Advanced Issues in springback

Advanced Issues in springback
Advanced Issues in springback

Advanced Issues in springback

Robert H.Wagoner a ,?,Hojun Lim b ,Myoung-Gyu Lee c

a Department of Materials Science and Engineering,Ohio State University,Columbus,OH 43210,USA

b

Computational Materials Science and Engineering Department,Sandia National Laboratories,P.O.Box 5800,Albuquerque,NM 87185,USA

c Graduate Institute of Ferrous Technology,Pohang University of Science an

d Technology (POSTEC),San 31,Hyoja-dong,Nam-gu,Pohang,

Gyeongbuk 790-784,South Korea a r t i c l e i n f o Article history:Received 8March 2012Received in ?nal revised form 24July 2012Available online 24August 2012Keywords:Springback B.Constitutive behavior B.Metallic material C.Finite elements C.Numerical algorithms

a b s t r a c t

For purposes of this review,springback is the elastically driven change of shape of a metal

sheet during unloading and following forming.Scienti?c advances related to this topic

have accelerated dramatically over roughly the last decade,since the publication of two

reviews in the 2004–2006timeframe (Wagoner,2004;Wagoner et al.,2006).The current

review focuses on the period following those publications,and on work in the ?rst author’s

laboratory.Much of this recent work can be categorized into ?ve main topics.

(1)

Plastic constitutive equations (2)

Variable Young’s modulus (3)

Through-thickness integration of stress (4)

Magnesium (5)Advanced high strength steels (AHSS)The ?rst two subjects are related to accurate material representation,the third to

numerical procedures,and the last two to particular classes of sheet materials.The princi-

pal contributions in these areas were summarized and put into context.

ó2012Elsevier Ltd.All rights reserved.

1.Introduction

‘‘Springback’’in the present context refers to the elastically-driven change of shape that occurs following a sheet forming operation when the forming loads are removed from the work piece.It is usually undesirable,causing problems such as in-creased tolerances and variability in the subsequent forming operations,in assembly,and in the ?nal part.These effects typ-ically degrade the appearance and quality of the products being manufactured.

Springback involves small strains,similar in magnitude to other elastic deformation of metals.As such,it was formerly considered a simple phenomenon relative to the large-strain deformation required for forming.Nonetheless,appreciation for the subtleties of springback in two areas has grown dramatically.In particular,high precision is needed for the large-strain plastic response that directly affects the stresses in the body before removal of external forces.The unloading,while nominally linear elastic for most cases,can show remarkable departures from an ideal linear law.

Interest in springback as a research area and application area is substantial and is growing rapidly.A previous review in April 2005(Wagoner et al.,2006)showed that the word ‘‘springback’’appeared in virtually no standard dictionaries at the time although the term had been in use since at least the 1940’s.A search of the ISE Web of Science database (Thomson Sci-enti?c)identi?ed 334published technical papers published since 1980.A Google search found 26,800references to the word ‘‘springback.’’

0749-6419/$-see front matter ó2012Elsevier Ltd.All rights reserved.https://www.360docs.net/doc/f318176628.html,/10.1016/j.ijplas.2012.08.006

?Corresponding author.Tel.:+16142922079;fax:+16142926530.

E-mail address:wagoner.2@https://www.360docs.net/doc/f318176628.html, (R.H.Wagoner).

4R.H.Wagoner et al./International Journal of Plasticity45(2013)3–20

Today,many dictionaries include the term‘‘springback.’’(Example:Free Merriam-Webster–https://www.360docs.net/doc/f318176628.html,/dictionary/springback).A search conducted on February29,2012,shows the following changes over the interven-ing7years using topics in the Web of Knowledge(Thomson Reuters)and in a World Wide Web search with Google:

20052012Increase Web of Knowledge Publications3341428428% Google/‘‘springback’’26,800499,0001862% Google/‘‘spring-back’’N/A1759,000–It appears that there has been more information and interest in springback in the past7years than in all years previously.

The current review starts from where two review papers published in2004and2006(Wagoner,2004;Wagoner et al., 2006)left off.It focuses on new advances since then,more particularly on work performed in the?rst author’s laboratory. (Neither of these limitations is strictly followed,but this simple statement captures the intent.)Five recent topics in spring-back are discussed in sections of this document:

(1)Plastic constitutive equations.

(2)Variable Young’s modulus.

(3)Through-thickness integration of stress.

(4)Magnesium.

(5)Advanced high strength steels(AHSS).

The?rst two subjects are related to accurate material representation,the third to numerical procedures,and the last two to particular classes of sheet materials.

2.Overview

Before looking at new advances,it will be useful to summarize brie?y the?eld of springback in a general way.For a more comprehensive treatment,the previous reviews are recommended(Wagoner,2004;Wagoner et al.,2006).

Many reports of springback data must be critically evaluated before accepting the results.While many kinds of experi-ments have been performed,most of them do not control the sheet tension directly,thus making reproducibility and accu-racy problematic.Examples of the kinds of geometries used include cylindrical tooling(Yu and Johnson,1983;Yuen,1990; Sanchez et al.,1996),L-bending(Livatyali and Altan,2001;Mkaddem and Saidane,2007;Gau and Kinzel,2001),U-bending (Chen and Ko?,2007;Liu et al.,2002;Hino et al.,1999;Sudo et al.,1974;Chakhari et al.,1984),V-bending(Hino et al.,1999; Chakhari et al.,1984;Zhang et al.,1997;Tekaslan et al.,2006;Tekiner,2004)and stretch-bend tests(Hino et al.,1999;Ueda et al.,1981;Kuwabara et al.,1996).

In order to reproduce springback under mechanical conditions similar to industrial practice while at the same time pro-viding the ability to control sheet tension,tool radius(R/t)and contact friction,the draw-bend springback(DBS)test was developed(Carden et al.,2002)from earlier designs used for friction testing(Wenzloff et al.,1992;Haruff et al.,1993;Val-lance and Matlock,1992).As shown in Fig.1,a strip of sheet metal is formed around a circular tool(roller)and the front actuator applies a constant displacement rate while the back actuator provides for a constant restraining force.Rollers can be set to free,driven or?xed conditions to alter the friction condition between the tool and the specimen.Draw-bend

R.H.Wagoner et al./International Journal of Plasticity45(2013)3–205 testing has been used widely for springback experiments and corresponding simulations(Carden et al.,2002;Li et al.,(1998, 1999a,1999b,2002);Geng et al.,2000;Geng and Wagoner,2002;Wagoner et al.,2000).

