FEM modeling of compressive deformation behaviour of aluminum cenosphere syntactic foam (ACSF) under constrained condition

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1 Indian Journal of Engineering & Materials Sciences Vol. 19, April 2012, pp FEM modeling of compressive deformation behaviour of aluminum cenosphere syntactic foam (ACSF) under constrained condition Raghvendra Khedle a *, D P Mondal b, S N Verma a & Sanjay Panthi b a Department of Mechanical Engineering, Rajiv Gandhi Prodyogiki Vishwavidyalaya, Air Port Road, Bhopal , India b Advanced Materials and Processes Research Institute (CSIR-AMPRI), Bhopal , India Received 18 April 2011; accepted 16 April 2012 The deformation behavior of aluminum cenosphere syntactic foam (ACSF) as a function of porosity, shell thickness, shell volume fraction and cenosphere volume fraction has been studied using finite element modeling of a representative unit cell of the respective material under both constrained and unconstrained conditions. The volume fraction of cenosphere and its shell thickness varies from 5% to 65% and 1 µm to 4 µm, respectively. It has been noted that as cenosphere volume fraction decreases, the plateau stress and Young s modulus of these materials increases. While these values increase with increase in the shell thickness, i.e., shell volume fraction. The modulus and plateau stress increase considerably under constrained condition especially at low cenosphere volume fraction. The FEM predicted values are validated with experimental results and it is noted that the FEM predicted values are within the 12% variation of the experimental values. The proposed study thus shows that unit representative shell techniques are reasonably ideal and rapid method for predicting compressive deformation behavior of ACSF. Keywords: FEM, Aluminum cenosphere syntactic foam, Plateau stress, Micro-balloons Aluminum cenosphere syntactic foam (ACSF) are finding wide range of applications in aerospace and automobile due to their excellent combination of physical, tribological and mechanical properties 1-5. The cenosphere is hollow and spherical in shape used as a space holder in aluminum metal for making aluminum syntactic foam 6-9. The existence of these hollow particles along with stronger shell in the matrix results in a lower density, lower thermal coefficient, lower thermal conductivity and higher specific strength 8,9. ACSF exhibits higher strength, excellent energy absorbing capability and isotropic mechanical properties due to extensive strain accumulation at relatively high stress 9. These properties of ACSF are dependent on the size of micro-balloons and the preparation of the matrix material. There are two ways to change the properties of the respective material: first one is to change the volume fraction of cenosphere and second one is to use cenosphere of different wall thicknesses and sizes in the ACSF 11. A few investigations have been carried out on the ACSF to study the effect of size, shape, volume fraction and distribution of cenosphere on its deformation behavior. ACSF with different porosity fraction could be made using different methods such as stir casting and melt in *Corresponding author ( raghvendra056@yahoo.com) filtration 10. Analytical and empirical attempts have been made to predict compressive strength of ACSF by various investigations 7-9,11. The FE model predicated lower peak load, which is most likely due to the size effect exhibited by foam 12. Wu et al. 7 predicted the compressive strength of ACSFs under quassi-static condition with the following equation: σ csf = C (σ m (1-f) 3/2 +σ wall [f (1-(1-t/r) 3 ) 3/2 ] (1) Where, σ csf is the compressive strength of ACSFs, σ m is the yield strength of matrix, ƒ is the volume fraction of cenosphere, σ wall is the yield strength of cenosphere wall material, C is the empirical constant and t/r is the relative wall thickness of cenosphere (where t is wall thickness and r is radius of the cenosphere). They further reported that age hardened ACSFs exhibit higher plateau stress and high energy absorbing capacity as compare to the cast one. The above equation also states that the cenospheres with higher shell thickness provide higher plateau strength in ACSF. Similar kind of relation was also proposed by Balch and Dunand 8. Mondal et al. 11 proposed a semi-empirical relationship of plateau stress of ACSF with cenosphere volume fraction and cenosphere shell strength and porosity fraction considering load partitioning between cenosphere and the matrix. According to Mondal et al. 11 the plateau

