal separation at 40 nm. As illustrated, increasing the cohesive strength from 200 MPa to 1500 MPa reduces the maximum decohesion separation from 38.2 nm to 0.68 nm. This result reveals larger dependence of the decohesion normal separation on the cohesive strength. The effect of changing the critical normal separation distance is studied by considering four different values of normal separation as: 25, 50, 500, 1000 nm while maintain the cohesive strength at 310 MPa. Fig. 15 shows the effect of changing the critical normal separation distance on the evaluation of decohesion between Al2O3 nanoparticles and Al. Increasing the critical separation distance increases the normal separation. However, the increasing rate is decreased with increasing the critical separation. For example, increasing the critical separation distance to double, from 25 to 50 nm, increases the maximum separation from 19 to 33.7 nm with increasing 1.7 time. However, increasing the critical distance from 50 to 500 nm which is ten times, the maximum separation distance is increased from 33.7 to 99.1 nm which is almost 3 times. This highlight large influence of critical separation distance on the decohesion of Al2O3-Al interface at slightly small values while for large values the dependence is reduced.

5. Conclusion Nanomechanical elasto-plastic model is developed to predict the damage in nanocomposites using unit cell representative volume element and cohesive zone model for the first time. The proposed model is based on elasto-plastic isotropic strain hardening to simulate the elastic and plastic hardening occurs inside the matrix, and exponential cohesive law to simulate the interface decohesion between metal matrix and reinforcement nanocomposite. The model is implemented using finite element framework. Commercial pure Al as a matrix and Al2O3 as reinforcement, are used to manufacture Al-5%Al2O3 nanocomposite by using high energy ball milling. Microstructure

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analysis are performed to investigate the production of nanosize particles and to illustrate a uniform distribution of reinforcement particles through matrix. Based on the obtained results, the most finding can be summarized as:•

Metal matrix nanocomposites can be efficiently manufactured with homogenous distribution and reduced reinforcement particle size using high-energy ball milling.

•

The proposed numerical model enables the understanding of damage imitation and propagation in elasto-plastic nanocomposites. Particularly, the deformation, stress-strain behavior and damage shape were predicted with good accuracy using the proposed model.

•

Considering debonding between matrix and reinforcement nanoparticle in the simulation shows lower stress prediction than considering fully bonded interface resulting in better correlation with experimental results after yielding of the matrix. This result indicates clearly that the assumption of considering fully bonded interface between reinforcement and matrix in elasto-plastic nanocomposites is misleading assumption.

•

The cohesive ultimate interface strength and the critical normal separation distance are two important parameters that influence the decohesion initiation and propagation of elasto-plastic nanocomposites. Increasing the cohesive strength highly reduced the maximum decohesion separation which highlight the larger dependence of decohesion behavior on the ultimate interface strength.

Acknowledgment This work was funded by the Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah, under grant No. (D-118-135-1440). The authors, therefore, acknowledge with thanks DSR technical and financial support.

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List of Figures Figure 1. Tensile test setup (a) experimental setup with extensometer position and (b) photo of Al5%Al2O3 nanocomposite sample after test. Figure 2. UCRVE model with meshing and boundary conditions. Figure 3. A comparison between experimental tensile test of pure Al metal and proposed elastoplastic model. Figure 4. Comparison of presented UCRVE model with cohesive interface and fully bonded interface and experimental results of Lloyd [64]. Figure 5. SEM micrographs of Pure Al and Al-5%Al2O3 nanocomposite powders after high-energy ball milling. Figure 6. XRD analysis of Al and Al-5%Al2O3 nanocomposite powders after high-energy ball milling. Figure 7. SEM micrographs of Al-5%Al2O3 nanocomposites at two different spots of the sample in (a) and (b) and EDX of squares 1 and 2 in (c) and (d). Figure 8. Mapping analysis of Al-5%Al2O3 nanocomposite. Figure 9. The representation of real microstructure of Al-Al2O3 nanocomposite and the unit cell representative volume element. Figure 10. Stress-stain behavior of Al and Al-5%Al2O3 nanocomposite. Figure 11. Equivalent plastic strain at full load for Al-5%Al2O3 nanocomposite considering fully bonded interface and CZM interface. Figure 12. Shear plastic strains and hydrostatic pressure for Al-5%Al2O3 nanocomposites considering fully bonded and CZM interfaces. Figure 13. CZM normal separation (µm) of Al-5%Al2O3 nanocomposite. Figure 14. Effect of cohesive strength the decohesion separation (µm) between Al2O3 nanoparticle and Al matrix. Figure 15. Effect of critical normal separation on the decohesion separation (µm) between Al2O3 nanoparticle and Al matrix. 21

\

Figure 1. Tensile test setup (a) experimental setup with extensometer position and (b) photo of Al5%Al2O3 nanocomposite sample after test. 22

Figure 2. UCRVE model with meshing and boundary conditions.

23

Figure 3. A comparison between experimental tensile test of pure Al metal and proposed elastoplastic model.

24

Figure 4. Comparison of presented UCRVE model with cohesive interface and fully bonded interface and experimental results of Lloyd [64].

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Figure 5. SEM micrographs of Pure Al and Al-5%Al2O3 nanocomposite powders after high-energy ball milling.

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Figure 6. XRD analysis of Al and Al-5%Al2O3 nanocomposite powders after high-energy ball milling.

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Figure 7. SEM micrographs of Al-5%Al2O3 nanocomposites at two different spots of the sample in (a) and (b) and EDX of squares 1 and 2 in (c) and (d).

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Figure 8. Mapping analysis of Al-5%Al2O3 nanocomposite.

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Figure 9. The representation of real microstructure of Al-Al2O3 nanocomposite and the unit cell representative volume element.

30

Figure 10. Stress-stain behavior of Al and Al-5%Al2O3 nanocomposite.

31

Figure 11. Equivalent plastic strain at full load for Al-5%Al2O3 nanocomposite considering fully bonded interface and CZM interface.

32

Figure 12. Shear plastic strains and hydrostatic pressure for Al-5%Al2O3 nanocomposites considering fully bonded and CZM interfaces.

33

Figure 13. CZM normal separation (µm) of Al-5%Al2O3 nanocomposite.

34

Figure 14. Effect of cohesive strength the decohesion separation (µm) between Al2O3 nanoparticle and Al matrix.

35

Figure 15. Effect of critical normal separation on the decohesion separation (µm) between Al2O3 nanoparticle and Al matrix.

36

List of Tables

Table.1 Properties of Al-SiC composite constituents, Lloyd [64].

Table.1 Properties of Al-SiC composite constituents, Lloyd [64].

Material

(123)

(423)

Al

76

0.33

208

0.2

SiC

427

0.17

-

-

37

I declare that I am the Corresponding Author for the manuscript under submission and I will be the sole contact for the Editorial process (including Editorial Manager and direct communications with the office). On behalf of all the authors, I declare that this manuscript is original, has not been published before (either as a conference proceeding or in a web-based journal) and is not currently being considered for publication elsewhere.

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