Springback predictions have been conducted using analytical methods and?nite element analysis(FEA).In general,the analytical approach assumes simpli?ed process and material properties.Analytical solutions for pure bending(Gardiner, 1957;Boklen,1953;Queener and De Angelis,1968;Marciniak et al.,1992;Hosford et al.,1993;Chan and Wang,1999; Yu et al.,1996)and bending with tension(Zhang et al.,1997;Kuwabara et al.,1996;Hosford et al.,1993;Chan and Wang, 1999;Yu et al.,1996;Crandall et al.,1961;Woo and Marshall,1959;Mickalich et al.,1988;Wenner,1983;Duncan and Bird, 1978;Kuwabara et al.,1995;Takahashi et al.,1996;Kuwabara et al.,1999)for various different hardening laws have been presented.More recent development of analytical solutions includes springback in creep age-forming processes(Jeune-champs et al.,2006),prediction of sidewall curl(Moon et al.,2008;Zhang et al.,2007),springback of magnesium alloys (Lee et al.,2008,2009),analytical models based on Hill’s yielding criterion and plane strain condition for U-bending and V-bending(Zhang et al.,2007a,b),and prediction of the draw-bend springback by a semi-analytical model(Lee et al.,2007).

Finite element analysis(FEA)is a well-established tool for analyzing and predicting sheet forming strains for various materials and test conditions.FE simulation of springback,however,is much more sensitive to numerical tolerances and to material model than forming simulations(Li et al.,1999b;Wagoner et al.,1997;Mattiasson et al.,1995;Lee and Yang, 1998).Numerical procedures that must be considered more critical for springback simulation include the spatial integration scheme(Li et al.,1999a,1999b;Lee and Yang,1998;He et al.,1996;Focellese et al.,1998;Narasimhan and Lovell,1999; Wagoner et al.,1999),element type(Li et al.,1998,1999a;Wang and Wagoner,2005)and time integration scheme such as implicit/implicit(Li et al.,1999a;Wagoner et al.,1997,1999;Hu et al.,1999;Lee et al.,2009b;Guo et al.,2002),expli-cit/implicit(Mattiasson et al.,1995;Lee and Yang,1998;He et al.,1996;Narasimhan and Lovell,1999;Papeleux and Pont-hot,2002;Lee,2005;Noels et al.,2004;Valente et al.,1999;Park et al.,1999),explicit/explicit(Montmayeur et al.,1999;Xu et al.,2004;Li et al.,1999),one-step approaches(Abdelsalam et al.,1999).Various material representations affect springback simulations signi?cantly:the unloading scheme(Yuen,1990;Li et al.,1999b;Wagoner et al.,1999;Tang,1987),strain hard-ening rule(Mickalich et al.,1988;Wenner,1983;Zhang and Lee,1995;Han et al.,1999),evolution of elastic properties (Chakhari et al.,1984;Morestin and Boivin,1996;Yu,2009;Eggertsen and Mattiasson,2009),plastic anisotropy(Chakhari et al.,1984;Geng et al.,2000;Geng and Wagoner,2002;Wagoner et al.,2000;Ragai et al.,2005;Verma and Haldar,2007; Gomes et al.,2005),Bauschinger effect(Gau and Kinzel,2001;Kuwabara et al.,1996;Geng et al.,2000;Kuwabara et al., 1999;Focellese et al.,1998;Zhang and Lee,1995;Baba and Tozawa,1964;Tozawa,1990;Pourboghrat and Chu,1995;Yos-hida and Uemori,2002;Firat,2007;Firat and Kaftanoglu,2008;Bouvier et al.,2005;Dongjuan et al.,2006)and anticlastic curvature(Carden et al.,2002;Li et al.,2002)are prominent examples.

In practice,springback is controlled in only two basic ways:

(1)by increasing sheet tension(Carden et al.,2002;Mickalich et al.,1988;Kuwabara et al.,1995;Zhang and Lee,1995;

Cho et al.,2003;Moon et al.,2003;Song et al.,2007;Padmanabhan et al.,2008;Sunseri et al.,1996;Liu,1988)to reduce springback,and/or

(2)by compensating the shape of tooling to achieve a?nal target shape after springback(Gan and Wagoner,2004;Ling-

beek et al.,2005;Wagoner et al.,2007;Kara?llis and Boyce,1996;Cheng et al.,2007).

The?rst method has dominated the solution to the problem of springback for the past century,and is still the mainstay. Upon increased sheet tension,the stress gradient through the thickness of the sheet is reduced and hence the bending mo-ment and the total springback is decreased.In addition to reducing springback itself,it greatly reduces the variability inher-ent with changes in material behavior.The only downside–it is a signi?cant one–is that increasing sheet tension promotes sheet splitting,particularly with newer high strength materials that typically have lower formability.Die compensation avoids this problem,but requires very accurate springback prediction and measurement,and it may not reduce the scatter of springback caused by typical process and material variations.

Perhaps the major driving force for the rapid increase of interest in springback is the rapidly increasing speci?cation of AHSS by automakers,particularly to grades such as dual-phase(DP)steel,transformation-induced plasticity(TRIP)steel,and twinning-induced plasticity(TWIP)steel.These steels represent unique challenges because in general they have higher strength/ductility combinations than traditional autobody steels and they make use of either very coarse microstructures (DP steels)or strain-induced transformations and complex hardening behavior(TRIP and TWIP steels).These differences manifest themselves in very large hardening transients following a stress reversal,large changes of elastic‘‘modulus’’follow-ing plastic deformation,and high temperatures attained by the plastic work in areas of large strain.It is not coincidental that much of the current work on springback focuses on these aspects.

