Constitutive Modeling of Additive Manufactured Ti-6Al-4V Cyclic Elastoplastic Behaviour

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1 TECHNISCHE MECHANIK, 36, 1-2, (2016), ubmitted: September 7, 2015 Contitutive Modeling of Additive Manufactured Ti-6Al-V Cyclic Elatoplatic Behaviour K. I. Kouroui, D. Agiu, C. Wang, A. Subic Metal additive manufacturing technique have been increaingly attracting the interet of the aeropace and biomedical indutry. A particular focu ha been on high value and complexity part and component, a there the advantage offered by additive manufacturing are very ignificant for the deign and production organiation. Variou additive manufacturing technique have been teted and utilized over the pat year, with laer-baed technology being among the preferred olution e.g. elective laer melting / intering (SLM / SLS). Fatigue qualification, a one of the primary deign challenge to meet, impoe the need for extenive material teting. Moreover, thi need i amplified by the fact that currently there i very limited in-ervice experience and undertanding of the ditinct mechanical behaviour of additively manufactured metallic material. To thi end, material modelling can erve a a mediator, neverthele reearch particular to additively manufactured metal i alo quite limited. Thi work attempt to identify the cyclic elatoplatic behaviour characteritic of SLM manufactured Ti-6Al-V. A et of uniaxial tre and train controlled mechanical tet have been conducted on a-built SLM coupon. Phenomena critical for engineering application and interrelated to fatigue performance (mean tre relaxation, ratcheting) have been examined under the prim of contitutive modeling. Cyclic platicity model have been uccefully employed to imulate the tet reult. Moreover, a preliminary analyi ha been conducted on the difference oberved in the elatoplatic behaviour of SLM and conventionally manufactured Ti-6Al-V and their poible connection to material performance in the high cycle fatigue regime. 1 Introduction Additive manufacturing of three-dimenional metallic component involve laer aited depoiting and melting of powder metallic material layer-by-layer, tarting from computer aided deign. A additive manufacturing (unlike traditional ubtractive manufacturing) i not contrained by geometry or hape, the deign paradigm behind additively manufactured component i fundamentally different a it i driven by function (with form following function). Thi approach offer ignificant opportunitie for light-weighting by identifying key functional feature and then organically developing the minimal geometry that will upport thee function. Furthermore, thi allow for multiple part to be replaced by a ingle more complex component by integrating or merging a number of different function into a ingle component. To achieve thi, we ue different computational method, uch a tructural and hape optimiation method baed on evolutionary algorithm or topographic optimiation algorithm (Leary et al., 2009; Huang et al., 2012; Leary et al., 2013a; Leary et al., 2013b). In the pat 20 year, additive manufacturing technology ha developed from imple three dimenional (3D) printer ued to generate non-tructural rein into a ophiticated manufacturing proce capable to produce object without the ue of tool. Mot recently, the focu ha been hifted from polymer to metal, primarily aiming to cover the need of the aeropace, biomedical and automobile indutry. Weight reduction of metallic part uing additive manufacturing procee and topographic tructural optimiation could go beyond 50% compared to traditional computational and manufacturing method applied to the ame part and material. High preciion manufacturing of Titanium alloy, uch a the Ti-6Al-V, i of primary importance for the biomedical and aeropace indutry, due to the high cot involved and the engineering ignificance of the application. Variou additive manufacturing technique have been developed, with elective laer melting (SLM) being one of the mot commonly ued. The SLM proce emerged between the late 1980 and early 1990 (Vrancken et al., 2012). The SLM technique ue an infrared fiber laer which aemble olid layer out of looe powder material. In principle, a thin layer of looe powder i initially levelled acro a proceed platform and elected area of the powder are melted and conolidated, via a canning laer beam, in a erial pattern (Simonelli et al., 2012). In comparion with the conventional manufacturing technique, SLM offer many advantage, uch a the reduction of production tep, high level of flexibility, high efficiency in the ue of material ue and a near 57

