Materials and Design 157 (2018) 1–11

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Materials and Design

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Development of interfacial stress during selective laser melting of TiCreinforced TiAl composites: Influence of geometric featureof reinforcement

Chenglong Ma, Dongdong Gu ⁎, Donghua Dai, Hongmei Zhang, Lei Du, Han ZhangCollege of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nanjing 210016, Jiangsu Province, PR ChinaJiangsu Provincial Engineering Laboratory for Laser Additive Manufacturing of High-Performance Metallic Components, Nanjing University of Aeronautics and Astronautics, Yudao Street 29, Nan-jing 210016, Jiangsu Province, PR China

H I G H L I G H T S G R A P H I C A L A B S T R A C T

• A meso-scale thermal-stress couplingmodel of SLM fabricated TiC/TiAl com-posites was established.

• Stress development in the interface be-tween TiC particle and the TiAl matrixwas illuminated.

• Higher thermal shocking resistance wasachieved when using sphere-shapedreinforcement.

⁎ Corresponding author at: College of Materials ScieUniversity of Aeronautics and Astronautics, Yudao StreProvince, PR China.

E-mail address: dongdonggu@nuaa.edu.cn (D. Gu).

https://doi.org/10.1016/j.matdes.2018.07.0300264-1275/© 2018 Elsevier Ltd. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 5 June 2018Received in revised form 4 July 2018Accepted 13 July 2018Available online xxxx

In this work, interfacial stress evolution behavior of TiC reinforced TiAl composites fabricated by selective lasermelting were investigated, based on a meso-scale finite element model solely including a single reinforcing par-ticle. The results implied that stress concentration always emerged where the maximum temperature gradientexisted. As the laser beam successively moving from the left side of powder bed to the right side, the matrixaround TiC particle underwent a solid-to-liquid-to-solid transfer process, as a result of which the interface lo-cated at left side and right side of TiC particle experienced a transformation from a compressive stress to a tensilestress. But the top edge of TiC particle always suffered from the tensile stress. Two different types of reinforcedparticle, namely sphere-shaped particle and cubic particle, were analyzed in this work. For the sphere-shapedone, the calculated plastic flow stress in the interface was higher than the corresponding simulated Von Misestress during the solidifying period, while the opposite result was obtained for the cubic one. It indicated thathigher thermal shock resistance could be obtained for sphere-shaped TiC reinforced composites which was fur-ther verified by the experiment results.

© 2018 Elsevier Ltd. All rights reserved.

Keywords:Selective laser meltingTiAl-based compositesInterfacial stress

nce and Technology, Nanjinget 29, Nanjing 210016, Jiangsu

1. Introduction

Recently, more and more attentions have been paid to the selectivelaser melting (SLM) investigations of Ti-Al-based alloys which possesshigh melting point, high specific strength and stiffness, excellent creepresistance and fatigue resistance [1–4]. Introduction of SLM technology

2 C. Ma et al. / Materials and Design 157 (2018) 1–11

efficiently overcomes the challenge of poor formability of TiAl alloys in-duced by the lower ambient ductility and toughness during conven-tional processes [5]. Also, the nature of net shape forming of SLMfurther extends the application of Ti-Al-based alloys in aerospace areawhere a mass of high-temperature components with complex configu-ration are demanded. Note that, at present, the highest working tem-perature for TiAl components mostly fluctuate at 760 °C. Previousinvestigations have indicated that by addition of reinforcing particles,the highest working temperature can be increased to 800–900 °C, ac-companying elevated high-temperature properties [6]. Nevertheless,some new problems emerge. C. Kenel et al. [7] attempted to preparecomplex structures by SLM of an oxide dispersion strengthened (ODS)γ-TiAl alloy. The results implied that the larger cracking tendencyexisted within the as-fabricated ODS γ-TiAl alloy.

