2003 WJTA American Waterjet Conference
August 17-19, 2003 y Houston, Texas
Paper 6-A
MATHEMATICAL MODELING OF ULTRA HIGH PRESSURE
WATERJET PEENING
S. Kunaporn
Walailuk University
Nakhonsithammarat, Thailand
M. Ramulu
University of Washington
Seattle, Washington, USA
M. Hashish
Flow International
Kent, Washington, USA
ABSTRACT
Waterjet peening is a recent promising method in surface treatment. It has potential to induce
compressive residual stresses that benefit the fatigue life of materials similar to the conventional
shot peening process. However, there are no analytical models that incorporate process
parameters, i.e. supply pressure, jet exposure time, and nozzle traverse rate etc., to allow
predicting the optimized peening process. Mathematical modeling of high pressure waterjet
peening was developed in this study to describe the relation between the waterjet peening
parameters and the resulting material modifications. Results showed the possibility of using the
proposed mathematical model to predict an initial range for effective waterjet peening under the
variation of waterjet peening conditions. The high cycle fatigue tests were performed to validate
the proposed model and fatigue test results showed good agreement with the predictions.
Organized and Sponsored by the WaterJet Technology Association
1. INTRODUCTION
Effects of the impacting high pressure waterjet on the solid target have been of interest among
researchers [1-13] not only to understand the mechanisms associated with jet material interface
but also to apply waterjet in material removal processes such as cleaning, cutting, and paint
removal etc. An additional application of the high-pressure waterjet to surface treatment was
realized as early as 1984 in inducing compressive residual stress to enhance fatigue strength [1].
The process now is known as water peening. Water peening is similar to shot peening except it
uses high-pressure droplets that are disintegrated in the waterjet flow field instead of solid shots.
Fig. 1 illustrates the schematic of changes in jet structure with distance from the nozzle. The
high-velocity droplets that benefit for peening are typically found in the transition region of jet
structure.
In shot peening, the contact pressure resulting by the impact of the solid shot is represented in a
form of a Hertzian pressure distribution [14-15]. The Hertzian pressure distribution was used in
a numerical analysis as an interfacial load on to a material’s surface to evaluate shot peening
performance. Waterjet peening is still lacking for theoretical developments if compared to shot
peening. The criteria for peening for any applied peening conditions on a specific target material
have not yet well defined. This might due to the complexity of the jets in the waterjet peening
operation, which involves many variables and conditions. However, some studies have been
experimentally and numerically performed to describe the effects of waterjet on the material
target. For example, Leach and Walker [16], and Rehbinder [17] presented the pressure
distribution across the jet stream in parabolic and exponential forms, respectively. Powell and
Simpson [18] subsequently employed the Leach and Walker parabolic pressure distribution to
predict the residual stress state of the elastic half-space due to the impinging jet for a rock cutting
application. Most recently, Daniewicz et al. [7] attempted to predict the material response in
waterjet peening by using finite element analysis. The jet was assumed to be stationary with the
impact pressure equal to the stagnation pressure, calculated by neglecting process parameters
that were involved in the waterjet peening process such as standoff distance, nozzle feed rate etc.
Results in their study showed under prediction of compressive residual stress in the material
target compared to experiments.
This paper presents the results of recent study on waterjet peening of 7075-T6 aluminum alloy
using ultra high-pressure waterjet. The study aimed at formulating the mathematical model of
waterjet peening for evaluating the effects of high impact jet on material as well as optimizing
the process. The analytical study of the waterjet peening process is presented and results are
discussed and verified with experiments.
2. MATHEMATICAL MODELING OF WATERJET PEENING
In this study, we have assumed the moving jet in the waterjet peening operation (Fig. 2) as a
stationary jet to avoid the complications of the effects of shear pressure that are possibly induced
by the movement of the jet along the surface. Therefore, the simplified stationary jet imposes
only a normal pressure onto the contact area. The approach used for the modeling of moving jet
in waterjet peening is based on an understanding of a basic knowledge of a jet structure for
peening in relations to the concept of elastic-plastic response of material to the impact jet. The
magnitude of the interfacial impact pressure resulting from waterjet on the material is derived.
The predicted impact pressure is subsequently used to predict the initial effective range for
peening. The initial range defined by the model is the range of applied peening conditions that is
sufficient to initiate yielding on the target but does not cause surface erosion.
Based on an elastic-plastic theory, the material will initiate yielding when the interfacial pressure
is equal to C ⋅ Sy , where C is a constant value that depends upon the geometry of the contact and
the yield condition and Sy is the yield strength of the material. For Poisson’s ratio ν = 0.3, the
constant values C for the onset of yielding was found to be 1.59 and 1.51 under the Hertz
pressure and the uniform pressure acting on a semi-infinite body, respectively [19]. Therefore,
following this concept, the minimum compact pressure, that is sufficient to induce plastic
deformation in the target, can be estimated if the properties of the target and the geometry of the
impact pressure are known.
Considering the jet structure from Fig. 2, it was assumed that the momentum of a liquid jet
outflow from the nozzle remained constant between the nozzle and the point of the impact. A
change of momentum, M, with the control volume, cv, is equal to the impulse force, F, acting
normal to the target surface. The momentum,  is given as ∫ Vρ V ⋅ dA , where V is the velocity
cv
and dA is the element area on a plane perpendicular to the direction of the velocity. The
momentum conservation of the jet from the jet nozzle exit (1) to the contact area (2) gives
(∫ VρV ⋅ dA)1
= (∫ VρV ⋅ dA)2
(1)
Assuming the jet velocity at the nozzle, V1, exit as Ve , and V2 is the impact velocity at the target
defined as Vim , thus Eq. (1) is written as:
π

