Revista Mexicana de Ingeniería Química
ISSN: 1665-2738
[email protected]
Universidad Autónoma Metropolitana Unidad
Iztapalapa
México
Veleva, L.; García-González, A.; Pérez, G.
FRACTAL QUANTIFICATION OF ALUMINUM PITTING CORROSION INDUCED BY HUMID
TROPICAL CLIMATE
Revista Mexicana de Ingeniería Química, vol. 12, núm. 1, 2013, pp. 65-72
Universidad Autónoma Metropolitana Unidad Iztapalapa
Distrito Federal, México
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de Ingenierı́a Quı́mica
Academia Mexicana de Investigación y Docencia en Ingenierı́a Quı́mica, A.C.
Revista Mexicana de Ingeniería Química
Volumen 12, Número 1, Abril 2013
Vol. 12,
No. 1 (2013) 65-72
CONTENIDO
ISSN 1665-2738
1
Volumen 8, número 3, 2009 / Volume 8, number 3, 2009
FRACTAL QUANTIFICATION OF ALUMINUM PITTING CORROSION INDUCED
BY HUMID TROPICAL CLIMATE
1
CUANTIFICACIÓN FRACTAL DE LA CORROSIÓN DE ALUMINIO POR
TROPICAL HÚMEDO
213 Derivation
and application
of the Stefan-Maxwell
equations
PICADURAS
INDUCIDA
POR EL
CLIMA
∗
(Desarrollo y aplicación de
ecuaciones
de Stefan-Maxwell)
L.las
Veleva,
A. Garcı́a-González
, and G. Pérez
Stephen Whitaker
Departamento de Fı́sica Aplicada, Centro de Investigación y Estudios Avanzados del Instituto Politécnico
Nacional, Unidad-Mérida, Antigua carretera Mérida-Progreso Km.6, C.P. 97310, Mérida, Yucatán, México.
Biotecnología / Biotechnology
Received 4 of February 2012; Accepted 11 of November 2012
245 Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo
Abstract
During three annual exposure periods, aluminum samples of wire, used for transmission of high voltage electricity, were exposed
intemperizados en suelos y sedimentos
at outdoor atmospheric marine-coastal and rural environments, located in the humid tropical climate of Yucatan Peninsula, in
the Mexican(Biodegradation
gulf. In atmospheric
conditions
the naturally
formed
aluminum
oxide
layer can beweathering
destroyed by
modeling
of sludge
bioreactors
of total
petroleum
hydrocarbons
in the
soilpresence of
chlorides, causing pitting localized corrosion attack, difficult for evaluation. The concepts of fractal geometry and self-similarity
and sediments)
were used in this study for evaluation of the pitting corrosion as a function of time, making a statistics of the frequency of
S.A.
S. Huerta-Ochoa,
C.A.data
Lucho-Constantino,
L. Aguilera-Vázquez,
A. Jiménezappearance of
pitsMedina-Moreno,
versus the area occupied
by them. The
showed that the distribution
of the pits follows
a power law. The
exponent of González
self-similarity
between 1.7-1.9 and it is relatively stable with the progress of corrosion progress. The progress
y M. varied
Gutiérrez-Rojas
of pits in area and frequency is more pronounced in time in the marine-coastal atmosphere, compared to pitting developed in
259 Crecimiento, sobrevivencia y adaptación de Bifidobacterium infantis a condiciones ácidas
rural- urban one. The concepts of fractal geometry and self-similarity can quantify the extent of localized corrosion with time, as
nondestructive
form and
rapid method.
(Growth,
survival
and adaptation of Bifidobacterium infantis to acidic conditions)
Keywords: L.
aluminum,
fractal quantification,
atmospheric
corrosion, pitting
corrosion, self-similarity.
Mayorga-Reyes,
P. Bustamante-Camilo,
A. Gutiérrez-Nava,
E. Barranco-Florido
y A. AzaolaResumen Espinosa
Durante tres años, se expusieron muestras de alambre de aluminio (usadas para el transporte de electricidad de alto voltaje), en
265 Statistical approach to optimization of ethanol fermentation by Saccharomyces cerevisiae in the
dos diferentes atmósferas, en una marina-costera y la otra rural-urbana, en el clima tropical húmedo de la penı́nsula de Yucatán,
en el golfo de
México.ofEn
estas condiciones
de exposición, la capa de óxido natural del aluminio puede ser destruida en presencia
presence
Valfor®
zeolite NaA
de cloruros, causando picaduras localizadas por el ataque corrosivo, lo que dificulta su análisis. Los conceptos de geometrı́a de
fractales y auto-similaridad
se utilizaron
la evaluaciónetanólica
de la corrosión
por picaduracerevisiae
en funciónendel
tiempo, de
haciendo una
(Optimización estadística
de para
la fermentación
de Saccharomyces
presencia
estadı́stica de
la
frecuencia
de
aparición
de
picaduras
contra
el
área
superficial
ocupada
por
estas.
Los
datos
muestran
que la
zeolita Valfor® zeolite NaA)
distribución de picaduras sigue una ley de potencias. El exponente de auto-similaridad varió entre 1.7-1.9 y es relativamente
Inei-Shizukawa,
H. A. Velasco-Bedrán,
F. Gutiérrez-López
H. Hernández-Sánchez
estable con G.
el avance
de la corrosión.
El aumento del G.
tamaño
del área de las and
picaduras
y en frecuencia, es más pronunciado
con el tiempo en la atmósfera marina-costera, en comparación con la rural-urbana. Los conceptos de geometrı́a de fractales y
auto-similaridad
predecir
la extensión
de la corrosión localizada de aluminio con el tiempo, de una forma no destructiva
Ingenieríapueden
de procesos
/ Process
engineering
y rápida.
271 Localización de una planta industrial: Revisión crítica y adecuación de los criterios empleados en
Palabras clave: aluminio, cuantificación fractal, corrosión atmosférica, corrosión por picadura, auto-similaridad.
esta decisión
1
(Plant site selection: Critical review and adequation criteria used in this decision)
Introduction
J.R. Medina, R.L. Romero y G.A. Pérez
Aluminum is widely used metal for transmission of
high voltage electricity and in construction industry.
∗ Corresponding
Thermodynamically it is very active and immediately
corrodes when is produced (high level of free energy
and high negative potential value -1.67 V) (Evans,
1965; Szklarska-Smialowska, 1971; Foley, 1986;
author. E-mail: [email protected]
Publicado por la Academia Mexicana de Investigación y Docencia en Ingenierı́a Quı́mica A.C.
65
Figure
Figure 1.
1. Schematic
Schematic presentation
presentation of
of cross-sections
cross-sections of
of non
non uniform
uniform (localized)
(localized) forms
forms of
of corrosio
corrosio
attacks.
attacks.
Veleva et
al./ Revista
Mexicana de
Ingenierı́a Quı́mica
Vol. 12,
No. 1 (2013)
65-72
Veleva
Veleva et
et al./
al./ Revista
Revista Mexicana
Mexicana de
de Ingenierı́a
Ingenierı́a Quı́mica
Quı́mica Vol.
Vol. 12,
12, No.
No. 11 (2013)
(2013) XXX-XXX
XXX-XXX
ions
ions (for
(for example,
example, airborne
airborne salinity
salinity in
in marine-coastal
marine-coastal
environments).
The
presence
of
metal
environments). The presence of metal impurities
impurities (Fe,
(Fe,
78
Cu)
78
Cu) increases
increases the
the pitting
pitting process
process in
in depth
depth and
and pit
pit
79
diameter,
79
diameter, which
which is
is rate-controlled
rate-controlled by
by the
the oxygen
oxygen (O
(O22))
80
cathodic
80
cathodic reduction
reduction on
on the
the metal
metal inclusions.
inclusions.
81
A
variety
of
atmospheric
81 progress
Aandvariety
of ofatmospheric factors,
factors, climatic
climatic
Table
Table 1.