2 136 INDIAN J ENG. MATER. SCI., APRIL 2012 stress decreases with cenosphere volume fraction while densification strain increases linearly with cenosphere volume fraction. According to Balch et al. 9 the compressive deformation of ACSF at quasi-static and dynamic conditions varies very marginally with strain rate. They expressed the strain rate sensitivity parameters,, of ACSF with the following equation: = σ d σ σ q 1 In (ε / ε * d q ) (2) Where, σ d and σ q are the flow stress at dynamic and quasi-static condition respectively, σ* is the flow stress at given strain (generally 0.05) under a reference strain rate of 0.001/s, and are strain rate at dynamic and quasi-static test condition (0.001/s) respectively. The value of for ACSF was measured in the range of to which is quite low. There is hardly any attempt executed on the deformation behavior of ACSF numerically. The deformation behavior of microsphere and matrix during deformation of ACSF has not been reported in the literature. This could be studied in depth, through finite element simulation. Detailed modeling of material and to study deformation behavior in microscale needs more complex computation work and is very time consuming. However, computation work could be made easier and faster significantly through modeling of representative unit cell model using 2D finite element simulation. The deformation behavior of composite materials has been studied using similar techniques and obtained reasonably good results. When the foam undergoes compressive deformation and it gets compacted in direction, parallel to the loading axis without giving any significant deformation along the perpendicular direction to the loading axis depending on the porosity fraction. ACSF is a material which belongs to category between foam and dense material. When these materials are deformed under constrained condition, their deformation behavior may differ from that under unconstrained condition. The extent of difference may vary with the porosity fraction. These aspects have not been examined so far. The present paper aims at 2D finite element simulation of the compressive deformation of ACSF under constrained and unconstrained condition as a function of the volume fraction of cenosphere, cenosphere shell wall thickness and porosity fraction. FEM Simulation In the present study, the effective properties (yield stress and Young s modulus) are determined numerically considering different thickness and volume fraction of cenosphere in ACSF. The modeling and the analyses are carried out using FEM programme developed at CSIR-AMPRI Bhopal. In the simulation, the distribution of cenosphere considered to be uniform in aluminum matrix in a hexagonal array. The process is axis-symmetric about y-axis and it is symmetric about x-axis. Therefore, in this study quarter geometry is used to carry out the parametric study, where, quarter of the representative cell represents a cylindrical system in which the matrix is taken as the material one and spherical cenosphere taken to be reinforced material as shown in Fig.1. The finer mesh is used in the Fig. 1a Unit cell model of ACSF in unconstrained condition (r=21 to 45 µm, T=1 to 4 µm); 1b Unit cell model of ACSF in constrained condition (T=1 to 4 µm and r=21 to 45 µm)

3 KHEDLE et al.: ALUMINIUM CENOSPHERE SYNTACTIC FOAM 137 cenosphere shell to see the stress strain variation while in the matrix fine mesh is or near the cenosphere shell and it goes coarser towards the ends. A typical mesh is shown in Fig. 1. Size of the matrix is 50 µm 50 µm. Cenosphere shell thickness varies from 1 µm to 4 µm for each representative volume fraction of the cenosphere particle. This leads to variation in porosity fraction and cenosphere shell volume fraction at fixed cenosphere volume fraction. The cenosphere volume fraction varies from 5% to 65% in matrix structure of the ACSF. Unconstrained condition Boundary conditions are specified by taking into account the symmetry of the system. In Fig. 1a, the nodal displacement on CD is considered to be zero in the x-direction due to axial symmetry and CB is constrained in the y-direction representing the plane of symmetry. Compressive displacements are applied at the top of the horizontal surface AD. Constrained condition Boundary conditions are specified taking into account the symmetry of the system. In Fig. 1b, the nodal displacement on CD is considered to be zero in the x-direction due to axial symmetry, CB is constrained in the y-direction representing plane of symmetry and AB is constrained in x-direction. When a vertical displacement is applied at the top surface the vertical faces must continue to be vertical while the distance between them changes. The displacement is applied incrementally to simulate the overall deformation of ACSF. The maximum displacement applied to the top surface is 10% of the total length of specimen and simulation is carried out in 100 steps (program run for hundred steps). This simulation carried out to study the parameters like strain, yield stress and Young s modulus and these parameters are related with volume fraction of cenosphere, porosity fraction, shell thickness and shell volume fraction. Von-Mises yield criterion in conjunction with the following standard power law flow curve was used for the plastic deformation of the matrix 9,10 : n σ ε = σ y ε y (3) Where, σ y, ε, ε y and n are the flow stress, yield strength, effective strain, yield strain and strain hardening exponent of the material. The material properties used in the simulation are shown in Table 1. Result and Discussion Flow behavior Flow curves under constrained and unconstrained condition for ACSF derived from FEM with 5% to 65% volume fraction of cenosphere with shell thickness of 1 µm are shown in Fig. 2. It is noted from Table 1 Material properties used in FEM analysis S.No. Property Material-1 Material-2 Aluminium matrix Cenosphere 01 Young s modulus 70GPa 200GPa 02 Poisson s ratio Strain hardening co-efficient 04 Yield Strength 260MPa 600MPa Fig. 2 Comparison of flow behavior with different cenosphere volume fractions in constrained (c) and unconstrained (uc) conditions