2 π 2 
Ve2  d n2  = Vim
 d im 
4

4

(2)
where dim and dn are the diameter of the waterjet at the point of the impact and at the nozzle exit,
respectively. The droplet diameter at the point of the impact, dim, is denoted in this model as the
equivalent droplet d eq . From Eq. (2), d eq is then given as:
d eq =
Ve
dn =
Vim
2 ps  d n 


ρ  Vim 
(3)
where ps is the pump pressure releasing from nozzle exit.
During the peening operation, it is assumed here that the motion of the jet produces uniform
pressure across the contact area. Therefore, the impinging normal point force acting on the
surface due to each droplet is calculated in relation to the pressure as:
Fd = pc
2
πd eq
(4)
4
where pc is the collapse pressure.
Substituting Eq. (3) into Eq. (4), we obtain
πd n2  Ve 
2
V

 = pc An  e
Fd = pc
4  Vim 
 Vim
where An is the cross sectional area of the nozzle and is equal to



π
4
2
(5)
d n2 .
To consider the phenomena of the full stream of the jet, we assume that the surface is repeatedly
struck by multiple impacts of single droplet. As a result, the exposure time of solid target under
repeated impacts needs to be obtained. By considering the jet structure as shown in Fig. 2, the
exposure time will be designated by t p and it is the time of the jet over the contact area, 2a,
which is given as t p =
2a
, where u is the nozzle traverse speed and 2a is the contact diameter,
u
which is equal to d n + 2 SOD tan
α
for this jet structure. Note that the impact area, 2a, used in
2
this model is considered as an equivalent area similar to the area resulting by the round jet. The
contact areas resulting from using different jet types (as shown in Fig. 3) will be simply
considered as the equivalent area similar to the round jet in the model. With this exposure time,
the total volume of liquid, V L , coming out form the nozzle is V L = AnVe t p , where An is the
nozzle area, Ve is the jet velocity at the nozzle exit.
In the view of the full stream jet, the number of the droplets in the total volume of the jet, defined
as the droplet intensity, I, is equal to the ratio of the total waterjet volume, V L , to the volume of a
single equivalent droplet, Vd eq . Then I is obtained by
I=
AnVe t p
VL
=
droplets in the jet
π 3
Vd eq
d eq
6
(6)
The term “site” is introduced in this model as an area on the surface that is equal to the crosssectional area of one equivalent droplet as graphically shown in Fig. 2. Therefore, a number of
A
sites per contact area on the surface, A* , is A* = a , where Aa and Adeq are the cross-section
Ad eq
of the contact surface of the jet and the cross section of the equivalent droplet that is given in Eq.
(3).
From the assumption that the droplet distribution is uniform over the contact area and all droplets
have the same diameter and are in the spherical shape, the number of impacts of the droplets per
contact area, N, is defined by

