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Geometrical characterization of surface roughness and its application to fatigue crack initiation
57
Materials Science and Engineering, 21 (1975) 57--62 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
Geometrical Characterization of Surface Roughness and its Application to Fatigue Crack Initiation*
P.S. MAIYA
Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (U.S.A.) (Received June 6, 1975)
SUMMARY
A direct mathematical method to determine the important geometrical parameters relative to surface roughness has been discussed. The surface-roughness characteristics that were produced on low-cycle fatigue specimens of Type 304 stainless steel by a silicon carbide grinding technique have been avaluated. An attempt has been made to establish a correlatlon between the shape and depth of the surface grooves and the fatigue crack-initiation life determination from fatigue specimens with wellcharacterized surface roughness. This analysis has been extended to existing measurements of the surface topography developed in initially smooth specimens of aluminum subjected to torsional fatigue. The quantitative description of the kinetics of such surface topographical changes is expected to yield valuable information pertinent to the crack-initiation process.
INTRODUCTION
Surface roughness is known to have considerable influence on important material properties such as fatigue [1,2] and friction and wear [3,4]. It is also expected to play a significant role in stress-corrosion cracking, because the crack-initiation process in a specimen can be delayed b y the introduction of a finer surface finish [ 5]. In many practical situations, the properties are, in addition, affected b y the metallurgical changes in the surface layers * Work supported by the U,S. Energy Research and Development Administration.
(e.g., phase changes, micro cracking, and introduction of residual stresses) induced b y various finishing processes. Only when the geometrical effects are satisfactorily separated from other effects associated with surface integrity, can the influence of the specific surface treatment on properties be better understood. A geometrical description of surface roughness is often useful in correlating the physical geomtry of surfaces with the measured surfacesensitive properties. For example, it is known that fatigue cracks in most cases initiate at a free surface, and this situation makes fatigue life sensitive to surface roughness. From a study of fatigue properties of specimens with well-characterized surface roughness, it is possible to establish a relation between the shape and depth of the surface grooves and their effect in reducing the fatigue life. In the present paper, the characterization of surface roughness and its relation to fatigue crack-initiation properties will be discussed. Also smooth specimens develop localized slip steps and notch-peak geomtry when subjected to cyclic stress or strain [6 - 8], which eventually leads to crack initiation and its subsequent propagation to failure. The development of surface topography associated with plastic instability effects in fatigue has been the subject of numerous investigations [9 - 11], b u t a quantitative description of the kinetics of changes in surface topography during fatigue tests is lacking because of the experimental difficulties associated with such studies. The present report also includes a discussion on how the surface roughness that develops in an initially smooth sepcimen during fatigue can be analyzed to obtain information concerning the variation of the geo-
58
metrical parameters with strain range or with the number of cycles. As has been pointed out [12], the component of surface roughness related to the amplitude of waveform alone is insufficient to describe surface roughness. An additional parameter related to the spacing, namely, the wavelength, is necessary to provide a description of the surface texture. The surface roughness produced by processes such as grinding and machining is usually recorded by conventional stylus methods in which a surface-measuring instrument (e.g., Talysurf) traces the surface profile, and the electrical signal that represents the profile curve can be sent to an analog computer to obtain values for the geometrical characteristics [4]. The present paper reports a straightforward mathematical analysis of surface-roughness profiles produced on the low-cycle fatigue specimens (hourglass shape) of Type 304 stainless steel. The surface roughness was produced circumferentially by grinding on silicon carbide paper with different grit sizes. A Talysurf instrument* was used to trace the surface profile. The profiles were then analyzed to obtain numerical values for the several surface-roughness paramaters. The geometrical parameters were then used to determine the possible correlation with fatigue crack-initiation life.
2 L
2rrkx,
Ak = ~ / y cos ~ -
2 L
Bk = ~ f
y sin
N--1
2rrkx
Ak cos - - ~ - + Bk sin
27rkx ~
dx.
(4)
0
The 2N amplitude measurements were made on a profile of length L at 2N points along the X-axis, starting from origin 0, either at equal intervals or at the locations of peaks and valleys. From the amplitude data, the 2N Fourier coefficientswere evaluated from eqns. (2) - (4). The integration was carried out numerically using the trapezoidal rule. The various surface-roughness parameters are defined as follows: The average depth of surface grooves is L
1
Rav=~f
If(x) Ldx.