During SLM processing, a complicated heat, mass and momentumtransfer within laser-induced molten pool is involved, due to the peri-odic rapid heating-cooling process and nonequilibrium solidificationbehavior [8–12]. Specially, for SLM of metal matrix composites(MMCs), taking into account the difference in thermal physical proper-ties such as thermal expansion coefficient between reinforcing particlesand the matrix, complicated cyclic stresses including thermal stress,contraction stress and structure stress are consequently induced bythe above multi-physical thermal behaviors [13,14]. In this condition,it should be paid more attention on the interfacial stress between rein-forcing particle and the matrix which mainly results from thermalstress. As shown in Fig. 1a, according to the classical Selsing's model,the temperature dependent residual interfacial stress between reinforc-ing particle and the matrix can be described as [15]:

P Tð Þ ¼ A αm Tð Þ−αR Tð Þð Þ Ts−Tð Þ 1þ υm Tð Þ2Em Tð Þ þ 1−2υR Tð Þ

ER Tð Þ� �−1

ð1Þ

where α(T), ν(T), E(T) are temperature dependent thermal expansioncoefficient, temperature dependent Poisson's ratio and temperature de-pendent Young's modulus, respectively; the subscript m and R are onbehalf of thematrix and reinforcingparticle, respectively; A is a constantrelated to the stress relaxation; Ts is the operating temperature. Obvi-ously, the larger the difference in thermal expansion coefficient andtemperature difference, the higher the interfacial stress. Meanwhile,stress concentration is always prone to occur on the edge of reinforcingparticle. Upon the interfacial stress excessing the strength of the matrixmaterial or reinforced particle, interfacial micro-cracks are initiated andpropagated rapidly, as shown in Fig. 1b. C. Lee et al. [16] also found thecracks tended to initiated at the reinforced particle or defect due to theaccumulated tensile residual stress in the laser clad composite layer.Hence, it is indispensable for strict process control of interfacial ther-mal/stress behavior during SLM processing of ceramic particle rein-forced MMCs. For example, D.D. Gu et al. [17] successfully realized theformation of gradient interface between WC particle and Ni-matrix byapplying an optimized processing parameter, thus efficiently suppress-ing the cracking. B. Cheng et al. [18] found that the 45° inclined linescanning strategy could significantly reduce residual stresses of SLM-fabricated parts. However, understanding exactly for stress evolution

Fig. 1. (a) The schematic of interfacial stress between reinforced particle and the matrix durinshowing micro-cracks emerging on the edge of particle.

in the interface is the first step to achieving it. In fact, in views ofmeso-scale of molten pool, real-time monitoring for stress evolutionin the interface is hardly to be achieved. In this case, numerical simula-tionmethod plays a crucial role in understanding the formation processand evolutionmechanism of inner stress, aswell as predicting deforma-tion and cracking behavior of as-fabricated part during SLM processing[19–21]. AhmedHussein et al. [22] investigated the stressfields in single316 L stainless steel layer built on the powder bed without support inSLM by finite element simulation method. High Von Mise stress waspredictedwithin the overlapping layerwhich caused by the cyclic melt-ing and cooling rates. But, to the best of my knowledge, few numericalsimulation investigations on the interfacial stress behavior between re-inforcing particle and the matrix during SLM processing have been re-ported, which can provide an important guiding significance forquality control of SLM-fabricated metal matrix composite components.

In this paper, a multi-phase finite element model including the ma-trix phase, reinforcement phase, and the substrate was established, inorder to reveal the interfacial stress transfer behavior during SLM ofTiC reinforced Ti-Al composites. Meanwhile, reinforcing particles withdifferent geometric features were introduced into the matrix, furtherexhibiting the influence of particle geometric feature on stressdistribution.

2. Modeling approach

2.1. Numerical model establishment and material properties

To better disclose interfacial stress evolution behavior and simulta-neously eliminate the coupling effect among reinforcing particles, ameso-scale finite elementmodel solely including single reinforcing par-ticle was established, as shown in Fig. 2. Reinforcing particle was em-bedded into the matrix, locating at the upper region of powder layer.Moreover, to further understand the influence of particle morphologyon interfacial stress, sphere-shaped particle and cubic particle weremodeled, respectively (Fig. 2). In this model, the dimension of powderlayer model was 175 μm× 87.5 μm× 30 μm, the dimension of substratemodel was 175 μm× 87.5 μm × 68 μm and the sizes of reinforcing par-ticles were set as 10 μm. Also, the nonlinear relationship of materialsproperties with temperature was considered, including thermal con-ductivity κ(T) [23,24], the constant pressure special heat capacity Cp(T) [23,24], elasticity modulus E(T) [23,25] and coefficient of thermalexpansion αCTE(T) [26], as shown in Fig. 3.

