鉸鏈?zhǔn)姐@模板鉆床夾具設(shè)計(jì)含CAD圖,鉸鏈,模板,鉆床,夾具,設(shè)計(jì),CAD Ji LiHuang GaoGary J. Chenge-mail: gjchengpurdue.eduSchool of Industrial Engineering,Purdue University,West Lafayette, IN 47906Forming Limit and Fracture Modeof Microscale Laser DynamicFormingThe microscale laser dynamic forming (LDF) process is a high strain rate microfabrica-tion technique, which uses a pulse laser to generate high pressure by vaporizing andionizing an ablative coating, and thus produces complex 3D microstructures in thin foils.One of the most important features of this technique is ultrahigh strain rate (typically1067s?1), which is theoretically favorable for increasing formability. However, due tothe lack of measurement techniques in microscale and submicroscale, the formability ofworkpieces in LDF is hardly studied. In this article, experiments were carried out onaluminum foils to study the forming limits and fracture of thin films in LDF. The defor-mation depth was measured by an optical profilometer and the formed feature was ob-served using a focused ion beam and a scanning electron microscope. Meanwhile, a finiteelement model based on a modified JohnsonCook constitutive model and a JohnsonCook failure model was developed to simulate the mechanical and fracture behaviors ofmaterials in LDF. Experimental results were used to verify the model. The verified modelwas used to predict the forming limit diagram of aluminum foil in LDF. The forming limitdiagrams show a significant increase in formability compared with other metal formingprocesses. ?DOI: 10.1115/1.4002546?Keywords: laser shock, microforming, high strain rate, fracture, forming limit diagram,thin film1IntroductionMicroscale laser dynamic forming ?LDF? is a novel microfab-rication technique to produce 3D microstructures with a compli-cated shape in thin foils. In the LDF process, a pulsed laser isfocused onto a workpiece, which is coated with ablative coating.As the ablative coating vaporizes and ionizes into plasma, a strongshock wave is induced in the workpiece, causing plastic deforma-tion. As a result, the workpiece deforms into a mold and takes the3D shape of the mold. As a shock induced high strain rate formingprocess, the advantages of laser shock peening ?LSP? and metalforming are combined in the LDF process ?1,2?.The LDF technique is particularly attractive to the electronicsindustry for its ability to form complex micro-3D shapes. With thefast growth of 3D microsystems, methods to manufacture 3D mi-croscale devices and components are highly needed. Comparedwith conventional sheet forming techniques, for example, stamp-ing and deep drawing, LDF is not limited by tooling dimensionsbecause the expansion of the plasma generated by laser pulse isresponsible for exerting pressure onto the workpiece. Comparedwith other microfabrication techniques, such as lithography-basedmanufacturing, LDF is cheap, fast, and suitable for forming dif-ferent materials and various 3D shapes.Figure 1 shows two microlaser dynamic formed features inwhich ?a? is a sample deformed into a square mesh and ?b? is asample deformed into a mold with hexagonal cavity arrays. Bothstructures are in micrometer scale. The figure shows that complexmicro-3D shapes can be perfectly fabricated by LDF.Moreover, one of the unique characteristics of LDF is ultrahighstrain rate ?typically 107s1? generated by the short shock pres-sure ?with a duration of less than 100 ns?. It is reported that theductility of materials increases significantly at a high strain rate?36?. In particular, better formability ?compare with conventionalhydroforming? has been observed and studied in electromagneticforming ?EMF?, in which the strain rate reaches 104s1?35?.The increase in the necking strains of the workpiece can be ex-plained by the increase in the strain rate sensitivity of materialswith the increase in strain rate especially when the strain rate isabove 103s1?7?. Besides high strain rate sensitivity, inertial ef-fects are also significant at high strain rates and can delay insta-bility and rupture ?6,8?. As a forming process with a strain rate1000 times higher than EMF, it is expected that LDF can signifi-cantly increase the formability of materials. However, due to thelack of testing techniques in microscale and submicroscale, theforming limits of workpieces in LDF have not been studied be-fore. There is a need to study the forming limit and fracture ofmaterials during LDF.In this article, ultrathin aluminum foils are deformed in micro-size molds by LDF. The deformation of the foils is measured by aWYKO HD3300 optical profiler. The formed features are ob-served under a scanning electron microscope ?SEM?. A focusedion beam ?FIB? is used to cut the formed feature and view thecross section. The deformation limit and fracture of the foils aredecided in experiments. Numerical simulation is conducted to pre-dict when and where fracture can occur in the workpiece in theforming operation. In order to accurately represent the materialresponse