A V t
I
I
n e p
=
=
N=
*
π
Aa / Ad eq 
3
A
 d eq
 6



A V t
Aa
n e p
÷
=
π
 Ad eq 
3

 d eq

 6
 π
2
  (2a ) 
÷ 4
 (7)
  π 2 
d eq 
 

  4
The number of impacts of the droplets per contact area, N, can be simplified to
N=
3 d nVim
2 (2a )u
(8)
Considering the full stream of the jet, the total impact force due to the stream of the jet onto
material surface is equal to the resulting force of each single droplet multiplied by the total
number of the impacts, N. As a result, the total impact force, Fimpact , can be calculated by
π
Fimpact = N ⋅ Fd = N ⋅
4
2
pc d eq
(9)
By knowing the impact force, the impact pressure due to the impact of the stream jet is then
obtained by assuming that the jet movement across the contact area produces a uniform pressure.
Thus the impact pressure of waterjet can be given as:
Pimpact =
Fimpact
Aa
=
N⋅
π
π
4
4
2
pc d eq
(10)
(2a )
2
Substituting Eq. (3), and Eq. (8) into Eq.(10), the impact pressure can be expressed as:
3
Pimpact =
3
3  d n  2 pc
 d   ps
= 3  n  ⋅ 

 Ve
Vim
2u  2a 
 2a   ρ ⋅ Vim
  pc 
 ⋅ 

  u 
(11)
From the perspective of the collapse pressure under the impact of the high velocity jet, the
magnitude of the pressure developed by an imploding droplet on the target is a highly localized
water-hammer pressure [20-23]. This high magnitude of the water hammer pressure is assumed
to be responsible for the plastic deformation at the point of the impact, which influences the
residual stress and strength properties. Therefore, it is used as the collapse pressure to
characterize the pressure and the force at the interface. The water- hammer pressure, pw, was
given as [20]:
p w = ρC oVo
(12)
where
is the fluid density, Co is the compressive wave velocity of the liquid, and Vo is the
collapse velocity of the jet. If we substitute Eq. (12) into Eq. (11), the impact pressure can be
finalized in terms of the major peening parameters as:

3

dn
 d n  ps
= 3 Co 
Pimpact = 3 C o 

 d + 2SOD tan α
 2a  u
 n
2

3

 p
 s
 u


(13)
The mathematical model of the impact pressure (Eq.13) is used to further predict the final
standoff distance for waterjet peening that can initiate yielding in a material. Based on the
theory of elasticity as discussed previously, the minimum impact pressure required to initiate
yielding of a material under the impact of the jets, Py, is defined as when it is equal to C ⋅ S y . If
this value is substituted into Eq. (13), a final standoff distance, SOD f , meaning the largest
standoff distance that gives the interface pressure at the threshold of plastic deformation can be
estimated as follows:
1/ 3