2.2. Heat source model and thermal-mechanics coupling model

In consideration of the complicated heat, mass and momentumtransfer behavior during SLM processing, some necessary assumptionsare proposed in order to make the problem mathematically tractable,including: (1) the heat flux from the laser beam follows the Gaussiandistribution; (2) the whole powder bed is considered to be isotropicand continuous material; (3) the coefficient of convection betweenpowder bed and the environment is assumed to be constant and the ini-tial temperature is defined as the ambient temperature (namely 25 °C);

g SLM processing; (b) SEM image of SLM-fabricated TiC reinforced Ni-based composites,

Fig. 2. The three-dimensionalmeso-scale finite elementmodel including a single reinforced particle. Here two different types of reinforced particles (the cubic one and the sphere-shapedone) with the same size were modeled.

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(4) the heat generated by phase transformation and themigration of re-inforced particlewithin themolten pool during SLMof TiC/TiAl compos-ites is ignored.

With regard to heat source model, the laser beam was modeled asvolume heat source with Gaussian energy distribution which met theEq. (2) as follows [27]:

q x; y; zð Þ ¼ 3csAp

πH 1−1e3

� � exp −3cs

logHz

� � x2 þ y2� �

0BB@

1CCA ð2Þ

where P is the laser power, A is the laser absorptivity of powder mate-rial, H is the height of the heat source, cs is the shape coefficient, equalto 3/(R0)2, and R0 is the laser beam radius at which the heat flux densityfalls to its 1/e2 at the center of the laser beam (here, 70 μm).

Fig. 3. The thermal physical parameters of the matrix and reinforced particle: (a) thermal cexpansion (CTE).

During the laser processing, the transient spatial temperature distri-bution T (x, y, z, t) within the as-fabricated part satisfies the differentialequation:

ρ∂ Cp Tð Þ � T� �

∂t¼ ∂

∂xκ Tð Þ � ∂T

∂x

� �þ ∂∂y

κ Tð Þ � ∂T∂y

� �

þ ∂∂z

κ Tð Þ � ∂T∂z

� �ð3Þ

where ρ is the density of powder material. Subsequently, the thermalstress analysis was performed based on the above simulated tempera-ture data of all nodes and, the corresponding thermal-stress couplingrelationship which met the yield criterion, flow rule, hardening ruleand thermal elastoplastic constitutive equations, etc. During the

onductivity; (b) special heat capacity; (c) elasticity modulus; (d) coefficient of thermal

4 C. Ma et al. / Materials and Design 157 (2018) 1–11

thermal stress analysis process, there existing the following equilibriumequation within any element in the SLMmodel:

dFf ge þ dRf ge ¼ K½ �e dδf ge ð4Þ

dRf ge ¼Z

B½ �T Cf gdTdV ; K½ �e ¼Z

B½ �T D½ � B½ �dV ð5Þ

where {dF}e is the nodal force increment vector of a mesh-cell, {dR}e isthe thermal-induced equivalent nodal force increment vector, {dδ}e isthenodal displacement increment vector, and [K]e is the stiffnessmatrixof element, [B] stands for thematrix related to element strain vector, {C}represents the vector related to temperature and [D] is the elastic orelastoplastic matrix. By integration of stiffness matrix of all elementsand all nodal force vector, the equilibrium equation of the wholemodel could be obtained:

XdFf ge þ dRf ge� � ¼ X

dRf ge� � ¼ XK½ �e� �

dδf ge ð6Þ

Note that, in consideration of no imposed loading force during SLMprocessing, the stress field of powder bed and substrate are in self-balance, as a result of which∑{dF}e is equal to zero. Besides, the strainincrement {dε}e could be described as:

dεf ge ¼ B½ � dδf ge ð7Þ

Then, according to Eq. (7), the thermal elastoplastic stress could beknown by the following equation:

dσf g ¼ D½ � dεf g− Cf gdT ð8Þ

By solving the above equations, the stress or strain evolution processand the corresponding deformation behavior can be obtained.

3. Experiment investigation

The rawpowdermaterials including 10wt% TiC particles and 90wt%TiAl alloy powders were used. Before SLM consolidation, the raw pow-der materials were uniformly mixed by the high-energy Pulverisette 6planetary mono-mill (Fritsch GmbH, Germany). Specially, to verify thesimulation results, near-sphere and irregular TiC particles were applied,respectively. Then, during SLM processing, the same processing

Fig. 4. Temperature contour images of reinforced pa

parameters were chosen, including laser power of 100 W, scanningspeed of 200 mm/s, layer thickness of 30 μm and laser spot diameterof 70 μm. Subsequently, the microstructure of SLM-fabricated TiC/Ti-Alcomposite was characterized by a Zeiss Sigma 04–95 field emissionscanning electronmicroscope (FESEM) (Carl Zeiss AG, Germany), to ob-serve whether cracks forms in the interface.