to short duration loading and to simulate the deformationbehavior in LDF, an appropriate constitutive model, as well as aductile failure model, is required. The widely used constitutivemodel developed by Johnson and Cook ?9? is adopted and modi-fied to be suitable for describing the material behavior at an ultra-high strain rate range. The JohnsonCook damage model, whichaccounts for the effects of stress triaxiality, strain rate, and tem-perature ?10?, is used as the ductile failure criterion. The fracturelaser intensity and foil deformation are used to determine the pa-rameter for strain rate effect. The theoretical simulations are vali-dated with experimental data. Finally, forming limit diagramsContributed by the Manufacturing Engineering Division of ASME for publicationin the JOURNAL OFMANUFACTURINGSCIENCE ANDENGINEERING. Manuscript receivedNovember 5, 2009; final manuscript received June 10, 2010; published onlineOctober 19, 2010. Assoc. Editor: Zhongqin Lin.Journal of Manufacturing Science and EngineeringDECEMBER 2010, Vol. 132 / 061005-1Copyright 2010 by ASMEDownloaded From: http:/manufacturingscience.asmedigitalcollection.asme.org/ on 10/19/2013 Terms of Use: http:/asme.org/terms?FLDs? of workpieces are plotted from the simulation results,which gives a useful reference for predicting the formability ofmaterials in microscale LDF.2ExperimentsIn this work, laser dynamic forming experiments were per-formed on ultrathin aluminum foils ?Lebow Co. Inc., Bellevue,WA?. The foil contains about 99% aluminum. Two foil thick-nesses were used ?2.5?m and 4?m?.The schematic of the LDF experiment is shown in Fig. 2. Itconsists of a laser source, confining media, a workpiece with ab-lative coating on the surface, and a mold. The laser used forplasma generation is a short pulse Q-switch neodymium dopedyttrium aluminum garnet laser ?ContinuumSurelite III? with awavelength of 1064 nm. The pulse width of the laser is 5 ns, andthe focused beam diameter is 46 mm with a Gaussian profile.Glass is used as the confining media. Graphite painting is sprayedon the aluminum foil as the ablative coating. The size of thedeformed region ranges from about 10?m to 50?m. An XYstage is used to control the position of the mold.Two rectangular mold openings with different sizes were usedfor forming the workpiece. They were cut on titanium plate byFIB. A SEM picture of the mold is shown in Fig. 3. The dimen-sions of the two molds used are given in Table 1. In this study, themolds are deeper than the deformation depth of the sample.During the forming process, the workpiece deforms into themold and takes the 3D shape of the mold. Both 2.5?m and4?m thick aluminum foils were deformed into the two rectan-gular molds. For each combination of mold size and foil thick-ness, multiple samples were deformed with increasing laser inten-sity until a laser intensity level sufficient to initiate the fracture ofthe foil is reached.The depths of the deformed features at various laser intensitiesare measured by a WYKO HD3300 optical profiler. The relation-ship between laser intensity and deformation until failure of theworkpiece can be obtained.3Modeling3.1Shock Pressure Calculation. According to Fabbro et al.?11?, the laser shock pressure can be calculated byFig. 1Features formed by micro laser dynamic forming: a arrays of micro squares; b repeated hexagonal shapesFig. 2Schematic setup of laser dynamic forming processFig. 3A mold mold 1 cut by FIBTable 1Parameters of two molds used for LDFMold 1Mold 2Length ?m?4842Width ?m?1612Depth ?m?15?15Fillet ?m?44061005-2 / Vol. 132, DECEMBER 2010Transactions of the ASMEDownloaded From: http:/manufacturingscience.asmedigitalcollection.asme.org/ on 10/19/2013 Terms of Use: http:/asme.org/termsdL?t?dt=2ZP?t?1?I?t? = P?t?dL?t?dt+32?ddt?P?t?L?t?2?where L?t? is the thickness of the interface at time t, I?t? is thelaser intensity at time t, and P?t? is the laser shock pressure gen-erated at time t.From Eqs. ?1? and ?2?, the peak value of shock pressure inducedby laser pulse can be calculated. It is proportional to the squareroot of laser intensity and is independent of laser pulse duration,which can be calculated byP ?GPa? = 0.01?2?+ 3?1/2Z1/2?g/cm2s? ? I01/2?GW/cm2?3?where?is the fraction of absorbed energy ?typically equal to 0.1?,I0is the laser intensity, and Z is calculated by2/Z = 1/Z1+ 1/Z2?4?where Z1and Z2are the impedances of the confining media ?glass?and the target material ?metal?, respectively.The calculated curves of P?t? according to different laser inten-sities are plotted in Fig. 4 and are inputted intoABAQUS6.8 usinga subroutine.3.2Constitutive Model. During the LDF process, the mate-rial experiences very high strain rates, and hence a constitutivemodel that accounts for the influence of strain rate is required.Among many material models considering strain rate effects, theJohnsonCook model is most widely used. The JohnsonCookmodel is given as follows, which describes the equivalent stress?as a function of plastic strain ?, strain rate ? , and temperature T:?