1. Coefficients
Coefficients of
of σσ for
for different
different time
time of
of Aluminum
Aluminum corrosion
corrosion
progress
and aggressivity
aggressivity
of
82
conditions
and
air-chemical
pollutants,
determines
the
environment:
Rural
urban
(RU)
and
Marine
coastal
(MC)
test
sites,
located
humid
tropical
climate.
82 inconditions
and
air-chemical
pollutants,
determines
the
environment: Rural urban (RU) and Marine coastal (MC) test sites, located in humid tropical climate.
83
corrosiveness
(i.e.
aggressivity)
of
the
atmosphere
83
corrosiveness (i.e. aggressivity) of the atmosphere
Environment
84
and
Environment
-2
-2
84
and contributes
contributes to
to the
the metal
metal corrosion
corrosion process
process in
in
Exposition
MC
σ
(µm
Exposition time
time RU
MC σσ (µm
(µm-2))
RU σ (µm-2))
85
distinct
ways
(Evans,
1965;
Bockris
and
85
distinct ways (Evans, 1965; Bockris and Khan,
Khan,
86
1994;
33 months
0.0422
0.0170
86
1994; Lee
Lee and
and Baker,
Baker, 1982;
1982; ISO
ISO 9223:92,
9223:92, 1992;
1992;
months
0.0422
0.0170
87
Leygraf
and
Graedel,
2000).
Climatic
characteristics
87
Leygraf
and
Graedel,
2000).
Climatic
characteristics
99 months
0.0259
0.0336
88
play
months
0.0259
0.0336
88
play aa key
key role
role on
on the
the atmospheric
atmospheric electrochemical
electrochemical
89
corrosion
process
and
to
be
able
to
fully
understand
12
months
0.0243
0.0289
89
corrosion
process
and
to
be
able
to
fully
understand
12 months
0.0243
0.0289
90
this
corrosion
phenomenon,
it
is
very
important
90
this corrosion phenomenon, it is very important to
to
91
properly
describe
the
environment
that
causes
metal
91
properly
describe
the
environment
that
causes
metal
Fig.
1.
Pourbaix
diagram
(potential
vs
pH)
for
Fig. 1. Pourbaix diagramo (potential vs pH) for 92 degradation. The most important factors related to the
degradation. The most important factors related to the
Aluminum
Aluminum in
in water
water at
at 25
25oC
C [Veleva
[Veleva L.,
L., Kane
Kane R.
R. 9392 climate
and
on
that
are
represented
93
climate
and its
its effect
effect
on
that material
material
are[Veleva
represented
(2003)].
Figure
2.
Pourbaix
diagram
(potential
vs
pH)
for
Aluminum
in
water
at
25ºC
L.,
(2003)].
Figure 2. Pourbaix diagram (potential vs pH)
for
Aluminum
in
water
at
25ºC
[Veleva
L., Kane
Kane R.
R.
94
by
a
combination
of
(a)
air
temperature
94
by a combination of (a) air temperature (T)
(T) and
and
(2003)].
95
relative
(2003)].
95
relative humidity
humidity (RH)
(RH) values,
values, often
often described
described as
as
96
the
temperature-humidity
complex
(THC),
96
the temperature-humidity complex (THC), (b)
(b) annual
annual
97
values
97
values of
of pluvial
pluvial precipitation,
precipitation, and
and (c)
(c) time
time of
of wetness
wetness
98
(TOW),
during
which
an
electrolyte
(moisture)
98
(TOW), during which an electrolyte (moisture) exists
exists
Fig.
presentation
of
cross-sections
of
on
metal
surface
and
Fig. 2.
2.1.Schematic
Schematic
presentation
of
cross-sections
of non
non 9999(localized)
Figure
Schematic
presentation
of
cross-sections
of
non
uniform
of
corrosion
on the
theforms
metal
surface
and corrosion
corrosion occurs.
occurs. In
In recent
recent
Figure
1.
Schematic
presentation
of
cross-sections
of
non
uniform
(localized)
forms
of
corrosion
uniform
100
years,
attacks.
uniform (localized)
(localized) forms
forms of
of corrosion
corrosion attacks.
attacks.
100
years, the
the parameter
parameter TOW
TOW has
has received
received special
special
attacks.
101
attention,
since
it
is
the
fundamental
101
attention, since it is the fundamental parameter
parameter that
that
102
relates to the time during which the corrosion cell
Graedel,
Graedel, 1989;
1989; Bockris
Bockris and
and Khan,
Khan, 1994;
1994; Wiersma
Wiersma 102 relates to the time during which the corrosion cell
103
(anode-cathode) can operate (ISO 9223:92, 1992;
and
and Hebert,
Hebert, 1991;
1991; Meakin
Meakin et
et al.,
al., 1993;
1993; SzklarskaSzklarska- 103 (anode-cathode) can operate (ISO 9223:92, 1992;
104
Cole et al., 1995; Dean and Reiser, 1995; Veleva et
Smialowska,
1999;
Pourbaix,
1974).
According
to
the
Smialowska, 1999; Pourbaix, 1974). According to the 104 Cole et al., 1995; Dean and Reiser, 1995; Veleva et
105
al.,
1997; Tidblad, 2000; Veleva and Alpuche-Aviles,
electrochemical
Pourbaix
Diagram
(Fig.
1),
aluminum
electrochemical Pourbaix Diagram (Fig. 1), aluminum 105 al., 1997; Tidblad, 2000; Veleva and Alpuche-Aviles,
106
2002;
Veleva and Kane, 2003). Based on statistical
could
get
three
possible
states
known
for
this
metal
could get three possible states known for this metal 106 2002; Veleva and Kane, 2003). Based on statistical
107
analysis
of the T-RH complex, it was previously
(and
its
alloys):
passivity,
immunity
and
corrosion
(and its alloys): passivity, immunity and corrosion 107 analysis of the T-RH complex, it was previously
108
shown
that
the tropical humid climate presents high
(active
state)
(Pourbaix,
1974).
There
is
a
region
of
pH
(active state) (Pourbaix, 1974). There is a region of pH 108 shown that the tropical humid climate presents high
109
annual
values
of TOW, from 4800 h to 8500 h per year,
(from
4
to
9)
and
electrochemical
potentials
where
the
(from 4 to 9) and electrochemical potentials where the 109 annual values of TOW, from 4800 h to 8500 h per year,
110
respectively
for
rural-urban and marine-coastal areas
metal
reach
passivity,
due
to
the
formation
of
a
very
metal reach passivity, due to the formation of a very 110 respectively for rural-urban and marine-coastal areas
111
of
Southeaster
Mexico.
Besides, the
thin
(transparent),
hydrated
oxide
layer
(Al
O
·H
O)
2
3
2
the TOW
TOW occurs
occurs in
in
thin (transparent), hydrated oxide layer (Al2 O3 ·H2 O) 111 of Southeaster Mexico. Besides,
o
112
temperature
range
of
20-25
oC (Veleva et. al., 1997)
with
a
low
porosity,
well
adherent
to
the
metal.
The
with a low porosity, well adherent to the metal. The 112 temperature range of 20-25 C (Veleva et. al., 1997)
113
and
both
factors
contribute to a much accelerated
passive
layer
the
for
aluminum
very
good
Figure
2.
(potential
pH)
water
25ºC
[Veleva
L.,
both
factors
passive
layer is
isdiagram
the reason
reason
forvs
very in
good
Figure
2. Pourbaix
Pourbaix
diagram
(potential
vsaluminum
pH) for
for Aluminum
Aluminum
in
water at
at113
25ºCand
[Veleva
L., Kane
Kane R.
R. contribute to a much accelerated
(2003)].
114
corrosion
process,
especially
corrosion
resistance
when
exposed
to
atmospheric
(2003)].
114
corrosion
process,
especially in
in the
the marine
marine coastal
coastal
corrosion resistance when exposed to atmospheric
115
regions
(Veleva
and
Alpuche-Aviles,
2002;
Veleva
conditions,
free
of
chloride
ions.
