Abstract

The indentation formed on a metallic component by the high-velocity impingement of a small object can fracture the component, and this is known as foreign object damage. In this type of dynamic indentation, it is necessary to consider the effects of work hardening, strain rate hardening, and thermal softening in the impinged material. In this study, in order to consider these effects, the expanding cavity model based on a spherical formulation is modified via the Johnson–Cook constitutive equation for the dynamic indentation problem. Additionally, an equation is developed based on energy conservation and the modified expanding cavity model to predict the size of the indentation formed by an impingement of a solid sphere (EPIS). The distributions of equivalent plastic strain, equivalent plastic strain rate, temperature, and equivalent von Mises stress obtained via the expanding cavity model were in good agreement with the data obtained from the finite element analysis (FEA). Furthermore, it was demonstrated that EPIS accurately predicted the indentation size formed on various metallic materials at several impingement velocities in the range of 50–300 m/s. Consequently, EPIS can be effectively applied to an impingement problem of a hard sphere onto a sufficiently thick ductile material within 300 m/s without any help of FEA.

References

References
1.
Cowles
,
B. A.
,
1996
, “
High Cycle Fatigue in Aircraft Gas Turbines—An Industry Perspective
,”
Int. J. Fract.
,
80
(
2–3
), pp.
147
163
. 10.1007/BF00012667
2.
Chen
,
X.
, and
Hutchinson
,
J. W.
,
2002
, “
Particle Impact on Metal Substrates With Application to Foreign Object Damage to Aircraft Engines
,”
J. Mech. Phys. Solids
,
50
(
12
), pp.
2669
2690
. 10.1016/S0022-5096(02)00022-4
3.
Oakley
,
S. Y.
, and
Nowell
,
D.
,
2007
, “
Prediction of the Combined High- and Low-Cycle Fatigue Performance of Gas Turbine Blades After Foreign Object Damage
,”
Int. J. Fatigue
,
29
(
1
), pp.
69
80
. 10.1016/j.ijfatigue.2006.02.042
4.
Maleki
,
E.
,
Unal
,
O.
, and
Kashyzadeh
,
K. R.
,
2018
, “
Fatigue Behavior Prediction and Analysis of Shot Peened Mild Carbon Steels
,”
Int. J. Fatigue
,
116
, pp.
48
67
. 10.1016/j.ijfatigue.2018.06.004
5.
Tabor
,
D.
,
1951
,
The Hardness of Metals
,
Oxford University Press, University of Oxford
,
Oxford, England, UK
.
6.
Big-Alabo
,
A.
,
Harrison
,
P.
, and
Cartmell
,
M. P.
,
2015
, “
Contact Model for Elastoplastic Analysis of Half-Space Indentation by a Spherical Impactor
,”
Comput. Struct.
,
151
, pp.
20
29
. 10.1016/j.compstruc.2015.01.005
7.
Almasri
,
A. H.
,
Olimat
,
S.
, and
Al Zubi
,
M.
,
2017
, “
Analytical and Numerical Simulation of Dynamic Indentation for Different Indenter Shapes
,”
J. Appl. Mech. Eng.
,
6
(
5
), p.
1000286
. 10.4172/2168-9873.1000286
8.
Miao
,
H. Y.
,
Larose
,
S.
,
Perron
,
C.
, and
Lévesque
,
M.
,
2010
, “
An Analytical Approach to Relate Shot Peening Parameters to Almen Intensity
,”
Surf. Coat. Technol.
,
205
(
7
), pp.
2055
2066
. 10.1016/j.surfcoat.2010.08.105
9.
Sundararajan
,
G.
, and
Tirupataiah
,
Y.
,
2006
, “
The Localization of Plastic Flow Under Dynamic Indentation Conditions: I. Experimental Results
,”
Acta Mater.
,
54
(
3
), pp.
565
575
. 10.1016/j.actamat.2005.09.022
10.
Sundararajan
,
G.
, and
Tirupataiah
,
Y.
,
2006
, “
The Localization of Plastic Flow Under Dynamic Indentation Conditions: II. Analysis of Results
,”
Acta Mater.
