Method of evaluating workability in cold pilgering
Journal of Materials Processing Technology 212 (2012) 1687–1693
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Journal of Materials Processing
Technology
j o u r n a l h o m e p a g e :w w w.e l s e v i e r.c o m /l o c a t e /j m a t p r o t e
c
Method of evaluating workability in cold pilgering ?
Hideaki Abe a ,?,Munekatsu Furugen b
a ZircoProducts Co.,Ltd.,1-13Chofu Minatomachi,Shimonoseki 752-0953,Japan
b
Furugen and Makino Laboratory Inc.,1-26Satsukigaoka,Nisinomiya 662-0875,Japan
a r t i c l e
i n f o
Article history:
Received 12October 2011
Received in revised form 6February 2012Accepted 11March 2012
Available online 18 March 2012
Keywords:Cold pilgering Workability
Compression test Zirconium alloy Stainless steel Titanium alloy
a b s t r a c t
A new method of evaluating the workability of a tube in cold pilgering has been studied on the basis of material deformability and the effects of process conditions.A circumferential compression test of a tube is con?rmed to be an effective evaluation method for deformability.The critical reduction in height upon crack initiation in the compression test is also found to be a good measure of material deformability.Systematic cold pilgering tests and the numerical analysis of cold pilgering are conducted.As a result,the ratio of radial strain to circumferential strain during pilgering is a good indicator of process conditions,and a common mechanism of inner ?ssure formation during pilgering in stainless steel,titanium alloy,and zirconium alloy is proposed.Finally,a suitable expression for workability is obtained by considering material deformability and the effects of pilgering conditions.These ?ndings will assist the selection of appropriate pilgering conditions to prevent the formation of ?ssures on the inner surface of a tube.
? 2012 Elsevier B.V. All rights reserved.
1.Introduction
High-quality metallic seamless tubes,including those made of stainless steel,titanium (Ti)alloy,and zirconium (Zr)alloy,are generally fabricated by cold working followed by a subsequent heat treatment to obtain dimensional accuracy and good mechan-ical properties,i.e.,high strength and high ductility.Fig.1shows the process ?ow of a seamless tube fabricated by cold working.First,a heat-treated hollow billet is extruded.The extruded tube is annealed if necessary.Subsequently,the tube is repeatedly cold-worked and heat-treated.Finally,the surface of the tube is ?nished by pickling,polishing,or blasting.Cold working includes cold draw-ing and cold pilgering.Cold pilgering is suitable for metals that are dif?cult to deform owing to its compressive reduction mode;Stinnertz (1988)reported that it is widely applied to tube manufac-ture and plays an important role in high-quality tube making.The objective of the present study is to develop a method of evaluating the workability of a tube in cold pilgering.
Fig.2shows an illustration of the cold pilgering process.The tools used are a pair of roll dies and a mandrel.The roll dies have a decreasing caliber from the inlet to the outlet on the outer surface.In pilgering,the roll dies are rotated and simultaneously
?This manuscript was accepted as an original article by the editorial committee of the Japan Society for Technology of Plasticity,after the peer review by two reviewers,and it appeared in the Journal of the Japan Society for Technology of Plasticity in volume 52,number 605in 2011in Japanese.
?Corresponding author.Tel.:+81832461272;fax:+81832468921.E-mail address:abe@zpc.co.jp (H.Abe).
reciprocated,and the rate of reduction of the outer diameter depends on the caliber.The mandrel,which has a tapered shape in the rolling direction,is located inside the tube.The diameter and wall thickness are gradually reduced with increasing number of forming steps while applying a lubricant,and the tube is elon-gated in the axial direction.In each forming step,the mother tube is advanced and rotated in the idle zone at a predetermined feed rate and turn angle,respectively,to repeatedly perform rolling during cold pilgering.
A large cross-sectional reduction is possible in cold pilgering compared with that in cold drawing.However,?ssures on the inner surface of the tube may be formed under unsuitable operating con-ditions because the tube is ?attened during rolling.Preventing the formation of such ?ssures is a very important issue in cold pilgering.
Various studies on ?ssure formation in cold pilgering have been reported.Bembenek et al.(1981)conducted cold working tests on austenitic stainless-steel tubes and quantitatively discussed the relation between the reduction mode and inner ?ssure formation.They indicated that a suitable ratio of wall reduction to diameter reduction (i.e.,the reduction mode or Q -factor)was crucial for pre-venting inner ?ssures.Dunstan and Johnson (1988)reported the results of cold working tests on Ti alloy and Zr alloy tubes,which indicated that a reduction with high Q -factor is effective for pre-venting ?ssures.Stinnertz (1990)reported the formation of inner ?ssures in the case of reduction with a Q -factor of less than 1.Abe et al.(1991)studied the effect of the Q -factor on the inner ?ssure formation of a Zr-lined Zircaloy-2tube by performing systematic cold pilgering tests and considering the plastic deformation state during cold pilgering.
0924-0136/$–see front matter ? 2012 Elsevier B.V. All rights reserved.doi:10.1016/j.jmatprotec.2012.03.012
1688H.Abe,M.Furugen/Journal of Materials Processing Technology212 (2012) 1687–1693 Bil let→Heat treatment→Extr usion→Anneal ing→
→Finishin g
Fig.1.Process?ow of cold-working tubes.
However,the formation of inner?ssures was subsequently
observed in the cold pilgering of Zircaloy-2tubes subjected to rapid
quenching during the process,and their formation could not be
explained by only the Q-factor.Abe et al.(1994)investigated the
effects of cold pilgering parameters,including the Q-factor and
reduction in area,on the inner?ssure formation of Zr alloy tubes
subjected to rapid quenching.In their study,a compression test was
performed on Zr alloy tube shells to evaluate material deformabil-
ity,and the relation between cold pilgering parameters and?ssure
formation was obtained.Abe et al.(2000)studied the effect of the
roll die caliber on the quality of Zr alloy tubes and proposed an
appropriate caliber design for high-reduction cold pilgering.Abe
and Furugen(2010)studied inner?ssure formation and the factors
affecting it in Zr alloy tubes.In their study,a compression test was
proved to be a useful measure for evaluating the deformability of
Zr alloy tube shells.The compressive properties of the tube shells,
which were related to the heat treatment conditions in the process,
affected inner?ssure formation in cold pilgering.
In the present paper,we present a comprehensive study of
inner?ssure formation in cold pilgering,in which both mate-
rial deformability and the effects of cold pilgering conditions are
considered.The test materials used are two stainless steels,a Ti
alloy,and two Zr alloys.The investigation of material deformabil-
ity includes the metallurgy and compressive property of each test
material.Systematic cold pilgering tests and the numerical anal-
ysis of cold pilgering are conducted to determine the effects of
pilgering conditions on inner?ssure formation.From the inves-
tigation results,a common mechanism of inner?ssure formation
for the test materials is revealed.In the discussion,the results in
the above-mentioned previous studies(Abe et al.,1994;Abe and
Furugen,2010)are referred to.A circumferential compression test
is proposed as a means of measuring deformability.Finally,the
relationship between the material deformability of tubes and the
pilgering conditions is discussed.
2.Experimental
2.1.Materials
The chemical compositions of the?ve materials tested,i.e.,two
stainless steels(M1and M2),one Ti alloy(M3),and two Zr alloys
(M4and M5),are shown in Table1.M1is a typical
austenitic
Fig.2.Cold pilgering process.
Table1
Test materials.