=?A + B?0?n?1 + C ln? ? 0?1 T?m?5?where ? 0is equal to 1 and the temperature is defined asT?=T TrTmelt Tr?6?where Tris a reference temperature and Tmeltis the melting tem-perature of the material. The five material constants are A, B, n, C,and m. In the laser dynamic forming process, there is no signifi-cant temperature change, so the third set of the brackets, whichrepresents the temperature dependence of stress, is not considered,i.e., T?=0. The value of m is not needed as well.In this work, the properties of commercial pure aluminum areadopted for a numerical study of the mechanical behavior of theworkpiece. Commercial pure aluminum is also known as alumi-num alloy 1100, which contains a minimum of 99.0% aluminum.The density, Youngs modulus, and Poisson ratio are given inTable 2, and the JohnsonCook equation parameters are given inTable 3 ?12?.However, there is a problem in using the JohnsonCook modelin the simulation of LDF, that is, the underestimation of flowstress by the JohnsonCook model at an ultrahigh strain raterange. It is reported ?7,13? that the flow stress increases stronglywith strain rate for aluminum when the strain rate is above103s1. In other words, the strain rate sensitivity of pure alumi-num becomes quite large in a high strain rate range ?strain rate?103s1?. Meanwhile, at a low strain rate ?strain rate ?103s1?,the flow stress slightly increases with strain rate. The reason forthis transition is the different mechanisms for dislocation motion.At a low strain rate, the dislocation motion is controlled by eitherlattice resistance or discrete obstacles, while at a high strain rate,viscous phonon drag becomes dominant ?14,15?.As seen in Eq. ?1?, the flow stress increases linearly with anatural logarithm of strain rate ?ln? /? 0? in the JohnsonCookmodel. As discussed above, this relationship no longer holds at ahigh strain rate. When the strain rate is above 103s1, Klopp et al.?7? gave the value of strain rate sensitivity m, which is 0.254. Inlaser dynamic forming, a very high strain rate can be obtained,ranging from 106to 107s1. In order to describe the materialbehavior more accurately, the JohnsonCook model is modifiedinto two expressions; one is valid for a low strain rate, and theother is used at a high strain rate range. The critical strain rate ? cis 103s1. The modified model is given as follows:?=?A + B?0?n?1 + C ln? ? 0?,? ? ? c?7a?=?A + B?0?n?C0? ? c?m,? ? ? c?7b?where C0=1+C ln? c/? 0? and the strain rate sensitivity is m=0.254 ?7?.The relationships between stress and plastic strain rate calcu-lated by the modified model are in agreement with the reportedexperimental results ?7,13?.3.3Failure Model. Aluminum is a typical ductile metal.When an aluminum foil is deformed by LDF, high pressure pulseexerts on it and the material is suddenly pulled into the moldopening, resulting in thinning and plastic deformation of thesample. If the tensile stress in the sample exceeds the fracturestrength, ductile fracture occurs by nucleation and the growth ofmicroscopic voids. The ductile failure model considered in thisFig. 4Calculated temporal distribution of laser shock pres-sure according to different laser intensityTable 2Properties of aluminumDensityYoungs modulusPoisson ratio2.71 g/cm272 GPa0.33Table 3Values of parameters in JohnsonCook model foraluminumABnC140 MPa75.2 MPa0.64740.0125Journal of Manufacturing Science and EngineeringDECEMBER 2010, Vol. 132 / 061005-3Downloaded From: http:/manufacturingscience.asmedigitalcollection.asme.org/ on 10/19/2013 Terms of Use: http:/asme.org/termswork is the computational fracture model of JohnsonCook ?10?.It is based on damage accumulation and has the formW =?eqp?f?8?where W is the damage to a material element, ?eqpis the incre-ment of accumulated plastic strain, and ?fis the accumulated plas-tic strain to failure under the current conditions of stress triaxial-ity, strain rate, and temperature. When W reaches 1, the damagecriterion is met. Once the failure criterion is met at any element,the deviatoric components of stress at that failed element are sentto zero, and the failed element will be deleted from the subsequentcalculation by activating element deletion algorithm available inABAQUS6.8. It ensures that the pressure stress in deleted elementsis made to vanish during the subsequent analysis. The form of thefailure strain proposed by Johnson and Cook is given by?f=?d1+ d2exp?d3?m?eq?1 + d4ln? eqp? 0?1 + d5T TrTm Tr?9?where d1,.,d5are material constants,?mis the average of thethree normal stresses,?eqis the von Mises equivalent stress, ? eqpisthe plastic equivalent strain rate, and ? 