,
54
(
3
), pp.
577
586
. 10.1016/j.actamat.2005.09.021
11.
Clough
,
R. B.
,
Webb
,
S. C.
, and
Armstrong
,
R. W.
,
2003
, “
Dynamic Hardness Measurements Using a Dropped Ball: With Application to 1018 Steel
,”
Mater. Sci. Eng. A
,
360
(
1–2
), pp.
396
407
. 10.1016/S0921-5093(03)00499-4
12.
Johnson
,
K. L.
,
1970
, “
The Correlation of Indentation Experiments
,”
J. Mech. Phys. Solids
,
18
(
2
), pp.
115
126
. 10.1016/0022-5096(70)90029-3
13.
Narasimhan
,
R.
,
2003
, “
Analysis of Indentation of Pressure Sensitive Plastic Solids Using the Expanding Cavity Model
,”
Mech. Mater.
,
36
(
7
), pp.
633
645
. 10.1016/S0167-6636(03)00075-9
14.
Wang
,
Z.
,
Basu
,
S.
,
Murthy
,
T. G.
, and
Saldana
,
C.
,
2016
, “
Modified Cavity Expansion Formulation for Circular Indentation and Experimental Validation
,”
Int. J. Solids Struct.
,
97–98
, pp.
129
136
. 10.1016/j.ijsolstr.2016.07.035
15.
Hill
,
R.
,
1950
,
The Mathematical Theory of Plasticity
,
Oxford University Press
,
University of Oxford, Oxford, England, UK
.
16.
Gao
,
X. L.
,
Jing
,
X. N.
, and
Subhash
,
G.
,
2006
, “
Two New Expanding Cavity Models for Indentation Deformations of Elastic Strain-Hardening Materials
,”
Int. J. Solids Struct.
,
43
(
7–8
), pp.
2193
2208
. 10.1016/j.ijsolstr.2005.03.062
17.
Zhang
,
T.
,
Wang
,
S.
, and
Wang
,
W.
,
2018
, “
Determination of the Proof Strength and Flow Properties of Materials From Spherical Indentation Tests: An Analytical Approach Based on the Expanding Cavity Model
,”
J. Strain Anal. Eng. Des.
,
53
(
4
), pp.
225
241
. 10.1177/0309324718754960
18.
Hopkins
,
H. G.
,
1960
,
Progress in Solid Mechanics Vol. 1
,
North-Holland Publishing Co.
,
Amsterdam, The Netherlands
.
19.
Johnson
,
G. R.
, and
Cook
,
W. H.
,
1983
, “
A Constitutive Model and Data for Metals Subjected to Large Strains, High Temperatures
,”
Proceedings of the 7th International Symposium on Ballistics
,
The Hague, The Netherlands
,
Apr. 19–21
, pp.
541
548
.
20.
Luis
,
J.
, and
Castellanos
,
P.
,
2012
, “
Temperature Increase Associated With Plastic Deformation Under Dynamic Compression: Application to Aluminium Alloy Al 6082
,”
J. Theor. Appl. Mech.
,
50
(
2
), pp.
377
398
.
21.
Nicholas
,
J. F.
,
1959
, “
The Dissipation of Energy During Plastic Deformation
,”
Acta Metall.
,
7
(
8
), pp.
544
548
. 10.1016/0001-6160(59)90190-7
22.
Mason
,
J. J.
,
Rosakis
,
A. J.
, and
Ravichandran
,
G.
,
1994
, “
On the Strain and Strain Rate Dependence of the Fraction of Plastic Work Converted to Heat: An Experimental Study Using High Speed Infrared Detectors and the Kolsky Bar
,”
Mech. Mater.
,
17
(
2–3
), pp.
135
145
. 10.1016/0167-6636(94)90054-X
23.
Ravichandran
,
G.
,
Rosakis
,
A. J.
,
Hodowany
,
J.
, and
Rosakis
,
P.
,
2002
, “
On the Conversion of Plastic Work Into Heat During High-Strain-Rate Deformation
,”
AIP Conf. Proc.
,
620
, pp.
557
562
. 10.1063/1.1483600
24.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press, University of Cambridge
,
Cambridge, UK
.