3.Plastic constitutive equations

3.1.2006status

Accurate springback prediction requires knowing the stress state throughout the body before unloading,which is con-trolled by the plastic response of the material during forming.Features of the material model that can often be ignored in

6R.H.Wagoner et al./International Journal of Plasticity45(2013)3–20

satisfactory forming simulations must be taken into account for springback simulations.The dominant example of such a feature studied in recent years is the Bauschinger effect,1which is seldom considered in applied sheet metal forming simula-tions,but which can change springback magnitudes by a factor of2Geng et al.(2000).That result utilized a form of kinematic hardening(Armstrong et al.,1966;Dafalias and Popov,1976;Krieg,1975;Chaboche et al.,1979;Ristinmaa,1995;Jiang and Kurath,1996)based on Armstrong–Frederick-type hardening rules(Chaboche et al.,1979,1987;Chaboche,2008,1991;Chab-oche and Rousselier,1983;Chaboche and Nouailhas,1989;Ohno and Wang,1991,1993;Jiang and Sehitoglu,1996;Khan and Huang,1995),with a two-surface plasticity formulation.It allowed modeling of so-called‘‘permanent softening’’following a path change by incorporating a bounding surface that translates and expands according to a mixed hardening rule(Hodge, 1957;Cris?eld,1991).This hardening law has been implemented for plane-stress thin-shell elements in conjunction with three anisotropic yield criteria:Hill’48(Hill,1948,1950;Mellor et al.,1978),Barlat’s three-parameter yield function(Barlat Yld89) Barlat and Lian,1989and Barlat’s Yld96(Barlat et al.,1997).When proper material anisotropy and non-proportional path hard-ening were incorporated,springback simulations agreed with measurements within the experimental scatter(Geng et al., 2000).

3.2.Advances since2006

Nonlinear hardening models incorporating kinematic hardening have been widely adopted to improve the accuracy of the sheet metal forming simulations.Three main nonlinear hardening models used to predict springback accurately are:(1) Armstrong-Frederick type hardening models,(2)multi-surface-type hardening models and(3)a novel hardening model without simple kinematic hardening.

3.2.1.Armstrong–Frederick type hardening model

Among many models describing the?ow stress characteristics with the change of strain paths such as Bauschinger effect, transient behavior,and permanent softening,Armstrong–Frederick type non-nonlinear kinematic hardening models domi-nated before2005and remain prevalent,with new variations still being introduced.Choi et al.(2006)proposed an aniso-tropic hardening model describing an anisotropic evolution by rotation of the yield function combined with the common non-linear kinematic hardening concept.A comprehensive review on Armstrong–Frederick type hardening models is avail-able in the recent review article by Chaboche(Lee et al.,2005)where the modeling capabilities of various nonlinear kine-matic hardening models are compared in the context of predicting ratcheting effect.

The role of path changes on applied springback predictions was quanti?ed.Chaboche(2008)assessed various hardening models by the springback of a U-shaped rail.Springback prediction using the kinematic hardening underestimated the springback,while isotropic hardening overestimated it.Oliveira et al.(2007)studied the in?uence of hardening model on springback and found that not only must strain-path changes be accommodated,but also the magnitude of strain attained by each strain-path segment.

3.2.2.Multi-surface-type hardening model

Recently,conventional two-surface models,such as the ones proposed by Krieg(1975)and Dafalias and Popov(1976), were integrated and extended in a uni?ed mathematical context to incorporate anisotropy,the Bauschinger effect,transient behavior,and permanent softening(Lee et al.,2007).As shown in Fig.2,the inner loading and outer bounding surfaces were decomposed into isotropic and kinematic hardening parts,thus providing a?exible implementation to accommodate com-plex material behavior.A simple but effective stress-update algorithm was introduced with a supplemental numerical treat-ment to resolve so-called overshooting problem.

The draw-bend springback of aluminum alloy5754-O sheet was predicted(Lee et al.,2007)within the experimental scat-ter using the non-quadratic anisotropic yield function Yld2000-2d(Barlat et al.,2003)and tension/compression experiments. Comparisons with standard Chaboche-type(or Armstrong–Frederick type)hardening models showed that it is essential to consider permanent softening as shown in Fig.3.A standard method to characterize the change of the loading direction is not clear for general stress states and paths.In terms of the single surface model,particularly Armstrong-Frederick type non-linear kinematic hardening model,various modi?cations have been made mainly to include the permanent softening ob-served at large plastic strain upon reversal loading(Geng and Wagoner,2002;Choi et al.,2006).Note that the Chaboche-type hardening model used in Fig.3is the standard combined isotropic-nonlinear kinematic hardening model that cannot reproduce the permanent softening.More rigorous models modi?ed from this2-parameter model have been able to repro-duce the permanent softening successfully.

Among other hardening models based on two-surface schemes,the Yoshida–Uemori(Y–U)model Yoshida et al.(2002)is gaining popularity in part because it has relatively few parameters to be determined and it has been implemented into the commercial FE software Pam-Stamp(ESI/PSI,1995).It assumes kinematic hardening of the loading surface and combined isotropic-kinematic hardening for the bounding surface,with both surfaces based on Hill’s yield function(Hill,1948).The model reproduces the Bauschinger transient similar to a general two-surface model,but it allows for work hardening stag-1We refer to the Bauschinger effect in its most general meaning as the evolution of hardening under non-proportional paths,particularly after a path reversal such as is encountered in a tension/compression test.

nation at large plastic strain at the expense of additional complexity.It is unclear whether accounting for work hardening stagnation is critical for the accurate prediction of springback or not.Recently,Ghaei et al.(2010)proposed an implicit stress integration algorithm for Y–U model for ABAQUS (ABAQUS,2006)and applied it to a channel draw springback of DP 600steel sheet.Predicted springback angles using Y–U and Chaboche-type hardening models were in good agreement with experi-ments,although the accuracy was enhanced by taking into account reduced elastic modulus.

3.2.3.Hardening model without simple kinematic hardening approach

Kinematic hardening models,whether involving one or two yield surfaces,still invoke the translation and expansion of a ?xed surface shape,thus preserving the direction of normals at given locations.A new approach presented by Barlat et al.(2011)describes the smooth change of yield surface shape by homogenous yield function-based anisotropic hardening (HAH).The homogeneous yield function consists of a stable component associated with a general anisotropic yield function and a ?uctuating component which distorts the overall shape of the yield surface.The yield surface shape is ?attened oppo-site from the active stress state during the proportional loading,but this ?uctuating component does not affect the shape of the yield surface near the active stress state.The HAH approach leads identical plastic ?ow stress response to the isotropic hardening for the monotonous loading,but the Bauschinger effect and transient hardening behavior can be ef?ciently repro-duced by the appropriate control of ?uctuating component during continuous and reverse loading.In this regard,the HAH model is similar to the combined isotropic-kinematic hardening,but does not involve the translation of the yield surface.

The new feature in the HAH model is an introduction of a microstructure deviator which memorizes the previous defor-mation history and controls the continuous evolution of yield surface distortion during multiple strain path changes.