(5)
o
The root-mean-square (rms) value* for profile
is R ms "
[f(x)[ 2 dx I
.
(6)
The average wavelength [12] is c f
Ao
(3)
and
ANALYSIS OF SURFACE-ROUGHNESS PROFILE
The appearance of a typical surface profile (schematic) recorded for a ground surface, using a Talysurf instrument, is shown in Fig. 1. In general, the profile is described by a Fourier series
ux
0
Xav = 27r 0 f
If(x) Idx (7)
L If'(x)ldx
o
27rkx )
k=l
2rrNx
+ A N cos ~
LINE
/V/S/CENTER
(1)
where Ao, Ak, Bk(k = 1, 2, ..., N - - 1), a n d A N are the Fourier coefficients. The Fourier coefficients are given by
vv 'v v v
[JvV L
a-
0
L
2 A0 = ~ - f_ y dx, o * T h e vertical a n d h o r i z o n t a l r e s o l u t i o n s o f t h e T a l y s u r f i n s t r u m e n t u s e d in the present w o r k are b e t t e r t h a n 0.01 a n d 4 p m , r e s p e c t i v e l y ,
(2)
Fig. 1. S u r f a c e - r o u g h n e s s profile.
* T h e d i s t i n c t i o n b e t w e e n t h e average a n d r m s values is n o t o f p r a c t i c a l i m p o r t a n c e in t h e present paper.
59
determining analytically the rms properties of the profile, namely, Rrms, k ~ s and Z2. For example, using orthogonality relations such as
and the rms wavelength is f
[f(x)]adx
0
/
Xrms = 27r . . . .
(8) [f'(x)] 2
where f(x) = y - - a, a = 1/1, f L y d x , and the prime denotes differentiation. Physically. a is the distance between the center line and the 0x axis (Fig. 1). From eqns. (6) and (8), it follows that [f'(x)]2 dx
1
27r
-
0
21r
(9)
where Z1 is the rms of the first derivative (slope) of the profile. The quantities given by eqns. (5), (6) and (7) have been determined by using the standard techniques of numerical integration. Another useful geometrical parameter that indicates the sharpness or degree of curvature of the "hills" and "valleys" is the rms of the second derivative of the profile defined by Z2 =
L
f [f"(x)] 2 dx
7
21rkx
27rk'x
t O, k ¢ k'
L~C°s~-dx=(
o
o
Rrms/)~rms -
L
r_j cos
(11)
L / 2 , k = k'
we find that Rrms, h~m~and Z 2 can be expressed in terms of the Fourier coefficients as follows: N
1
1/2
Rrms=~~.[~- k=l G (A2"FB2)TZ'2N1
(12)
1/2
Xrms=27r
+ ~
h=l
X
L--,
\
(2T~NANI 2t L / j
(A 2 +B2) + A
+ ~-L
!
1/2
+ ~
(13)
and
4 .
(10)
I
0
The parameters Z1 and Z2 may be of importance in fatigue and friction and wear properties. A determination of which parameter is the most important may depend upon a particular application. For example, the Z1 characteristics have been found to be more useful than Z2 in predicting the frictional behavior of cold-worked disks [4]. The Fourier representation of a surface profile also provides a convenient m e t h o d of
k=l
[2~rN\ 4
2~
The rms values can thus be determined from eqns. (12) - (14), which involve the summation of the Fourier coefficients. The cut-off length L was chosen such that L ~ X for better representation of surface profile. The m a x i m u m depth of surface roughness was also determined from the profile amplitude measurements.
TABLE 1 Values for g e o m e t r i c a l p a r a m e t e r s related to surface r o u g h n e s s for T y p e 304 stainless steel Surface preparation
Ray (pm)
Rrms (pm)
Mechanically polished*
--
0.0075
<0.027
0.032 0.393 2.758
0.0386 0.482 3.736
0.18 1.8 8.9
G r o u n d o n silicon carbide p a p e r 6 0 0 grit 2 4 0 grit 50 grit
Rmax (pm)
~av (pm) --
19.0 23.2 83.0
* T h e values for this case were d e t e r m i n e d b y i n t e r f e r o m e t r i c t e c h n i q u e s .