4. Results

4.1. Temperature distribution profile and thermal behavior

Fig. 4a shows the surface temperature distribution profiles of thesphere-shaped TiC ceramic particle at different laser irradiation time.The predictedmaximum temperature Tmax and the corresponding posi-tion of Tmax occurred to experience a consecutive change. At t = 262.5μs, the Tmax was continuously increased to 2623.3 °C and subsequentlythe Tmax got decreased abidingly which indicated the laser beam leftaway from the particle. Besides, it was worthy to be paid attention onthe temperature difference ΔT between top surface and bottom surfaceof reinforced particle. Before the Tmax of TiC particle reached 2623.3 °C(Fig. 4a–c), the ΔT showed a relatively higher value of N700 °C withinthe small scale of 10 μm. As the laser irradiation time further increasing(Fig. 4d–h), the ΔT continuously got reduced and was just only ~128 °Cwhen the accumulated irradiation time reached 700 μs. Fig. 5a and b fur-ther give the temperature gradient G contour images of reinforced par-ticle and the surrounding matrix, respectively corresponding to t1 =87.5 μs and t2 = 700 μs. At the initial stage (namely t1 = 87.5 μs), theG gradually increased within the reinforced particle along the z-axis di-rection and the maximum temperature gradient Gmax was N8.57 × 107

°C/m. However, for the surroundingmatrix, the G distribution was sub-jected to perturbation to some extent, in consideration of the differencein thermal conductivity between thematrix and reinforced particle. As aresult, transfer of the heat flux induced by laser beam was held back inthe interface between the matrix and reinforced particle, especiallyalong the direction perpendicular to the isoline of G (as shown theblack arrow), thus leading to a great G emerging at the interface(Fig. 5a). As the laser beam was far away from the reinforced particle,the G decreased significantly to ~6.79 × 107 °C/m (Fig. 5b).

To allow for the prediction and evaluation of interfacial temperatureand subsequent stress behavior, some crucial points located at the inter-face between the matrix and reinforcing particle, namely bottom pole

rticle surface at different laser irradiation time.

Fig. 5. The temperature gradient distribution profiles on the Z-X section at (a) t1= 87.5 μs and (b) t2= 700 μs; (c) the schematic of positions of the selected crucial points in the interface;(d) temperature-time curves of all selected points; (e) the temperature gradient distribution along the x-axis and z-axis directions (t = 87.5 μs).

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(BP), left pole (LP) and top pole (TP), and the centroid of volume of re-inforcing particle (CV) were selected, as shown in Fig. 5c. The corre-sponding temperature evolution curves of all selected points aredepicted in Fig. 5d. In views of the melting point (~1450 °C) of the ma-trix, four various periods were determined according to the state of thematrix around the reinforcing particle: period I, the solid-to-melt trans-fer period (0–112.5 μs); period II, the full melting period (112.5–362.5μs); period III, the melt-to-solid transfer period (362.5–568.75 μs); pe-riod IV, the full solidified period (568.75–700 μs). Then, Fig. 5e furtherdemonstrates the G distributions of all selected points along the z-axisdirection and x-axis direction at t = 87.5 μs. It was not difficult to seethat the temperature change was relatively andante with the lower Gwithin the reinforced particle, while showing a sharp fluctuation withthemuch higherG in the interface. Differently, along the z-axis direction,G of the matrix side was lower than that of the particle side in the inter-face, but the opposite result was obtained along the x-axis direction.

Fig. 6. (a) The Von Mise stress and (b) the strain rate evolu

4.2. Thermal stress evolution and interfacial stress distribution

During SLM processing, the complicated thermal behavior inducedby Gaussian distribution of laser energy and ultra-rapidly heating/cooling nature results in the complexity and dissimilarity of thermalstress distribution within different laser melting elements. Specially,the added reinforcing particle with different non-liner thermal physicalproperties from that of thematrix further enhances the above complex-ity. Fig. 6 shows the stress-time and the strain rate-time curves of thechosen points. Specially, although BP was not the first to suffer fromthermal shock, the predicted stress value of BP was the maximum dur-ing period I (Fig. 6a). Subsequently, it was found that the Von Misestress of all points declined rapidly with the laser irradiation time in-creasing during the period II. However, for TP, its stress value showeda factitious change during the later stage of period II, getting a slight in-crease. With the laser irradiation time further increasing (during period

tion curves of all selected points as a function of time.