Symbol Material Content(mass%)
M1
Stainless steel
18%Cr–8%Ni–Fe
M222%Cr–6%Ni–3%Mo–Fe
M3Ti alloy3%Al–2.5%V–Ti
M4
Zr alloy
1.3%Sn–0.2%Fe–0.1%Cr–0.05%Ni–Zr
M5 1.0%Sn–0.2%Fe–0.19%Cr–0.12%Ni–Zr
stainless steel(Type304),and M2is a dual-phase stainless steel
(Type329).M3is an?+?-type Ti alloy that is widely used as an
aerospace material.M4and M5are Sn–Fe–Cr–Ni–Zr alloys;M4is
a typical material used in the nuclear industry called Zircaloy-2.
A billet of each tested material was extruded to form a tube
shell,as shown in Fig.1.The tube shells of the two stainless steels
and Ti alloy were cold-worked and heat-treated twice before the
cold pilgering tests.The Zr alloy tube shells were annealed at about
650?C before the cold pilgering tests.The?-quenching method for
the billets differed between the two Zr alloy tubes.The billet of M4
was quenched from the?-phase to the?-phase in the solid state
using water,whereas that of M5was quenched with ice-mixed
brine while in a hollow shape to obtain a high cooling rate.All the
tubes were fully annealed to remove the residual stress before the
cold pilgering test.
https://www.sodocs.net/doc/e14316399.html,pression test
The sampling of specimens and the compression test method
are shown in Fig.3.Specimens were obtained from three direc-
tions,i.e.,the radial,circumferential,and axial directions,of the
tube.The specimens were solid cylinders of4mm or8mm diame-
ter and8mm height;their surfaces were?nished to form smooth
surfaces with a roughness of0.8?m Ra.The compression test was
performed in an Instron test machine at room temperature.Both
the top and bottom sides of the specimens were lubricated with oil,
and the compression speed was kept constant at5mm/min.Dur-
ing compression,the actual displacement and load were recorded
continuously;thus,crack initiation in the specimens was clearly
observed.The critical reduction in height, c,upon crack initiation
was calculated using
c=ln
H
h
,(1)
where H is the height of the specimen before the test and h is
the height of the specimen upon crack initiation.Also,the yield
strength was obtained from the recorded displacement and load.
The stainless-steel and Ti alloy specimens were obtained from
extruded tube shells of45mm outer diameter(OD)and7mm wall
thickness(WT).The Zr alloy specimens were obtained from tubes
of63.5mm OD and10.9mm WT before the cold pilgering
test.
https://www.sodocs.net/doc/e14316399.html,pression test.
H.Abe,M.Furugen/Journal of Materials Processing Technology212 (2012) 1687–16931689
Table2
Test pass schedules of stainless steels and Ti alloy.
Symbol Schedule(unit:mm)Rd Q
P1OD16×WT1.3→OD6.3×WT0.6880%0.7 P2OD16×WT1.3→OD7.5×WT0.5680% 1.1 P3OD16×WT1.3→OD8.3×WT0.5080% 1.5 P4OD16×WT1.3→OD9.5×WT0.4180% 2.4 P5OD16×WT1.3→OD11.2×WT0.3680% 4.2
2.3.Cold pilgering test
In the cold pilgering test of the stainless steels and Ti alloy,the mother tubes tested had an OD of16mm,a WT of1.3mm,were2m long,and were fabricated from tube shells by several cold work-ing and annealing processes.The test tubes were fully annealed and surface-conditioned to a roughness of0.2?m Ra by pickling or blasting.The test machine was a small cold pilger mill with a roll die diameter of100mm and a working zone length of180mm.The feed rate was2.5mm and the turn angle was75?.
The?ve test pass schedules for the stainless steels and Ti alloy are shown in Table2,together with the two cold pilgering parameters,i.e.,the reduction in area[Rd(%)]and reduction mode (Q-factor).The Q-factor represents the ratio of wall thickness reduc-tion to diameter reduction and is de?ned as Q=ln(t1/t0)/ln(d1/d0), where t0and t1are the wall thicknesses before and after pilger-ing,and d0and d1are the average diameters before and after pilgering,respectively.In the test,Rd was?xed at80%and the Q-factor was widely varied from0.7to 4.2.The depth of the inner?ssures was measured by observing the cross section of the cold-pilgered tubes using optical microscopy,and the inner?s-sures that formed during pilgering were observed by scanning electron microscopy(SEM).Also,the effect of the mother-tube grain size on the workability of M1was investigated by per-forming annealing at different temperatures before the pilgering test.
In the cold pilgering test of the Zr alloys,the mother tubes of 63.5mm OD,10.9mm WT,and2m length were fully annealed and surface-?nished to a roughness of0.2?m Ra by pickling.The cold pilgering test was performed using a75VMR-type mill man-ufactured by Meer with a roll die diameter of370mm and a working zone length of760mm.The feed rate was2mm and the turn angle was57?.The test pass schedules for the Zr alloys are shown in Table3.M4and M5were cold-pilgered using sched-ules Z1and Z2,respectively.The reductions were91%and87%, respectively,which are relatively high.The other?ve pass sched-ules from Z3to Z7were used in previous studies(Abe et al., 1994;Abe and Furugen,2010).The reduction in area Rd was widely varied from51%to91%and the Q-factor was varied from 1.0to3.8.The detection of?aws in the cold-pilgered tubes was performed by ultrasonic testing,penetration testing,and visual observation.
Table3
Test pass schedules of Zr alloy.
Symbol Schedule(unit:mm)Rd Q
Z1OD63.5×WT10.9→OD22.2×WT2.691% 1.5 Z2OD63.5×WT10.9→OD25.5×WT3.587% 1.3 Z3a OD63.5×WT10.9→OD34.0×WT4.677% 1.5 Z4a OD63.5×WT10.9→OD44.4×WT7.651% 1.0 Z5a OD63.5×WT10.9→OD40.0×WT6.064% 1.4 Z6a OD63.5×WT10.9→OD34.0×WT2.885% 2.6 Z7a OD63.5×WT10.9→OD37.0×WT2.286% 3.8
a Previously reported studies(Abe et al.,1994;Abe and Furugen,2010
).
Fig.4.Load chart in compression
test.
Fig.5.Specimen of Zr alloy M5after compression test.
3.Results
https://www.sodocs.net/doc/e14316399.html,pression test results
Typical graphs showing displacement versus compression load obtained from the compression test of the stainless steels and Ti alloy are shown in Fig.4.In all three directions,the two stainless steels did not form cracks up to a displacement of5mm,whereas the Ti alloy had slanting cracks.The two Zr alloys formed cracks in the compression test similar to those in the Ti alloy;the appearance of M5specimens after the compression test is shown in Fig.5.
The compression test results of all?ve materials are shown in Table4.In all three directions,M1and M2showed a critical reduc-tion in height, c,of more than1,and hardly any difference in yield strength(0.2%YS)was observed.Even M2,which has high strength, did not exhibit cracks in any direction.For the Ti alloy,a difference in yield strength was observed among the three directions,and both the circumferential and axial specimens had a much lower c.Both M4and M5had a difference in yield strength among the three directions and also had lower c values in all three directions. In particular,M5had an extremely low c in the circumferential direction.
The Ti alloy and Zr alloy tubes had lower compressive deforma-bility than the stainless-steel tubes and signi?cant anisotropy in the yield strength and c among the three directions.This result is related to the fact that Ti and Zr have only a few slip systems causing
Table4
Compression test result.
Radial Circumferential Axial
0.2%YS(MPa) c0.2%YS(MPa) c0.2%YS(MPa) c
M1361>1.0332>1.0345>1.0 M2732>1.0748>1.0719>1.0 M37510.547540.466160.42 M46350.697980.585360.69 M57130.489010.295730.61
1690H.Abe,M.Furugen /Journal of Materials Processing Technology 212 (2012) 1687–
1693
Fig.6.Cold pilgering test result in stainless steels and Ti alloy.
crystal deformation owing to their hexagonal close-packed (hcp)structure.Tenckhoff (1988)reported that Ti and Zr exhibit inher-ent crystallographic and mechanical anisotropies,and that an hcp structure has least deformability in the c-axis direction.In Abe and Furugen (2010),the existence of a relationship between the c -axis orientation ratio and the c values for the three directions in Zr alloy tube shells was con?rmed.