~rms
Rrras/
Z2
(~m)
krm s
(pm -1 )
~6
18.5 22.8 89.5
O.0O125
0.0021 0.021 0.042
0.00611 0.434 0.023
60 A P P L I C A T I O N TO F A T I G U E C R A C K I N I T I A T I O N
The variation of the surface-roughness parameters with the grit size of the silicon carbide paper for the fatigue specimens containing circumferential grooves is summarized in Table 1. The low-cycle fatigue tests have been performed under axial push - pull strain-cycling conditions at 593°C at a strain rate of 4 X 1 0 --~3 sec -1. From the fatigue-striation spacing measurements, the crack-initiation life No (number of cycles to initiate a crack length equal to 0.1 mm) has been determined. The technique for producing surface roughness and the fatigue test results can be found elsewhere [13]. Because surface roughness affects only No, it is meaningful to obtain a correlation b e t w e e n the parameter related to surface roughness and No. When the strain range is held constant and only the surface roughness is varied in fatigue tests, the relation between No and the geometrical parameter (which enhances the strain at the r o o t of surface notches produced b y grinding) is assumed to be of the following form: N o = A (surface-roughness parameter) - ~
(15)
where A and e are constants. Equation (15) is based on the Coffin - Manson relation for crack initiation, i.e., Ne = A ( A % ) - e where Aep is the plastic strain range. When Aep is held constant and only surface roughness increases, the effect of surface roughness m a y be considered to enhance the strain concentration [14] that depends on the surface-roughness 8.00
I
I rllll
i
8.00
I
7.75 -
7.50 -
7.25
2 ,~
7.0C
6.5C
0 ¸
--
6.25 10-2
I
i iliilll
I
I
Irl~lll
I 0 -I
I
r I111t1
tO 0
i0 I
Rma x ,/.Lm
Fig. 3. Fatigue crack-initiation life of surface roughness.
vs.
m a x i m u m depth
characteristics, as suggested in eqn. (15). Figures 2 - 4 show the correlation between R~s/Xm~s and No, Rmax and No, and R~ms and No, respectively, on log - log plots. Based on the correlation factor of linear regression for limited data, the amplitude, particularly the rms value (Rm~s) of the surface profile, gives better correlation with No (Fig. 4, correlation factor = --0.96) than the rms of the first derivative of the profile (Fig. 2, correlation factor = --0.89). However, more extensive data are needed to firmly establish this point of view and the importance of parameters such as Z2. Another useful application of the surface-
If'
8.2.~
r i ll[rl I
l
I IIIIII
I
I Illl;ll
I
I
i iii~ii
I
I I Illlll
I
f
I i iiii
I
I
7.75 -&OC 7.50
--
7.7.~ 7.5C
7,2E --
2 Z°
~'~ 7.0C
7.2.~
~OC
6.7~ - 6.7E -6.5C --
6.25'
rO-4
6.5C-l
i i~JIPi
I
t i irllJl
iO - 3
i I0 - Z
i i ill lO-r
vs.
I
[ IJlJll
i0-2
lO-i
i0 0
I IIIII
i0 i
R rms, ~m
R r m s / ~. r m s
Fig. 2. Fatigue crack-initiation life derivative of surface profile,
6.25 j jO-3
rms of the first
Fig. 4. Fatigue crack-initiation life profile.
vs.
