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7/30/2019 L thuyt t bin

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L thuyt t binDi tc dng ca ti, cc vt liu mt mc no s thc hin s chy t t. Hin tng

ny gi l t bin (t ch Creep - t bin).tnh t bin ca kim loiung cong t bin. ng cong ca cc th nghim ko vi ti v nhit khng i c vtrn hnh 1. Trc honh biu din thi gian t, trc tung biu din ko di tng i = l/l0 y ll ko di tuyt i, cn l0 l di ban u. Khi t ti, thanh nhn bin dng tc thi0 (on OA). Bin dng tc thi c th l n hi hay n do.on ABc trng cho s gim

vn tc t bin v gi l giai on th nht (hay chuyn tip) ca t bin; di ca on nytng i ngn. Vn tc bin dng thc t l hng s trn on BC; phn ny gi l giai on thhai ca t bin (hay l giai on chy nht). Th nghim s kt thc hoc bng s b "gy" tiim C, hoc bng s ph hoi "nht" ko theo s hnh thnh ch tht. Trong trng hp sau cphn t bin nhanh dn CD.Nu ng sut ln, giai on th hai c th xy ra trong thi gian

ngn.

ng cong chng. Nu di thanh b ko lun lun l hng s ( = const) th ng sut trongthanh s gim theo thi gian v xy ra s chng ng sut. Hin tng ny c gii thch bng stng bin dng t hin trong thanh, do phn bin dng n hi gim i. S chng c c

trng bng s gim t ngt ca ng sut u qu trnh (hnh 2).

Hnh 1: ng cong t bin. Hnh 2: ng cong chng ng sutS chng lm cn tr s lm vic ca cc lin kt bu lng, lin kt nn, cc l xo v.v... Mc khcdo s chng m cc ng sut nhit v cc ng sut ban u ti cc phn t ca cu trc gim mtcch t ngt. Hin tng chng c nghin cu trc tip nh cc my th nghim lm chng.

T bin nguc. Nu ti mt thi im no ta ct ti th di ca thanh sau khi ct ti sgim dn. Hin tng ny gi l s phc hi hay l t bin ngc. Ch c mt phn bin dng

thuc giai on th nht ca t bin c phc hi. S phc hi c trong cc kim loi a tinh thv c lin quan n tnh khng thun nht ca s t ti ca cc tinh th trong cc n tinh th s

phc hi rt t. Thng th c th b qua hiu ng t bin ngc khi ng sut bin i chm.Hiu ng ny c th rt ln khi ng sut thay i tun hon.

T bin khi t ti li. Sau khi ct ti vt liu c t bin ngc. Khi t ti tr li nh hn mctrc, vn tc t bin t u ln hn vn tc t bin trc khi ct ti, nhng sau nhanh

chng tr v gi tr trc (hnh 3).


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Hnh 3 : T bin khi chu ti lp liHnh 4 : Cc ng cong t bin ca tbp

cthnh phn 0,31/C ; 0,540//Mn ; 0,11/Si ;2,05/Ni ; 0,83/Cr ; 0,45//Mo nhit (l 450oC.

Do , s bin dng li mt thi im no ph thuc rt t vo s gin on. Mc d vy trongthc t vn xy ra trng hp bin dng tng cng, khi t bin c gin on, ln hn so vi t

bin khng c gin on.S ph thuc vo ng sut. gii thch s ph thuc ca vn tc vo ng sut ta lm cc thnghim vi cc cch t ti khc nhau. Trn hnh 4 ch ra cc kt qu th nghim trong mt thi

gian di vi thp c t hp kim nhit 450 0C.Cc ng cong ca cc th nghim trong thi gian ngn ni chung c dng tng t mc d vn

tc t bin thng tip tc gim. Trong trng hp ny nn xc nh vn tc trung bnh ca tbin trong khong chn.

Cc kt qu th nghim v t bin rt ri rc, v vy cn phi lm ng u cc kt qa t binny, thng t c iu bng cch lp cc im th nghim trong li lgarit.

Theo cc th nghim, vn tc t bin giai on th hai II l hm n iu, tng nhanh ca ngsut 1. Cc im thi nghim trong li lgarit thng tp trung gn mt ng thng no ,

iu ny xc nhn c s ph thuc ly thaII = B11m (l) y h s t bin B1 v s m t bin ml cc hng s c trng cho vt liu cho nhit

cho. Thng thng s m t bin ln hn n v v i khi n 10 - 12 v hn na.Vi cc ng sut rt nh vn tc bindng t l vi ng sut, iu ny khngph hp vi nh lut (1). S thiu htny ca s ph thuc ly tha khng chobin v min ng sut rt b nh hngrt t n tnh t bin ca ton chi tit.