The difference in c between M4and M5can be explained by the effect of the cooling rate in billet ?-quenching,as described in Abe and Furugen (2010).Namely,the cooling rates of M4and M5were about 30?C/s and over 100?C/s,respectively.The differ-ence in the cooling rate affected the compressive deformability of the tube shells.The compressibility is related to the dislocation density in the matrix.Yang and Adamson (1989)studied the dis-location behavior of Zircaloy-4during quenching and annealing,and found that the rapid water quenching of a Zircaloy-4specimen induced a large amount of dislocation in the matrix that could not be annihilated by subsequent annealing at 650?C or a lower tempera-ture.Onchi et al.(1980)reported that the channeling of dislocations led to inhomogeneous plastic deformation in Zircaloy-2.Wechsler (1972)stated that dislocation channeling is produced by quenching or irradiation in many metals,including Zircaloy-4.Thus,the tube shell M5,which was fabricated by extremely rapid quenching and annealing at 650?C,exhibited less deformability than M4owing to its larger number of remaining dislocations.
Kudo and Aoi (1967)studied the relation between stress and crack initiation during compression tests on annealed steel sam-ples.The obtained reduction in height was from 0.6to 1.8.The compression test results revealed that the Ti alloy and Zr alloy tube shells in the present test had lower deformability than the annealed steel samples.
3.2.Cold pilgering test results of stainless steels and Ti alloy
The measurement results for the inner ?ssure depth of the cold-pilgered stainless-steel and Ti alloy tubes are shown in Fig.6.A marked difference could be seen among the ?ve test passes as well as among the three materials.In the lower-Q -factor passes (P1and P2),deep ?ssures were observed,whereas in the higher-Q -factor passes (P3,P4,and P5),shallow wrinkles were observed.This result is in agreement with those in Bembenek et al.(1981)and Dunstan and Johnson (1988).
In pass schedule P1,where the effect of the cold pilgering condi-tions was signi?cant,the Ti alloy tube (M3)had the deepest ?ssures of 10?m,followed by the dual-phase stainless steel (M2)with 8?m ?ssures and the austenitic stainless steel (M1)with 6?m ?ssures.In pass P2,where the effects of the pilgering conditions as well as the material were observed,the Ti alloy had deep ?ssures,while the two stainless steels had shallow ?ssures.In passes P3and P4,where a difference among the materials was observed,only the Ti alloy had ?ssures.In pass P5,where the effect of the
pilgering
Fig.7.Grain-size effect in austenitic stainless steel.
conditions was manifest,all material tubes had shallow wrinkles.The Ti alloy had deeper inner ?ssures than the stainless steels in all the passes.The pilgering test results correspond to the behavior of c for the materials.
The result of the test on the austenitic stainless steel with differ-ent mother-tube grain sizes is shown in Fig.7.A mother tube with coarser grains had deeper ?ssures after pilgering than that with ?ner grains.
Fig.8shows the inner surface during pilgering.Images were obtained by SEM observation of the austenitic stainless-steel tube during P1,which resulted in the deepest ?ssures for all three mate-rials.Even when the mother tube (Position 1)had a smooth surface,the tube had a rough inner surface in the early stage of pilgering (Position 2).The roughness on the inner surface changed into wrin-kles at Position 3.Eventually,deep ?ssures were formed on the inner surface at the ?nishing point of pilgering (Position 4).Similar results were observed for the other materials in this study.A sim-ilar result for a Zr-lined Zircaloy-2tube was also reported in Abe et al.(1991).
The effect of the grain size of the mother tube on the inner ?ssure depth,as shown in Fig.7,is related to the roughness observed at Position 2.In general,a metal workpiece with coarser grains is likely to exhibit roughness on the surface after cold working;such rough-ness is referred to as “orange peel”.Because the roughness is formed in the early stage of pilgering,the grain size of the mother tube affects the depth of ?ssures in pilgering.In addition,the inherent deformation systems of materials,such as slip and twin systems,are expected to affect the formation of ?ssures.
3.3.Cold pilgering test results of Zr alloys
The results of the cold pilgering test of the Zr alloy tubes are shown in Table 5,together with the pilgering parameters and the c values in the circumferential direction.In the present study,pil-gering tests No.1and No.2were conducted for tube shells M4and M5,respectively.The results of 16other tests were reported in Abe et al.(1994)and Abe and Furugen (2010).The 18tube shells had various c values from 0.29to 0.73;this variation is caused by the different thermal histories of the process,as already mentioned.That is,tube shell M4in test No.1was subjected to a moderate cool-ing rate (about 30?C/s)during billet quenching,while tube shell M5in test No.2was subjected to an extremely high cooling rate (over 100?C/s).The tube shells in tests No.3to No.8were fabricated by
H.Abe,M.Furugen/Journal of Materials Processing Technology212 (2012) 1687–1693
1691
Fig.8.Propagation of inner?ssure during pilgering in austenitic stainless steel at P1.
a method involving rapid billet quenching(about100?C/s).In con-
trast,the tube shells in tests No.9to No.18were fabricated by a
combination of three different cooling rates(i.e.,100?C/s,30?C/s,
and15?C/s)during billet quenching and various annealing tem-
peratures from649?C to788?C as described in Abe and Furugen
(2010).
Tube shell M4in test No.1,having the higher c of0.59,had
no?ssures on the inner surface after the cold pilgering with91%
reduction.In contrast,tube shell M5in test No.2,having the lower
c of0.29,ha
d deep?ssures of about0.2mm after th
e pilgering with
87%reduction.The relative values of c for the two materials in the
compression test are in qualitative agreement with the degree of
?ssure formation obtained in the cold pilgering test.
However,the18cold pilgering test results shown in Table5
cannot be explained by only considering the circumferential c.
Neither can they be explained by only considering the cold pilgering
parameters(Rd and Q-factor).Hence,it is necessary to discuss the
workability of cold pilgering by considering both the measure of
material deformability c and the pilgering conditions.This will be
discussed in the next section.
4.Discussion
4.1.Analysis of cold pilgering
Furugen and Hayashi(1984)developed a method of numeri-
cal analysis for investigating cold pilgering.Their analytical model
was the?rst attempt to estimate the plastic deformation state
in pilgering.Most subsequent studies on the analysis of cold pil-
gering have cited this study.Monkawa et al.(1985)reported an
Table5
Pilgering test result of Zr alloys.
No.Pass schedule Circumferential, c Pilgering test result
Rd Q
1Z191% 1.50.58Good
2Z287% 1.30.29Deep?ssure
3a Z287% 1.3
0.40Deep?ssure
4a Z377% 1.5Fissure 5a Z451% 1.0Good 6a Z564% 1.4Good 7a Z685% 2.6Good 8a Z786% 3.8Good
9a
Z451% 1.00.58Good
10a0.43Fissure
11a0.56Good
12a0.61Good
13a0.73Good
14a0.71Good
15a0.71Good
16a0.58Good
17a0.64Good
18a0.58Good
a Previously reported studies(Abe et al.,1994;Abe and Furugen,2010).improvement in the lifetime of cold pilgering tools by applying results obtained using the analysis method.Finite element(FE) analysis has also been used to investigate cold pilgering.Lodej et al. (2006)reported a three-dimensional FE analysis of tubes subjected to cold pilgering,citing the study of Furugen and Hayashi,and their results corresponded well with those obtained using the analytical model.Hence,the analysis method of Furugen and Hayashi is use-ful for estimating the plastic deformation state and is utilized in the following discussion.