rms o f surface
61
I0 P~jt k,I rnm,q
(i)
I
(2)
T
mm
0J mini
~mm
"I
(S)
Fig. 5. Surface topography of pure aluminum specimens 1, 2 and 3 cycled, respectively, with _+1.5 X 10 ~ 3 -+3.0 X 10-3, and 4.5 X 10-3 reversed surface shear-strain amplitudes for 10,000 cycles (Ronay, ]966). roughness analysis is illustrated by a consideration of the results published by R o n a y [15,16] on aluminum. The surface contour changes that take place in an initially smooth specimen subjected to fatigue tests are believed to be the result of irreversible displacements on the slip planes. The kinetics of such surface shape changes are important in understanding the crack-initiation mechanisms. Figure 5 shows the surface contour changes in the high-purity aluminum specimens cycled with +1.5 X 10 -3, _+3.0 X 10 -3 and -+4.5 X 10 -3 reversed surface shear-strain amplitudes for 10,000 cycles. A Leitz - Forster surface measuring instrument was used to measure the surface c o n t o u r of the specimens. The reported grain diameter of the specimens is ~ 1 0 0 - 200 pm. The amplitude measurements were made on an enlargement of Fig. 5. The Fourier analysis of the surface topography shown in the Figure yields the results listed in Table 2. It should be emphasized that the changes in the geometrical quantities with strain amplitude or with number of cycles can be quantitatively determined. Both ~ and
R increase with an increase in strain amplitude for a predetermined number of cycles; the increase in R is more marked than the increase in k. The increase in k with an increase in strain amplitude may indicate that the number density for crack-initiation sites decreases as the strain amplitude increases. The relation between k and grain size should be of importance to the role that grain boundaries play in crack initiation. The variation in the amplitude with number of cycles or with strain range is of particular interest in mechanistic and modeling studies [7,8] concerned with crack initiation.
ACKNOWLEDGEMENTS
The author is grateful to Ms. Maria Ronay and Academic Press, New York, for granting permission to use Fig. 5, to S. Srinivas for numerous helpful discussions and to N.F. Fiore for his useful comments on the manuscript. The continuing support and encouragement of R.W. Weeks are appreciated. The work was
TABLE 2 Values for geometrical parameters to describe surface roughness that developed in aluminum during torsional fatigue. The surface profile used for Fourier analysis was obtained from ref. 14. surface shear strain amplitude
Ray (pm)
Rrms (pm)
Rmax (pm)
~av (pro)
)krms (pm)
Rrms/
Z2
~rms
(P m - l )
+1.5 X 10 - 3 +3.0 X 10 - 3 -+4.5 X 10 - 3
0.917 3.909 14.789
1.164 5.235 18.755
2.259 11.880 28.820
372.4 670.7 970.0
376.4 714.5 1004.6
0.000309 0.000733 0.0187
0.000397 0.000559 0.000909
62
supported by the U.S. Energy Research and Development Administration.
REFERENCES 1 O.J. Horger and H.R. Neifert, Symp. on Surface Treatment of Metals, Am. Soc. Metals, 1941, p. 279. 2 E. Siebel and M. Gaier, Engr. Dig., 18 (1957) 190. 3 M.J. Furey, Trans. Am. Soc. Lub. Eng., 6 (1963) 49. 4 N.O. Myers, Wear, 5 (1962) 182. 5 R.M. Latanision and R.W. Staehle, in R.W. Staehle e t al. (eds.), Proc. Conf. on Fundamental Aspects of Stress Corrosion Cracking, Natl. Assoc. Corrosion Engrs., 1969, p. 241. 6 M.H. Raymond and L.F. Coffin, Trans. ASME, Basci Engineering, Series D, 85 (1963) 548.
7 C. Laird and A.R. Krause, Intern. J. Fracture Mech., 4 (1968) 219. 8 F.A. McClintock, in D.C. Drucker and J.J. Gilman (eds.), Fracture of Solids, Interscience, New York, 1963, p. 65. 9 P.J.E. Forsyth, J. Inst. Metals, 82 (1953 - 54) 449. 10 W.A. Wood, S.McK. Cousland and K.R. Sargant, Acta Met., 11 (1963) 643. 11 P. Charsley and N. Thompson, Phil. Mag., 8 (1963) 77. 12 R.C. Spragg and D.J. Whitehouse, Proc. Inst. Mech. Engrs., 185 (1970 - 71) 47. 13 P.S. Maiya and D.E. Busch, Met. Trans. to be published. 14 P.S. Maiya, to be published. 15 M. Ronay, in H. Liebowitz (ed.), Fracture - An Advanced Treatise, Vol. III, Academic Press, New York, 1971, p. 431. 16 M. Ronay, Tech. Rept. No. 34., Inst. for the study of Fatigue and Reliability, Columbia University, New York, 1966.