2 net hape production. However, there are everal important effect that need to be avoided: internal tree development, occurring from teep temperature gradient and high cooling rate during the manufacturing proce, and increaed poroity. All the effect have an impact on the mechanical behaviour of the material under cyclic loading and low or high cycle fatigue. Ti-6Al-V i one of metal alloy employed for SLM produced part, mainly for application of high value, performance and complexity, due to it high trength and trength-to-weight ratio. A wide pectrum of mechanical propertie over a range of temperature can be achieved by varying the microtructure of the dualphae Ti-6Al-V through appropriate heat treatment and thermomechanical proceing (Zhang et al., 2007). However, heat treatment add time and cot to the production proce, reducing partly the advantage offered by additive manufacturing. Moreover, cutomiation of the microtructure may be achieved through altering the SLM manufacturing parameter. In thi cae the a-built material can be utilied without further proceing or treatment, which i highly preferable from a manufacturing cot point of view. Variou reearcher have examined the monotonic and high cycle fatigue behaviour of SLM Ti-6Al-V, neverthele it elatoplatic repone under cyclic loading ha not been invetigated in much detail, e.g. Leuder et al. (2013). In thi context, modelling and imulation of the cyclic elatoplatic behaviour of a-built SLM Ti-6Al-V i expected to complement the knowledge of reearcher and engineer aiming to identify the characteritic of uch alloy. Thi tudy aim to provide a et of preliminary reult from a computational work conducted on the imulation of the cyclic elatoplatic repone of a-built SLM Ti-6Al-V through the implementation of rate independent platicity model. For thi purpoe, experimental reult are utilied, obtained from an ongoing tet campaign conducted at the Centre for Additive Manufacturing of RMIT Univerity. 2 Platicity Model Many rate-independent platicity model for metal material imulation have been developed over the pat thirty year. However, only a relatively mall fraction of thee model enjoy today a wide acceptance by the reearch community and the indutry. Three well etablihed platicity model (Multicomponent Armtrong-Frederick model, Multicomponent Armtrong-Frederick model with threhold term and Ohno-Wang model) are utilied to model and imulate the behaviour of a-built SLM Ti-6Al-V. Moreover, a more recently propoed platicity model (Multicomponent AF with Multiplier) i included in thi invetigation, in an effort to compare and contrat it performance with thi et of widely accepted model. 2.1 Multicomponent Armtrong-Frederick (MAF) The Multicomponent Armtrong-Frederick (MAF) model i in practice a uperpoition of a number of Armtrong-Frederick (AF) (Armtrong and Frederick, 1966) back-tre term (Chaboche et al., 1979). Thi addition of AF term, commonly three for mot application, produce a more effective repreentation of the tranient and tabilied tre-train curve when compared to a model with a ingle AF term. In practice, each of the different back-tre term capture the different feature of the hyterei loop. The uniaxial formulation of the MAF model i provided by the following et of equation: a = a i, for i = 1,2,3 (1) Where, a i the total backtre and a i the added backtree, each governed by equation: ( ) i i i i p a = c a a ε (2) Dot over quantitie hown in equation (2) and elewhere denote the time derivative (rate) of backtre p platic train ε. The model material parameter are repreented by (backtre aturation value). c i (backtre evolution pace) and a and The MAF model ha been employed extenively in many application by both cientit and engineer. It i incorporated a a tandard feature in mot commercial finite element analyi oftware (e.g. Abaqu, ANSYS), however it ha very limited capabilitie in imulating ratcheting effectively. A erie of modification have been propoed to account for thi drawback, epecially in relation to the improvement of multiaxial ratcheting imulation. i a i 58