6 C. Ma et al. / Materials and Design 157 (2018) 1–11

III), the stress of BP, CV and LP occurred to get increased apparentlywhile the stress of TP tended to decrease successively. When the laserbeam was far away from the reinforcing particle, the residual stress ofall points reached a steady state. Fig. 6b further gives the strain rate evo-lution curves of these points as a function of time. Due to the existenceof ultrahigh temperature gradient and temperature change rate, thestrain rate got a prominent fluctuation during the period I and II dueto the thermal-stress coupling relationship. However, during the periodIII and IV, the particle surface temperature tended to became steady,thus contributing to a very small strain rate.

According to stress evolution features shown in Fig. 6a, the initialstage and the solidified stage were two crucial stages. For the former,the matrix and the reinforced particle simultaneously underwent ahuge thermal shock and consequently the maximum stress value wasachieved in this stage, which might play an important role in crack ini-tiation within reinforced particle. For another, although the thermalstress level was lower than that in the initial period, it was still enoughtomake thematrix fractured in consideration of the fact that thematrixaround reinforced particle had got solidified completely. Fig. 7 respec-tively displays the stress distribution in the interface between the ma-trix and sphere-shaped reinforcing particle at t1 = 87.5 μs and t2 =700 μs. As for the case in the initial period, a high thermal stress regionwith the maximum Von Mise stress σmax value of 204 MPa formedaround the sphere-shaped particle (Fig. 7a and b). Furthermore, theVon Mises stress contour on the sphere-shaped reinforcing particlewas shown in Fig. 7c, from which the position of the predicted σmax

was found to be consistent with that of the predicted Gmax. Noted that,the σmax value on the reinforcing particle reached 401 MPa, higher~200 MPa than that within the surrounding matrix. With regard to theas-solidified one, the predicted stress in the matrix around reinforcedparticle was relatively uniform with a value of approximately 167 MPa(Fig. 7d and e). In this condition, the σmax on the reinforced particle sur-face was also lowered, only 272 MPa (Fig. 7f). To better understand theinterfacial stress transfer behavior, the contours and curves of stresscomponents distribution in X (S11), Y (S22), and Z (S33) direction forthe above two cases were demonstrated in Figs. 8 and 9, respectively.In the initial stage, for all stress components, the matrix surroundingthe left-side and right-side of reinforced particle exhibited a compressive

Fig. 7. The VonMise stress distribution contours on the Z-X section of laser processed track andferent time: (a)–(c) t1 = 87.5 μs and (d)–(f) t2 = 700 μs.

stress state and the matrix in the vicinity of TP showed a tensile stressstate (Fig. 8a–c). Especially for stress component S33, the matrix belowthe BP of reinforced particle also showed a tensile stress state. Withinthe reinforced particle, compressive stress dominated for the S11 andS22 stress components, while S33 in a tensilemodewas predicted. Addi-tionally, near the TP of reinforced particle, a small tensile stress emergedfor S11 and S22. Based on the Fig. 8d–f, themaximum compressive stressreached ~320MPa near the LP of particle for S22 and the interfacial stresswas−246MPa in this case (Fig. 8e). Along the z-axis direction, themax-imum tensile emerged at the position of TP of particle, reaching~300 MPa (Fig. 8f). For the solidified stage, all stress components almostexhibited a tensile stress statewith a relatively homogenous stress distri-bution (Fig. 9a–c). The maximum stress value for all stress componentswas below 100 MPa. Along the x-axis direction, a slight compressivestress was predicted (Fig. 9d–f).

4.3. The influence of geometric feature of reinforcing particle on interfacialstress distribution

Generally, sphere-shaped reinforcing particle is recommended, dueto the equal and larger radius of curvature in the interface betweenthematrix and reinforcing particle whichmeans that there is no appar-ent stress concentration existing during laser manufacturing process.Nevertheless, to givemore insight into the influencemechanismof geo-metric feature of reinforcing particle on the interfacial stress distribu-tion during SLM processing, the corresponding simulation work byusing a cubic reinforced particle has been performed, as revealed inFig. 10. The surface temperature distribution profile of cubic reinforcedparticle in the initial stage is shown in Fig. 10a. The Tmax was 2399.61 °C,apparently higher than that of sphere reinforced particle. Meanwhile,both the predicted Gmax and σmax emerged at the same position, show-ing a good consistency (Fig. 10b and c). The σmax showed a value of305 MPa which was lower significantly than that of sphere reinforcedparticle. Then, some crucial points were also chosen, including leftupper vertex (LUV), left lower vertex (LLV), right upper vertex (RUV),right lower vertex (RLV) and centroid of volume (CV) of reinforced par-ticle. The temperature, Von Mise stress and the strain rate of thesepoints as a function of time are further displayed in Fig. 10d–f. By

the corresponding full-dimensional stress distribution images of reinforced particle at dif-

Fig. 8. The stress distribution contour images of different stress component on the Z-X section at t1=87.5 μs: (a) S11; (b) S22; (c) S33. And the corresponding stress-distance curves alongthe x-axis and z-axis direction of (d) S11, (e) S22, (f) S33.