0is a reference strain rate.Similar to the JohnsonCook constitutive model, the temperatureeffect is not considered in this study because LDF is a cold work-ing process.This failure strain expression is extended from the fracturestrain proposed by Hancock and Mackenizie ?16? for proportionalloading with constant stress triaxiality, which has the form?f= ?n+?exp?3?m2?eq?10?where ?nis the nucleation strain and?is a material characteristic?17?. The criterion was partly based on the RiceTracey voidgrowth equation ?18? and partly on experimental results.For forming the same material, the stress triaxiality does notvary significantly, and so do the constants d1, d2, and d3. Thus, thereported values of d1, d2, and d3for aluminum are adopted ?19?,which are given in Table 4.Material constant d4defines the effect of plastic strain rate onthe fracture strain. In the case of high strain rate dynamic fracture,the effect of strain rate is much more significant than in the qua-sistatic case, so the value of d4varies at a high strain rate. In thisstudy, the value of d4is determined by coupling experimental andcomputational results.4Results and Discussion4.1Experimental Results. In the LDF experiment, a work-piece is deformed into a mold with a microsize rectangular open-ing and takes the 3D shape of the mold. Figure 5?a? shows thetypical deformed feature after LDF. As the workpiece is irrevers-ibly deformed in LDF, high strain localization zones formed atsidewalls of the feature and the material around these zones be-came thinner. At strain localization zones, cracks form by thenucleation, growth, and coalescence of submicro- and microvoids?20?, which further causes failure of the sample as the plasticdeformation increases.It is already known that ductile fracture is caused by the forma-tion of submicro- and microvoids under tensile stress, which con-sists of three stages: ?1? void nucleation, ?2? void growth, and ?3?void coalescence. However, the mechanisms for void nucleationand growth are very different for different materials deformed atdifferent strain rate regimes. Therefore, the fracture that occurs inmicro-LDF process has its own features.Generally speaking, void nucleation occurs at impurities in amaterial, such as grain boundaries, inclusions, and dislocationpileups ?20?, and the first two kinds are the most common. How-ever, instead of grain boundaries and inclusions, we guess thatdislocation pileups are the major void nucleation sites in the LDFprocess. This can be explained by several reasons. First, under theimpact of pulsed pressure shock, dislocation density in samplesincreases dramatically, providing a large amount of dislocationpileups for void nucleation. Meanwhile, highly dense dislocationsform subgrain structures in the sample ?1?, which can also play therole of void nucleation location. Second, ultrathin foils are formedin micro-LDF. Because the thickness of the foil is only severalmicrons, which is comparable to the grain size, only one layer orat most several layers of grains are stacking in the thickness di-rection of the sample. That means grain boundaries available forvoid nucleation are much less compared with the bulk material.Table 4Values of parameters in JohnsonCook failure modelfor aluminumd1d2d30.140.141.5Fig. 5Typical deformed samples of aluminum foils. a A fea-ture fabricated by LDF foil thickness is 2.5?m, laser intensityis 0.13 GW/cm2, and mold 1 is used. b A fractured featurefoil thickness is 2.5?m, laser intensity is 0.27 GW/cm2, andmold 1 is used.061005-4 / Vol. 132, DECEMBER 2010Transactions of the ASMEDownloaded From: http:/manufacturingscience.asmedigitalcollection.asme.org/ on 10/19/2013 Terms of Use: http:/asme.org/termsThus, grain boundaries are not the main nucleation sites in micro-LDF. Similarly, as pure aluminum foil is used in the experiment,inclusions, which are very common void nucleation locations inalloys, are not the main nucleation sites either.After nucleation, voids start to grow under tensile stress. Al-though the widely used mechanism for void nucleation is vacancydiffusion, dislocation emission based mechanism should be re-sponsible for void growth in LDF. In LDF experiments, the load-ing time for the pressure pulse is less than 50 ns, and the strainrate produced in the sample is as high as 107s1. As a result,there is no sufficient time for the diffusion process to take place.In other words, the velocity of diffusion is too slow to drive thenucleated voids to grow in LDF. Lubarda et al. ?21? proposed adislocation emission mechanism for void growth at high strainrate regime. During the plastic deformation process, two types ofdislocation, prismatic dislocation loop and shear loop, are emittedfrom the surface of voids to relax stress concentration and thusmake the voids grow gradually. The emission of prismatic dislo-cation loop is further studied by Ahn and Sofronis ?22?.Therefore, high density dislocations generated in the LDF pro-cess and subgrain structures formed by dislocations are importantfactors for fracture in LDF by influencing the nucleation andgrowth of voids. The number and size of voids grow with local-ized plastic strain. When the localized plastic strain reaches acritical value, both the number and size of voids are large enoughfor the voids to connect to each other and coalesce, resulting infra