3 2.2 Multicomponent Armtrong-Frederick with Threhold term (MAF-T) The ratcheting deficiencie aociated with the MAF model were improved with the introduction of a fourth backtre which included a threhold term (Chaboche, 1991). Thi model i abbreviated a MAF-T (MAF with Threhold term). The threhold tre level, controlled by the correponding term, ignifie a tranition point whereby up to it the kinematic hardening rule develop linearly and over that point it evolve according to the original AF rule (nonlinearly). The motivating factor behind the introduction of the threhold term wa to reduce the rate of ratcheting predicted by the MAF model by tiffening the loading curve and relaxing the unloading curve. Similarly to the MAF model the total back tre in the MAF-T model i given by the addition of different backtre, a per equation (1). For the uniaxial cae, for four backtree, the following et of equation apply: ( ) i i i i p a = c a a ε, for i = 1,2,3 (3) a i p a i = ci ai ai 1 ε, for i = () a i Where, the model material parameter are repreented by aturation value) and a i (threhold term). The ymbol 2.3 Ohno-Wang (O-W) c i (backtre evolution pace), repreent the Macaulay bracket. a i (backtre The Ohno-Wang (O-W) model (Ohno and Wang, 1993a; Ohno and Wang, 1993b) originally acted a a multilinear model, unlike to the MAF and MAF-T model, which predicted no uniaxial ratcheting. In order to overcome thi iue a multiplier wa added to the dynamic recovery term of the AF backtre, which introduced a light nonlinearity to each of the defined backtre equation. The uniaxial formulation of the O-W model i a follow [again, for four added backtre term, a per equation (1)]: ( ) i i i i p a = c a a ε, for i = 1,2,3 (5) m a i p a i = c i ai ai ε, for i = (6) a i Where, the model material parameter are repreented by c i (backtre evolution pace), a i (backtre aturation value) and m (multiplier). The multiplier i calculated with reference to ratcheting or mean tre relaxation data. A hown by Bari and Haan (2000) for mall value of m, the higher the predicted ratcheting rate i. 2. Multicomponent AF with Multiplier (MAFM) The Multicomponent AF with Multiplier (MAFM) model wa introduced a an improved alternative to the MAF- T model (Dafalia et al., 2008). A a conequence of the incorporation of the threhold term in the original MAF model, an un-phyical linear portion of the hyterei loop wa formed. However, the MAFM model i able to improve thi iue without affecting the ratcheting imulation accuracy (Dafalia et al., 2008). Thi wa achieved with the introduction of a multiplier term into one of the AF backtree. The multiplier i ued to adjut the rate at which aturation of the backtre occur, without affecting the aturation level. Thi operation i analogou to the MAF-T model threhold term, without the need to check the exceedance of a threhold (which i a computationally expenive tak). The uniaxial formulation of MAFM model, for four backtree [obeying to an additive decompoition, a per equation (1)], i given by the following et of equation: ( ) i i i i p a = c a a ε, for i = 1,2,3 (7) ( ) ( ) * * * p a i = c i + ci ai ai ai ai ε, for i = (8) 59

4 With * a (dimenionle multiplier) given by: ( ) * * * * p a = c a a ε (9) Where, the model material parameter are repreented by * * c (backtre evolution pace), i * a i (backtre aturation value), c ( a multiplier backtree evolution pace) and a ( a multiplier backtre aturation value). 2.5 Iotropic Hardening A nonlinear iotropic hardening rule wa alo incorporated along each of the kinematic hardening model examined. Thi addition wa deemed neceary for the effective imulation of the trong cyclic oftening characteritic of the material under tudy (Ti-6Al-V). The governing equation (in uniaxial tre pace) for the yield tre ( k ) i provided below: ( ) p k = ck k k ε (10) Where, c k the parameter controlling the evolution pace and 3 Experimental Data * k the aturation value of the yield tre ( k ). The experimental data utilied for the purpoe of thi computational tudy were obtained from mechanical tet previouly conducted at the RMIT Univerity Centre for Advanced Manufacturing. Thee tet data come from tet performed on cylindrical cro ection pecimen of a-built SLM Ti-6Al-V material manufactured with an SLM Solution SLM 250 HL machine. Thi manufacturing equipment ha a rated power of 00 W under continuou laer mode and a minimal laer pot ize of 80 micron. The pecimen have been fabricated with a laer power of 175 W, at a laer canning peed of 710 mm/, 120μm hatch pacing and a 30μm powder layer thickne. The platform wa preheated to 200 C prior to the building proce and each pecimen had a total of 2,76 built layer. The microtructure of the obtained pecimen wa examined with the ue of optical microcopy (Phaiboonworachat, 201). Ti-6Al-V alloy are compoed of two phae, the α-phae (Hexagonal Cloe Packed, HCP tructure) and the β-phae (Body Centered Cubic, BCC), while a α+β phae can be preent imultaneouly. The examined SLM pecimen ample revealed the preence of a martenitic microtructure (α -phae). In particular, the characteritic needle haped thin lamella (lath martenite) of the α -phae have been oberved (Figure 1a). Moreover, prior β-phae acicular haped column, with random orientation, have been identified on the SLM material urface (Figure 1b). The length of the prior β-phae column ha been meaured a 183.8μm. Figure 1. SLM Ti-6Al-V microtructure micrograph preenting (a) needle haped thin lamella α -phae and (b) characteritic β-phae acicular haped column. 60