7C. Ma et al. / Materials and Design 157 (2018) 1–11

comparisonwith the case of sphere reinforced particle, the period III gotextended,which indicated the solidification process initiated in advance(Fig. 10d). For the stress evolution, it should be noted that the stress ofall points decreased successively with the laser irradiation time increas-ing (Fig. 10e). During period I, the stress value of LUV was the highestreaching ~290MPa, in views of this position suffering from the thermal

Fig. 9. The stress distribution contour images of different stress component on the Z-X section atthe x-axis and z-axis direction of (d) S11, (e) S22, (f) S33.

shockfirstly. Subsequently, the stress of LUV declined rapidly during pe-riod II. However, the stress value of LUV and LLV occurred to be in asteady uptrend during the period III. As the laser beam was far awayfrom the reinforcing particle, the residual stress of all points reached asteady state. Fig. 10f further depicts the strain rate-time curves of theabove chosen points. Positive strain rate was just obtained during the

t2= 700 μs: (a) S11; (b) S22; (c) S33. And the corresponding stress-distance curves along

Fig. 10. The (a) temperature, (b) temperature gradient and (c) VonMise stress distribution contours of reinforced particle at t1= 87.5 μs; (d) temperature-time, (e) VonMise stress-time,and (f) strain rate-time curves of all selected points.

8 C. Ma et al. / Materials and Design 157 (2018) 1–11

period I for LUV, RUV and RLV. As well, the strain rate showed a drasticfluctuation in the initial stage and got a steady state in the solidifiedstage. Furthermore, Fig. 11 gives the X-Z sectional distribution contoursof stress component S11, S22, and S33 in the solidified stage (t = 700μs). Similar as the case of sphere reinforced particle, tensile stressmode dominated for all stress components and the σmax value reached111 MPa.

5. Discussion

5.1. Thermal stress transfer behavior in the interface

As the laser beam interacts with the TiAl-based alloy powder layerwhere a single TiC particle is embedded, the matrix material experi-ences a rapid melting process, simultaneously accompanying anultrahigh temperature gradient (Figs. 4 and 11). For a single materialsuch as TiAl-based matrix, the thermal stress σ can be described as(αCTEEΔT)/(1-2ν) where αCTEE is roughly a constant (1.51–1.56MPa/°C) here due to the opposite change rule of αCTE and E as a functionof temperature [28]. For the adjacent nodesN1 andN2with temperature

Fig. 11. The stress distribution contour images of different stress comp

T1 and T2 respectively, assuming that the nodeN lies betweenN1 andN2,as the node N1 and node N2 infinitely approaches (namely Δx ≈ 0),thermal stress σ(N) of node N can be estimated as:

σ Nð Þ ¼ αCTE T1ð ÞE T1ð Þ1−2ν

T1−T0ð Þ−αCTE T2ð ÞE T2ð Þ1−2ν

T2−T0ð Þ

≈αCTE T1ð ÞE T1ð Þ

1−2νT1−T2ð Þ ¼ αCTE T1ð ÞE T1ð Þ

1−2νG Nð ÞΔx

T1NT2ð Þ ð9Þ

Obviously, σ(N) has a positive relationship with the temperaturegradient G(N) of node N. Consequently, it can be speculated that higherthermal stress tends to form in the region with larger temperature gra-dient, in consideration of the constraining effect between adjacentmelt-ing elements. According to Fig. 5a, along the building direction, thelargest Gwithin thematrix emerges at the TP and BP of reinforcing par-ticle at t = 87.5 μs. As a result, the σmax within the matrix is obtainednear the same positions (Fig. 7a and b). Similarly, for the reinforcingparticle, the σmax is inclined to exist at the TP of particle where theGmax is found to form (Figs. 5a and 7c).With regard to the stress compo-nent, as shown in Fig. 8, along the x-axis direction, a great stress differ-ence as high as 150–300MPa within a very small scale of 1–2 μm forms

onent on the Z-X section at t2 = 700 μs: (a) S11; (b) S22; (c) S33.