Hnh 5. nh hng ca nhit V tnh ng dng ca cc ung cong t bin. Cc ng cong t bin (xem hnh 4) thng

c th xem nhit nh ng dng vi nhau khi vi s ph thuc ly tha, chng c th cbiu din di dng

1c = 1(t)1m (2)Hm 1(t) t l vi ng cong no trong cc ng cong t bin. Vi gi tr. thi gian

khng ln hm ly tha l mt xp x tt1(t) = At (0 <


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nh hng ca nhit . Khi ng sut c nh, vn tc nh nht ca t bin tng theo nhit vi quy lut hm m:

(3)

y C,N l cc hng s, Tl nhit tuyt i.Cc ng cong t bin cc nhit khc nhau v vi cng ng sut c v trn hnh 5.h s B1 v s m m,ni chung, ph thuc vo nhit . Thng trong khong nhit cho

trc, s m mthc t c th coi l khng i, nhit ch lm thay i h s B1. Trong trnghp ny c s ph thuc n gin vo nhit .

T bin trong cc trng thi ng sut phc tp thung c nghin cu cc th nghim lbin ca cc ng thnh mng. Ta a ra cc kt lun c bn t cc th nghim ny.

Nu vi nhit cho trc kim loi n nh, tc l trong n khng c s bin i pha, th plc thy tnh khng nh hng n t bin, s thay i th tch l bin dng n hi.

Trong cc iu kin t ti n gin, cc phng trnh ca ten x ng sut v vn tc bin dngtrng nhau. Cc kt qu th nghim cho thy s xp x ng dng ca cc ten x ng sut v vn

tc bin dng. C s ph thuc gia cc cng ng sut tip i v cc vn tc bin dng trti c trng cho vt liu cho vi nhit cho trc.

Khi t ti phc tp tnh t bin lin h vi s tng tnh d hng ca bin dng v do n phthuc vo cc t ti. Vi s t ti phc lp bin i t ngt nhng s ph thuc n gin nu

ra trn khng cn ng na.


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Mathematical Models of ViscoelasticBehaviour

In these models springs and dashpots are used to simulate the elastic and viscous components ofthe stress/stain response.The spring (elastic component of the response) obeys the relations for tensile and shear stress

The dashpot (viscous component of the response) obeys the relations for tensile and shearstress

Simple models using combinations of springs and dashpots do not correspond directly todiscrete molecular structures, but they do aid in understanding how the materials willrespond to stress/strain variations. In general, the more complex the model the better theexperimental fit, but the greater the number of experimental constants required. We shallonly describe the simplest of these models, developing these only for tensile stress.(a)

Maxwell Model

This consists of a spring and dashpot in series

Figure: Maxwell Model


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Equilibrium EquationAssuming constant area, equilibrium of forces gives

Deformation Equation

or from above


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giving

This is the governing equation of the Maxwell Model.(i)Creep

For a constant applied stress,

ie the strain increases linearly with time, being given by

(ii)RelaxationFor a constant strain

Solving this equation with at t = 0,

(iii)RecoveryWhen the stress is removed there is instantaneous recovery of the elastic strain.


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This model is acceptable as a first approximation to relaxation behaviour, but isinadequate for prediction of creep and recovery.

(b)Kelvin or Voigt Model

This consists of a spring and dashpot in parallel

Figure: Kelvin or Voigt Model

Equilibrium EquationThe applied load is supported by the spring and the dashpot


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Deformation Equation

Thus

giving

This is the governing equation of the Kelvin or Voigt Model.(i)Creep

For a constant applied stress,

Solving this differential equation for total strain,

(ii)RelaxationFor a constant strain


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ie the stress is constant, with the predicted response being that of an elasticmaterial - no relaxation(iii)Recovery When the stress is removed

Solving this equation with the initial condition at the time of stress removal

This model is acceptable as a first approximation to creep and recovery behaviour,

but is inadequate for prediction of relaxation.

Various compromises involving aspects of both models have been proposed. All involveincreased complexity.

In general, equations of the form

are favoured to model viscoelastic behaviour.

>From these simple models, we can obtain some insight into the criterion by which we can judgewhether the polymer melt system will be predominantly viscous or elastic in its behaviour. Using

the Maxwell model, for constant stress ( ) the strain in time t is

The terms on the right hand side contribute equally to the strain when : i.e., when

, the relaxation time. For shear stresses this relaxation time is .


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For processing times, t < tr, the system is predominantly elastic.For processing times, t > tr, the system is predominantly viscous.

Effect of Elasticity

When a tensile or shear stress is applied to a polymer melt, the molecules partially uncoilbecoming preferentially aligned in the direction of the applied stress. On removing the stress themolecules tend to regain their random configuration. This recovery leads to a contraction in the

direction of stress, in the case of tension and in the case of shear.

The elastic modulus depends not only on the polymer but also on the processing

conditions.

Its effects are observed in die-swell (most significant in short dies - why?) and in theWeissenberg effect (polymer appears to climb rotating shaft in stirred tank - cf. normal vortex).

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