dn
  3C o p s 

− 1 =
SOD f =



α
P u 
 2 tan α
2 tan   y

2
2
dn
1/ 3


  3C o p s 

− 1
 C ⋅ S u 


y



(14)
The constant C is a value depending on the geometry of the interfacial pressure based on elastic
theory, which can be estimated by FEA. With the known C value, the final standoff
distance, SOD f , can be estimated for any given waterjet peening condition by the proposed
mathematical model.
The variation of all process parameters, ps, dn, u and  will give the level of impact pressure that
can be used to estimate the standoff distance at which the jet has no effects on the material target.
. A schematic representation is plotted in Fig. 4 to describe how each parameter relates to the
p
predicted final standoff distance, SODf. As follows from the figure, SODf increases as s and ps
u
increase, and u and decrease.
As previously discussed, the constant value C is dependent on the geometry of the interfacial
pressure and properties of the target body. In order to estimate the SOD f using the proposed
Eq. 14, it is necessary to define C. Previous study has been performed to define the constant
value C using finite element analysis [24-25]. Results showed that the constant C value of 1.59
given for the surface loading of the theoretical Hertzian pressure could be initially used for the
prediction of an effective peening range by Eq. 14.
3. EXPERIMETAL VERIFICATION
3.1
Experimental Setup: High Cycle Fatigue Testing
The test specimens were fabricated into hour glass, circular cross section fatigue life rotating
bending test specimens (Fig. 5). After fabrication, the gage section of each test specimen was
surface treated by waterjet peening under conditions. To verify how peening conditions affects
the fatigue limit of Al7075-T6, tests with different variations of ps and SOD for waterjet peening
on the test specimens were made. These variations were chosen such that the proposed
mathematical model used to predict the peening range could be verified. The peening conditions
were listed in Tables 1. The waterjet peening system employed a high-pressure pump with
control unit, capable of generating pump pressures, ps, up to 400 MPa. The pressurized water
was controlled and directed through a 0.3-mm sapphire orifice before entering a nozzle specially
designed for the purpose of waterjet peening. The nozzle was oriented perpendicular to the
surface of the test specimen. With the test specimen fixed in a holder, the nozzle was moved and
adjusted to obtain an appropriate nozzle-to-surface standoff distance, SOD (Fig. 2).
Both peened and unpeened hour-glass, circular cross section fatigue life test specimens were
fatigue life tested in completely reversed rotating bending (R= Smin/Smax = -1) until fracture. A
commercial R.R. Moore rotating bending fatigue test machine (4-point flexure) was used at
rotational speeds up to 10,000 RPM at alternating stress, S, that ranged from 200 to 430 MPa.
The number of cycles to fracture, along with corresponding applied stress amplitude were
recorded for each test for later analysis.
3.2
Results of High Cycle Fatigue Testing
It is apparent that the degree of fatigue improvements is strongly dependent on peening
conditions as observed in the S-N curves Fig.5 to Fig.7. The fatigue improvement was found
under some peening conditions (e.g. SK-F1-FT1-1 for ps of 103 MPa, SK-F1-FT2-1 for ps of 207
MPa, and SK-F1-FT3-1 for ps of 310 MPa). The maximum degree of fatigue improvement was
about 20%-25% as compared to the unpeened condition. For each applied supply pressure in this
waterjet peening study, the variation of standoff distance has an effect on the degree of fatigue
improvement. Fatigue endurance limit of was found to decrease with increasing standoff
distances.
According to the proposed mathematical model developed based on the multiple impacts of the
droplets as previously given in Eq. 14, the SODf or the maximum standoff distance at which
waterjet peening can induce plastic deformation was estimated for the applied peening conditions
as listed in Table 1. For u = 12.7 mm/s, dn = 0.33 mm, and = 20°, the proposed mathematical