4 138 INDIAN J ENG. MATER. SCI., APRIL 2012 this figure that flow curves have no sharp yield point. The material gradually changes from yield to plastic region, without showing any sudden increase in stress irrespective of boundary condition. The strain hardening effect in the plastic region reduces with increase in cenosphere volume fraction. The important fact is that the ACSF with higher volume fraction of cenosphere behaves like a foam material. It is also noted that the Young s modulus as well as yield stress decreases with increase in cenosphere volume fraction. It is further noted that the ACSF under constrained condition provides higher stress value than unconstrained condition when cenosphere volume fraction is less than 50%. Under constrained condition, ACSF is also exhibiting higher stain hardening rate in the plastic region. In elastic region, ACSF behaves almost similarly in both constrained and unconstrained conditions. This is primarily because of the fact that the elastic strain is accommodated by the elastic compaction of cenosphere and the frictional stress is very low at the interface of constrained condition. At lower volume fraction of cenosphere, ACSF exhibited considerably higher stress in constrained condition than that under unconstrained condition. Effect of cenosphere volume fraction The elastic modulus of ACSF is calculated as the ratio of the stress to the applied strain over the top surface in the elastic range. To simplify and generalize the graph, the plateau stress and elastic modulus of the foam is normalized with respect to that of the matrix material. Where normalized yield stress and Young s modulus is the ratio of computed yield stress (0.2% proof stress) and modulus of ACSF to those of dense matrix alloys. The normalized yield stress of ACSF under constrained condition as a function of cenosphere volume fraction is shown in Fig. 3a. It is noted from this figure that yield stress decreases with increase in cenosphere volume fraction. This figure also states that yield stress increases with increase in cenosphere shell thickness. Figure 3b similarly depicts that Young s modulus of ACSF under constrained condition decreases with increase in cenosphere volume fraction. This figure further shows that Young s modulus increases with increase on cenosphere shell thickness. Similar trend of experimental observations are reported, when the tests are conducted under unconstrained condition. It is further noted that up to 40% cenosphere fraction, yield stress and modulus decrease linearly with cenosphere fraction. Beyond 40% cenosphere, yield stress and modulus decrease rapidly and non-linearly with cenosphere fraction. This attributed to the fact that the yield stress and modulus of ACSF follow approximately the rule of mixture when it contains cenospheres less than 40%. At higher fraction of cenosphere ( 50%), ACSF behaves like foam materials and under such circumstances the yield stress and modulus starts decreasing non-linearly and rapidly with cenosphere fraction. The cenosphere shell contains empty space within itself. Hence, the normalized yield stress and normalized Young s modulus of ACSF are plotted as a function of porosity fraction at different shell thickness in Figs 4a and 4b, respectively. It is evident from these figures that both Fig. 3a Variation of normalized yield stress with cenosphere volume fraction for different cenosphere shell thicknesses (T) at constrained condition (c ) Fig. 3b Variation of normalized Young's modulus with cenosphere volume fraction at different cenosphere shell thicknesses (T) at constrained condition (c)