In cold pilgering,the tube is rolled asymmetrically because it is rotated by57?or75?in each forming step.In the analysis,the tube cross section is divided into four sections,including two web parts and two?ange parts,as illustrated in Fig.9.In each section, the average stress and strainεare calculated in the radial(r),cir-cumferential(?),and longitudinal(l)directions.The analysis using the method of Furugen and Hayashi was performed to enable a discussion of the pilgering test results.
The analysis results of austenitic stainless steel at pass P3are shown in Fig.10. ij andεij in the?gure denote the stress and strain in the i-direction in tube section j,respectively.In the web part (section1),where the entire inner surface of the tube is in contact with the mandrel,the stresses in all three directions are compres-sive;the large radial strain is compressive and the circumferential strain is very small.In the?ange part(section2),the radial and axial stresses are compressive and tensile,respectively;the large circumferential strain is compressive and the small radial strain is tensile.The behaviors of the stress and strain during pilgering are the same for all the pass schedules regardless of the material tested.
The plastic deformation state during pilgering affects the forma-tion of inner?ssures.Hardly any?ssures are formed in the web part, because all three stresses are compressive and the radial and cir-cumferential strains are compressive and tensile,respectively.On the other hand,the?ange part is subject to a larger compressive stress and the circumferential strain is compressive.In addition, the inner surface is free,that is,it is partially in contact with the mandrel.Consequently,in the?ange part,?ssures are more likely to form on the inner surface.
The present analysis results indicated a signi?cant difference in the strain history in the?ange part during pilgering among the pass schedules.A comparison of three pass schedules(P1,P3,and P5) applied to the austenitic stainless-steel tubes is shown in Fig.11. The three passes had different strain histories,that is,P1had both a larger circumferential compressive strain and a larger radial
tensile Fig.9.Partition of a tube-section in analysis.
1692H.Abe,M.Furugen /Journal of Materials Processing Technology 212 (2012) 1687–
1693
Fig.10.Numerical analysis result of the cold pilgering in austenitic stainless steel at P3.
strain than P3and P5.The strain history during pilgering is likely to affect the formation of inner ?ssures on the cold-pilgered tubes.Hence,we next discuss the validity of applying the strain ratio in the ?ange part (?εr /ε?)max ,which approximately indicates the slope of the strain history in Fig.11,as an indicator of the pilgering conditions.
4.2.Fissure formation mechanism
Fig.12shows the formation mechanism of an inner ?ssure,which is derived from both the experimental and analytical results.Even when a mother tube has a smooth surface,it has a rough inner surface in the early stage of pilgering.In this stage,both the grain size and the inherent slip systems of the material affect the degree of roughness.As working proceeds,the rough inner surface becomes wrinkled.In the case of pilgering with a large (?εr /ε?)
max
Fig.11.Strain history (εr –ε?)in ?ange part during
pilgering.
Fig.12.Mechanism of inner ?ssure during cold pilgering.
in the ?ange part,the wrinkles are likely to develop into ?ssures owing to the high circumferential compressive strain;hence,a low-deformability material with a low circumferential c is likely to develop deep inner ?ssures on pilgered tubes.
4.3.Workability in stainless steels and Ti alloy
Fig.13shows the cold pilgering test results for the two stainless steels and the Ti alloy,where the ?ssure depth is plotted against the strain ratio in the ?ange part (?εr /ε?)max .The strain ratio was con?rmed to be a good indicator of the cold pilgering conditions.In most previous studies,inner ?ssure formation has been discussed in terms of the Q -factor.In the present study,the strain ratio in the ?ange part has been found for the ?rst time to be an indicator of the plastic deformation state in cold pilgering,which leads to ?s-sure formation.In the ?gure,the effect of material deformability is also manifest.The ?gure shows the workability of the stainless-steel and Ti alloy tubes in cold pilgering.In practice,it is possible to prevent inner ?ssure formation by selecting an appropriate strain ratio in the ?ange part depending on the material,using the results in the ?gure.In addition,the ?gure suggests that appropriate pro-cess conditions can be obtained by simultaneously considering the plastic deformation state and material deformability.
4.4.Workability in Zr alloys
Next,numerical analysis was performed for all seven pass schedules of the Zr alloy tubes,and the strain ratios in the ?ange part (?εr /ε?)max for all 18test pass schedules in Table 5were obtained.Fig.14shows the obtained strain ratios in the ?ange part,the circumferential c values,and the pilgering test results shown in Table 5.The pilgered tubes are classi?ed into three groups by inspection,namely,no ?ssures ( ),?ssures ( ),and deep ?ssures (?).The ?gure clearly shows the workability of the Zr alloy tubes in cold pilgering.When the material has good deformability,that is,a high c ,severe cold pilgering with a large strain ratio (?εr /ε?)max is possible.In contrast,when the material has a low c ,cold pilger-ing must be carried out with a small (?εr /ε?)max to prevent ?ssure formation.
A criterion curve for ?ssure formation is next discussed on the basis of the theory of ductile fracture,assuming the relation (function of process condition indicator)×(measure of mate-rial deformability)=constant.Oyane (1972)studied the
criteria
Fig.13.Workability of stainless steels and Ti alloy in cold pilgering.
H.Abe,M.Furugen/Journal of Materials Processing Technology212 (2012) 1687–1693
1693
Fig.14.Workability of Zr alloys in cold pilgering.
leading to ductile fracture strain in metal forming.Toda et al.(1988)
studied the failure of a workpiece in cold forging on the basis of
Oyane’s study.Here,we discuss the application of a similar rela-
tion to the cold forging process.In the study,the stress during cold
forging was used as an indicator of the process conditions.However,
stress should not be selected as indicator of the process conditions
in cold pilgering,because radial stress is negligible in the?ange
part.Hence,the above-mentioned strain ratio of the?ange part is
selected as an indicator of the process conditions,and the critical
reduction in height c is used as a measure of material deformabil-
ity.
The proposed formula of the criterion curve is
1?1
a
εr
ε?
· c=b,(2)
where(?εr/ε?)is the maximum ratio of the radial strain to the circumferential strain in the?ange part, c is the critical reduction in height in the circumferential compression test,and a and b are constants.
From all18cold pilgering test results of Zr alloys,we obtain a=0.45and b=0.25and the obtained criterion curve is shown in Fig.14.The test results of the stainless steels were referred to in the discussion of workability in the case of a high c;namely,even when c is higher than1,cold pilgering at a strain ratio higher than 0.35is impossible.Moreover,the pilgering test results of the Ti alloy tube are consistent with the relation shown in Fig.14.These results will enable a manufacturer to choose appropriate cold pilgering conditions for Zr alloy tubes.