Materials Science and Engineering, 21 (1975) 57--62 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands
Geometrical Characterization of Surface Roughness and its Application to Fatigue Crack Initiation*
P.S. MAIYA
Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (U.S.A.) (Received June 6, 1975)
SUMMARY
A direct mathematical method to determine the important geometrical parameters relative to surface roughness has been discussed. The surface-roughness characteristics that were produced on low-cycle fatigue specimens of Type 304 stainless steel by a silicon carbide grinding technique have been avaluated. An attempt has been made to establish a correlatlon between the shape and depth of the surface grooves and the fatigue crack-initiation life determination from fatigue specimens with wellcharacterized surface roughness. This analysis has been extended to existing measurements of the surface topography developed in initially smooth specimens of aluminum subjected to torsional fatigue. The quantitative description of the kinetics of such surface topographical changes is expected to yield valuable information pertinent to the crack-initiation process.
INTRODUCTION
Surface roughness is known to have considerable influence on important material properties such as fatigue [1,2] and friction and wear [3,4]. It is also expected to play a significant role in stress-corrosion cracking, because the crack-initiation process in a specimen can be delayed b y the introduction of a finer surface finish [ 5]. In many practical situations, the properties are, in addition, affected b y the metallurgical changes in the surface layers * Work supported by the U,S. Energy Research and Development Administration.
(e.g., phase changes, micro cracking, and introduction of residual stresses) induced b y various finishing processes. Only when the geometrical effects are satisfactorily separated from other effects associated with surface integrity, can the influence of the specific surface treatment on properties be better understood. A geometrical description of surface roughness is often useful in correlating the physical geomtry of surfaces with the measured surfacesensitive properties. For example, it is known that fatigue cracks in most cases initiate at a free surface, and this situation makes fatigue life sensitive to surface roughness. From a study of fatigue properties of specimens with well-characterized surface roughness, it is possible to establish a relation between the shape and depth of the surface grooves and their effect in reducing the fatigue life. In the present paper, the characterization of surface roughness and its relation to fatigue crack-initiation properties will be discussed. Also smooth specimens develop localized slip steps and notch-peak geomtry when subjected to cyclic stress or strain [6 - 8], which eventually leads to crack initiation and its subsequent propagation to failure. The development of surface topography associated with plastic instability effects in fatigue has been the subject of numerous investigations [9 - 11], b u t a quantitative description of the kinetics of changes in surface topography during fatigue tests is lacking because of the experimental difficulties associated with such studies. The present report also includes a discussion on how the surface roughness that develops in an initially smooth sepcimen during fatigue can be analyzed to obtain information concerning the variation of the geo-
58
metrical parameters with strain range or with the number of cycles. As has been pointed out [12], the component of surface roughness related to the amplitude of waveform alone is insufficient to describe surface roughness. An additional parameter related to the spacing, namely, the wavelength, is necessary to provide a description of the surface texture. The surface roughness produced by processes such as grinding and machining is usually recorded by conventional stylus methods in which a surface-measuring instrument (e.g., Talysurf) traces the surface profile, and the electrical signal that represents the profile curve can be sent to an analog computer to obtain values for the geometrical characteristics [4]. The present paper reports a straightforward mathematical analysis of surface-roughness profiles produced on the low-cycle fatigue specimens (hourglass shape) of Type 304 stainless steel. The surface roughness was produced circumferentially by grinding on silicon carbide paper with different grit sizes. A Talysurf instrument* was used to trace the surface profile. The profiles were then analyzed to obtain numerical values for the several surface-roughness paramaters. The geometrical parameters were then used to determine the possible correlation with fatigue crack-initiation life.
2 L
2rrkx,
Ak = ~ / y cos ~ -
2 L
Bk = ~ f
y sin
N--1
2rrkx
Ak cos - - ~ - + Bk sin
27rkx ~
dx.
(4)
0
The 2N amplitude measurements were made on a profile of length L at 2N points along the X-axis, starting from origin 0, either at equal intervals or at the locations of peaks and valleys. From the amplitude data, the 2N Fourier coefficientswere evaluated from eqns. (2) - (4). The integration was carried out numerically using the trapezoidal rule. The various surface-roughness parameters are defined as follows: The average depth of surface grooves is L
1
Rav=~f
If(x) Ldx.