5 KHEDLE et al.: ALUMINIUM CENOSPHERE SYNTACTIC FOAM 139 modulus and yield stress follow the similar trend of variation with porosity fraction. It is further noted that up to certain porosity fraction (30-50%) both these response parameters decrease with increase in the porosity fraction. But above this, porosity fraction decreases nonlinearly and rapidly. It may be noted that the critical porosity fraction decreases with increase in cenosphere shell thickness. This is attributed to the fact that porosity fraction decreases with increase in cenosphere shell thickness. The cenosphere shells are not supported with any materials from inner side as these are hollow. But because of the wider thickness, the cenosphere shell could withstand higher load or load partitioning by increases cenosphere shell. Effect of shell wall thickness To examine the effect of cenosphere shell wall thickness and the shell volume fraction, the shell volume fraction for different volume fractions of cenosphere in ACSF is calculated. The normalized yield stress and normalized modulus of ACSF under constrained condition are plotted as a function of shell wall volume fraction in Figs 5a and Fig 5b, respectively. These figures show that both the normalized yield stress and normalized Young s modulus increase with increase in cenosphere shell volume fraction. The slopes of the lines in all the cases are almost same. This demonstrates that, the rate of increase in stress and modulus with cenosphere shell thickness at different cenosphere volume fraction is almost same. This also demonstrates that the yield stress and Young s modulus varies linearly with shell thickness. This might be due to the fact that Fig. 4a Variation of normalized yield stress with porosity fraction at different cenosphere shell thicknesses (T) at constrained condition (c) Fig. 5a Variation of normalized yield stress at different volume fractions (V f ) with shell thickness fraction at constrained condition (c) Fig. 4b Variation of normalized Young's modulus with porosity fraction at different cenosphere shell thicknesses (T) at constrained condition (c) Fig. 5b Variation of normalized Young s modulus at different volume fractions (V f ) with shell thickness fraction at constrained condition (c)

6 140 INDIAN J ENG. MATER. SCI., APRIL 2012 the interaction stress between cenosphere shell and the matrix is negligible. Comparison of normalized Yield stress and modulus under constrained and unconstrained conditions The comparison of normalized Young s modulus and normalized yield stress of ACSF as a function of cenosphere volume fraction are shown in Figs 6a and 6b, respectively. It is evident from these figures that yields stress and Young s modulus in both the conditions decrease with increase in cenosphere volume fraction. When the cenosphere shell thickness increases, the values of normalized yield stress and modulus increase in both the conditions. It is further evident from these figures that yield stress and modulus of ACSF under constrained condition are considerably higher than that obtained under unconstrained condition when cenosphere volume fraction is less than 60%. It is evidently noted that at 65% of cenosphere fraction, ACSF exhibits almost same value of yield stress and modulus both under constrained and unconstrained conditions. It is further noted, that, under constrained condition, at 65% cenosphere and shell thickness of 1 µm, ACSF exhibits marginally less yield stress and modulus as compared to that under unconstrained condition. The comparison of normalized yield stress and normalized Young s modulus of ACSF are plotted as a function of porosity fraction at different shell thicknesses in Figs 7a and 7b, respectively. It is evident from these figures that the values of normalized yield stress and normalized Young s modulus decrease Fig. 6a Variation of normalized yield stress at different shell thicknesses (T) of cenosphere with cenosphere volume fraction in constrained (c) and unconstrained (uc) conditions Fig. 7a Variation of normalized yield stress at different shell thicknesses (T) of cenosphere with porosity fraction in constrained (c) and unconstrained (uc) conditions Fig. 6b Variation of normalized Young's modulus at different shell thicknesses (T) of cenosphere with cenosphere volume fraction in constrained (c) and unconstrained conditions (uc) Fig. 7b Variation of normalized Young s modulus at different shell thicknesses (T) of cenosphere with porosity fraction in constrained (c) and unconstrained (uc) conditions

7 KHEDLE et al.: ALUMINIUM CENOSPHERE SYNTACTIC FOAM 141 with porosity fraction under constrained and unconstrained conditions. It is also noted that variation of the normalized yield stress and normalized modulus of ACSF under unconstrained condition is slightly different from that in constrained condition. In case of unconstrained condition, yield stress and modulus vary almost linearly with porosity fraction for the entire porosity range unlike in constrained condition. In case of constrained condition, it is noted that up to 55% porosity fraction, the yield stress is greater than that under unconstrained condition. But, beyond 55%, the yield stress under both the condition is almost same. However, modulus behaves differently. It is also observed that modulus under constrained condition becomes less than that in unconstrained condition when porosity fraction is greater than 50% depending on the cenosphere shell thickness. When the cenosphere shell thickness is 1 µm, the normalized modulus under unstrained condition becomes less than that under constrained condition at porosity fraction greater than 55%. This