9C. Ma et al. / Materials and Design 157 (2018) 1–11

in the left or right interface, which can be attributed to the existence of ahuge G difference in this region (Fig. 5e). Along the z-axis direction, es-pecially for S33, tensile stress concentration occurs in the interface (TPand BP), as well resulting from the predicted G induced by the heatflux transfer along the depth direction and thermal conductivity differ-ence between the matrix and reinforced particle.

5.2. Thermal shock resistance and thermal stability

J. Hunt et al. [28] defined two performance indexes, namely σYS/(EαCTE) and κ/αCTE, to respectively evaluate the thermal shock resistanceand thermal stability during laser-based additive manufacturing pro-cessing,whereσYSwas the yield strength. Based on the thermal physicalproperties κ and αCTE of the matrix (TiAl-based alloy) and reinforcedparticle (TiC), the κ/αCTE evolution behavior as a function of temperatureis revealed in Fig. 12a. Obviously, the thermal stability of the reinforcedparticle is apparently higher than that of thematrix. J. Hunt et al. furtherpointed out that a good thermal shock resistance combined with excel-lent thermal stability demands the maximized σYS/(EαCTE) and κ/αCTE.However, the κ/αCTE value depends on the inherent property ofmaterialand has no direct relationship with additive manufacturing processing,which indicates that the σYS/(EαCTE) should be paid more attention on.N. J. Harrison et al. [29] suggested Ultimate Tensile Strength (UTS,σUTS) was more applicable over yield strength when involved the frac-ture. Note that, UTS of the matrix or reinforcing particle is not a con-stant, but as a function of temperature T and strain rate _ε . Manyresearchers have carried out extensively the investigations on materialbehavior at high strain rates and elevated temperatures. According to

Fig. 12. (a) the thermal stability κ/αCTE evolution tendencywith temperature; (b) the calculatedcalculated plastic flow stress σ values at different periods for the cubic particle case.

Zener and Hollomon's work [30], Zener-Hollomon factor was put for-ward to describe the influence of T and _ε on plastic flow stress σ:

Z ¼ _ε expQRT

� �¼ A sinh ασð Þ½ �n ð10Þ

where Q is activation energy, R is ideal gas constant, A, α, and n areconstants independent of T and _ε. Plastic flow stress σ is usually definedas the yield limit at a certain temperature, strain, and strain rate. Due tothe unavailable formula based on UTS, T and _ε, here the thermal shockresistance is described as σ/(EαCTE). YuWang et al. [30] had establishedthe correlation between plastic flow stress and Zener-Hollomon factorin TiAl-based alloys at high temperature, where the Q value was322.3 kJ/mol and the plastic flow stress σ was expressed as:

σ ¼ 1:176� 108 arcsinh 4:333� 10−9Zh i0:3856

ð11Þ

However, the αCTE is usually inversely related to E, thus resulting inthe ineffectual discussion for the denominator (EαCTE). Hence, an inte-grated performance indicator χ is further proposed to evaluate thecrack susceptibility of an alloy, which is described as:

χ ¼ σσT T;Cp;αCTE

� � ð12Þ

where σT (T, Cp, αCTE) is thermal stress corresponding to the simulatedVon Mise stress. In this case, to avoid hot cracks, the inequation χ N 1is required to be met. Based on the Eq. (11) as well as the predictedstrain rate and temperature data from the simulated results, the

plastic flow stress σ values at different periods for the sphere-shaped particle case; (c) the

Fig. 13. SEM images of the interface between thematrix and reinforced particlewith (a) sphere-shapedmorphology and (b) cubic shape in the solidifiedmicrostructure of SLM-processedTiC/TiAl composites.