model predicted that SODfs for three different supply pressures of 103, 207, and 310 MPa were
33mm, 42 mm, and 48 mm, respectively. Observations from fatigue testing results showed that
the specimens waterpeened at the standoff distances less than the predicted SODf, did show an
improvement of fatigue life in a comparable amount to that of shot peening. The conditions that
showed the improvement of fatigue limits were SK-F1-FT1-1 for ps of 103 MPa, SK-F1-FT2-1
for ps of 207 MPa, and SK-F1-FT3-1 for ps of 310 MPa.
In contrast, the conditions that applied standoff distances greater than the predicted SODf showed
no or slight improvement of fatigue limits. Such conditions were SK-F1-FT1-2 and SK-F1-FT13 (ps of 103 MPa) and SK-F1-FT2-2 and SK-F1-FT2-3 (ps of 207 MPa), and SK-F1-FT1-3 (ps of
310 MPa). The roughness measurement of these fatigue test specimens showed no apparent
changes in surface roughness parameters. Therefore, it is possible that the waterjet under these
conditions might not induce sufficient plastic deformation at the surface to improve its fatigue
limit. This observation is in agreement to the prediction from the proposed mathematical model.
However, it is important to note that the number of fatigue tests for some conditions are small
that might not be enough to establish the fatigue test results for such conditions. However, the
deduction of the fatigue results might be possible from the tendency that was observed in their SN curves.
4. CONCLUSION
The mathematical modeling based on the multiple impacts of the jets has been proposed to
estimate the contact pressure and the feasible peening range. Fatigue results showed that the
proposed mathematical model might be a practical tool to predict the initial waterjet peening
range since results showed some agreement between the fatigue study and the proposed model.
Fatigue life improvement by waterjet peening was observed in the specimen waterpeened under
the effective conditions predicted by the proposed model. Fatigue results did show that the
viability of the proposed mathematical model that predicted the effective range for waterjet
peening. With this observation, the proposed mathematical model could be used as the initial
means to find out the optimal range for waterjet peening. However, more studies on other metals
are necessary to perform in order to validate the model.
5. REFERENCES
1. Salko, D., “Peening by Water”, Proceedings of 2nd International Conference on Shot Peening,
ICSP-2, Chicago, Illinois, 14-17 May 1984, Edt. Fuchs, H.O., American shot peening
Society, New Jersey, pp. 37-38.
2. Blickwedel, H., Haferkamp, H., Louis, H. and Tai, P.T., “Modification of Material Structure
by Cavitation and Liquid Impact and Their Influence on Mechanical Properties,” Erosion by
Liquid and Solid Impact, Proc. 7th International Conference on Erosion by Liquid and Solid
Impact, 7-10 September 1987, pp.31.1-31.6.
3. Mathias, M., Gocke, A. and Pohl, M., “The residual stress, texture and surface changes in
steel induced by cavitation”, Wear, Vol. 150, 1991, pp. 11-20.
4. Yamauchi, Y., Soyama, H., Adashi, Y., Sato, K., Shindo, T., Oba, R., Oshima R., and
Yamabe, M., “Suitable Region of High-Speed Submerged Water Jets for Cutting and
Peening,” JSME International Journal, Series B, Vol.8, No.1, 1995, pp.31-38.
5. Tonshoff, H.K., Kross, F. and Marzenell, C., “High-pressure water Peening – a New
Mechanical Surface-Strengthening Process”, Annals of the CIRP Vol. 46, No. 1, 1997, pp
113-116.
6. Hirano, K., Enmoto, K., Hayashi, M., Oyamada, O., Hayashi, E., and Shimizu, S., “Stress
Corrosion Cracking Mitigation by Water Jet Peening”, PVP, Plant System/Components
Aging Management, ASME 1997, Vol. 349, pp.89-93.
7. Daniewicz, S.R., and Cummings, S.D., “Characterization of Water Peening Process”,
Transaction of the ASME, Vol. 121, July 1999, pp. 336-340.
8. Krull, P., Nitschke-Pagel, Th., and Wohlfahrt, H., “ Stability of Residual Stresses in Shot
Peened and High Pressure Water Peened Stainless Steels at Elevated Temperature”, The 7th
International Conference on Shot Peening, Warsaw, Poland, 1999.