(5)
o
The root-mean-square (rms) value* for profile
is R ms "
[f(x)[ 2 dx I
.
(6)
The average wavelength [12] is c f
Ao
(3)
and
ANALYSIS OF SURFACE-ROUGHNESS PROFILE
The appearance of a typical surface profile (schematic) recorded for a ground surface, using a Talysurf instrument, is shown in Fig. 1. In general, the profile is described by a Fourier series
ux
0
Xav = 27r 0 f
If(x) Idx (7)
L If'(x)ldx
o
27rkx )
k=l
2rrNx
+ A N cos ~
LINE
/V/S/CENTER
(1)
where Ao, Ak, Bk(k = 1, 2, ..., N - - 1), a n d A N are the Fourier coefficients. The Fourier coefficients are given by
vv 'v v v
[JvV L
a-
0
L
2 A0 = ~ - f_ y dx, o * T h e vertical a n d h o r i z o n t a l r e s o l u t i o n s o f t h e T a l y s u r f i n s t r u m e n t u s e d in the present w o r k are b e t t e r t h a n 0.01 a n d 4 p m , r e s p e c t i v e l y ,
(2)
Fig. 1. S u r f a c e - r o u g h n e s s profile.
* T h e d i s t i n c t i o n b e t w e e n t h e average a n d r m s values is n o t o f p r a c t i c a l i m p o r t a n c e in t h e present paper.
59
determining analytically the rms properties of the profile, namely, Rrms, k ~ s and Z2. For example, using orthogonality relations such as
and the rms wavelength is f
[f(x)]adx
0
/
Xrms = 27r . . . .
(8) [f'(x)] 2
where f(x) = y - - a, a = 1/1, f L y d x , and the prime denotes differentiation. Physically. a is the distance between the center line and the 0x axis (Fig. 1). From eqns. (6) and (8), it follows that [f'(x)]2 dx
1
27r
-
0
21r
(9)
where Z1 is the rms of the first derivative (slope) of the profile. The quantities given by eqns. (5), (6) and (7) have been determined by using the standard techniques of numerical integration. Another useful geometrical parameter that indicates the sharpness or degree of curvature of the "hills" and "valleys" is the rms of the second derivative of the profile defined by Z2 =
L
f [f"(x)] 2 dx
7
21rkx
27rk'x
t O, k ¢ k'
L~C°s~-dx=(
o
o
Rrms/)~rms -
L
r_j cos
(11)
L / 2 , k = k'
we find that Rrms, h~m~and Z 2 can be expressed in terms of the Fourier coefficients as follows: N
1
1/2
Rrms=~~.[~- k=l G (A2"FB2)TZ'2N1
(12)
1/2
Xrms=27r
+ ~
h=l
X
L--,
\
(2T~NANI 2t L / j
(A 2 +B2) + A
+ ~-L
!
1/2
+ ~
(13)
and
4 .
(10)
I
0
The parameters Z1 and Z2 may be of importance in fatigue and friction and wear properties. A determination of which parameter is the most important may depend upon a particular application. For example, the Z1 characteristics have been found to be more useful than Z2 in predicting the frictional behavior of cold-worked disks [4]. The Fourier representation of a surface profile also provides a convenient m e t h o d of
k=l
[2~rN\ 4
2~
The rms values can thus be determined from eqns. (12) - (14), which involve the summation of the Fourier coefficients. The cut-off length L was chosen such that L ~ X for better representation of surface profile. The m a x i m u m depth of surface roughness was also determined from the profile amplitude measurements.
TABLE 1 Values for g e o m e t r i c a l p a r a m e t e r s related to surface r o u g h n e s s for T y p e 304 stainless steel Surface preparation
Ray (pm)
Rrms (pm)
Mechanically polished*
--
0.0075
<0.027
0.032 0.393 2.758
0.0386 0.482 3.736
0.18 1.8 8.9
G r o u n d o n silicon carbide p a p e r 6 0 0 grit 2 4 0 grit 50 grit
Rmax (pm)
~av (pm) --
19.0 23.2 83.0
* T h e values for this case were d e t e r m i n e d b y i n t e r f e r o m e t r i c t e c h n i q u e s .