critical value decreases with increase in cenosphere shell thickness. Demonstration of the cenosphere shell thickness play an important role on the deformation response of the ACSF. The comparison of normalized yield stress and normalized Young s modulus of ACSF are plotted as a function of shell thickness fraction at different cenosphere volume fractions in Figs 8a and 8b, respectively. It is evident from these figures that the value of normalized yield stress and normalized Young s modulus in constrained and unconstrained conditions increase as volume fraction of cenosphere decreases and shell thickness fraction increases. It is also noted that the curves of normalized yield stress at higher volume fraction of cenosphere are almost same in both the conditions. The curves of normalized Young s modulus at higher volume fraction of cenosphere are parallel in constrained and unconstrained conditions, wherein the normalized modulus in unconstrained condition is significantly higher than that in constrained condition. In case of lower volume fraction of cenosphere (especially less than 50%), the ACSF behaves like dense materials and having greater Poisson ratio and has sufficient amount of lateral strain in case of unconstrained condition. Under constrained condition, this lateral deformation is suppressed and resulting in higher amount of interaction stress at the interface between ACSF and the boundary resisting the deformation. When cenosphere volume fraction is greater than 50% and especially at 60 or 65%, ACSF behaves like foam. The Poisson ratio becomes almost negligible and thus the lateral stress and the interaction stress/frictional stress at the boundary became almost zero. However, some kind of tri-axial stress at the surface is generated which leads to further deformation of the ACSF and thus the yield stress and modulus decreased. The other cause in this case may be due to consideration of zero coefficient of friction with the ACSF and constrained boundary. Thus when, the volume fraction of cenosphere increased significantly, the interaction stress becames almost zero. When cenosphere volume fraction becomes less than 60%, there is insufficient amount of lateral strain. Thus, under such condition, even through the coefficient of friction at the interface between ACSF and constrained boundary is considered to be zero, because of the higher extent of lateral deformation (due to considerably higher solid fraction), there exists significant amount of interaction Fig. 8a Variation of normalized yield stress at different volume fraction (V f ) with shell thickness fraction in constrained (c) and unconstrained (uc) conditions Fig. 8b Variation of normalized Young's modulus at different volume fractions (V f ) with shell thickness fraction in constrained (c) and unconstrained (uc) conditions

8 142 INDIAN J ENG. MATER. SCI., APRIL 2012 stress at the interface, in addition, to the tri-axial state of stress. This leads to significantly higher value of yield stress and modulus under constrained condition. At higher cenosphere fraction ( > 60%), because of tri-axial state of stress and the minimum lateral strain, some kinds of back stress is generated at the interface which might leads to greater degree of shear deformation of the matrix and finally leading to decrease in yield stress and modulus marginally, in the constrained condition then that in unconstrained condition Experimental validation For experimental validation of the model, first ACSF with varying volume fraction of cenospheres are prepared using the methodology described elsewhere 11. The Al-2014 matrix alloy used as and its chemical compositions are given in Table 2. The micrographs of ACSF at lower and higher magnification are shown in Figs 9a and 9b, respectively. It is evident from these figures that cenospheres are distributed quite uniformly and the shells of cenosphere are porous in nature. It is further noted that the interface bonding between the cenosphere shell and the matrix are reasonably sharp and strong. The average size of cenosphere used for making ACSF was 85 ± 6 µm and its average shell thickness was 4 to 5 µm. The compression test was carried out at a strain rate of 0.01/s. Two different approaches were used for testing under unconstrained and constrained conditions. In case of unconstrained condition, the specimens were compressed in an open platform (platen). Whereas, in case of constrained condition, the samples were kept in a channel located at the center of the die. The diameter of the channel in the die was equal to the diameter of the sample. So that during compression of the sample deformation may not take place in lateral direction (perpendicular to loading direction).the diameter of the punch was also equal to the diameter of the sample as well as the channel of the die. For compression testing sample of 10 mm in diameter and 15 mm in height was used. The normalized yield stress and modulus of the experimental values and the FEM predicted values are given in Table 3. The Table 2 Chemical composition of 2014 Al alloy (in wt %) Si Fe Cu Mn Mg Cr Zn Ti Al 0.76± ± ± ± ± ± ± ± ±1.1 Table 3 Comparison of FEM results with experimental values S.No Cenosphere volume fraction % Normalized Young s modulus (constrained condition) Normalized yield stress(constrained condition) Normalized Young s modulus (unconstrained condition) Normalized yield stress(unconstrained condition) FEM Experiment FEM Experiment FEM Experiment FEM Experiment ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±0.04 Fig. 9a Uniform distribution of cenosphere in ACSF Fig. 9b Bonding between cenosphere shell and matrix alloy