5.Conclusion
The workability of seamless tubes in cold pilgering was investi-gated on the basis of both material deformability and the effects of process conditions.The materials investigated were two stainless steels,a Ti alloy,and two Zr alloys.A compression test was per-formed to evaluate the material deformability of tube shells.Cold pilgering tests,in which the pilgering parameters and the deforma-bility of materials were varied systematically,and the numerical analysis of cold pilgering were conducted.The compression test results revealed that the Ti alloy and Zr alloy tube shells had lower circumferential deformability than those made from stain-less steels owing to their slip systems resulting from their hcp structure.The workability results obtained in the cold pilgering tests corresponded well with the material deformability results in the compression test.Accordingly,the circumferential compres-sion test of a tube shell was proved to be a useful evaluation method, that is,the critical reduction in height upon crack initiation c is a good measure of material deformability.The results of numeri-cal analysis indicated that the maximum ratio of the radial strain to the circumferential strain in the?ange part during pilgering (?εr/ε?)max is a good indicator of the pilgering conditions.As a result,a common mechanism of inner?ssure formation during cold pilgering in stainless steel,Ti alloy,and Zr alloy was proposed.In practice,it is possible to prevent inner?ssure formation by select-ing an appropriate strain ratio(?εr/ε?)max for stainless-steel and Ti alloy tubes.A criterion curve of workability for Zr alloy tubes in cold pilgering was obtained by combining the circumferential material deformability given by c and the plastic deformation state in the ?ange part given by(?εr/ε?)max.The obtained?ndings will assist the selection of appropriate process conditions that will prevent inner?ssure formation for future materials not yet subjected to cold pilgering.
References
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285–306.
Abe,H.,Takeda,K.,Uehira,A.,Anada,H.,Furugen,M.,2000.A new fabrication process for Zr-lined Zircaloy-2tubing.In:ASTM STP1354,pp.425–459.
Abe,H.,Furugen,M.,2010.Method of evaluating workability in cold pilgering of zirconium alloy tube.Materials Transaction51,1200–1205.
Bembenek,Z.,Wiesner,H.,Starek,J.,1981.New?ndings in the?eld of grooving pilger mills for the cold rolling of austenitic seamless tubes.In:Proceeding of 3rd Japan–Czechoslovakia Joint Symposium,pp.135–153.
Dunstan,P.G.,Johnson,R.T.,1988.Factors in?uencing I.D.crack propagation in tube pilgering.In:Proceeding of Conference Sources&Prevention Defects in Tubes, Bars Shapes Arizona,pp.48–56.
Furugen,M.,Hayashi,C.,1984.Application of the theory of plasticity to the cold pilgering of tubes.Journal of Mechanical Working Technology10,273–286. Kudo,H.,Aoi,K.,1967.Effect of compression test condition upon fracturing of a medium carbon steel.Journal of the Japan Society for Technology of Plasticity 29,971–976.
Lodej,B.,Niang,K.,Montmitonnet,P.,Aubin,J.-L.,2006.Accelerated3D FEM com-putation of the mechanical history of the metal deformation in cold pilgering of tubes.Journal of Materials Processing Technology177,188–191.
Monkawa,M.,Ueda,S.,Kojima,K.,Furugen,M.,1985.Stress analysis on the roll and mandrel of a cold pilger mill.In:Proceeding of3rd International Conference on Steel Rolling,pp.351–358.
Onchi,T.,Kayano,H.,Higashiguchi,Y.,1980.The inhomogeneous deformation behavior of neutron irradiated Zircaloy-2.Journal of Nuclear Materials88, 226–235.
Oyane,M.,1972.Criteria of ductile fracture strain.Bulletin of the Japan Society of Mechanical Engineers15,1507–1513.
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英语中的比较级与最高级 详解
比较级与最高级 1.as...as 与(not) as(so)...as as...as...句型中，as的词性 第一个as是副词，用在形容词和副词的原级前，常译为“同样地”。第二个as是连词，连接与前面句子结构相同的一个句子(相同部分常省略)，可译为“同..... He is as tall as his brother is (tall) . (后面的as 为连词) 只有在否定句中，第一个as才可换为so 改错: He is so tall as his brother.（X） 2.在比较状语从句中，主句和从句的句式结构一般是相同的 与as...as 句式中第二个as一样，than 也是连词。as和than这两个连词后面的从句的结构与前面的句子大部分情况下结构是相同的，相同部分可以省略。 He picked more apples than she did. 完整的表达为: He picked more apples than she picked apples. 后而的picked apples和前面相同，用did 替代。 He walked as slowly as she did.完整表达为: He walked as slowly as she walked slowly. she后面walked slowly与前面相同，用did替代。
3.谓语的替代 在as和than 引导的比较状语从句中，由于句式同前面 主句相同，为避免重复，常把主句中出现而从句中又出现的动词用do的适当形式来代替。 John speaks German as fluently as Mary does. 4.前后的比较对象应一致 不管后面连词是than 还是as,前后的比较对象应一致。The weather of Beijing is colder than Guangzhou. x than前面比较对象是“天气”，than 后面比较对象是“广州”，不能相比较。应改为: The weather of Bejing is colder than that of Guangzhou. 再如: His handwriting is as good as me. 应改为: His handwriting is as good as mine. 5.可以修饰比较级的词 常用来修饰比较级的词或短语有: Much,even,far,a little,a lot,a bit,by far,rather,any,still,a great deal等。 by far的用法: 用于强调，意为“...得多”“最最...”“显然”等，可修饰形容词或副词的比较级和最高级，通常置于其后，但是若比较级或最高级前有冠词，则可置于其前或其后。
The way常见用法
The way 的用法 Ⅰ常见用法： 1)the way+ that 2)the way + in which（最为正式的用法） 3)the way + 省略（最为自然的用法） 举例：I like the way in which he talks. I like the way that he talks. I like the way he talks. Ⅱ习惯用法： 在当代美国英语中，the way用作为副词的对格，“the way+ 从句”实际上相当于一个状语从句来修饰整个句子。 1)The way =as I am talking to you just the way I’d talk to my own child. He did not do it the way his friends did. Most fruits are naturally sweet and we can eat them just the way they are—all we have to do is to clean and peel them. 2）The way= according to the way/ judging from the way The way you answer the question, you are an excellent student. The way most people look at you, you’d think trash man is a monster. 3）The way =how/ how much No one can imagine the way he missed her. 4）The way =because
人教版(新目标)初中英语形容词与副词的比较级与最高级
人教版（新目标）初中英语形容词与副词的比较级与最高级 （一）规则变化： 1．绝大多数的单音节和少数双音节词，加词尾-er ，-est tall—taller—tallest 2．以不发音的e结尾的单音节词和少数以-le结尾的双音节词只加-r，-st nice—nicer—nicest , able—abler—ablest 3．以一个辅音字母结尾的重读闭音节词或少数双音节词，双写结尾的辅音字母，再加-er，-est big—bigger—biggest 4．以辅音字母加y结尾的双音节词，改y为i再加-er，-est easy—easier—easiest 5．少数以-er，-ow结尾的双音节词末尾加-er，-est clever—cleverer—cleverest, narrow—narrower—narrowest 6．其他双音节词和多音节词，在前面加more，most来构成比较级和最高级 easily—more easily—most easily （二）不规则变化 常见的有： good / well—better—best ; bad (ly)/ ill—worse—worst ; old—older/elder—oldest/eldest many / much—more—most ; little—less—least ; far—farther/further—farthest/furthest
用法： 1．原级比较：as + adj./adv. +as（否定为not so/as + adj./adv. +as）当as… as中间有名字时，采用as + adj. + a + n.或as + many / much + n. This is as good an example as the other is . I can carry as much paper as you can. 表示倍数的词或其他程度副词做修饰语时放在as的前面 This room is twice as big as that one. 倍数+as+adj.+as = 倍数+the +n.+of Your room is twice as larger as mine. = Your room is twice the size of mine. 2．比较级+ than 比较级前可加程度状语much, still, even, far, a lot, a little, three years. five times,20%等 He is three years older than I (am). 表示“（两个中）较……的那个”时，比较级前常加the（后面有名字时前面才能加冠词） He is the taller of the two brothers. / He is taller than his two brothers. Which is larger, Canada or Australia? / Which is the larger country, Canada or Australia? 可用比较级形式表示最高级概念，关键是要用或或否定词等把一事物（或人）与其他同类事物（或人）相分离 He is taller than any other boy / anybody else.