However,
even
115
regions
(Veleva
and
Alpuche-Aviles,
2002;
Veleva
conditions, free of chloride ions. However, even
116
and
Kane,
2003;
Corvo
et
al.,
1997;
Veleva
and
in
noncontaminated
atmosphere,
when
aluminum
116
and
Kane,
2003;
Corvo
et
al.,
1997;
Veleva
and
in non- contaminated atmosphere, when aluminum
117
Maldonado,
1998;
Santana-Rodriguez
et
al.,
2003).
itit is
in
contact
with
humidity
(water),
after
a
long
117
Maldonado,
1998;
Santana-Rodriguez
et
al.,
2003).
is in contact with humidity (water), after a long
118
The reports note that the humid tropical climate
exposure
exposure time
time the
the passive
passive layer
layer can
can be
be destroyed
destroyed and
and 118 The reports note that the humid tropical climate
119
is extremely aggressive, according to ISO 9223:92
corrosion
corrosion attack
attack appears
appears focused
focused in
in small
small and
and specific
specific 119 is extremely aggressive, according to ISO 9223:92
120
(1992), for the widely used standard metals (zinc,
locations
locations on
on the
the metal
metal surface,
surface, referred
referred to
to as
as corrosion
corrosion 120 (1992), for the widely used standard metals (zinc,
121
copper, low carbon steel and aluminum), compared to
pits
pits (up
(up to
to 100
100 µm
µm deep)
deep) (Fig.
(Fig. 2).
2). This
This type
type of
of 121 copper, low carbon steel and aluminum), compared to
122
the aggressivity of different temperate climates.
localized
localized corrosion
corrosion can
can be
be observed
observed on
on aluminum
aluminum and
and 122 the aggressivity of different temperate climates.
its
Corrosion
its alloys
alloys (Szklarska-Smialowska,
(Szklarska-Smialowska, 1971;
1971; Foley,
Foley, 1986;
1986; 123
123
Corrosion attack
attack by
by pitting
pitting is
is difficult
difficult for
for
Graedel,
1989;
Bockris
and
Khan,
1994;
Wiersma
124
evaluation.
Different
types
of
tests
Graedel, 1989; Bockris and Khan, 1994; Wiersma 124 evaluation.
Different types of tests have
have been
been
and
developed
and Hebert,
Hebert, 1991;
1991; Meakin
Meakin et
et al.,
al., 1993;
1993; SzklarskaSzklarska- 125
125
developed for
for pitting
pitting corrosion
corrosion (ISO
(ISO 11463-93,
11463-93, 1993;
1993;
Smialowska,
1999;
McCafferty,
2003;
Burstein
et
al.,
126
ASTM
Guide
G46-94,
2005;
Kelly,
Smialowska, 1999; McCafferty, 2003; Burstein et al., 126 ASTM Guide G46-94, 2005; Kelly, 2005),
2005), based
based
2004).
on
2004). ItIt is
is often
often induced
induced by
by the
the presence
presence of
of chloride
chloride 127
127
on physical
physical and
and chemical
chemical methods.
methods. The
The exposures
exposures
76
76
77
77
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43
44
44
45
45
46
46
47
47
48
48
49
49
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22
www.rmiq.org
www.rmiq.org
www.rmiq.org
Veleva
et
Revista
Mexicana
Ingenierı́a
Quı́mica
Vol.
No.
1 (2013)
65-72
Veleva
Veleva
etetal./
al./al./
Revista
Revista
Mexicana
Mexicana
de
dede
Ingenierı́a
Ingenierı́a
Quı́mica
Quı́mica
Vol.
Vol.
12,
12,12,
No.
No.
11(2013)
(2013)
XXX-XXX
XXX-XXX
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of
of coupons
coupons to
to natural
natural environments
environments or
or solutions
solutions that
that
simulate
simulate service
service conditions
conditions are
are extremely
extremely valuable
valuable
tests,
tests, due
due to
to their
their direct
direct applicability.
applicability. However,
However, mass
mass
loss
loss measurement,
measurement, which
which characterizes
characterizes the
the rate
rate of
of
uniform
uniformmetal
metalcorrosion,
corrosion,can
canbe
beextremely
extremelymisleading
misleading
for
forpitting
pittinglocalized
localizedcorrosion.
corrosion. Badly
Badlypitted
pittedspecimens
specimens
can
can exhibit
exhibit negligible
negligible mass
mass loss
loss ifif the
the attack
attack isis
extremely
extremely localized.
localized. There
There are
are several
several ways
ways in
in
which
which pitting
pitting can
can be
be described,
described, giving
giving aa quantitative
quantitative
expression
expression to
to indicate
indicate its
its significance,
significance, to
to predict
predict the
the
life
life of
of material.
material. Some
Some of
of the
the more
more commonly
commonly used
used
methods
methods for
for examination
examination and
and evaluation
evaluation of
of pitting
pitting
corrosion
corrosion are
are described
described in
in ISO
ISO 1146-93
1146-93 (1993)
(1993) and
and
ASTM
ASTM GG 46
46 (1998)
(1998) (Kelly,
(Kelly, 2005),
2005), although
although for
for most
most
cases
cases no
no single
single method
method isis sufficient
sufficient by
by itself:
itself: (a)
(a)
standard
standardrating
ratingcharts
chartsfor
forpits
pitsin
interms
termsof
ofdensity,
density,size,
size,
and
and depth;
depth; (b)
(b) metal
metal penetration
penetration expressed
expressed in
in terms
terms
of
ofthe
themaximum
maximumpit
pitdepth;
depth;(c)
(c)application
applicationof
ofstatistics
statistics
to
to the
the analysis
analysis of
of corrosion
corrosion pitting
pitting data;
data; (d)
(d) loss
loss in
in
mechanical
mechanical properties
properties (tensile
(tensile strength,
strength, elongation,
elongation,
fatigue
fatiguestrength,
strength,impact
impactresistance
resistanceand
andburst
burstpressure),
pressure),
ifif pitting
pitting isis the
the predominant
predominant form
form of
of corrosion
corrosion and
and
the
the density
density of
of pitting
pitting isis relatively
relatively high.
high. ItIt should
should be
be
stressed
stressedthat
thatsome
someof
ofthe
thementioned
mentionedabove
abovemethods
methodsare
are
destructive
destructiveas
asprocedures.
procedures.
While
While prediction
prediction of
of localized
localized penetration
penetration rate
rate
remains
remains aa goal
goal of
of electrochemical
electrochemical testing,
testing, recent
recent
applications
applications of
of statistics
statistics to
to the
the corrosion
corrosion process
process
appear
appear promising.
promising. Another
Anothertechnique
technique which
whichdoes
doesnot
not
appear
appear to
to have
have received
received much
much attention
attention isis the
the use
use
of
of nondestructive
nondestructive image
image analysis
analysis of
of corroded
corroded metal
metal
surface
surface morphology.
morphology. Although
Although the
the method
method isis more
more
time
timeconsuming
consumingthan
thanmass
masschange
changemeasurements,
measurements,this
this
one
one has
has the
the potential
potential of
of allowing
allowing the
the required
required data
data
to
to be
be easily
easily gathered
gathered and
and combined
combined with
with statistical
statistical
analysis
analysis of
of aa sufficient
sufficient number
number of
of images
images (sample
(sample
area),
area), deriving
deriving the
the progress
progress of
of pit-size
pit-size distribution
distribution in
in
corrosion
corrosionpatterns
patternsor
orpitting
pittingpenetration.
penetration.
Nowadays
Nowadays fractal
fractal concepts
concepts have
have become
become
increasingly
increasingly popular
popular when
when trying
trying to
to quantitatively
quantitatively
characterize
characterizeapparently
apparentlyirregular
irregularor
ordisordered
disorderedobjects
objects
(Mandelbrot,
(Mandelbrot, 1983;
1983; Vicsek,
Vicsek, 1989;
1989; Gordon
Gordon etet al.,
al.,
2001).