5 A comparion of the microtructure of the SLM material to a wrought material wa alo conducted. Unlike to the needle haped lamella oberved in the SLM material (Figure 2a), the wrought material i dominated by a pheroidite microtructure containing α-phae and β-phae (bright area and dark port repectively, hown in Figure 2b). Figure 2. Comparion of the microtructure of (a) SLM Ti-6Al-V and (b) wrought Ti-6Al-V. The pecimen were teted under train and tre controlled loading hitorie, ummaried in the Table 1 and Table 2 correpondingly. The tet control (input) parameter for both loading hitorie are the following: Strain Controlled Tet: Symmetric (zero mean train) cycling at different train amplitude ( ε a ) for a given number of cycle (150 cycle or lower, where the pecimen experienced a failure) (Table 1); Stre Controlled Tet: Non-ymmetric cycling under different combination of mean tre ( σ ) and tre amplitude ( σ ) pair, until pecimen failure (Table 2). a m Loading Hitory Strain Amplitude ε a Number of Cycle Tet 1 ±1.0% 150 Tet 2 ±1.5% 150 Tet 3 ±2.0% 150 Tet ±2.5% 88* *pecimen failure Table 1. Strain controlled loading hitorie. 61

6 Loading Hitory Stre Amplitude σ a Mean Stre σ m Minimum, Maximum σ, σ Stre ( ) min max Tet 1 15 MPa ( -850, +880 ) MPa 865 MPa Tet 2 35 MPa ( -830, +900 ) MPa Tet 3 30 MPa ( -85, +905 ) MPa 875 MPa Tet 0 MPa ( -835, +915 ) MPa Table 2. Stre controlled loading hitorie. The tet data (reult) are not preented independently in thi ection but in conjunction with the obtained imulation reult in the next ection of thi paper. However, ome important obervation are highlighted here, a thee are relevant to the objective and focu of thi tudy. In particular, the cyclic tet performed on the abuilt SLM material, reulting in elatoplatic behaviour, ignify important feature related to the fatigue performance of uch material. Figure 3 preent the hyterei loop obtained from the a-built SLM Ti-6Al-V train controlled tet in comparion with previouly publihed experimental data (Mayeur et al., 2008). Figure 3. Stre train hyterei loop obtained from the train controlled teting of a-built SLM Ti-6Al-V at different train level (repreented by the olid line) compared to previouly publihed tet data for wrought Ti- 6Al-V (Mayeur et al., 2008). By examining Figure 3 it i noticed that the SLM material exhibit, for each of the four train level, a trong cyclic oftening behaviour. Moreover, the yield tre, ranging from approximately 917 MPa to 1,096 MPa, i achieved at relatively low train. Thi caue a compreion in the hape of the hyterei loop, which i conitent with the brittle nature of the a-built SLM material and it low capacity to undertake platic deformation during cyclic loading (low platic deformation diipation). Thi particular feature of the tudied SLM material i evident in the hyterei loop correponding to ±1% train level, a compared to experimental reult for wrought Ti-6Al-V, obtained from the literature (Mayeur et al., 2008), both hown in Figure 3. It i alo noticed that the a-built SLM material exhibit a higher load capacity at the expene of reduced ductility. In ummary, one may conclude that: High trength and low ductility under cyclic loading are the primary characteritic oberved, which are oppoed to lower value applicable for wrought Ti-6Al-V; Cyclic oftening behaviour oberved at all train level i alo of notice; Platic deformation diipation, approximated by the area encloed by the hyterei loop, i lower for the SLM Ti-6Al-V a compared to wrought alloy. Thi, in turn, i believed to have a negative effect on the low and high cycle fatigue life of the material, a previouly reported by Leuder et al. (2013) and Xu et al. (2015). 62