For

R.H.Wagoner et al./International Journal of Plasticity 45(2013)3–207

example,the yield surface locus evolution during uni-axial tension followed by equi-biaxial tension is shown in Fig.4where microstructure deviator continuously saturates from initial uni-axial loading direction to equi-biaxial direction.The FE sim-ulations for the NUMISHEET’93U-channel benchmark showed that the new approach captures the Bauschinger effect,tran-sient hardening behavior and permanent softening in cyclic stress–strain curves,which resulted in good agreement with experimentally measured springback (Lee et al.,2012,in press ).Other approaches have also introduced the distortion of the yield function (Francois,2001;Feigenbaum and Dafalias,2007,2008).

In real forming process,the deformation is more complex such that neither stress state nor the strain path does not follow that of the simple uni-axial deformation.Instead,the deformation usually involves a signi?cant strain change which leads to the development of more complicate constitutive models for the ?nite element simulation of sheet metal forming.For this purpose,physical descriptions of the microstructure changes during deformation (Teodosiu and Hu,1998;Haddadi et al.,2006)to account for the Bauschinger effect were proposed.For example,Teodosiu and Hu.(1998)and Haddadi et al.(2006)used a tensorial form of dislocation structures developed during reverse loading and combined this microstructure change effect with the conventional nonlinear kinematic hardening.The microstructure change by the description of the dis-location structure during strain path change was also considered in the crystal plasticity approach to explicitly investigate the slip activities among slip systems in polyscrystals (Peeters et al.,2000;Li et al.,2003;Holmedal et al.,2008;Kim et al.,2012).Based on this dislocation density based hardening model,the effect of strain-path change on the springback predic-tion or on the two-stage deep drawing was investigated by using ?nite element analysis (Oliveira et al.,2007;Haddag et al.,2007;Thuillier et al.,2010).The advanced constitutive models could predict the complex material behavior during stain path change under uni-axial condition.However,there was no signi?cant in?uence of the stagnated hardening or stress over-shooting during reverse or cross-loading on springback compared to that predicted by the phenomenological isotropic-non-linear kinematic hardening models which could also predict the Bauschinger effect.

Although the physically-based hardening models or dislocation-based models have been applied to the forming and springback simulations,these models usually require many parameters.For example,the model by Teodosiu and Hu (1998)has 13parameters to describe the evolutions of state variables including fourth-and second-order tensors.Recently,the HAH model was successfully extended to describe more complex material behavior during strain path change such as cross-loading (Barlat et al.,in press ).With 8hardening parameters,the extended model could predict measured stress-strain responses of an EDDQ steel sheet sample during various two-step tension tests.Especially,the ?ow stress overshooting and work hardening stagnation with very low or negative strain hardening rate for cross-loading conditions could be captured reasonably.

4.Variable Young’s modulus

4.1.2006status

Morestin and Boivin (1996)identi?ed the signi?cant role of an ‘‘elastic modulus effect’’in springback prediction while Ghosh et al.(Luo and Ghosh,2003;Cleveland et al.,2002)made detailed measurements for an aluminum alloy

and

hardening model in p -plane.The yield locus evolution during uni-axial tension uni-axial tension (Barlat et al.,2011).

R.H.Wagoner et al./International Journal of Plasticity45(2013)3–209 high-strength steel.Various mechanisms for the nonlinear unloading behavior following plastic deformation have been pro-posed over the years:residual stress(Hill,1950),anelasticity(Lubahn et al.,1961;Zener,1948),damage evolution(Yeh and Cheng,2003;Halilovic et al.,2009),twinning or kink bands in HCP alloys(Caceres et al.,2003;Zhou et al.,2008;Zhou and Barsoum,2010a,2010b),and piling up and relaxation of dislocation arrays(Morestin and Boivin,1996;Luo and Ghosh,2003; Cleveland et al.,2002;Yang et al.,2004).

AHSS show large deviations from linear unloading according to the usual Young’s modulus following plastic deformation (Morestin and Boivin,1996;Luo and Ghosh,2003;Cleveland et al.,2002;Yeh and Cheng,2003;Caceres et al.,2003;Yang et al.,2004;Augereau et al.,1999).Springback prediction can be improved signi?cantly by adjusting the value of an apparent ‘‘elastic modulus’’(Morestin and Boivin,1996;Yu,2009;Halilovic et al.,2009;Fei and Hodgson,2006;Zang et al.,2007;Li et al.,2002;Pourboghrat et al.,1998;Eggertsen and Mattiasson,2010;Vrh et al.,2008;Ghaei et al.,2008;Kubli et al.,2008; Sun and Wagoner,2011;Kim et al.,2009;Andersson et al.,2002;Yamamura et al.,2002;Bjorkhaug et al.,2004;Yao et al., 2002;Nguyen et al.,2004;Wagoner and Li,2007).Up to2006and beyond,nearly all proposed practical approaches adopt a chord modulus(Morestin and Boivin,1996;Yu,2009;Luo and Ghosh,2003;Fei and Hodgson,2006;Zang et al.,2007;Li et al.,2002;Ghaei et al.,2008;Kubli et al.,2008)that varies with plastic strain.The chord modulus uses a linear slope of stress–strain data from joining two points obtained from just before unloading and zero applied stress.It is readily incorpo-rated in?nite element(FE)simulations by adopting a different value of Young’s modulus(which may or may not be allowed to vary with the plastic strain before unloading).Unfortunately,such treatments,while convenient,do not capture the non-linearity of the unloading response.This means that partial unloading(to a?nal value of residual stress,for example)will occur with signi?cant errors of strain(corresponding to errors of?nal shape after springback).

4.2.Advances since2006

Li et al.Sun and Wagoner(2011)examined the nature of the so-called‘‘modulus effect’’and then proposed and developed a corresponding novel continuum description.Simple tensile experiments of loading and unloading of DP780and DP980 steels showed that the effect was not markedly strain-rate dependent,as would be expected on the basis of classical anelas-ticity.The observed unloading chord modulus was reduced in some cases by30%relative to Young’s modulus.Simple con-siderations rule out damage evolution as the origin of such a large effect;such alloys show very little damage before fracture under sheet forming conditions(Kim et al.,2009).