10 C. Ma et al. / Materials and Design 157 (2018) 1–11

calculated plastic flow stress of different selected crucial point is illumi-nated in Fig. 12b and c under various laser irradiation time. Consideringthat the matrix surrounding reinforced particle experiences the solid-to-liquid transfer process during the period I and exists in a form of liq-uid phase during theperiod II, the period III and IV are twomain danger-ous stages. For the case with sphere-shaped TiC particle, the yield limitsof all chosen points (BP, LP and TP) reach over 150 MPa (Fig. 12b), ap-parently higher than the predicted Von Mise stress value (Fig. 6a), as aresult of which χ N 1 is obtained and the interface between the matrixand reinforced particle can avoid the initiation ofmicro-crack. However,for the case with cubic TiC particle, during the period IV, the calculatedyield limits of LUV, LLV and RLV are below 150MPa at t=700 μs whenthe simulated VonMise stresses of LUV, LLV and RLV respectively reach172 MPa, 208 MPa and 210 MPa, thus contributing to χ b 1. Withoutdoubt, the matrix in the interface, especially in the vicinity of vertexesof cubic TiC particle, will be inclined to be subjective tomicro-crack for-mation. Hence, it can be concluded that sphere-shaped reinforced parti-cle is more favorable to enhance the thermal shock resistance ofcomposites. Fig. 13 further gives the corresponding SEM images of theinterface structure between thematrix and reinforced particle with dif-ferent geometric feature. It was not difficult to find that a good interfacebonding was obtained for the sphere-shaped particle, while severecracking occurred in the vicinity of the vertex of near-cubic particle.Specially, the cubic reinforced particle itself also got broken and severalcracks run through the particle, which might be attributed to the cycliccompression-tensile stress induced by the track-by-track and layer-by-layer nature of SLM technology.

6. Conclusion

Themain challenge for additivemanufacturing ofmetal matrix com-posites stems from interfacial stress induced by complicated cyclic ther-mal behavior between thematrix and reinforcing particle. Inappropriatelaser processing parameters or powder propertiesmight result in forma-tion of huge interfacial stress, thus inducing the initiation and propaga-tion ofmicro-cracks. In this study, interfacial stress evolution behavior ofTiC reinforced TiAl composites fabricated by selective lasermeltingwereinvestigated, based on a meso-scale finite element model solely includ-ing a single reinforcing particle. Some crucial conclusions can be drawnas follows:

(1) The stress concentration always emerged where the maximumtemperature gradient existed, namely in the interface. As thelaser beam successively moving from the left side of powderbed to the right side, the matrix around TiC particle underwenta solid-to-liquid-to-solid transfer process, as a result of whichthe interfacial stress at left side and right side of TiC particletransformed from a compressive stress to a tensile stress. How-ever, the interfacial stress on top edge of TiC particle was always

in a tensile stress state. Besides, in the whole interaction processbetween the laser beam and powder bed, the interfacial stressfirstly decreased consecutively due to the melting period andthen, occurred to get bounced in views of solidified constraint.

(2) The influence of geometric feature of reinforcing particle, namelysphere-shaped particle and cubic particle, on stress evolution be-havior was further investigated. Based on the predicted temper-ature and strain rate, the plastic flow stress σwas calculated. Forthe sphere-shaped one, the calculated σ in the interface washigher than the simulated Von Mise stress during the solidifyingperiod, while for the cubic one, the opposite result was obtained.It indicated that sphere-shaped reinforced particle could effi-ciently enhance the thermal shock resistance of compositeswhich was also verified by the experiment results.

Authors contributions section

1. Chenglong Ma proposed the idea of development of interfacialstress between the matrix and reinforced particle, and wrotethis manuscript;

2. DongdongGu provided the crucial advices and gave a lot of construc-tive discussions;

3. Donghua Dai established the meso-scale thermal-stress couplingmodel;

4. Hongmei Zhang performed the SLM experiments of TiC reinforcedTiAl composites;

5. Lei Du performed the simulation calculation and analyzed the tem-perature/stress field data;

6. Han Zhang conducted the SEM characterization of the interface be-tween the matrix and reinforced particle.

Acknowledgement

The authors gratefully acknowledge the financial support from theNational Natural Science Foundation of China (Nos. 51735005), the Na-tional Key Research and Development Program “Additive Manufactur-ing and Laser Manufacturing” (No. 2016YFB1100101), the NSFC-DFGSino-German Research Project (No. GZ 1217), the Key Research andDe-velopment Program of Jiangsu Provincial Department of Science andTechnology of China (No. BE2016181), and the Priority Academic Pro-gram Development of Jiangsu Higher Education Institutions. ChenglongMa thanks the financial support from the Funding for Outstanding Doc-toral Dissertation in NUAA (No. BCXJ17-05) and Postgraduate Research& Practice Innovation Program of Jiangsu Province (No. KYCX17-0253).

Data availability

The raw/processed data required to reproduce these findings cannotbe shared at this time as the data also forms part of an ongoing study.

11C. Ma et al. / Materials and Design 157 (2018) 1–11

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