7 Numerical Implementation Each of the platicity model, namely MAF, MAF-T, O-W and MAFM, wa implemented numerically in Matlab. The model parameter were obtained with the ue of the applicable (for each model) methodology and conequently optimied through a manual iterative fine-tuning proce. In particular, the proce outlined in Bari and Haan (2000) and Dafalia et al. (2008) wa ued to determine the material parameter. The value for the c i and i a parameter were calculated with reference to the tabilied cyclic tre-train curve, while the * * parameter which control the ratcheting rate ( a, c, a and m ) were determined with reference to ratcheting data. Adjutment of thee parameter wa made until the model could capture ufficiently the amount of ratcheting for a particular load cae. It wa important that uch parameter adjutment wa double-checked againt the tabilied cyclic tre-train repone to enure the imulation of the tabilied tre-train curve wa not compromied. The iotropic hardening value ( c k, k ) were etimated by fitting the uniaxial integrated iotropic hardening equation to tre range veru accumulated platic train data in order to define the relationhip between thee two meaure. The final et of material parameter obtained through the aferomentioned proce, ummaried in Table 3, wa utilied for the imulation of the experimental reult. MAF MAF-T O-W MAFM Initial yield tre ( σ ) 90 MPa Y Elaticity Modulu ( E ) 101 GPa Backtre Model Parameter a MPa MPa MPa MPa a 1 1 a 2 2 a 3 3 a Iotropic hardening parameter c ,50 00 a MPa MPa 7.7 MPa MPa c a MPa MPa 21.0 MPa MPa c a MPa MPa 9.57 MPa c a 15 * a 15 * c 1,700 m 0.10 c 2 k k 180 Mpa Table 3. Material parameter for platicity model (MAF, MAF-T, O-W and MAFM) 63

8 5 Reult The imulation reult obtained for the different model are compared againt tet data for each of the different loading hitorie (train / tre controlled) hown in Table 1 and Table 2. Thee are preented and dicued in detail in the following ection. 5.1 Strain Controlled Reult The tabilied hyterei loop at each train level (1.0%, 1.5%, 2.0% and 2.5%) are preented in Figure.It i oberved that all model are capable to capture effectively the hape and characteritic of the loop. Figure. Hyterei loop obtained from the train controlled tet, under different train level, in comparion with computational reult for the MAF, MAF-T, O-W and MAFM model. A cloer look at the cyclic hardening behaviour of the material wa conidered of interet. Thi wa performed through the calculation of the cyclic hardening factor (Η ) at different train level. The cyclic hardening factor ( Η ) i given by the following equation: σ Η= at σ σ 0 0 (11) Where, where cycle. σ at the tre amplitude i in the firt cycle and σ 0 i the tre amplitude of any number of The reult (experimental and computational) are preented in Figure 5. All model perform fairly acceptable. However, one may note that the lat point of the experimental curve (correponding to 2.5% train) wa not captured by any model. Thi wa attributed to the fact that thi point correpond to the prematurely failed pecimen (at 88 cycle), which did not allow the cyclic phenomenon evolve fully (no tabiliation occurred). 6

9 Figure 5. Cyclic Hardening Factor at different train level. Comparion of experimental veru computational reult for different model. The material mean tre relaxation wa alo invetigated. For thi purpoe, the tre amplitude variation wa plotted againt the number of cycle until aturation, both for experimental and computational reult. Figure 6 preent the obtained reult for each of the different train level and for all model compared. One may note that the model perform better at higher train level (2.0% and 2.5%), capturing quite well the experimental curve. All model have imilar behaviour in term of curve fitting, however a cloer look at each model performance i dicued in greater detail in the equel. 65