A new class of strain was identi?https://www.360docs.net/doc/f318176628.html,d‘‘Quasi-Plastic–Elastic(QPE)strain,’’it is recoverable(elastic-like)but energy dissipative(plastic-like).A3-D continuum constitutive law was devised to account for the three types of deformation behav-ior separated by two transition surfaces,one between linear elastic and QPE modes,and one between QPE and plastic modes. The QPE theory reproduced nonlinear loading and unloading curves following stress/strain path changes in a natural and highly accurate way.The magnitude of the QPE strain was found to be proportional to?ow stress or elastic strain.The stress–strain behavior upon unloading depended only on the magnitude of the stress change after plastic deformation.Most surprising,the QPE relationship was found to be identical for two alloys when unloaded from the same?ow stress,Fig.5(a).

Fig.5(b)compares experimental unloading-loading data in tension with various constitutive models.The QPE model cap-tures accurately all known features of the modulus effect whereas elastic or chord models do not.The initial unloading fol-lowing plastic deformation occurs elastically according to the handbook value of Young’s modulus,until some critical stress

(a)

(a)Relationship between dissipated energy and stress at unloading of

approaches for unloading and reloading following tensile deformation for DP

10R.H.Wagoner et al./International Journal of Plasticity45(2013)3–20

Table1

Average draw-bend springback angle simulation errors of DP980for normalized sheet tensions of0.3,0.6,0.8,and0.9.

Elastic(E o),Isotropic hardening Elastic(E o),Chaboche Chord[E(e)],Chaboche QPE,Chaboche Average error18.0o8.5o 5.3o 2.6o

is reached.At that point,a new constitutive behavior representing QPE is entered,with corresponding nonlinear unloading and energy absorption.Reloading follows a similar process,again transitioning from elastic behavior to QPE behavior and ?nally to plastic/elastic/QPE behavior at yielding.

Table1show that springback predictions based on the QPE constitutive behavior are much more accurate than existing representations.A standard Chaboche-type plastic model,even with three component back stress evolution rule,cannot be ?tted to reproduce the QPE effect adequately.However,the plastic work hardening behavior on reloading might be able to be modeled more accurately by introducing additional back-stress tensor.Draw-bend springback simulations using the QPE model agreed with experiments to within3degrees whereas other standard model formulations showed5–18degrees in average error.

5.Through-thickness integration

5.1.2006status

Industrial FE simulation of complex sheet is carried out using shell elements almost exclusively because they make the simulations much faster by reducing the number of degrees of freedom relative to solid elements.This was true in2006and remains so today.For a given number of degrees of freedom,shell elements offer the possibility to treat stress variations through the thickness very accurately by using large number of integration points(IP).(The equivalent treatment with solid elements adds more elements and degrees of freedom,thus making the computation time unrealistically long.)In spite of this advantage,most simulations of industrial sheet forming operations rely on small numbers of integration points through the thickness,typically3or5.Some commercial programs for sheet forming analysis in the past did not make provision for more than7or9integration points.

Reports were made between1999and2002by Li et al.(2002)and Wagoner et al.(1999)that25-to-51IP were required to assure1%numerical accuracy for springback simulations,depending on the bend ratio,R/t,and the magnitude of sheet ten-sion.They recommended use of25IP for general springback analysis.This work set off a?urry of activity on the subject, including con?icting and contrary reports in the literature,particularly among users and developers of commercial software. Examples include reports that there is no difference in simulated springback for3to10IP(Andersson et al.,2002)or7to15 IP(Yamamura et al.,2002),and only marginal differences between5and20IP(Bjorkhaug et al.,2004).Some authors rec-ommended7or9IP(Xu et al.,2004;Yao et al.,2002;Nguyen et al.,2004)and one(Xu et al.,2004)even stated that7IP was optimal and larger number decreased the accuracy!(This would seem to be a mathematical impossibility,as was later ver-i?ed.See below.)

5.2.Advances since2006

In order to address this controversy,Wagoner and Li(2007)conducted analytical and numerical integration of bending moments for bending-under-tension of a beam.This removed numerical uncertainties associated with FE modeling.They evaluated the role of number of integration points(N IP)on the accuracy of the numerical integration alone under various conditions of varying R/t,sheet tension and strain hardening behavior.

The simulations showed that the springback error limit must be considered,not the error for a single,particular simula-tion.The actual integration error is oscillatory in terms of small changes of R/t and sheet tension,which has the appearance of scatter if not computed systematically.This means that it is possible to get a very accurate answer within the limiting envelope,but such a result is purely fortuitous.(This may explain the much better agreement between simulations and experiments when the experimental results are known in advance!)As shown in Fig.6(a),the numerical integration error limit depends on integration scheme and increases with increased sheet tension.No single integration scheme always per-formed best,but Gauss integration is preferred for the higher tension force range,where the interaction errors are largest.

Fig.6(b)and Table2show the effect of N IP and R/t on the accuracy of springback prediction.It was shown that the max-imum error increases with decreasing bending radius and N IP.More IP are required for low-strength steel than for high strength aluminum,because the lower bending moment corresponds to larger fractional errors,and because the stress-strain curve has more curvature.These results con?rmed the original recommendations of Li and Wagoner generally,although the predictions can be re?ned for particular cases.Therefore,reports of the adequacy of small N IP(3–9)for springback analysis should be critically examined before being https://www.360docs.net/doc/f318176628.html,rger N IP can always reproduce a continuous stress distribution,and therefore the post-forming bending moment,more accurately,but at the expense of increased computational time.

Burchitz and Meinders(2008)developed an adaptive through-thickness integration method which showed negligible dif-ference for N IP larger than20–25.Xia et al.(2006)showed that the details of the results can be modi?ed by the boundary conditions adopted.

R.H.Wagoner et al./International Journal of Plasticity45(2013)3–2011

Table2

Number of integration points(N IP)required to limit the springback values for low strength steel

using Gauss integration.

Max error1%5%10%50%

R/t=56826164

R/t=203818134

R/t=100221063

6.Magnesium

6.1.2006Status

Magnesium alloys were being increasingly considered for sheet forming applications because of their low density(lower than aluminum)and high strength(similar to aluminum).The principal problem was the low ductility in tension at room temperature(Roberts,1960;Bettles and Gibson,2005).Therefore,the main areas of research focused on the deformation mechanisms,improving ductility,and possible warm forming applications.