9. Soyama, H., “Improvement in Fatigue Strength of Silicon Manganese Steel SUP7 by Using a
Cavitating Jet”, JSME International Journal, Series. A, Vol. 43, No.2, 2000, pp173-177.
10. Colosimo, B.M., Monno, M., and Semeraro, Q., “ Process Parameters Control in Water Jet
Peening”, International Journal of Material and Product Technology, Vol. 15, No. ½, 2000,
pp.10-19.
11. Ramulu, M., Kunaporn, S., Jenkins, M.G., Hashish, M., and Hopkins, J., “ Fatigue
Performance of High Pressure Waterjet peened Aluminum Alloy”, 2000 ASME Pressure
Vessels and Piping Conference, Seattle, WA, July 23-27, 2000.
12. Kunaporn, S, Ramulu, M., Jenkins, M.G., Hashish, M., and Hopkins, J., “Ultra High Pressure
Waterjet Peening, Part I: Surface Characteristics”, 2001 WJTA American Waterjet
Conference, Minneapolis, MN, August 18-21, 2001, paper no 25.
13. Kunaporn, S, Ramulu, M., Jenkins, M.G., Hashish, M., and Hopkins, J., “Ultra High Pressure
Waterjet Peening, Part II: Fatigue Performance”, 2001 WJTA American Waterjet
Conference, Minneapolis, MN, August 18-21, 2001, paper no. 26.
14. Al-Obaid, Y.F., “A Rudimentary Analysis of Improving Fatigue Life of Metals by Shot
Peening”, Journal of Applied Mechanics, Vol.57, June 1990, pp. 307-312.
15. Al-Hassani, S.T.S., “ An Engineering Approach to Shot Peening Mechanics”, Proceedings of
2nd International Conference on Shot Peening, ICSP-2, Chicago, Illinois, 14-17 May 1984,
Edt. Fuchs, H.O., American shot peening Society, New Jersey, pp. 275-281.
16. Leach, S.J., and Walker, G.L., “The Application of High Speed Liquid Jets to Cutting”,
Philosophical Transactions, Royal Society of London Series A, Vol. 260, 1966, pp. 295-308.
17. Rehbinder, G, “ Some Aspects of the Mechanism of Erosion of Rock with a High Speed
Water Jet”, paper E1, 3rd International Symposium on Jet Cutting Technology, May, 1976,
Chicago, IL, pp. E1-1 to E1-20.
18. Powell, J.H., and Simpson, S.P., “Theoretical Study of the Mechanical Effects of Water Jets
Impinging on a Semi-Infinite Elastic Solid”, International Journal of Rock Mechanics and
Mining Science, Vol.6, 1969, pp. 353-364.
19. Tabor, D., The Hardness of Metals, The Clarendon Press, Oxford, 1951.
20. Blowers, R. W., “On the Response of an Elastic Solid to Droplet Impact”, Journal of Institute
Mathematics Applications (1969), Vol. 5, pp. 167-193.
21. Obara, T., and Bourne, N.K., and Field. J.E., “Liquid-Jet impact on liquid and solid surface,”
Wear, 1995, Vol. 186-187, pp. 38-394.
22. Johnson, W. and Vickers, G.W., “Transient Stress Distribution caused by Water-Jet Impact”,
Journal Mechanical Engineering Science, Vol. 15, No.4, 1973, pp. 302-310.
23. Hwang, J.B.G., and Hammitt, F.G., “On Liquid-Solid Impact Phenomena”, Journal of
Applied Physics, Mar 21-25, 1976, ASME, pp. 24-27. (Cavitations and Phosphate Flow
Forum, 1976.
24. Kunaporn, S., “An Experimental and Numerical Analysis of Waterjet Peening of 7075-T6
Aluminum Alloy”, Doctoral Dissertation, University of Washington, 2002.
25. Kunaporn, S, Ramulu, M.G., Hashish, M., “Finite Element Analysis of Residual Stress
induced by Ultra high Pressure Waterjet”, The 16th International Conference on Water
Jetting, Aix-en-Provence, France, 16-18 October 2002.
Table 1: Waterjet peening conditions of circular fatigue test specimens.
Test
Set
Test
specimen
s
7
SK-F1-FT1-1
3
SK-F1-FT1-2
3
SK-F1-FT1-3
7
SK-F1-FT2-1
3
SK-F1-FT2-2
3
SK-F1-FT2-3
9
SK-F1-FT3-1
3
SK-F1-FT3-2
Identification
FT1
FT2
FT3
No of.
ps
Actual
SOD
(MPa)
(mm)
u
(mm/s) passes Type
24
36
47
36
59
83
44
77
103
207
310
No. of
Predicte
Nozzle
jet
d SODf
32
12.7
12.7
(mm)
4
Fan
42
12.7
48
nozzle
solid
fluid flow
droplet
fluid flow
.
. .. .
. .
.. ..
.. . .
..
. .. .. . . .
. . . . .. . . .
. . . .
Initial Region
Applications: cutting, machining,
hole piecing etc.
Transition Region
Applications: cleaning, peening etc.
Final Region
Figure 1: Schematic of changes in jet structure with distance from the nozzle.
ps
Nozzle
dn
u
nozzle
nozzle direction
α
SOD
a
ps
dn
= supply pressure
= nozzle diameter
α = jet angle
SOD = standoff distance
u
= nozzle feed rate
a
= radius of a contact area
Impinging droplet point
force
Fd
π