2001). Fractal
Fractal geometry
geometry isis finding
finding many
many applications
applications
in
in material
material science.
science. AA preliminary
preliminary account
account of
of fractal
fractal
properties
propertiesof
ofsteel
steelcorrosion
corrosionpitting
pittinghas
hasbeen
beenreported
reported
by
by Costa
Costa etet al.
al. (1991)
(1991) and
and later
later the
the authors
authors use
use
aa Monte
Monte Carlo
Carlo simulation
simulation of
of localized
localized corrosion
corrosion
(Reigada
(Reigadaetetal.,
al.,1994).
1994). An
Anattempt
attemptisismade
madeto
tocorrelate
correlate
the
thefractal
fractaldimensions
dimensionsof
ofsurface
surfaceprofiles
profilesmeasured
measuredon
on
corroded
corrodedaluminum
aluminumspecimens
specimensimmersed
immersedin
in3%
3%NaCl,
NaCl,
with
withresults
resultsobtained
obtainedwith
withelectrochemical
electrochemicalimpedance
impedance
spectroscopy
spectroscopy (EIS)
(EIS) (Roberge
(Roberge and
and Trethewey,
Trethewey,
180
180
181
181
182
182
183
183
184
184
185
185
186
186
187
187
188
188
189
189
190
190
191
191
192
192
193
193
194
194
195
195
196
196
197
197
198
198
199
199
200
200
1995).
1995). Fractal
Fractal characterization
characterization of
of two-dimensional
two-dimensional
aluminum
aluminum foils
foils corrosion
corrosion fronts
fronts (in
(in pH=12,
pH=12, 1M
1M
NaCl
NaCl electrolyte),
electrolyte), controlled
controlled pontentiostatically,
pontentiostatically, was
was
reported
reported (Holten
(Holten etet al.,
al., 1994).
1994). The
The results
results show
show that
that
the
the fronts
fronts (at
(at the
the metal-electrolyte
metal-electrolyte interface)
interface) can
can be
be
described
describedin
interms
termsof
ofself-affine
self-affinefractal
fractalgeometry
geometryover
over
aasignificant
significantrange
rangeof
oflength
lengthscales.
scales.
In
In our
our study
study we
we present
present the
the progress
progress of
of pitting
pitting
corrosion
corrosionattach
attachon
onaluminum
aluminumafter
afterexposure
exposureto
tohumid
humid
tropical
tropical climate
climate (marine
(marine and
and rural
rural environments)
environments)
during
during one
one year,
year, as
as aa function
function of
of time,
time, making
making aa
statistics
statisticsof
ofthe
thefrequency
frequencyof
ofappearance
appearanceof
ofpits
pitsversus
versus
the
the area
area occupied
occupied by
by them.
them. The
The degree
degree of
of corrosion
corrosion
damage
damage manifests
manifests itself
itself in
in the
the severity
severity of
of corrosion
corrosion
and
and aggressivity
aggressivity of
of the
the environment.
environment. Since
Since corrosion
corrosion
results
resultsin
intexture
texturechanges
changesof
ofaametal
metalsurface,
surface,ititchanges
changes
its
its fractal
fractal dimension
dimension as
as well.
well. The
The concept
concept of
of fractals
fractals
and
and self-similarity
self-similarity were
were applied
applied for
for the
the study
study of
of the
the
phenomena
phenomenaof
oflocalized
localizedcorrosion
corrosionof
ofaluminum.
aluminum.
22 Materials
Materials and
and methods
methods
2.1
2.1 Sampling
Samplingand
andfield
fieldexposure
exposure
216
216
Wire
Wire samples
samples (1
(1 m
m and
and 3.1
3.1 mm
mm of
of diameter)
diameter) of
of
electrolytic
electrolyticaluminum
aluminum(99,
(99,999%),
999%),used
usedfor
forelectricity
electricity
transmission
transmission of
of high
high voltage,
voltage, were
were prepared
prepared as
as
open
open helix
helix specimens
specimens (exposed
(exposed vertically).
vertically). Their
Their
surface
surface encompasses
encompasses all
all exposure
exposure angles
angles and
and isis
oriented
oriented equal1y
equal1y with
with respect
respect to
to al1
al1 wind
wind directions,
directions,
which
whichusual1y
usual1ydetermine
determinethe
theprincipal
principalpollutants
pollutants(ISO
(ISO
9223:92,
9223:92, 1992).
1992). Therefore
Therefore itit isis recommended
recommended that
that
preference
preference be
be given
given to
to the
the comparison
comparison of
of metal
metal
corrosion
corrosion rates
rates obtained
obtained with
with open
open helix
helix specimens
specimens
when
when exposures
exposures are
are conducted
conducted in
in different
different climates
climates
and
and atat different
different geographical
geographical latitudes
latitudes (ISO
(ISO 9223:92,
9223:92,
1992;
1992; Veleva
Veleva and
and Maldonado,
Maldonado, 1998).
1998). After
After exposure
exposure
atat tropical
tropical climate,
climate, the
the samples
samples where
where chemically
chemically
treated
treated according
according to
to ISO
ISO 8407
8407 (1993),
(1993), removing
removing the
the
corrosion
corrosionproducts
productson
onthe
thealuminum
aluminumsurface.
surface.
217
217
2.2
2.2 Test
Testsite
sitecharacterization
characterization
201
201
202
202
203
203
204
204
205
205
206
206
207
207
208
208
209
209
210
210
211
211
212
212
213
213
214
214
215
215
218
218
219
219
220
220
221
221
222
222
223
223
224
224
225
225
226
226
During
Duringthree
threeannual
annualexposure
exposureperiods,
periods,aluminum
aluminumopen
open
helix
helixspecimens
specimenswere
wereexposed
exposedin
inaccordance
accordancewith
withISO
ISO
9226
9226 (1992)
(1992) atat outdoor
outdoor atmospheric
atmospheric corrosion
corrosion in
in two
two
test
test sites
sites located
located in
in the
the humid
humid tropical
tropical climate
climate of
of
the
the Yucatan
Yucatan Peninsula
Peninsula (Southeastern
(Southeastern Mexico,
Mexico, in
in the
the
Caribbean
Caribbean area):
area): marine-coastal
marine-coastal (MC)
(MC) environment
environment
(at
(atProgreso
ProgresoPort,
Port,21
21oo18’N,
18’N,89
89oo39’W),
39’W),30
30m
mfrom
fromthe
the
seashore
seashoreand
andaarural-urban
rural-urban(RU)
(RU)site
siteatatMerida,
Merida,30
30km
km
far
farfrom
fromthe
thesea
sea(Fig.
(Fig.3).
3).
www.rmiq.org
www.rmiq.org
www.rmiq.org
6733
Veleva
Revista
Mexicana
Ingenierı́a
Quı́mica
Vol.
No.
1 (2013)
65-72
Veleva
Veleva
et
et et
al./
al./al./
Revista
Revista
Mexicana
Mexicana
de
dede
Ingenierı́a
Ingenierı́a
Quı́mica
Quı́mica
Vol.
Vol.
12,
12,12,
No.
No.
11 (2013)
(2013)
XXX-XXX
XXX-XXX
264
264
265
265
2.3
2.3 Fractal
Fractal quantification
quantification
corrosion
corrosion
267
267
228
228
229
229
230
230
231
231
232
232
233
233
234
234
235
235
236
236
237
237
238
238
239
239
240
240
241
241
242
242
243
243
244
244
245
245
246
246
247
247
248
248
249
249
250
250
251
251
252
252
253
253
254
254
255
255
256
256
257
257
258
258
259
259
260
260
261
261
262
262
263
263
pitting
pitting
A
A fractal
fractal is
is defined
defined as
as “a
“a set
set for
for which
which the
the Hausdorff
Hausdorff
dimension
dimension strictly
strictly exceeds
exceeds the
the topological
topological dimension”
dimension”
268
268
and
and is
is less
less than
than the
the embedding
embedding dimension
dimension (Vicsek,
(Vicsek,
269
269
1999;
1999; Gordon
Gordon et
et al.,
al., 2001;
2001; Costa
Costa et
et al.,
al., 1991;
1991;
270
270
Bunde
Bunde and
and Havlin,
Havlin, 1991).