~rms
Rrras/
Z2
(~m)
krm s
(pm -1 )
~6
18.5 22.8 89.5
O.0O125
0.0021 0.021 0.042
0.00611 0.434 0.023
60 A P P L I C A T I O N TO F A T I G U E C R A C K I N I T I A T I O N
The variation of the surface-roughness parameters with the grit size of the silicon carbide paper for the fatigue specimens containing circumferential grooves is summarized in Table 1. The low-cycle fatigue tests have been performed under axial push - pull strain-cycling conditions at 593°C at a strain rate of 4 X 1 0 --~3 sec -1. From the fatigue-striation spacing measurements, the crack-initiation life No (number of cycles to initiate a crack length equal to 0.1 mm) has been determined. The technique for producing surface roughness and the fatigue test results can be found elsewhere [13]. Because surface roughness affects only No, it is meaningful to obtain a correlation b e t w e e n the parameter related to surface roughness and No. When the strain range is held constant and only the surface roughness is varied in fatigue tests, the relation between No and the geometrical parameter (which enhances the strain at the r o o t of surface notches produced b y grinding) is assumed to be of the following form: N o = A (surface-roughness parameter) - ~
(15)
where A and e are constants. Equation (15) is based on the Coffin - Manson relation for crack initiation, i.e., Ne = A ( A % ) - e where Aep is the plastic strain range. When Aep is held constant and only surface roughness increases, the effect of surface roughness m a y be considered to enhance the strain concentration [14] that depends on the surface-roughness 8.00
I
I rllll
i
8.00
I
7.75 -
7.50 -
7.25
2 ,~
7.0C
6.5C
0 ¸
--
6.25 10-2
I
i iliilll
I
I
Irl~lll
I 0 -I
I
r I111t1
tO 0
i0 I
Rma x ,/.Lm
Fig. 3. Fatigue crack-initiation life of surface roughness.
vs.
m a x i m u m depth
characteristics, as suggested in eqn. (15). Figures 2 - 4 show the correlation between R~s/Xm~s and No, Rmax and No, and R~ms and No, respectively, on log - log plots. Based on the correlation factor of linear regression for limited data, the amplitude, particularly the rms value (Rm~s) of the surface profile, gives better correlation with No (Fig. 4, correlation factor = --0.96) than the rms of the first derivative of the profile (Fig. 2, correlation factor = --0.89). However, more extensive data are needed to firmly establish this point of view and the importance of parameters such as Z2. Another useful application of the surface-
If'
8.2.~
r i ll[rl I
l
I IIIIII
I
I Illl;ll
I
I
i iii~ii
I
I I Illlll
I
f
I i iiii
I
I
7.75 -&OC 7.50
--
7.7.~ 7.5C
7,2E --
2 Z°
~'~ 7.0C
7.2.~
~OC
6.7~ - 6.7E -6.5C --
6.25'
rO-4
6.5C-l
i i~JIPi
I
t i irllJl
iO - 3
i I0 - Z
i i ill lO-r
vs.
I
[ IJlJll
i0-2
lO-i
i0 0
I IIIII
i0 i
R rms, ~m
R r m s / ~. r m s
Fig. 2. Fatigue crack-initiation life derivative of surface profile,
6.25 j jO-3
rms of the first
Fig. 4. Fatigue crack-initiation life profile.
vs.