Fd = pc  deq2 
4 
water droplet,
deq
2a
specimen
o o o o
o o o o o
o o o or o o
o o o o o o
o o o o o
o o o Contact area
Figure 2: Graphic representation of the waterjet peening process.
nozzle
r (mm)
round jet
fan jet
α = 20°
SOD = 45 mm
5000
4500
4000
3500
3000
Expected Pressure Distribution
2500
2000
1500
1000
500
0
-10.000
-5.000
0.000
5.000
10.000
Specimen
Figure 3: Schematic of pressure profile across a cross section of the jet
resulting from using different kinds of nozzles in the waterjet operation
Log (Pimpact)
Pimpact
Py= C⋅Sy


dn
= 3C0 
α
 d n + 2 SOD tan

2
SOD f
3

 ps

 u

SOD
P y : the minimum pressure distribution at which yielding can be initiated
SOD f : the maximum SOD that can be used in UHPWJ peening to initiate yielding
Figure 4: Pressure distribution curve.
Units: mm
R 203.2
9.27
6.27
19.05
87.37
Figure 5: Geometry and Dimensions of Hourglass,
Circular Cross-section Fatigue Life Test Specimens
Alternative Stress, Sa (MPa)
460
as machined specimens
420
SK-F1-FT1-1, ps = 103 MPa, SOD = 24 mm
380
SK-F1-FT1-3, ps = 103 MPa, SOD = 47 mm
SK-F1-FT1-2, ps = 103 MPa, SOD = 36 mm
340
300
260
220
180
104
105
106
107
108
109
Cycles to Failure, Nf
Figure 5: S-N curves for as-machined and waterjet-peened circular cross
section fatigue life test specimens set SK-F1-FT1 for ps = 103 MPa, u = 12.7 mm/s.
as machined specimens
SK-F1-FT2-1, ps = 207 MPa, SOD = 36 mm
SK-F1-FT2-2, ps = 207 MPa, SOD = 59 mm
SK-F1-FT2-3, ps = 207 MPa, SOD = 83 mm
Alternative Stress, Sa (MPa)
460
420
380
340
300
260
220
180
104
105
106
107
108
109
Cycles to Failure, Nf
Figure 6: S-N Curves for as-machined and waterjet-peened circular cross
section fatigue life test specimens set SK-F1-FT2 for ps = 207 MPa, u = 12.7 mm/s.
Alternative Stress, Sa (MPa)
460
as machined specimens
420
SK-F1-FT3-1, ps = 310 MPa, SOD = 44 mm
SK-F1-FT3-2, ps = 310 MPa, SOD = 77 mm
380
340
300
260
220
180
104
105
106
107
108
109
Cycles to Failure, Nf
Figure 7: S-N curves for as-machined and waterjet-peened circular cross
section fatigue life test specimens set SK-F1-FT3 for ps = 310 MPa, u = 12.7 mm/s.