1991). The
The fact
fact that
that the
the pits
pits
271
271
cover
cover aa finite
finite area
area on
on the
the metal
metal surface,
surface, give
give the
the
272
272
reason
reason to
to study
study their
their distribution
distribution using
using the
the concept
concept
273
273
of
of fat
fat fractal
fractal (Mandelbrot,
(Mandelbrot, 1983;
1983; Vicsek,
Vicsek, 1999).
1999).
274
274
The
The characterization
characterization analysis
analysis consists
consists in
in obtaining
obtaining
275
275
black
black and
and white
white images
images of
of pitted
pitted regions
regions on
on the
the
276
276
metal
metal surface.
surface. This
This is
is done
done in
in order
order to
to obtain
obtain
277
277
data
data on
on pit
pit density
density and
and pit
pit size,
size, during
during the
the time
time of
of
Fig.
Fig. 3.
3. Map
Map of
of Yucatan
Yucatan Peninsula
Peninsula (Southeastern
(Southeastern 278
278
corrosion
corrosion progress,
progress, distinguishing
distinguishing the
the influence
influence of
of
Mexico,
Mexico,3.
Caribbean
Caribbean
area).
Figure
Figure
3.
Map
Map of
ofarea).
Yucatan
Yucatan Peninsula
Peninsula (Southeastern
(Southeastern
Mexico,
Caribbean
Caribbean
area).
279
279 Mexico,
atmosphere
atmosphere
corrosive
corrosivearea).
aggressively
aggressively (pollution)
(pollution) of
of both
both
280
280
test
test sites.
sites. After
After elimination
elimination of
of corrosion
corrosion products,
products,
Periodically,
Periodically, at
at 1,
1, 3,
3, 6,
6, 9,
9, and
and 12
12 months,
months, three
three 281
281
33
33 samples
samples were
were cut
cut (1
(1 cm
cm of
of length
length of
of wire)
wire) from
from
replicate
replicate open
open helix
helix specimens
specimens were
were evaluated.
evaluated. Time
Time 282
282
helix
helix specimens
specimens that
that have
have been
been exposed
exposed at
at different
different
of
of wetness
wetness (TOW)
(TOW) values
values was
was calculated
calculated using
using aa 283
283
period
period to
to corrosion
corrosion in
in MC
MC and
and RU
RU test
test sites.
sites. Scanning
Scanning
statistical
statistical analysis
analysis of
of temperature-relative
temperature-relative humidity
humidity 284
284
Electron
Electron Microscope
Microscope (SEM),
(SEM), Phillips
Phillips XL-30
XL-30 ESEM
ESEM
(T-RH)
(T-RH) complex.
complex. Despite
Despite the
the close
close distance
distance between
between 285
285
(at
(at 0.3
0.3 Torr
Torr and
and work
work distance
distance of
of 7.7-12.5
7.7-12.5 mm),
mm), was
was
both
both test
test sites,
sites, the
the difference
difference in
in their
their daily
daily T-RH
T-RH 286
286
used
used for
for morphology
morphology analysis
analysis of
of aluminum
aluminum corroded
corroded
complex
complex makes
makes them
them interesting
interesting to
to study,
study, because
because they
they 287
287
surface.
surface.
show
show how
how variable
variable the
the tropical
tropical climate
climate can
can be
be [18].
[18].
288
288
The
The collected
collected 174
174 images
images where
where characterized
characterized
For
For example,
example, the
the RU
RU zone
zone is
is hotter
hotter that
that the
the MC
MC one,
one,
289
289
with
with the
the Image
Image JJ program,
program, defining
defining conversion
conversion factor
factor
however,
however, the
the MC
MC zone
zone is
is more
more humid
humid than
than the
the RU
RU
290
290
of
of pixels
pixels to
to area
area (µm
(µm22)) and
and running
running the
the program
program
environment,
environment, but
but the
the MC
MC shows
shows less
less fluctuation
fluctuation in
in
291
291
for
for statistical
statistical analysis
analysis of
of pitted
pitted areas
areas for
for one
one base
base
T-RH
T-RH values
values during
during the
the year.
year. We
We believe
believe that
that the
the
292
292
threshold
threshold and
and for
for thresholds
thresholds moved
moved to
to ±5%.
±5%.
described
described differences
differences are
are due
due to
to the
the influence
influence of
of the
the
293
293
The
The cumulative
cumulative frequency
frequency for
for pit
pit area
area was
was
permanent
permanent thermodynamic
thermodynamic buffering
buffering effect
effect of
of the
the sea
sea
294
294
calculated
calculated for
for each
each time
time and
and site
site of
of exposure.
exposure.
on
on TT and
and RH
RH for
for the
the MC
MC atmosphere.
atmosphere. On
On RU
RU zones,
zones,
295
295
The
The analyzed
analyzed data
data show
show power-law
power-law decay,
decay, whose
whose
this
this effect
effect is
is not
not present
present and
and TT and
and RH
RH show
show much
much
296
296
coefficient
coefficient and
and exponent
exponent can
can be
be finding
finding from
from log-log
log-log
larger
larger fluctuation
fluctuation during
during the
the night
night and
and day,
day, interrupting
interrupting
297
297
graphs.
graphs. Therefore,
Therefore, itit is
is clear
clear that
that we
we can
can use
use the
the
corrosion
corrosion process
process and
and introducing
introducing internal
internal stress
stress in
in
298
298
Korcak’s
Korcak’s exponent
exponent of
of self-similarity
self-similarity (s),
(s), as
as exponent
exponent
corrosion
corrosion metal
metal products.
products. Besides,
Besides, the
the annual
annual TOW
TOW
299
299
of
of fat
fat fractal
fractal (β)
(β) (Vicsek,
(Vicsek, 1999).
1999).
values
values (4,800
(4,800 hh in
in RU-site
RU-site and
and 8,400
8,400 hh in
in MC
MC one)
one)
300
300
The
The fractal
fractal characteristic
characteristic more
more important
important is
is that
that
have
have very
very different
different distribution
distribution of
of TOW
TOW in
in temperature
temperature
301
301
the
the fractal
fractal has
has aa dd lower
lower dimension
dimension value
value than
than need
need
regions.
regions. In
In the
the RU
RU site
site aa larger
larger percentage
percentage of
of TOW
TOW
302
include
the
the
object.
object. Armin,
However,
However,
there
there is
is
structures
structures
that
that
oto tree
Figure
Figure
4.
4.occurs
Menger
Menger
sponge
sponge
tree
iterations
iterations
with
D302
=include
1.8927,
1.8927,
[Bunde
[Bunde
Armin,
Havlin
Havlin
Shlomo.
Shlomo.
(1995)].
(1995)].
FF =
(54-66%)
(54-66%)
occurs
in
in the
the
20-25
20-25oto
C
C range,
range,
but
but in
in the
thewith
MC
MC D
303
303
D
D
=
=
d,
d,
but
but
show
show
a
a
fractal
fractal
behavior
behavior
[
[
Mandelbrot
Mandelbrot
FF
site
site 64-73%
64-73% of
of TOW
TOW is
is in
in the
the 25-30
25-30ooC.
C.
304
304
Benoit
Benoit B.,
B., (2004)].