rms o f surface
61
I0 P~jt k,I rnm,q
(i)
I
(2)
T
mm
0J mini
~mm
"I
(S)
Fig. 5. Surface topography of pure aluminum specimens 1, 2 and 3 cycled, respectively, with _+1.5 X 10 ~ 3 -+3.0 X 10-3, and 4.5 X 10-3 reversed surface shear-strain amplitudes for 10,000 cycles (Ronay, ]966). roughness analysis is illustrated by a consideration of the results published by R o n a y [15,16] on aluminum. The surface contour changes that take place in an initially smooth specimen subjected to fatigue tests are believed to be the result of irreversible displacements on the slip planes. The kinetics of such surface shape changes are important in understanding the crack-initiation mechanisms. Figure 5 shows the surface contour changes in the high-purity aluminum specimens cycled with +1.5 X 10 -3, _+3.0 X 10 -3 and -+4.5 X 10 -3 reversed surface shear-strain amplitudes for 10,000 cycles. A Leitz - Forster surface measuring instrument was used to measure the surface c o n t o u r of the specimens. The reported grain diameter of the specimens is ~ 1 0 0 - 200 pm. The amplitude measurements were made on an enlargement of Fig. 5. The Fourier analysis of the surface topography shown in the Figure yields the results listed in Table 2. It should be emphasized that the changes in the geometrical quantities with strain amplitude or with number of cycles can be quantitatively determined. Both ~ and
R increase with an increase in strain amplitude for a predetermined number of cycles; the increase in R is more marked than the increase in k. The increase in k with an increase in strain amplitude may indicate that the number density for crack-initiation sites decreases as the strain amplitude increases. The relation between k and grain size should be of importance to the role that grain boundaries play in crack initiation. The variation in the amplitude with number of cycles or with strain range is of particular interest in mechanistic and modeling studies [7,8] concerned with crack initiation.
ACKNOWLEDGEMENTS
The author is grateful to Ms. Maria Ronay and Academic Press, New York, for granting permission to use Fig. 5, to S. Srinivas for numerous helpful discussions and to N.F. Fiore for his useful comments on the manuscript. The continuing support and encouragement of R.W. Weeks are appreciated. The work was
TABLE 2 Values for geometrical parameters to describe surface roughness that developed in aluminum during torsional fatigue. The surface profile used for Fourier analysis was obtained from ref. 14. surface shear strain amplitude
Ray (pm)
Rrms (pm)
Rmax (pm)
~av (pro)
)krms (pm)
Rrms/
Z2
~rms
(P m - l )
+1.5 X 10 - 3 +3.0 X 10 - 3 -+4.5 X 10 - 3
0.917 3.909 14.789
1.164 5.235 18.755
2.259 11.880 28.820
372.4 670.7 970.0
376.4 714.5 1004.6
0.000309 0.000733 0.0187
0.000397 0.000559 0.000909
62
supported by the U.S. Energy Research and Development Administration.
REFERENCES 1 O.J. Horger and H.R. Neifert, Symp. on Surface Treatment of Metals, Am. Soc. Metals, 1941, p. 279. 2 E. Siebel and M. Gaier, Engr. Dig., 18 (1957) 190. 3 M.J. Furey, Trans. Am. Soc. Lub. Eng., 6 (1963) 49. 4 N.O. Myers, Wear, 5 (1962) 182. 5 R.M. Latanision and R.W. Staehle, in R.W. Staehle e t al. (eds.), Proc. Conf. on Fundamental Aspects of Stress Corrosion Cracking, Natl. Assoc. Corrosion Engrs., 1969, p. 241. 6 M.H. Raymond and L.F. Coffin, Trans. ASME, Basci Engineering, Series D, 85 (1963) 548.
7 C. Laird and A.R. Krause, Intern. J. Fracture Mech., 4 (1968) 219. 8 F.A. McClintock, in D.C. Drucker and J.J. Gilman (eds.), Fracture of Solids, Interscience, New York, 1963, p. 65. 9 P.J.E. Forsyth, J. Inst. Metals, 82 (1953 - 54) 449. 10 W.A. Wood, S.McK. Cousland and K.R. Sargant, Acta Met., 11 (1963) 643. 11 P. Charsley and N. Thompson, Phil. Mag., 8 (1963) 77. 12 R.C. Spragg and D.J. Whitehouse, Proc. Inst. Mech. Engrs., 185 (1970 - 71) 47. 13 P.S. Maiya and D.E. Busch, Met. Trans. to be published. 14 P.S. Maiya, to be published. 15 M. Ronay, in H. Liebowitz (ed.), Fracture - An Advanced Treatise, Vol. III, Academic Press, New York, 1971, p. 431. 16 M. Ronay, Tech. Rept. No. 34., Inst. for the study of Fatigue and Reliability, Columbia University, New York, 1966.