英语中的比较级和最高级
大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基础上变化的。分为规则变化和不规则变化。 规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加 -er 和 -est 构成。 great (原级) (比较级) (最高级) 2) 以 -e 结尾的单音节形容词的比较级和最高级是在词尾加 -r 和 -st 构成。wide (原级) (比较级) (最高级) 3)少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和 -est 构成。 clever(原级) (比较级) (最高级) 4) 以 -y 结尾,但 -y 前是辅音字母的形容词的比较级和最高级是把 -y 去掉,加上 -ier 和-est 构成. happy (原形) (比较级) (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该辅音字母然后再加 -er和-est。 big (原级) (比较级) (最高级) 6) 双音节和多音节形容词的比较级和最高级需用more 和 most 加在形容词前面来构成。 beautiful (原级) (比较级) (比较级) difficult (原级) (最高级) (最高级) 常用的不规则变化的形容词的比较级和最高级: 原级------比较级------最高级 good------better------best many------more------most much------more------most bad------worse------worst far------farther, further------farthest, furthest 形容词前如加 less 和 least 则表示"较不"和"最不 形容词比较级的用法: 形容词的比较级用于两个人或事物的比较,其结构形式如下: 主语+谓语(系动词)+ 形容词比较级+than+ 对比成分。也就是, 含有形容词比较级的主句+than+从句。注意从句常常省去意义上和主句相同的部分, 而只剩下对比的成分。
The way的用法及其含义(二)
The way的用法及其含义（二） 二、the way在句中的语法作用 the way在句中可以作主语、宾语或表语： 1.作主语 The way you are doing it is completely crazy.你这个干法简直发疯。 The way she puts on that accent really irritates me. 她故意操那种口音的样子实在令我恼火。The way she behaved towards him was utterly ruthless. 她对待他真是无情至极。 Words are important, but the way a person stands, folds his or her arms or moves his or her hands can also give us information about his or her feelings. 言语固然重要,但人的站姿,抱臂的方式和手势也回告诉我们他(她)的情感。 2.作宾语 I hate the way she stared at me.我讨厌她盯我看的样子。 We like the way that her hair hangs down.我们喜欢她的头发笔直地垂下来。 You could tell she was foreign by the way she was dressed. 从她的穿著就可以看出她是外国人。 She could not hide her amusement at the way he was dancing. 她见他跳舞的姿势，忍俊不禁。 3.作表语 This is the way the accident happened.这就是事故如何发生的。 Believe it or not, that's the way it is. 信不信由你, 反正事情就是这样。 That's the way I look at it, too. 我也是这么想。 That was the way minority nationalities were treated in old China. 那就是少数民族在旧中
英语比较级和最高级的用法归纳
英语比较级和最高级的用法归纳 在学习英语过程中，会遇到很多的语法问题，比如比较级和最高级的用法，对于 这些语法你能够掌握吗？下面是小编整理的英语比较级和最高级的用法，欢迎阅读！ 英语比较级和最高级的用法 一、形容词、副词的比较级和最高级的构成规则 1.一般单音节词和少数以-er，-ow结尾的双音节词，比较级在后面加-er，最高级 在后面加-est; (1)单音节词 如：small→smaller→smallest short→shorter→shortest tall→taller→tallest great→greater→greatest (2)双音节词 如：clever→cleverer→cleverest narrow→narrower→narrowest 2.以不发音e结尾的单音节词，比较在原级后加-r，最高级在原级后加-st; 如：large→larger→largest nice→nicer→nicest able→abler→ablest 3.在重读闭音节(即：辅音+元音+辅音)中，先双写末尾的辅音字母，比较级加-er，最高级加-est; 如：big→bigger→biggest hot→hotter→hottest fat→fatter→fattest 4.以“辅音字母+y”结尾的双音节词，把y改为i，比较级加-er，最高级加-est; 如：easy→easier→easiest heavy→heavier→heaviest busy→busier→busiest happy→happier→happiest 5.其他双音节词和多音节词，比较级在前面加more，最高级在前面加most; 如：bea utiful→more beautiful→most beautiful different→more different→most different easily→more easily→most easily 注意：(1)形容词最高级前通常必须用定冠词 the，副词最高级前可不用。 例句： The Sahara is the biggest desert in the world. (2) 形容词most前面没有the，不表示最高级的含义，只表示"非常"。 It is a most important problem. =It is a very important problem.
(完整版)the的用法
定冠词the的用法： 定冠词the与指示代词this ,that同源,有“那(这)个”的意思,但较弱,可以和一个名词连用,来表示某个或某些特定的人或东西. (1)特指双方都明白的人或物 Take the medicine.把药吃了. (2)上文提到过的人或事 He bought a house.他买了幢房子. I've been to the house.我去过那幢房子. (3)指世界上独一无二的事物 the sun ,the sky ,the moon, the earth (4)单数名词连用表示一类事物 the dollar 美元 the fox 狐狸 或与形容词或分词连用,表示一类人 the rich 富人 the living 生者 (5)用在序数词和形容词最高级,及形容词等前面 Where do you live?你住在哪? I live on the second floor.我住在二楼. That's the very thing I've been looking for.那正是我要找的东西. (6)与复数名词连用,指整个群体 They are the teachers of this school.(指全体教师) They are teachers of this school.(指部分教师) (7)表示所有,相当于物主代词,用在表示身体部位的名词前 She caught me by the arm.她抓住了我的手臂. (8)用在某些有普通名词构成的国家名称,机关团体,阶级等专有名词前 the People's Republic of China 中华人民共和国 the United States 美国 (9)用在表示乐器的名词前 She plays the piano.她会弹钢琴. (10)用在姓氏的复数名词之前,表示一家人 the Greens 格林一家人(或格林夫妇) (11)用在惯用语中 in the day, in the morning... the day before yesterday, the next morning... in the sky... in the dark... in the end... on the whole, by the way...