(2004)]. In
In these
these cases,
cases, when
when the
the volume
volume
305
305
V(l)
V(l) was
was compute,
compute, usually
usually called
called fat
fat fractal,
fractal, using
using
The
The airborne
airborne salinity
salinity (chlorides)
(chlorides) and
and SO
SO22 were
were
306
306
spheres
spheres the
the decrease
decrease size
size l,l, this
this converge
converge aa finite
finite value
value
monitored
monitored monthly,
monthly, according
according to
to ISO
ISO 9225
9225 (1992),
(1992),
307
307
whit
whit aa exponent
exponent no
no whole.
whole. In
In fat
fat fractal
fractal VV00 =
= V(0),
V(0), but
but
using
using the
the wet
wet candle
candle and
and sulphation
sulphation plate
plate methods,
methods,
308
308
V(l)
V(l) =
= ff(l),
(l), show
show aa power
power law
law with
with aa exponent,
exponent, which
which
respectively.
respectively. The
The MC
MC site
site presents
presents high
high concentration
concentration
309
309
is
is just
just aa rescale
rescale structure
structure value.
value. This
This can
can be
be expressed
expressed
of
of airborne
airborne salinity
salinity (annual
(annual average
average of
of chlorides
chlorides ≈
≈ 362
362
310
310
in
in
Farmer
Farmer
(1986)
(1986)
form
form
in
in
the
the
Eq.
Eq.
(1):
(1):
−2 −1
dd−1),), while
while the
the RU
RU atmosphere
atmosphere salinity
salinity is
is
mg
mg m
m−2
−2 −1
very
very low
low (10.21
(10.21 mg
mg m
m−2
dd−1)) and
and insignificant
insignificant from
from
V(L)
V(L) ≈
≈ VV00 +
+ Al
Alββ
(1)
(1)
the
the point
point of
of view
view of
of corrosive
corrosive attack.
attack. Both
Both test
test sites
sites
present
present low
low and
and very
very low
low annual
annual categories
categories of
of SO
SO22 311
311
where
where AA is
is aa constant
constant and
and ββ is
is an
an exponent
exponent that
that
aggressiveness,
aggressiveness, according
according to
to ISO
ISO 9223
9223 (1992).
(1992).
312
312
quantify
quantify the
the fractal
fractal properties.
properties.
266
266
227
227
of
of
68
44
www.rmiq.org
www.rmiq.org
www.rmiq.org
Figure
3.
Peninsula
(Southeastern
Mexico,
Caribbean
area).
Figure
3. Map
Map of
of Yucatan
Yucatan Peninsula
Peninsula (Southeastern
(SoutheasternMexico,
Mexico,Caribbean
Caribbeanarea).
area).
Figure 3.
Map
of
Yucatan
Veleva
et
al./
Revista
Mexicana
de
Ingenierı́a
Quı́mica
Vol.
12,
No.
1 (2013)
XXX-XXX
Veleva
Revista
Mexicana
Ingenierı́a
Quı́mica
Vol.
No.
1 (2013)
65-72
Veleva
et et
al./al./
Revista
Mexicana
dede
Ingenierı́a
Quı́mica
Vol.
12,12,
No.
(2013)
XXX-XXX
Veleva
et
al./
Revista
Mexicana
de
Ingenierı́a
Quı́mica
Vol.
12,
No.
11(2013)
XXX-XXX
atmosphere
(Fig.
5b)
more
pronounced
than
the
atmosphere(Fig.
(Fig. 5b)
5b)isis
ismore
morepronounced
pronouncedthan
thaninin
inthe
the
atmosphere
rural-urban
test
site
(Fig.
5a),
because
of
the
more
rural-urban
test
site
(Fig.
5a),
because
of
the
more
rural-urban
test
site (Fig.
5a), because
of the
more
accelerated
corrosion
progress,
due
the
very
high
acceleratedcorrosion
corrosionprogress,
progress,due
duetoto
tothe
thevery
veryhigh
high
accelerated
salinity
(chloride)
contamination.
After
6
months
of
salinity
(chloride)
contamination.
After
6
months
of
salinity
(chloride)
contamination.
After
6 months
of
corrosion,
the
pitting
attack
is
more
extended
on
the
corrosion,
the
pitting
attack
is
more
extended
on
the
corrosion,
thethe
pitting
attack
is more
extended
onmetal
the
surface
and
pits
penetrate
deeper
into
the
surface and
andthe
thepits
pitspenetrate
penetratedeeper
deeperinto
intothe
themetal
metal
surface
structure.
However,
the
formed
corrosion
products
structure. However,
However, the
theformed
formedcorrosion
corrosionproducts
products
structure.
also
can
act
as
physical
barrier
between
the
metal
also
can
act
as
physical
barrier
between
the
metal
also
canand
act the
as environment,
physical barrier
between
the fact
metal
surface
and
due
to
this
the
surface
and
the
environment,
and
due
to
this
fact
the
surface and the environment, and due to this fact the
corrosion
progress
goes
slowly.
This
effect
is
observed
corrosionprogress
progressgoes
goesslowly.
slowly.This
Thiseffect
effectisisobserved
observed
corrosion
333
in the
MC
zone,
where
the
corrosion
progress
more
333
theMC
MCzone,
zone,where
wherethe
thecorrosion
corrosionprogress
progressisis
ismore
more
333
ininthe
334
accelerated,
compared
to
that
in
the
RU
one,
and
334
accelerated, compared
comparedtotothat
thatininthe
theRU
RUone,
one,and
and
334
accelerated,
335
the
samples
show
less
pitting
formation
in
9
months,
335 the
thesamples
samplesshow
showless
lesspitting
pittingformation
formationinin9 9months,
months,
335
336
compared
to
that
months,
for
example.
336 compared
comparedto
tothat
thatinin
in666months,
months,for
forexample.
example.
336
337
After
analyzing
all
collected
SEM
images
337
After analyzing
analyzing all
all collected
collected SEM
SEM images
imagesofof
of
337
After
338
pitting
attack,
graphs
presenting
the
frequency
of
338 pitting
pitting attack,
attack, graphs
graphs presenting
presentingthe
thefrequency
frequency
of
338
of
2
339
pitting
events
as
function
their
area
(µc
2 2)) were
Fig.
sponge
iterations
with
D
339 pitting
pittingevents
eventsas
asaaafunction
functionofof
oftheir
theirarea
area(µc
(µc
were
) were
Fig. 4.
4. Menger
sponge to
to tree
tree iterations
iterations with
with D
DFFF ==
= 339
Menger sponge
to
tree
340
constructed,
following
the
methodology
described
1.8927,
[Bunde
Armin,
Havlin
Shlomo.
(1995)].
340 constructed,
constructed,
following
the
methodology
described
340
following
the
methodology
described
1.8927, [Bunde Armin,
Armin, Havlin
Havlin Shlomo.
Shlomo. (1995)].
(1995)].
341
above
in the
experimental
part
of this
study.
The
341
above
the[Bunde
experimental
partHavlin
thisstudy.
study. The
The
Figure
to
tree
iterations
with
D
==1.8927,
1.8927,
Armin,
Shlomo.
(1995)].
341
inin the
experimental
part
ofofthis
Figure 4.
sponge to
to tree
tree iterations
iterationswith
with
DFFabove
1.8927,
[Bunde
Armin,
Havlin
Shlomo.
(1995)].
4. Menger
Menger sponge
sponge
D
=
[Bunde
Armin,
Havlin
Shlomo.
(1995)].
Fgraphs
342
exhibited
a
good
fitting
to
the
power
law,
342 graphs
graphs exhibited
exhibited aa good
good fitting
fittingtotothe
thepower
powerlaw,
law,
342
An
example
for
these
fractals
is
the
Menger
sponge
An example for these
these fractals
fractalsisisthe
theMenger
Mengersponge
sponge 343 therefore can be presented the log-log form of these
343 therefore
thereforecan
canbe
bepresented
presentedthe
thelog-log
log-logform
formofofthese
these
343
(Bunde
shown
in
Fig.
4.
(Bunde and
1991), as
as shown
shown in
in Fig.
Fig. 4.
4.
and Havlin,
Havlin, 1991),
1991),
as
344
graphs
(Fig.