10 Figure 6. Cyclic Mean Stre Relaxation at different train level. Computational veru experimental reult for all model in comparion. An intereting analyi, from the point of view of material fatigue performance, ha been attempted via the calculation of the platic deformation energy diipation. The capacity of the SLM material to aborb platic energy wa conidered important for the completene of thi tudy, ince no uch reult have been reported in the pat, to the bet knowledge of the author. To thi end, the platic energy denity (correponding to the hyterei loop area) wa plotted againt the number of cycle, both for tet and imulated data. Figure 7 preent thee reult, while Figure 8 preent the percentile error (%error) between tet and imulated data for each model compared. A variation between model, in term of their capability to capture the tet data, i quite evident from thee reult. Thi obervation provide a ueful way to ae more accurately and perhap in a more repreentative way, the platicity model performance in reference to fatigue behaviour. However, an overall comparion of the model i neceary. Thi needed to be put under the prim of capturing the variou tet cae (train and tre controlled) and characteritic repone reulting from each loading cae. For thi purpoe, a ranking cheme i propoed a a imple way to obtain quantitative reult on the overall performance of the model. Thi cheme i preented in the equel. 66

11 Figure 7. Platic Strain Energy Denity, per cycle, for experimental and imulated reult. Figure 8. Platic Strain Energy Denity percentile error (%Error), per cycle, between experimental and computed reult for each of the model compared. 67

12 5.2 Stre Controlled Reult The invetigation of ratcheting behaviour (platic train accumulation under cyclic loading) of the SLM material (a-built Ti-6Al-V) wa a focal point for thi reearch. Such reult, experimental and computational, have not been reported o far, to the bet knowledge of the author, and were conidered important for the completene of thi work. A mentioned, a et of different loading hitorie wa utilied to obtain the ratcheting curve (a detailed in Table 2). Figure 9 preent the experimental and computational ratcheting reult for each tre pair, while Figure 10 preent the percentile error (%Error) between computational and experimental reult (for each of the model compared). One may notice that, again, the performance of the different model i varied, epecially when oberving the %Error curve. Thee finding are intrumental for the overall comparion and aement of the platicity model. Figure 9. Ratcheting train per cycle for each of the tre controlled loading cae for experiment and computed reult, for each of the model compared. 68

13 Figure 10. Ratcheting train per cycle percentile error (%Error) between experimental and computed reult for each of the model compared. 5.3 Overall Performance of the Model The need for a imple way to conduct an overall comparion i apparent by examining the variou reult obtained, for both train and tre controlled loading hitorie. The four platicity model have proven to be, in general, capable to imulate effectively complex elatoplatic phenomena. However, when it come to electing a model to be ued in actual engineering application it i not apparent or at leat eaily identifiable which would be the mot uitable one. For the engineering practitioner uch a deciion would be done on the bai of a good trade-off between the different characteritic, advantage and diadvantage of each model. Effectively, a ranking cheme could be conidered a a good tool to ait the deciion making proce. Such a ranking cheme i exemplified in thi tudy. The propoed coring cheme relie on a weighting matrix which aign different point at the variou level of percentile error (%error) achieved by each of the model. Lower performance (greater %Error) i aigned with lower point and the oppoite. For implicity, four different error level and dicrete point value were ued for thi example ranking cheme (Table ) Error < 5% 5% < Error < 10% 10% < Error < 20% Error > 20% Table. Weighting Matrix for coring cheme Employing the weighting matrix in all different cae lead to a coring table for each of the model compared (MAF, MAF-T, MAFM and O-W). Thee reult are preented in Table 5, where each model performance i noted (in term of the %error achieved). The different colour repreent the number of point aigned for each cae and when ummed a total (overall) core reult for each model (Table 6). 69