英语比较级和最高级的用法
More than的用法 A. “More than+名词”表示“不仅仅是” 1)Modern science is more than a large amount of information. 2)Jason is more than a lecturer; he is a writer, too. 3) We need more than material wealth to build our country.建设我们国家，不仅仅需要物质财富. B. “More than+数词”含“以上”或“不止”之意，如： 4)I have known David for more than 20 years. 5)Let's carry out the test with more than the sample copy. 6) More than one person has made this suggestion. 不止一人提过这个建议. C. “More than+形容词”等于“很”或“非常”的意思，如： 7)In doing scientific experiments, one must be more than careful with the instruments. 8)I assure you I am more than glad to help you. D. more than + (that)从句，其基本意义是“超过（=over）”，但可译成“简直不”“远非”.难以，完全不能（其后通常连用情态动词can） 9) That is more than I can understand . 那非我所能懂的. 10) That is more than I can tell. 那事我实在不明白。 11) The heat there was more than he could stand. 那儿的炎热程度是他所不能忍受的 此外，“more than”也在一些惯用语中出现，如： more...than 的用法 1. 比……多，比……更 He has more books than me. 他的书比我多。 He is more careful than the others. 他比其他人更仔细。 2. 与其……不如 He is more lucky than clever. 与其说他聪明，不如说他幸运。 He is more （a）scholar than （a）teacher. 与其说他是位教师，不如说他是位学者。 注：该句型主要用于同一个人或物在两个不同性质或特征等方面的比较，其中的比较级必须用加more 的形式，不能用加词尾-er 的形式。 No more than/not more than 1. no more than 的意思是“仅仅”“只有”“最多不超过”，强调少。如： --This test takes no more than thirty minutes. 这个测验只要30分钟。 --The pub was no more than half full. 该酒吧的上座率最多不超过五成。-For thirty years，he had done no more than he （had）needed to. 30年来，他只干了他需要干的工作。 2. not more than 为more than （多于）的否定式，其意为“不多于”“不超过”。如：Not more than 10 guests came to her birthday party. 来参加她的生日宴会的客人不超过十人。 比较： She has no more than three hats. 她只有3顶帽子。（太少了） She has not more than three hats. 她至多有3顶帽子。（也许不到3顶帽子） I have no more than five yuan in my pocket. 我口袋里的钱最多不过5元。（言其少） I have not more than five yuan in my pocket. 我口袋里的钱不多于5元。（也许不到5元） more than, less than 的用法 1. （指数量）不到，不足 It’s less than half an hour’s drive from here. 开车到那里不到半个钟头。 In less than an hour he finished the work. 没要上一个小时，他就完成了工作。 2. 比……（小）少 She eats less than she should. 她吃得比她应该吃的少。 Half the group felt they spent less than average. 半数人觉得他们的花费低于平均水平。 more…than,/no more than/not more than (1)Mr．Li is ________ a professor; he is also a famous scientist． (2)As I had ________ five dollars with me, I couldn’t afford the new jacket then． (3)He had to work at the age of ________ twelve． (4)There were ________ ten chairs in the room．However, the number of the children is twelve． (5)If you tel l your father what you’ve done, he’ll be ________ angry． (6)－What did you think of this novel? －I was disappointed to find it ________ interesting ________ that one． 倍数表达法 1. “倍数+形容词（或副词）的比较级+than+从句”表示“A比B大（长、高、宽等）多少倍” This rope is twice longer than that one.这根绳是那根绳的三倍（比那根绳长两倍）。The car runs twice faster than that truck.这辆小车的速度比那辆卡车快两倍（是那辆卡车的三倍）。 2. “倍数+as+形容词或副词的原级+as+从句”表示“A正好是B的多少倍”。
“the way+从句”结构的意义及用法
“tｈｅwａｙ+从句”结构的意义及用法 首先让我们来看下面这个句子: Ｒead the foｌloｗｉnｇpassagｅａnd talkａbout ｉt wi ｔh your classmaｔes．Try tｏｔeｌl whaｔyｏu thiｎk ｏf Tom aｎd ｏｆｔhe ｗay the chiｌｄrenｔrｅated ｈim. 在这个句子中，ｔhe waｙ是先行词,后面是省略了关系副词that或in whｉch的定语从句。 下面我们将叙述“the ｗaｙ+从句”结构的用法。 1.tｈe wａy之后，引导定语从句的关系词是tｈat而不是hoｗ,因此，<<现代英语惯用法词典＞＞中所给出的下面两个句子是错误的：Ｔhｉs is ｔｈeｗayｈowｉtｈａppened. This is the way how he ａlwａｙs treats me. 2．在正式语体中,thaｔ可被in which所代替;在非正式语体中，ｔhat则往往省略。由此我们得到theｗay后接定语从句时的三种模式：1) tｈe ｗaｙ＋ｔhａt-从句２）the way +ｉn whiｃh－从句3) the ｗay +从句 例如：Ｔｈe way(in whiｃh ，thａt) ｔhｅｓｅｃomｒade ｓloｏｋａｔｐrobｌems is wrong．这些同志看问题的方法
不对。 Ｔｈｅｗａy(that ,ｉn ｗhiｃh)yoｕ’ｒe doinｇit is comple ｔeｌy crａzy.你这么个干法,简直发疯。 Wｅａdmiｒｅd him for thｅｗay ｉｎｗhｉch he fａｃeｓdiｆficultieｓ． Waｌlａｃe ａｎd Ｄarwiｎｇreed ｏn the way ｉｎwhi ｃh ｄｉfｆｅrｅnt forms ｏf life had ｂegｕn.华莱士和达尔文对不同类型的生物是如何起源的持相同的观点。 Thｉs is ｔｈe ｗaｙ（tｈａｔ) hｅdｉd it. I lｉkeｄｔhe waｙ(ｔhat) ｓｈeｏｒganized ｔhe ｍeetｉng． 3.theｗay(tｈat)有时可以与hｏw(作“如何”解）通用。例如： That’s tｈe ｗaｙ(tｈaｔ) shｅspoke. = Tｈat’s how shｅspoke.
初中英语比较级和最高级讲解与练习
初中英语比较级和最高级讲解与练习 形容词比较级和最高级 一．绝大多数形容词有三种形式,原级,比较级和最高级, 以表示形容词说明的性质在程度上的不同。 1. 形容词的原级: 形容词的原级形式就是词典中出现的形容词的原形。例如: poor tall great glad bad 2. 形容词的比较级和最高级: 形容词的比较级和最高级形式是在形容词的原级形式的基 础上变化的。分为规则变化和不规则变化。 二．形容词比较级和最高级规则变化如下: 1) 单音节形容词的比较级和最高级形式是在词尾加-er 和-est 构成。 great (原级) greater(比较级) greatest(最高级) 2) 以-e 结尾的单音节形容词的比较级和最高级是在词尾加-r 和-st 构成。 wide (原级) wider (比较级) widest (最高级) 3) 少数以-y, -er, -ow, -ble结尾的双音节形容词的比较级和最高级是在词尾加 -er 和-est构成。 clever(原级) cleverer(比较级) cleverest(最高级)， slow(原级) slower(比较级) slowest (最高级) 4) 以-y 结尾,但-y 前是辅音字母的形容词的比较级和最高级是把-y 去掉,加上-ier 和-est 构成. happy (原形) happier (比较级) happiest (最高级) 5) 以一个辅音字母结尾其前面的元音字母发短元音的形容词的比较级和最高级是双写该 辅音字母然后再加-er和-est。 原形比较级最高级原形比较级最高级 big bigger biggest hot hotter hottest red redder reddest thin thinner thinnest 6) 双音节和多音节形容词的比较级和最高级需用more 和most 加在形容词前面来构 成。 原形比较级最高级 careful careful more careful most careful difficult more difficult most difficult delicious more delicious most delicious 7)常用的不规则变化的形容词的比较级和最高级: 原级比较级最高级 good better best 好的 well better best 身体好的 bad worse worst 坏的 ill worse worst 病的 many more most 许多 much more most 许多 few less least 少数几个 little less least 少数一点儿 （little littler littlest 小的） far further furthest 远（指更进一步，深度。亦可指更远） far farther farthest 远（指更远，路程）
way 用法