6).
The
graphs
show
only
the
central
part
344 graphs
graphs(Fig.
(Fig.6).
6).The
Thegraphs
graphsshow
showonly
onlythe
thecentral
centralpart
part
344
345
of
the
respective
curves.
For
very
small
pits
there
are
345 of
ofthe
therespective
respectivecurves.
curves.For
Forvery
verysmall
smallpits
pitsthere
thereare
are
345
346
difficulties
with
the
resolution
limit
of
the
images.
On
346 difficulties
difficulties
with
the
resolution
limit
of
the
images.
On
346
with
the
resolution
limit
of
the
images.
On
33 Results
Results and
discussion
and discussion
discussion
347
the
other
hand,
the
frequency
for
very
large
pits
quite
347 the
theother
otherhand,
hand,the
thefrequency
frequencyfor
forvery
verylarge
largepits
pitsisis
isquite
quite
347
348
low,
giving
rise
to
large
statistical
fluctuations.
The
348
348 low,
low, giving
givingrise
risetotolarge
largestatistical
statisticalfluctuations.
fluctuations. The
The
Figures
(5a)-(5b)
present
SEM
images
of
aluminum
Figures (5a)-(5b) present
present SEM
SEM images
images of
of aluminum
aluminum 349
349
accumulated
frequency
had
be
show
in
the
Eq.
(2):
349 accumulated
accumulatedfrequency
frequencyhad
hadbebeshow
showininthe
theEq.
Eq.(2):
(2):
surface
of
samples,
corroded
in
MC
and
RU
surface of samples, corroded
corroded in
in MC
MC and
and RU
RU
environments
exposure
times.
can
number
of
pits
with
area
larger
than
during different
different
environments during
different exposure
exposure times.
times. ItItIt can
can
number
numberof
ofpits
pitswith
witharea
arealarger
largerthan
thanaaa (2)
σ(a)
(2)
σ(a)
(2)
σ(a)==
=
be
pits
formed
in
the
marine
total
area
of
the
sample
that the
the intensity
intensity
of
be seen
seen that
intensity of
of pits
pits formed
formed in
in the
the marine
marine
total
totalarea
areaofofthe
thesample
sample
323
323
323
324
324
324
325
325
325
326
326
326
327
327
327
328
328
328
329
329
329
330
330
330
331
331
331
332
332
332
313
313
313
314
314
314
315
315
315
316
316
316
317
317
317
318
318
318
319
319
319
320
320
320
321
321
321
322
322
322
(a)
(a)
(a)
350
350
350
351
351
351
352
352
352
(b)
(b)
(b)
Fig. 5.
5. SEM
SEM
images
of
(pitting)
formed
surface
after
333and
666months
exposure
Fig.
(pitting)
formed
on
aluminum
surface
after
and
months
exposure
Fig.
5.
SEM5.
images
of localized
localized corrosion
corrosion
(pitting)corrosion
formedon
onaluminum
aluminum
surface
after1,1,
1,
and
monthsofof
of
exposureafter
Figure
SEM
images
of
localized
(pitting)
formed
on
aluminum
surface
Figure
corrosion
(pitting)
formed
on
aluminum
surface
after
and
in
rural-urban
(a)
and
marine-coastal
(b)
tropical
climate.
in
rural-urban
tropical
climate.
Figure
5.
SEM
images
of
localized
corrosion
(pitting)
formed
on
aluminum
surface
after1,1,
1,333and
and666
in rural-urban (a) and marine-coastal (b) tropical climate.
months of
months
(a)
and
marine-coastal
tropical
climate.
months
of exposure
exposure in
in rural-urban
rural-urban (a)
(a) and
andmarine-coastal
marine-coastaltropical
tropicalclimate.
climate.
www.rmiq.org
www.rmiq.org
www.rmiq.org
55
69
5
(b)
(b)
(b)
Figure 5. SEM images of localized corrosion (pitting) formed on aluminum surface after 1, 3 and 6
Figure 5. SEM images of localized corrosion (pitting) formed on aluminum surface after 1, 3 and 6
Figure
images
of localized
corrosion
(pitting)
formed
on climate.
aluminum
surface after 1, 3 and 6
months
of
exposure
in rural-urban
(a)
and marine-coastal
tropical
Veleva
et 5.
al./SEM
Revista
Mexicana
de Ingenierı́a
Vol. 12,
No.
1 (2013)
XXX-XXX
months
in rural-urban
(a) andQuı́mica
marine-coastal
tropical
climate.
Veleva
et of
al./exposure
Revista Mexicana
de Ingenierı́a
Vol. 12, No.
1 (2013)
XXX-XXX
months
exposure
inMexicana
rural-urban
(a) andQuı́mica
marine-coastal
tropical
climate.
Veleva
et
Revista
Ingenierı́a
Quı́mica
Vol.
No.
1 (2013)
65-72
Veleva
et of
al./al./
Revista
Mexicana
dede
Ingenierı́a
Quı́mica
Vol.
12,12,
No.
1 (2013)
XXX-XXX
353
353
353
354
354
354
355
355
355
356
356
356
357
357
357
358
358
358
359
359
359
360
360
360
361
361
361
362
362
362
363
363
363
364
364
364
365
365
365
366
366
366
367
367
367
368
368
368
369
369
369
370
370
370
371
371
371
372
372
372
373
373
373
6
6
70
6
Fig. 6. Log of accumulated frequency of pits vs. Log of their area, observed on corroded surface of aluminum
Fig. 6. Log of accumulated frequency of pits vs. Log of their area, observed on corroded surface of aluminum
Fig. 6. Log
of exposure
accumulated
frequency
of pitsinvs.
Log ofof
their
observed
onmonths,
corroded
surface
aluminum
samples,
after
in different
periods,
urban-rural
(Merida,
9 and
12
from
left of
to right)
and surface of
Figure
6. Log
of accumulated
pitsarea,
vs. 6,
Log
of their
area, observed
corroded
samples, after
exposure
in different
periods, infrequency
urban-rural
9 and
12 months,
from left on
to
right)
and surface of
Figure
6. Log
ofand
accumulated
frequency
of(Merida,
pits
vs. 6,
Log
ofoftheir
area,
observed
on
corroded
samples, after
exposure
in
different
periods,
in
urban-rural
(Merida,
6,
9
and
12
months,
from
left
to
right)
and12surface
marine-coastal
(Progreso
6,
9
12
months,
from
left
to
right)
environments
humid
tropical
climate.
Figure
6.
Log
of
accumulated
frequency
of
pits
vs.
Log
of
their
area,
observed
on
corroded
of
aluminum
after
exposure
in different
periods, in of
urban-rural
(Merida,
9 and
months,
marine-coastal
(Progresosamples,
6, 9 and 12
months,
from left
to right) environments
humid tropical
climate.6,
aluminum
samples,
after
exposure
in
different
periods,
in
urban-rural
(Merida,
6,
9
and
12 months,
marine-coastal
(Progreso
6,
9
and
12
months,
from
left
to
right)
environments
of
humid
tropical
climate.
aluminum
exposure in(Progreso
different 6,
periods,
in months,
urban-rural
6, 9 environments
and 12 months,
from
left tosamples,
right) andafter
marine-coastal
9 and 12
from(Merida,
left to right)
of
from left to right) and marine-coastal (Progreso 6, 9 and 12 months, from left to right) environments of
from left
to right)
and marine-coastal (Progreso 6, 9 and 12 months, from left to right) environments of
humid
tropical
climate.
humidpower
tropical
shows well defined
lawclimate.
scaling and a similarity 374 Conclusions
humid
tropical
climate.
shows well defined power law scaling and a similarity 374 Conclusions
shows
wellthat
defined
to
Eq. (1),
is: power law scaling and a similarity
to Eq. (1), that is:
to Eq. (1), that is:
σ(a) = σ0 a−s
(3)
σ(a) = σ0 a−s
(3)
σ(a) = σ0 a−s
(3)
for any length of exposure, in both environments. Here
for any length of exposure, in both environments. Here
length of of
exposure,
in bothand
environments.