9 KHEDLE et al.: ALUMINIUM CENOSPHERE SYNTACTIC FOAM 143 modulus and yield stress of foam samples were normalized with respect to that of dense matrix alloy. It is evident from Table 3, that predicted values of normalized yield stress and normalized modulus are in reasonably good agreement with the experimental values. It is further noted that the predicted values are 8-12% higher than the experimental ones. The marginally higher values in case of FEM predicted ones is due to the assumption taken during modeling: (i) shells are dense, (ii) coherent bonding between shells and matrix, (iii) uniform distribution of cenosphere, (iv) same size of each cenosphere, (v) matrixes are free from any defects and porosity and (vi) smooth cenosphere surface. But in practice: (i) the shells are porous (Fig. 9b), (ii) only mechanical bonding exists between shell and matrix (Fig. 9b), (iii) there exists some order of clustering (Fig. 9a), (iv) shells are not uniform in thickness (Fig. 9b) and (v) cenospheres are not uniform in size (Fig. 9a). Considering some of the above assumptions (variation in shell thickness and incoherent bonding) in the FE model, compressive deformation behavior of ACSF have been carried out. Further, in case of constrained condition, the frictional force is considered to be zero. This is because of the fact that the specimen surface and the die surface are lubricated with MoS 2 lubricant and the deformation under yielding is very low. However, in practice, there frictional force could not be reduced to zero. Because of the presence of pores, the constrained boundary condition is leading to triaxial stress. This may also cause some kind of variation between the experimental values and FEM predicted values. The variation within 8-12% of the experimental one could be considered as reasonably satisfactory, and this study thus demonstrates that representation modeling and deformation behavior of ACSF. Conclusions Following conclusion are made from this study: (i) FEM modeling of representative unit cell is fast and rapid technique for prediction and analysis of compressive deformation behaviour of aluminum cenosphere syntactic foam. (ii) Under constrained condition, syntactic foam exhibits reasonably higher stress and modulus as compared to that under unconstrained condition when the cenosphere volume fraction is less than 60%. At higher cenosphere fraction, the compressive deformation response of ACSF is found to be almost same in both constrained and unconstrained condition. (iii) The modulus and strength of ACSF increases with increase in cenosphere shell thickness, while decreases with increase in cenosphere volume fraction vis-à-vis porosity fraction. (iv) At higher volume fraction of cenosphere (>60%) or of porosity (>30~50%) depending on cenosphere cell thickness, the modulus of ACSF under unconstrained condition is greater than that under constrained condition. (v) FEM predicted values of yield stress and Young s modulus are found to be 8-12% higher than the experimental one. This is attributed to the assumptions taken during FE modeling of ACSF which are somehow not achieved in experimental material during its synthesis. This difference between FE and experimental results is primarily due to some order of clustering of cenospheres, non-uniform size of cenospheres and cenosphere shell thickness, rough cenosphere surface and incoherent bonding between cenosphere shell and the matrix. References 1 Alps A T & Zhang J, Scripta Metall Mater, 26 (1992) Surappa M K, & Rohatgai P K, J Mater Sci, 16 (1981) Prasad S V, Rohatgi P K, & Kosel T H, Mater Sci Eng A, 80 (1986) Zhao M, Wu G H, Dou Z, & Jiang L T, Mater Sci Eng A, 374 (2004) Rohatgi P K, Kim J K, & Guo R Q, Metall MaterTrans, 33 (2002) Wu G H, Dou Z Y, Jiang L T & Cao J H, Mater Lett, 60(2006) Wu G H, Dou Z Y, Sun D L, Jiang L T, Ding B S, & He B F, Scripta Mater, 56(2007) Balch D K, & Dunand D C, Acta Mater, 54 (2006) Balch D K, Dwyer J G, Davis G R, Cady & Dunand D C, Mater Sci Eng A, 17 (2005) Mondal D P, Ramakrishna N & Das S, Mater Sci Eng A, 433 (2006) Mondal, D P, Das S, Ramakrishna N & Uday Bhaskar K, Compos Pt (A), 40 (2009) Styles M, Composton P & Kalyanasundaram S, Compos Struct, 86 (2008) Dou Z Y, Jiang L T, Wu G H, Zhang Q, Xiu Z Y & Chen G Q, Scripta Mater, 57 (2007) Zhang H, Ramesh K T & Chin E S C, Acta Mater, 53 (2005)