表示“方式”、“方法”，注意以下用法： 1.表示用某种方法或按某种方式，通常用介词in(此介词有时可省略)。如： Do it (in) your own way. 按你自己的方法做吧。 Please do not talk (in) that way. 请不要那样说。 2.表示做某事的方式或方法，其后可接不定式或of doing sth。 如： It’s the best way of studying [to study] English. 这是学习英语的最好方法。 There are different ways to do [of doing] it. 做这事有不同的办法。 3.其后通常可直接跟一个定语从句(不用任何引导词)，也可跟由that 或in which 引导的定语从句，但是其后的从句不能由how 来引导。如： 我不喜欢他说话的态度。 正：I don’t like the way he spoke. 正：I don’t like the way that he spoke. 正：I don’t like the way in which he spoke. 误：I don’t like the way how he spoke. 4.注意以下各句the way 的用法： That’s the way (=how) he spoke. 那就是他说话的方式。 Nobody else loves you the way(=as) I do. 没有人像我这样爱你。 The way (=According as) you are studying now, you won’tmake much progress. 根据你现在学习情况来看，你不会有多大的进步。 2007年陕西省高考英语中有这样一道单项填空题： ——I think he is taking an active part insocial work. ——I agree with you_____. A、in a way B、on the way C、by the way D、in the way 此题答案选A。要想弄清为什么选A，而不选其他几项，则要弄清选项中含way的四个短语的不同意义和用法，下面我们就对此作一归纳和小结。 一、in a way的用法 表示：在一定程度上，从某方面说。如： In a way he was right.在某种程度上他是对的。注：in a way也可说成in one way。 二、on the way的用法 1、表示：即将来(去)，就要来(去)。如： Spring is on the way.春天快到了。 I'd better be on my way soon.我最好还是快点儿走。 Radio forecasts said a sixth-grade wind was on the way.无线电预报说将有六级大风。 2、表示：在路上，在行进中。如： He stopped for breakfast on the way.他中途停下吃早点。 We had some good laughs on the way.我们在路上好好笑了一阵子。 3、表示：(婴儿)尚未出生。如： She has two children with another one on the way.她有两个孩子，现在还怀着一个。 She's got five children，and another one is on the way.她已经有5个孩子了，另一个又快生了。 三、by the way的用法
英语比较级和最高级
形容词比较级和最高级的形式 一、形容词比较级和最高级的构成 形容词的比较级和最高级变化形式规则如下 构成法原级比较级最高级 ①一般单音节词末尾加 er 和 est strong stronger strongest ②单音节词如果以 e结尾，只加 r 和 st strange stranger strangest ③闭音节单音节词如末尾只有一个辅音字母， 须先双写这个辅音字母，再加 er和 est sad big hot sadder bigger hotter saddest biggest hottest ④少数以 y, er(或 ure), ow, ble结尾的双音节词， 末尾加 er和 est(以 y结尾的词，如 y前是辅音字母， 把y变成i，再加 er和 est，以 e结尾的词仍 只加 r和 st) angry Clever Narrow Noble angrier Cleverer narrower nobler angriest cleverest narrowest noblest ⑤其他双音节和多音节词都在前面加单词more和most different more different most different 1) The most high 〔A〕mountain in 〔B〕the world is Mount Everest，which is situated 〔C〕in Nepal and is twenty nine thousand one hundred and fourty one feet high 〔D〕 . 2) This house is spaciouser 〔A〕than that 〔B〕white 〔C〕one I bought in Rapid City，South Dakota 〔D〕last year. 3) Research in the social 〔A〕sciences often proves difficulter 〔B〕than similar 〔C〕work in the physical 〔D〕sciences. 二、形容词比较级或最高级的特殊形式：
高中英语的比较级和最高级用法总结
比较级和最高级 1.在形容词词尾加上―er‖ ―est‖ 构成比较级、最高级： bright（明亮的）—brighter—brightest broad（广阔的）—broader—broadest cheap（便宜的）—cheaper—cheapest clean（干净的）—cleaner—cleanest clever（聪明的）—cleverer—cleverest cold（寒冷的）—colder—coldest cool（凉的）—cooler—coolest dark（黑暗的）—darker—darkest dear（贵的）—dearer—dearest deep（深的）—deeper—deepest fast（迅速的）—faster—fastest few（少的）—fewer—fewest great（伟大的）—greater—greatest hard（困难的,硬的）—harder—hardest high（高的）—higher—highest kind（善良的）—kinder—kindest light（轻的）—lighter—lightest long（长的）—longer—longest loud（响亮的）—louder—loudest low（低的）—lower—lowest near（近的）—nearer—nearest new（新的）—newer—newest poor（穷的）—poorer—poorest quick（快的）—quicker—quickest quiet（安静的）—quieter—quietest rich（富裕的）—richer—richest short（短的）—shorter—shortest slow（慢的）—slower—slowest small（小的）—smaller—smallest smart（聪明的）—smarter—smartest soft（柔软的）—softer—softest strong（强壮的）—stronger—strongest sweet（甜的）—sweeter—sweetest tall（高的）-taller-tallest thick（厚的）—thicker—thickest warm（温暖的）—warmer—warmest weak（弱的）—weaker—weakest young（年轻的）—younger—youngest 2.双写最后一个字母,再加上―er‖ ―est‖构成比较级、最高级： big（大的）—bigger—biggest fat（胖的）—fatter—fattest hot（热的）—hotter—hottest red（红的）—redder—reddest sad（伤心的）—sadder—saddest thin（瘦的）—thinner—thinnest wet（湿的）—wetter—wettest mad（疯的）—madder—maddest 3.以不发音的字母e结尾的形容词,加上―r‖ ―st‖ 构成比较级、最高级：able（能干的）—abler—ablest brave（勇敢的）—braver—bravest close（接近的）—closer—closest fine（好的,完美的）—finer—finest large（巨大的）—larger—largest late（迟的）—later—latest nice（好的）—nicer—nicest ripe（成熟的）—riper—ripest
The way的用法及其含义(一)
The way的用法及其含义（一） 有这样一个句子：In 1770 the room was completed the way she wanted. 1770年，这间琥珀屋按照她的要求完成了。 the way在句中的语法作用是什么？其意义如何？在阅读时，学生经常会碰到一些含有the way 的句子，如：No one knows the way he invented the machine. He did not do the experiment the way his teacher told him.等等。他们对the way 的用法和含义比较模糊。在这几个句子中，the way之后的部分都是定语从句。第一句的意思是，“没人知道他是怎样发明这台机器的。”the way的意思相当于how；第二句的意思是，“他没有按照老师说的那样做实验。”the way 的意思相当于as。在In 1770 the room was completed the way she wanted.这句话中，the way也是as的含义。随着现代英语的发展，the way的用法已越来越普遍了。下面，我们从the way的语法作用和意义等方面做一考查和分析： 一、the way作先行词，后接定语从句 以下3种表达都是正确的。例如：“我喜欢她笑的样子。” 1. the way+ in which +从句 I like the way in which she smiles. 2. the way+ that +从句 I like the way that she smiles. 3. the way + 从句(省略了in which或that) I like the way she smiles. 又如：“火灾如何发生的，有好几种说法。” 1. There were several theories about the way in which the fire started. 2. There were several theories about the way that the fire started.
(完整版)初中英语比较级和最高级的用法
英语语法---比较级和最高级的用法 在英语中通常用下列方式表示的词:在形容词或副词前加more(如 more natural,more clearly )或加后缀 -er(newer,sooner )。典型的是指形容词或副词所表示的质、量或关系的增加。英语句子中，将比较两个主体的方法叫做“比较句型”。其中，像“A比B更……”的表达方式称为比较级；而“A最……”的表达方式则称为最高级。组成句子的方式是将形容词或副词变化成比较级或最高级的形态。 一、形容词、副词的比较级和最高级的构成规则 1．一般单音节词和少数以-er，-ow结尾的双音节词，比较级在后面加-er，最高级在后面加-est； （1）单音节词 如：small→smaller→smallest short→shorter→shortest tall→taller→tallest great→greater→greatest （2）双音节词 如：clever→cleverer→cleverest narrow→narrower→narrowest 2．以不发音e结尾的单音节词，比较在原级后加-r，最高级在原级后加-st； 如：large→larger→largest nice→nicer→nicest able→abler→ablest 3．在重读闭音节（即：辅音＋元音＋辅音）中，先双写末尾的辅音字母，比较级加-er，最高级加-est； 如：big→bigger→biggest hot→hotter→hottest fat→fatter→fattest 4．以“辅音字母＋y”结尾的双音节词，把y改为i，比较级加-er，最高级加-est； 如：easy→easier→easiest heavy→heavier→heaviest busy→busier→busiest happy→happier→happiest 5．其他双音节词和多音节词，比较级在前面加more，最高级在前面加most； 如：beautiful→more beautiful→most beautiful different→more different→most different easily→more easily→most easily