Here
sfor
is any
the exponent
self-similarity
σ is a constant.
s is the exponent of self-similarity and σ00 is a constant.
s is the
exponent σ
of0 self-similarity
σ0 is ausing
constant.
The
parameters
and s can be and
obtained
the
The parameters σ0 and s can be obtained using the
The parameters
and (3):
s can be obtained using the
logarithmic
form σof0 Eq.
logarithmic form of Eq. (3):
logarithmic form of Eq. (3):
log σ(a) = log σ0 − s log a
(4)
log σ(a) = log σ0 − s log a
(4)
log σ(a) = log σ0 − s log a
(4)
The value of σ0 can represent and reflect the corrosive
The value of σ0 can represent and reflect the corrosive
The value ofof
σ test
cansite
represent
reflectofthe
aggressivity
and theand
changes
thecorrosive
density
aggressivity of 0test site and the changes of the density
aggressivity
of test site
and the(see
changes
of The
the density
of
pits with corrosion
progress
Eq. 4).
results
of pits with corrosion progress (see Eq. 4). The results
of pitsthat
withthe
corrosion
(see Eq.
The results
show
values progress
of exponent
of 4).
self-similarity
show that the values of exponent of self-similarity
showbetween
that the1.7
values
of during
exponent
self-similarity
vary
and 1.9
the of
annual
corrosion
vary between 1.7 and 1.9 during the annual corrosion
vary between
1.7 andexposed
1.9 during
corrosion
period
of aluminum
in the
bothannual
test sites,
part
period of aluminum exposed in both test sites, part
period
of aluminum
exposedsome
in both
test for
sites,σ part
of
tropical
humid climate:
values
are
of tropical humid climate: some values for σ are
of tropical
humid
climate:
values
σ are
shown
in Table
1. These
resultssome
indicate
thatfor
σ change
shown in Table 1. These results indicate that σ change
shown in Tableis1.a function
These results
indicate
that corrosion
σ change
(dependency)
of time
of metal
(dependency) is a function of time of metal corrosion
(dependency)
is a functionofofenvironments.
time of metal corrosion
progress
and aggressively
progress and aggressively of environments.
progress and aggressively of environments.
374
375
375
375
376
376
376
377
377
377
378
378
378
379
379
379
380
380
380
381
381
381
382
382
382
383
383
383
384
384
384
385
385
385
386
386
386
387
387
387
388
388
388
389
389
389
390
390
390
391
391
391
392
392
392
393
393
393
394
394
394
395
395
395
396
396
396
397
397
397
398
398
398
Conclusions
The development of pitting has been studied as a
The development of pitting has been studied as a
The development
of pitting
has been
studied
as a
function
of time, making
a statistics
of the
frequency
function of time, making a statistics of the frequency
function
of time,
a statistics
of the
frequency
of
appearance
of making
pits versus
the area
occupied
by
of appearance of pits versus the area occupied by
of appearance
of show
pits versus
thedistribution
area occupied
by
them.
The data
that the
of the
them. The data show that the distribution of the
them.
The adata
show
thethedistribution
of the
pits
follows
power
law.that
Even
corrosion pitting
pits follows a power law. Even the corrosion pitting
pits follows
a power(depending
law. Even the
corrosion
appears
chaotically
of the
anodicpitting
sites
appears chaotically (depending of the anodic sites
appears chaotically
(depending
the anodic
location,
excess of Gibbs
energy,of etc.
factors, sites
the
location, excess of Gibbs energy, etc. factors, the
location,
of Gibbs
energy,
etc. the
factors,
the
nature
of excess
aluminum
obeys all
the time
principal
nature of aluminum obeys all the time the principal
nature of law
aluminum
obeys
the time the
corrosion
- a power
law.allTherefore,
theprincipal
concept
corrosion law - a power law. Therefore, the concept
corrosion
law - a can
power
law. Therefore,
the concept
of
self-similarity
be applied
for the study
of the
of self-similarity can be applied for the study of the
of self-similarity
can be applied
for the
study oftheir
the
phenomenon
of localized
corrosion,
describing
phenomenon of localized corrosion, describing their
phenomenon with
of localized
development
time. corrosion, describing their
development with time.
development
withof
time.
The exponent
self-similarity varies between 1.7
The exponent of self-similarity varies between 1.7
self-similarity
between
1.7
and The
1.9 exponent
and it is of
relatively
stable varies
with the
progress
and 1.9 and it is relatively stable with the progress
andcorrosion
1.9 and itprogress
is relatively
stable with
the progress
of
on aluminum
surface.
The
of corrosion progress on aluminum surface. The
of corrosion
progress
on aluminum
surface.
The
corrosion
progress
is more
accelerated
in marinecorrosion progress is more accelerated in marinecorrosion
progress is
marinecoastal
environment,
duemore
to itsaccelerated
high salinityin(chloride)
coastal environment, due to its high salinity (chloride)
coastal environment,
its high
(chloride)
contamination.
Duedue
totothis
fact salinity
the progress
of
contamination. Due to this fact the progress of
contamination.
to this isfactmore
the pronounced
progress of
pits
in area andDue
frequency
pits in area and frequency is more pronounced
pitstime,
in area
and frequency
more pronounced
in
compared
to pitting isdeveloped
in ruralin time, compared to pitting developed in ruralin time,
compared toThe
pitting
developed
ruralurban
atmosphere.
humid
tropical inclimate
urban atmosphere.
The humid tropical climate
urban atmosphere.
The humid
tropical
induces
accelerated progress
of pitting,
thatclimate
affect
induces accelerated progress of pitting, that affect
induces
accelerated
pitting,
thatof affect
the
aluminum
surfaceprogress
in very ofshort
period
time
the aluminum surface in very short period of time
the aluminum
surface
veryto short
period
time
(months),
extending
the in
attack
the dept
of theofmetal.
(months), extending the attack to the dept of the metal.
(months), extending the attack to the dept of the metal.
Table 1. Coefficients of σ for different time of
Table 1. Coefficients of σ for different time of
Table 1. Coefficients
of σ for different
time of
Aluminum
corrosion progress
and aggressivity
Aluminum corrosion progress and aggressivity
Aluminum
corrosion
and aggressivity
of environment:
Ruralprogress
urban (RU)
and Marine
of environment: Rural urban (RU) and Marine
of environment:
Rurallocated
urban (RU)
and Marine
coastal
(MC) test sites,
in humid
tropical
coastal (MC) test sites, located in humid tropical
coastal (MC) test sites,
located in humid tropical
climate.
climate.
climate.
Exposition
Environment
Exposition
Environment
Exposition
Environment
time
RU σ(µ m−2
)
MC σ(µ m−2
)
−2
time
RU σ(µ m −2)
MC σ(µ m−2
)
399
Acknowledgements
time
RU σ(µ m )
MC σ(µ m−2 )
399
Acknowledgements
3 months
0.0422
0.170
399
Acknowledgements
3 months
0.0422
0.170
months
0.0422
0.170
93 months
0.0259
0.0336
400
The
authors wish to acknowledge Mexican
9 months
0.0259
0.0336
400
The authors wish to acknowledge Mexican
9 months
0.0259
0.0336
12
months
0.0243
0.0289
400
The authors
wish
to support
acknowledge
Mexican
401
CONACYT
for its
financial
of this study
and
12 months
0.0243
0.0289
401
CONACYT for its financial support of this study and
12 months
0.0243
0.0289
401
CONACYT for its financial support of this study and
www.rmiq.org
www.rmiq.org
www.rmiq.org
www.rmiq.org
Veleva
et al./
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de Ingenierı́a
Quı́mica
12, No.
1 (2013)
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et al./
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we also thank Eng. William Cauich for his technical
assistance in SEM images.
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