25.
Nobre
,
J. P.
,
Diasa
,
A. M.
, and
Gras
,
R.
,
1997
, “
Resistance of a Ductile Steel Surface to Spherical Normal Impact Indentation: Use of a Pendulum Machine
,”
Wear
,
211
(
2
), pp.
226
236
. 10.1016/S0043-1648(97)00125-7
26.
Lubliner
,
J.
,
1990
,
Plasticity Theory
,
Macmillan
,
London, UK
, Chap. 4.
27.
Schwer
,
L.
,
2007
, “
Optional Strain-Rate Forms for the Johnson Cook Constitutive Model and the Role of the Parameter Epsilon_0
,”
Proceedings of the 6th European LS-DYNA Users’ Conference
,
Gothenburg, Sweden
,
May 29–30
.
28.
Sharma
,
P.
,
Chandel
,
P.
,
Mangla
,
V.
,
Mahajan
,
P.
, and
Singh
,
M.
,
2013
, “
Effect of Strain Rate on Constitutive Behavior of AA-5052H34
,”
Key Eng. Mater.
,
535–536
, pp.
60
63
. 10.4028/www.scientific.net/KEM.535-536.60
29.
Akbari Mousavi
,
S. A. A.
,
Ranjbar Bahadori
,
S.
, and
Shahab
,
A. R.
,
2010
, “
Numerical and Experimental Studies of the Plastic Strains Distribution Using Subsequent Direct Extrusion After Three Twist Extrusion Passes
,”
Mater. Sci. Eng. A
,
527
(
16–17
), pp.
3967
3974
. 10.1016/j.msea.2010.02.077
30.
Assadi
,
H.
,
Gärtner
,
F.
,
Stoltenhoff
,
T.
, and
Kreye
,
H.
,
2003
, “
Bonding Mechanism in Cold Gas Spraying
,”
Acta Mater.
,
51
(
15
), pp.
4379
4394
. 10.1016/S1359-6454(03)00274-X
31.
Zhang
,
X. C.
,
Lu
,
J.
, and
Shi
,
S. Q.
,
2011
, “
A Computational Study of Plastic Deformation in AISI 304 Induced by Surface Mechanical Attrition Treatment
,”
Mech. Adv. Mater. Struct.
,
18
(
8
), pp.
572
577
. 10.1080/15376494.2011.621828
32.
Gardenier
,
H. E.
,
Palazotto
,
A. N.
, and
Larson
,
R. A.
,
2012
, “
Development and Investigation of a Slotted Beam Impact Experiment for Intermediate Strain Rates
,”
J. Aerosp. Eng.
,
25
(
2
), pp.
294
307
. 10.1061/(ASCE)AS.1943-5525.0000112
33.
Niesłony
,
P.
,
Grzesik
,
W.
,
Jarosz
,
K.
, and
Laskowski
,
P.
,
2018
, “
FEM-Based Optimization of Machining Operations of Aerospace Parts Made of Inconel 718 Superalloy
,”
Procedia CIRP
,
77
, pp.
570
573
. 10.1016/j.procir.2018.08.220
34.
Schulze
,
V.
, and
Zanger
,
F.
,
2011
, “
Numerical Analysis of the Influence of Johnson-Cook-Material Parameters on the Surface Integrity of Ti-6Al-4V
,”
Procedia Eng.
,
19
, pp.
306
311
. 10.1016/j.proeng.2011.11.117
35.
Hill
,
R.
,
Storåkers
,
B.
, and
Zdunek
,
A. B.
,
1989
, “
A Theoretical Study of the Brinell Hardness Test
,”
Proc. R. Soc. Lond. A
,
423
(
1865
), pp.
301
330
. 10.1098/rspa.1989.0056
36.
Taljat
,
B.
, and
Pharr
,
G. M.
,
2004
, “
Development of Pile-Up During Spherical Indentation of Elastic Plastic Solids
,”
Int. J. Solids Struct.
,
41
(
14
), pp.
3891
3904
. 10.1016/j.ijsolstr.2004.02.033
You do not currently have access to this content.