The limited ductility of magnesium alloys made the solution of other application problems moot.For example,springback would be expected to be large because the Young’s modulus of magnesium is less than2/3that of aluminum,which itself exhibits large and problematic springback.A search of the Web of Knowledge(Thomson Reuters)through2005shows only two papers combining‘‘springback’’and‘‘magnesium’’as topics(a third paper found in the search is mostly about alumi-num-magnesium alloys).Chen and Huang(2003)showed that,as expected,forming at higher temperatures(and thus at lower stresses)reduced springback.In the other paper,Boger et al.introduced a large-strain tension-compression test that is particularly suited for revealing the widely differing strain hardening in tension and compression for magnesium alloys (Boger et al.,2005).

6.2.Advances since2006

The number of papers combining‘‘springback’’and‘‘magnesium’’since2006is38,as compared to2for all years previ-ously.Clearly,while still small,interest in the subject is increasing.Most of these more-recent papers focus on the special asymmetric plastic constitutive response of magnesium alloys(Lee et al.,2009a,b,2007;Kim et al.,2011,2009;Hama and Takuda,2011,2012;Supasuthakul et al.,2011;Hama et al.,2011;Tadano,2010),on the effects of elevated temperature or warm forming(Xiao et al.,2011;Greze et al.,2010;Hama et al.,2010;Gao et al.,2010;Ozturk et al.,2009;Palumbo et al., 2009;Kim et al.,2008;Bruni et al.,2006),or on special forming processes to mitigate problems(Kuo and Lin,2012;Gisario et al.,2011;Han and Lee,2011;Bunget et al.,2010;McNeal et al.,2009;Hino et al.,2009,2008;Palumbo et al.,2008).

Lou et al.(2007)measured the continuous,room temperature,large-strain,reverse-path hardening of Mg AZ31B and through metallography and acoustic emission associated the unusual features to twinning,untwining,and their exhaustion at room temperature.That work made use of the Boger tension–compression device(Boger et al.,2005)and the results were incorporated in complex plasticity formulations for FE implementation based on combined hardening models(Li et al.,2008, 2010),on two-surface models(Lee et al.,2007,2008),and on visco-plastic polycrystal models(Choi et al.,2009).From ap-proaches such as these,the room-temperature springback was computed using FE modeling(Lee et al.,2009b)and analytical models(Lee et al.,2008,2009a;Kim et al.,2009).

The two-surface approach(Lee et al.,2008)is based on a modi?ed Drucker–Prager yield function to incorporate the strength differential effect.Simulations based on this approach predict the springback of magnesium at room temperature

12R.H.Wagoner et al./International Journal of Plasticity45(2013)3–20

much better than conventional approaches,including the presence of a knee in the variation of springback angle with back force,Fig.7.

The drawback of conventional hardening model is clear from the comparison between measured and simulated spring-back results shown in Fig.7.Various Armstrong–Frederick type isotropic-kinematic hardening models have been reasonably well applied for the springback prediction of cubic crystals such as aluminum and steels.The evolution of back stress in the AF-type nonlinear hardening model is fundamentally exponential for a monotonic uni-axial loading,which is well suited for the standard plastic?ow stress behavior shown in cubic crystals.However,HCP materials such as magnesium alloys and titanium alloys having strong basal texture show signi?cant strength differential,asymmetric plastic?ow stress between tension and compression.Moreover,the shape of?ow stress curves during twinning(or untwining)dominant deformation such as tension followed by compression is unusually in?ected,which makes the conventional hardening law dif?cult to be directly applicable.

Measurements of the springback of magnesium under controlled draw-bend conditions have been carried out at room temperature(Lee et al.,2009b,2007).Such springback measurements,Fig.8,show the expected large magnitudes corre-sponding to the low Young’s modulus(maximum angles of100–120degrees vs.60degrees for aluminum(Carden et al., 2002),but also some unusual features.In contrast to aluminum alloys(Carden et al.,2002),AZ31B magnesium alloys show an increase or?at aspect of springback for increasing sheet tension at lower values but a more rapid decrease after a critical point,such as was presented in Fig.8.

R.H.Wagoner et al./International Journal of Plasticity45(2013)3–2013 Measurements of springback have also been performed at elevated temperature(Hama et al.,2010).For temperatures above200°C,which coincide with large reductions of?ow stress and ductility increases to practical magnitudes,springback is drastically reduced or eliminated.

The most recent work in the area of springback of magnesium alloys combines several of the aspects noted above.In par-ticular,Piao et al.(2011)developed an elevated-temperature,tension–compression testing capability suitable to for measur-ing the strain hardening under non-proportional loading as a function of temperature(i.e.as twinning disappears and slip becomes easier).A new procedure(Piao et al.,in press)makes use of this procedure in a single test to determine the presence or absence of twinning and a semi-quantitative estimate of the area of fraction of twins.

7.Advanced high-strength steels(ahss)

7.1.2006Status

Springback was known to be one of the major problems limiting their widespread adoption of advanced high-strength steels(AHSS Wagoner,2006.Fig.9compares the springback of traditional high-strength steel and AHSS with nominally the same yield stress.Evidently AHSS’s have more dramatic behavior that needed to be understood.

Advances in plastic constitutive equations for AHSS have been addressed implicitly in earlier sections of this paper and will not be addressed again here.Pertinent to springback,AHSS,and in particular dual-phase(DP)steels,have several aspects that make them distinct from traditional mild and high strength/low alloy steels:

Strength-to-modulus ratios similar to aluminum alloys.

High strain hardening concurrent with high strength.

Very large plastic work products and thus high temperatures developed during deformation.

Very large non-isotropic hardening effects after path reversals.

Very large‘‘modulus’’changes when unloading after large plastic strains.

By2006,steels of the era2had been shown not to exhibit time-dependent springback,even at periods up to7years after forming(Wang et al.,2004).This intriguing phenomenon,?rst reported in1997(Wagoner et al.,1997)for aluminum alloys, refers to the change of a formed part’s shape for up to a year after forming.Results and analysis(Wang et al.,2004)showed that time-dependent springback is caused by room-temperature creep driven by residual stresses in the equilibrated body after forming.Conditions that produce high internal stresses relative to the yield stress favor time-dependent springback.

