1、MUGHRABI ET AL ON CYCLIC SUP IRREVERSIBILITIES 11 b/M 0 i f .Q-nm b)FIG.1Evolution of surface roughness by random irreversible cyclic slip in a planar-slip ma-terial.Cu-30at.%Zn,aty-=10;see text for details,(a)Experimentally observed roughness profile.N=5 X 10.From Lukds and Klesnil 38.Courtesy of t
2、he authors and of Akademie-Verlag.(b)Surface roughness profile generated by computer simulation.The profile corre-sponds to N=1.5 X IW cycles for p=0.5%.From Ref 15.n=100,then/J would have been found to be twice as large as in the examples given.The main conclusions from this comparison between comp
3、uter simulation and observation are that in a planar-slip alloy such as Cu-30at.%Zn glide is largely reversible in the bulk but not at the surface 13 and that the slip irre-versibility at the surface increases with increasing Ypj.The slip irreversibility at the surface is rather small in absolute nu
4、mbers but,because of the relatively large value of n,the effect on the roughness profile,compare Eq 3,is signifi-cant.Again,the question remains at what stage critical crack nuclei form which can develop into Stage I shear cracks such as those observed by Katagiri and co-workers 45.Cyclic Strain Loc
5、alization in Persistent Slip Bands The most prominent cause of fatigue crack initiation in wavy-slip fee metals fatigued in the high-cycle range is the localization of cyclic strain in persistent slip bands(PSBs)8,9,13,28,29,35,46-49.It has been demonstrated in ex-periments on single crystals of sev
6、eral fee metals that a threshold value of Ypj exists below which PSBs do not form 13,28,29,50.Up to this threshold value so-called bundles or veins of clustered primary edge-dislocation dipoles MUGHRABI ET AL ON CYCLIC SLIP IRREVERSIBILITIES 15 FIG.2Formation of extrusions by emergence of PSB-matrix
7、 interface dislocations(sche-matically).M is matrix:a is axial stress.After Ref 14.(a)Arrangement of interface dislocations corresponding to an interstitial-type dislocation-dipole layer.All other microstructural features(edge dislocation walls,screw dislocations)have been omitted for the sake of cl
8、arity,(b)Extru-sions formed by emergence of interface dislocations.where D is the dimension of the PSB measured in the direction of b.The elastic compressive internal strain is given by mb-f.=r sat tint *v(7)Hence int int-tv(8)where E is Youngs modulus of elasticity.With Cy*6 X 10*,at is found to be
9、=6 MPa.A more rigorous calculation yields a slightly smaller value 14.Under the action of the applied stress a,the interface dislocations tend to glide out of the crystal at A and A during the tensile phases and at B and B during the compressive phases of cycling,respectively.This process leads to t
10、he formation of extrusions on both sides of the PSB,as indicated in Fig.2b.Depending on the ability of the vacancy-type defects to migrate and to escape from the PSBs into the matrix,EGM consider two cases 14.At low temperatures the vacancy-type defects cannot leave the PSB.The ex-trusions attain th
11、eir maximum height when all interface dislocations have left the crystal.Thus the total height of the extruded material(in the direction of b)is given by e=mb CJ D(9)Copyright by ASTM Intl(all rights reserved);Mon Dec 7 13:11:40 EST 2015Downloaded/printed byUniversity of Washington(University of Was
12、hington)pursuant to License Agreement.No further reproductions authorized.16 FATIGUE MECHANISMS In Other words,the heights of the extrusions on either side of the crystal are 0.5e.For a specimen of 3 mm diameter(D 4.2 mm),0.5e 1.2 fim.Essmann and co-workers called these extrusions which cease to gro
13、w after all interface dislocations given by Eq 6 have left the crystal,static extrusions.As-suming that the emergence of the interface dislocations is not hindered seri-ously by other processes,static extrusions are expected to form rather rapidly at the rate at which steady-state conditions are app
14、roached.At higher temperatures at which the vacancy-type defects become mobile,EGM consider the possibility that some of them can escape into the matrix.In this case the lost vacancies are replaced continuously by subsequent disloca-tion annihilation processes.Thus the number of interstitial-type di
15、slocation-dipoles constituting the multipolar PSB-matrix interface dislocation layer will continue to increase beyond the value given by Eq 6,giving rise to continuously growing extrusions.The kinetics of this process have not been formulated quantitatively so far.EGM have noted that this process ca
16、n only operate effec-tively in a thin PSB layer(5 to 10 nm)at the PSB-matrix interface,since point defects located further away from the matrix will probably anneal out at dislocations within the PSB-walls before reaching the matrix.Thus continu-ous extrusion growth is considered to be a more probable process in very thin PSBs(such as those prevailing in fatigued age-hardened alloys)than in PSBs of about 1 iim thickness,as observed in pure fee metals.Surface Roughening by Random Irreversible Gli