14 Simulation Reult Model Stre Controlled Strain Controlled Ratcheting Rate Mean Stre Relaxation Hyterei Loop (1t Cycle) Cyclic Hardening (H value) Platic Deformation Energy Tet 1 Tet 2 Tet 3 Tet Tet 1 Tet 2 Tet 3 Tet Tet 1 Tet 2 Tet 3 Tet Tet 1 Tet 2 Tet 3 Tet Tet 1 Tet 2 Tet 3 Tet MAF 0.0% 70.5% 55.7% 10.% 6.2% 6.8% 0.8%.% 9.5% 7.% 1.9% 7.7% 71.8% 19.9% 1.% 23.8% 10.8% 6.0% 7.9%.9% MAFT 25.% 3.1% 23.6% 6.1% 5.6% 6.3% 0.8% 7.7% 9.3% 6.6% 15.0% 7.9% 63.8% 20.5% 1.3% 27.6% 9.8% 6.6% 9.0% 5.1% MAFM 7.3% 5.2% 5.0% 16.7% 5.1% 6.7% 1.0% 0.8% 8.9% 6.6% 18.1% 8.0% 63.0% 23.2% 3.9% 30.0% 5.7% 7.3% 9.0% 3.1% O-W 11.0% 12.2% 8.0% 17.7%.% 7.7% 0.8% 1.% 9.3% 9.7% 15.9% 7.9% 65.3% 2.2% 3.1% 22.3% 12.8% 8.6% 7.1% 3.8% Table 5. Score Matrix reult for each model compared - Average Error% for each tet cae examined. MAF MAFT MAFM O-W Table 6. Overall core for each model The total (overall) core obtained for each model may be ued a a decriptor of the overall performance of the model, in comparion to other model. From thi example one may notice that the difference between model may be rather mall (in term of point collected), however ome model do tend to perform better when examining their overall characteritic (e.g. MAFM and O-W, a compared to the implet MAF and the widely ued MAF-T). Of coure, thi coring cheme i not the only applicable or the bet available (in term of accuracy) to conduct a repreentative comparion. Thi example intend primarily to highlight the importance of uch (imple) coring cheme for deciion making procee. Thee can be particularly ueful for engineering practitioner conidering to employ advanced platicity model, a oppoed to built-in model in commercial finite element oftware (uch a the rather imple MAF model). 6 Concluion Thi tudy aimed to identify the baic cyclic elatoplatic characteritic of a-built SLM Ti-6Al-V and moreover ae the capability of contitute model to imulate thi behaviour. The four model employed in thi regard were ucceful in imulating complex phenomena ariing from uniaxial train and tre controlled loading hitorie. Thi reearch i one of the few invetigation reported to date on SLM material. Phenomena aociated with the fatigue performance of thi cla of metal can be captured with reaonable accuracy with thi et of model, with ome of the model being more promiing (a indicated by thi rough comparion). Engineering deign conideration, epecially for application where high and low cycle fatigue i a critical operating factor, can benefit from thee mechanical teting and imulation reult. Moreover, thee finding can be helpful a a bai and initiator for further tudie on a-built SLM Ti-6Al-V, for which very few publihed data exit. Another intereting finding wa that the cyclic platicity model compared, quite widely ued by indutry and academia, have a varied performance under different loading cae and parameter. A coring cheme, for the aement of their overall performance, can be utilied for a quick and eay comparion. Thi can be epecially ueful for practicing engineer wihing to go beyond the claic MAF model or, it derivative, MAF-T model. A more ophiticated coring cheme (e.g. utiliing dicrete and non-dicrete value weighing matrice), a oppoed to the example ued, could lead to the development of a more comprehenive tool for reearcher and engineer. Thi tudy ha alo provided the ground for the MAFM model to confirm it value not only a an alternative to the MAF-T model but moreover a a veratile model capable to imulate the behaviour of variou clae of metal alloy (Kouroui and Dafalia, 2013; Dafalia et al., 2008). However, a more detailed analyi and implementation of the MAFM model for other metal alloy, and in the multiaxial regime, i conidered neceary for it further validation. 70