7.2.Advances since2006

With the exception of time-dependent springback,which will be addressed below,only a few recent key AHSS references will be cited.Through-thickness variations of material properties(‘‘banding’’)in AHSS were associated with signi?cant springback differences(Gan et al.,2006).Constitutive equations for1-D(Sung et al.,2010)and3-D plasticity(Sun and Wag-oner,2011;Sun et al.,2009;Kim et al.,2011;Sun and Wagoner(submitted for publication)were introduced and shown to allow accurate simulation of springback(Kim et al.,2011;Chung et al.,2008)and formability(Kim et al.,2011).Modulus changes were found to?t into a new constitutive framework(Kim et al.,2011)and patterns of multi-axial path hardening were identi?ed and found amenable to interpretation by nonlinear kinematic hardening theories(Sun et al.,2009,submitted for publication).

The remainder of this section will?nish with a closer look at time-dependent springback of AHSS.Contrary to the status in2006,Lim et al.(2012)reported the?rst observations of time-dependent springback of steels,in particular AHSS grades of DP600,DP800,DP980,and TRIP780.Similar to aluminum alloys,but opposite of traditional steels,all AHSS showed a linear increase of the springback angles with log time for the?rst few days to weeks(Fig.10(b)).The magnitude of time-dependent springback decreased with increasing back force and tool radius,consistent with the behavior of aluminum and with a room-temperature creep mechanism.The?nal time-dependent shape change of AHSS was approximately1/3of that observed for aluminum alloys under similar test conditions and was up to18%and6%of the total springback for Al6022-T4and DP600, respectively.

The mechanism of time-dependent springback of AHSS was found to be room-temperature creep,similar to aluminum alloys.The principal alternative,anelasticity,was found to exhibit kinetics more than an order of magnitude faster than time-dependent springback.Details of room temperature creep predictions for DP600was carried out,Fig.11.Although good qualitative agreement was found,simulations over-estimated the time-dependent springback angle.However,pre-dicted time-dependent springback using time hardening and strain hardening creep laws showed better prediction than the model adopting steady-state creep law,by a factor of2–3(Lim et al.,2012).

While the choice of creep law is important(and standard ones from tensile tests do not give perfect predictions),other constitutive effects were minor,in all cases less that2%on initial springback angle,and less than7%on?nal time-dependent 2Steels tested included DQSK(drawing quality,silicon-killed steel),AKDQ(aluminum-killed,drawing quality steel)and HSLA(high strength low alloy steel).

shapes after U-channel forming and springback of an AHSS(DP600)and traditional high-strength steel(HSLA

(b)

AHSS and(b)time-dependent springback angles for DP600(Lim et al.,2012

R.H.Wagoner et al./International Journal of Plasticity45(2013)3–2015 springback angle.Examples that were tested include detailed strain hardening law,plastic anisotropy,strain rate sensitivity and FE mesh size.Deformation-induced heating is another complication for draw-bend springback of AHSS(Sung et al., 2010;Kim et al.,2011).A thermo-mechanical FE model of the DBS test for DP980showed that incorporating the thermal effect changed the springback angle by8%.

8.Concluding remark

Although the capability of the springback prediction has been signi?cantly improved in terms of the elastic–plastic con-stitutive equations and relevant FEM modeling as described in the previous sections,there are still remaining sources of uncertainty that should be considered in the future investigations.The topics that might be further improved in the spring-back analysis are:

(1)Constitutive model considering the effect of different strain paths

(2)Friction

(3)Temperature

(4)New press technology

The?rst subject becomes more important as the emergence of the advanced high-strength steels since the conventional forming technology might not be applicable to successfully form parts within expected shape accuracy.In this case,the mul-ti-stage forming technology might be necessary to improve both formability and shape accuracy,which may be optimized by the?nite element modeling that takes the effect of different strain paths into account.Several plastic constitutive models have been proposed to capture the stress-strain responses under load reversal,cross-loading condition with previous defor-mation histories(Oliveira et al.,2007;Haddag et al.,2007;Thuillier et al.,2010;Barlat et al.,in press).For example,the springback of U-channel type with or without pre-tension was proposed as a benchmark problem of Numisheet2011 (2011),which resulted in signi?cant scatters among participants depending on their applied constitutive models.The work on the stain path effect may be especially needed in areas related to the strain-induced transformation of austenite to mar-tensite and the consequent creation of anisotropic mechanical behavior,and the resultant effect of such anisotropic behavior on springback(Lee et al.,2007).

The second and third topics,friction and temperature,are usually coupled to each other.Besides an understating of con-stitutive behavior of advanced high strength steels,it is also necessary to understand the interaction between material and tool surface,or frictional behavior,and temperature dependency on the springback.Especially for the AHSS,it might be imperative to investigate the change of friction conditions during forming because the sheet materials experience variable deformation rate,temperature and pressure between blank and tool.The in?uence of the temperature in the cold forming was proved to be signi?cant in terms of the temperature dependent plastic?ow curve and friction coef?cient(Barlat et al., 2003;Yoshida et al.,2002).For example,in the real continuous forming conditions the temperature rise might be as high as 60–80°C with the AHSS,which in?uences the?ow stress curves,friction,necking and springback.Therefore,more robust measurements of stress–strain behavior and friction by taking the temperature effect into account will be necessary for bet-ter simulation of springback in the sheet metal forming.

To introduce more?exible control of the forming speed,frictional behavior and materials’temperature during forming of advanced high strength steels,a new generation of presses,so called servo presses,emerged with the capability to control the stroke of all of the moving components of the stamping tool.The advantages of servo press were well documented by the previous articles(Osakada,2010;Tamai et al.,2010).The primary feature of the servo press is able to control slide action independently by a set of powerful servo motors,which is not possible with traditional presses.Therefore with this servo press technology the displacement path can be liberally de?ned with respect to not only the position and speed but also the direction.Another advantage of servo press is that slide velocity can be controlled throughout the forming process.Since the number of achievable slide motions is inde?nite,the computer simulation technology to optimize them is more crucial for the sheet metal forming with servo press.The constitutive equations should be compatible with path dependent mechan-ical behavior,including the effect of strain rate and the friction change as a function of forming speed and temperature. Acknowledgements

This work was supported by the National Science Foundation(Grant CMMI0727641),the Department of Energy(Contact DE-FC26-02OR22910),the Auto/Steel Partnership,and the National Research Foundation of Korea(Grant NRF-2010-220-D00037).Thanks are due the many authors whose work was cited here.Special acknowledgement to collaborators who con-tributed to this work extensively over many years:Kwansoo Chung(Seoul National University),David K.Matlock(Colorado School of Mines),Michael L.Wenner(G.M.Research,retired),James G.Schroth(G.M.Research),James R.Fekete(formerly General Motors,now at NIST Boulder),Sean R.Agnew(University of Virginia),Thomas B.Stoughton(G.M.Research),Fredric Barlat(Pohang University of Science and Technology),and Myoung-Gyu Lee(formerly of Ohio State University,now at Po-hang University of Science and Technology).

16R.H.Wagoner et al./International Journal of Plasticity45(2013)3–20

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文档管理系统可行性研究

文档管理系统 可行性研究报告 The Report of Feasibility Studies 专业:计算机科学与技术 班级: 姓名: 报告日期:

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人事档案、照片档案、实物档案、会计档案、基建档案、工程档案、客户关系档案等等。符合国家档案局发布的《归档文件整理规则》(最新标准)。 档案管理一体化系统 主要功能 主要包括收文管理、行文管理、合同管理、档案管理、查询管理、用户管理、系统维护等七大模块。可以存储并读取各种格式的电子文档。内置完备的打印格式,并可自定义打印格式,各类登记簿实现了流水、满页打印。可设置为网络版,实现局域网或广域网上多台计算机数据库的共享。支持打印、读取条形码,支持读取员工卡,为档案文件的借阅登记提供了更多方便。 提供完美的解决方案 经验出发,从管理领先角度思考如何优化图文管理效益,从而针对各大企业的管理需求,设计出乾坤DMS图文管理系统。「乾坤图文管理系统」透过计算机化接口,提供用户可以关键词或编号索引快速轻松搜寻档案,并结合管理人员的文件调阅权限,审阅签核流程;再者,透过电子化的档案集中存放,不仅保障文件安全性,可防止非经授权的图文数据流出,同时也能视需求调阅不同版本,管理经验得以传承,企业知识也可妥善保存应用。

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度保证企业的文件安全。 2、共享、学习企业文件 文件管理系统通过内部网络将文件资本进行共享,让更多的人分享到企业文件资本,拓宽部门和员工的知识范围。 3、应用、增值文件资本 文件管理平台构建面向企业业务流程的文件管理系统,使得工作过程中显形知识结构化,隐形知识显形化。 通过文件的不断重复应用,实现文件增值。有效的规避了人员升迁流动所造成了关键业务领域的损失,让业务运行不辍。 4、提升企业竞争力 创造企业新竞争价值,增加企业利润,降低企业成本,提高企业效率。建立企业新文化,鼓励思想自由,培育创新精神。 通过减少反应时间来提高为客户服务的水平,通过快速向市场提供产品和服务来增加收入。 二、文件管理系统的建设要求 首先是支持的文件内容要全面,从文件管理的内容角度,至少应该包括: ?对信息的发布,比如直接发布各种内容 ?对文档的管理,如各类DOC、XLS、PPT等文件 ?对数据信息的管理,如各类报表等等 有利于充分利用文件: ?对链接的处理:在内容中可以互相链接,它是有效利用文件的非常重要的环节 ?强有力的索引能力,特别是全文检索 ?对于动态数据的强有力查询能力,比如可以根据各种条件进行查询

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企业文档管理系统的基本功能 建立一套规范的文档管理系统在企业信息化建设的过程中是必不可少的,是企业规范化管理的重要一步。随着科技的不断进步,文档管理系统可以提供的功能已不再局限于单纯的文档集中管理,文档管理系统可以帮你做什么,都搞清楚了吗? 企业文档管理系统的含义: 企业文档管理系统提供给企业一个易用,安全,高效的文档管理软件。通过该系统软件,企业可以集中存储和管理海量的文档和各类的数字资产(如Office文档,视频,音频,图片,等等),系统提供了严谨和灵活的权限管理机制和文档共享机制。 当前,市面上的各类文档管理系统多种多样,但其实概括起来,常用功能基本包含以下五项:

1、集中存储:文档管理系统通过集中存储的形式,将企业原先散乱存放在员工个人办公设备上的文档统一存储在一个地方,实现文档的集中管理以及合理共享。 2、快速检索:方便快捷的让用户在海量的文档中搜索到急需的文档。 3、文档编辑:用户可以直接在文档管理系统中编辑文档,依据软件产品的不同,还可细分为支持在线编辑或需要下载到本地后再编辑。但总体上,一款优秀的文档管理系统,其编辑模式都不需要用户改变原有的操作习惯。 4、权限管理:系统必须支持权限控制,系统管理员可根据员工所属岗位、部门设置不同的文档使用权限,普通用户仅可在其权限范围内执行相关的操作。 5、文档保护:系统须对文档进行必须要加密保护,无轮是存储或是传输过程中,确保企业文档的安全。 除了上述常用的基本功能之外,像云盒子这类的基于企业私有云环境下的文档管理系统,还集成了即时通讯、客户端多平台漫游、移动办公等多项功能。如此,企业不仅仅可对内部的文档进行规范化管理,更可利用其它功能来提高日常办公效率。

文档管理系统的功能及优势介绍-中文

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图书管理系统需求分析文档

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是主要功能是以工作室选方向功能和工作室出勤点到功能为主。因此我们需要一个更为完善的系统网站。 目前图书管理系统管理网站已有学生做出来了,但系统的侧重点是图书借阅功能。对于此类功能并不能满足用户的其他需求,但是对于已选工作室方向的同学们来说却并不实用。因为该系统未对已选工作室的学生进行需求分析。而我们的网站是针对已经选好方向的学生来说的,它能够更方便的让已选工作室方向的学生和老师进行沟通,更方便的让学生们知道其他工作的进展情况,能够很好的督促大家努力的去学习。 2、建设目标 我们的系统旨在方便学生们的借阅、在线阅读和学生们对各个阅读进度的了解以及老师对学生阅读情况的了解和老师对其他安排进度的了解等。 一个工程的完成,一个是不能够做到很完善的,则就需要小组一起完成,一起学习沟通合作,要让我们大家感到小组的快乐合作。并完成任务。 具体建设目标如下: a.减少对图书管理工作的人力与费用; b.提高处理图书的速度; c.提高图书管理的精度; d.促进教务工作信息化管理。 3、系统拓展 系统网站拓展至全省各大高校学院 三、系统功能需求功能分析 1、系统可行性分析 (1)、技术可行性:技术人员有c#语言做基础,学习采用语言,

文档管理系统详细设计书

档案管理软件子系统模块详细设计说明书

版本历史记录

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