15 7 Acknowledgment The upport of the Centre for Advanced Manufacturing of RMIT Univerity i acknowledged. Moreover, we would like to thank particularly Profeor Milan Brandt and Dr Shoujin Sun, of RMIT Univerity, for their aitance in matter related to SLM material characteritic and manufacturing proce. Reference Armtrong, P.J.; Frederick, C.O.: A mathematical repreentation of the multiaxial Bauchinger effect. G.E.G.B. Report RD/B/N, 731 (1966) Bari, S.; Haan, T.: Anatomy of coupled contitutive model for ratcheting imulation. Int. J. Plat., 16, (2000), Chaboche, J. L.;, Dang-Van, K.; Cordier, G.: Modelization of the train memory effect on the cyclic hardening of 316 tainle teel. In: Fifth International Conference on SMiRT, Berlin, Germany (1979). Chaboche, J.L.: On ome modification of kinematic hardening to improve the decription of ratchetting effect. Int. J. Plat., 7, (1991), Dafalia, Y.F.; Kouroui, K.I.; Saridi, G.J: Multiplicative AF kinematic hardening in platicity. Int. J. Sol. Struct., 5, (2008), Huang, S.; Leary, M.; Ataalla, T.; Probt, K.; Subic, A.: Optimiation of Ni Ti hape memory alloy repone time by tranient heat tranfer analyi. Mat. De., 35, (2012), Kouroui, K.I.; Dafalia, Y.F.: Contitutive modeling of Aluminum Alloy 7050 cyclic mean tre relaxation and ratcheting. Mech. Re. Comm., 53, (2013), Leary, M.; Maciej, M.; Lumley, R.; Subic, A.: An integrated cae tudy of material election, teting and optimization. In: Proceeding of the 17th International Conference on Engineering Deign (ICED 09), 7, Stanford Univerity, Palo Alto, CA, USA. (2009) Leary, M.; Babaee, M.; Brandt, M.; Subic, A.: Feaible build orientation for elf-upporting fued depoition manufacture: A novel approach to pace-filling teelated geometrie. Adv. Mat. Re., (2013a), Leary, M.; Shidid, D.; Mazur, M.; Brandt, M.; Subic, A.: Topographic optimization with variable boundary condition: Enabling optimal deign of interacting component, In: Proceeding of the International Conference on Engineering Deign, ICED, 9, (2013b). Leuder, S.; Thone, M.; Riemer, A.; Niendorf, T.; Troter, T.; Richard, H.A.; Maiera, H.J.: On the mechanical behaviour of titanium alloy TiAl6V manufactured by elective laer melting: Fatigue reitance and crack growth performance. Int. J. Fat., 8, (2013), Mayeur, J.R.; McDowell, D.L.; Neu, R.W.: Crytal platicity imulation of fretting of Ti-6Al-V in partial lip regime conidering effect of texture. Comp. Mat. Sci., 1, (2008), Ohno, N.; Wang, J.D.: Kinematic hardening rule with critical tate of dynamic recovery, part I: formulation and baic feature for ratchetting behaviour. Int. J. Plat., 9, (1993a), Ohno, N.; Wang, J.D.: Kinematic hardening rule with critical tate of dynamic recovery, part II: Application to experiment of ratchetting behavior. Int. J. Plat., 9, (1993b), Phaiboonworachat, A.; Cyclic Elato-platic Behaviour of Additive Manufactured Metal, Final Year Project, RMIT Univerity, Melbourne, Autralia, (201). Simonelli, M.; Te, Y.Y.; Tuck, C.: Further undertanding of Ti-6Al-V elective laer melting uing texture analyi, In: 23rd Annual Int. Solid Freeform Fabrication Symp., 80, (2012). 71

16 Vrancken, B.; Thij, L.; Kruth, J-P; Van Humbeeck, J.: Heat treatment of Ti6AlV produced by Selective Laer Melting: Microtructure and mechanical propertie. J. Alloy Compd, 51, (2012), Xu, W.; Sun, S; Elambaeril, J.; Liu, Q.; Brandt, M.; Qian, M.: Ti-6Al-V additively manufactured by elective laer melting with uperior mechanical propertie. JOM, 67, (2015), Zhang, M.; Zhang, J.; McDowell, D.L.: Microtructure-baed crytal platicity modeling of cyclic deformation of Ti-6Al-V. Int. J. Plat., 23, (2007); Addre: K. Kouroui, Department of Mechanical, Aeronautical and Biomedical Engineering, Univerity of Limerick, Limerick, Ireland; School of Aeropace, Mechanical and Manufacturing Engineering, RMIT Univerity, Melbourne, VIC, Autralia D. Agiu, School of Aeropace, Mechanical and Manufacturing Engineering, RMIT Univerity, Melbourne, VIC, Autralia C. Wang, School of Aeropace, Mechanical and Manufacturing Engineering, RMIT Univerity, Melbourne, VIC, Autralia A. Subic, School of Aeropace, Mechanical and Manufacturing Engineering, RMIT Univerity, Melbourne, VIC, Autralia 72