cuantificación fractal de la corrosión de aluminio por picaduras

$: Cuantificación fractal de la corrosión de aluminio por picaduras$
Revista Mexicana de Ingeniería Química

CONTENIDO

Volumen 8, número 3, 2009 / Volume 8, number 3, 2009

213 Derivation and application of the Stefan-Maxwell equations

(Desarrollo y aplicación de las ecuaciones de Stefan-Maxwell)

Stephen Whitaker

Biotecnología / Biotechnology

245 Modelado de la biodegradación en biorreactores de lodos de hidrocarburos totales del petróleo

intemperizados en suelos y sedimentos

(Biodegradation modeling of sludge bioreactors of total petroleum hydrocarbons weathering in soil

and sediments)

S.A. Medina-Moreno, S. Huerta-Ochoa, C.A. Lucho-Constantino, L. Aguilera-Vázquez, A. Jiménez-

González y M. Gutiérrez-Rojas

259 Crecimiento, sobrevivencia y adaptación de Bifidobacterium infantis a condiciones ácidas

(Growth, survival and adaptation of Bifidobacterium infantis to acidic conditions)

L. Mayorga-Reyes, P. Bustamante-Camilo, A. Gutiérrez-Nava, E. Barranco-Florido y A. Azaola-

Espinosa

265 Statistical approach to optimization of ethanol fermentation by Saccharomyces cerevisiae in the

presence of Valfor® zeolite NaA

(Optimización estadística de la fermentación etanólica de Saccharomyces cerevisiae en presencia de

zeolita Valfor® zeolite NaA)

G. Inei-Shizukawa, H. A. Velasco-Bedrán, G. F. Gutiérrez-López and H. Hernández-Sánchez

Ingeniería de procesos / Process engineering

271 Localización de una planta industrial: Revisión crítica y adecuación de los criterios empleados en

esta decisión

(Plant site selection: Critical review and adequation criteria used in this decision)

J.R. Medina, R.L. Romero y G.A. Pérez

Revista Mexicanade Ingenierıa Quımica

1

Academia Mexicana de Investigacion y Docencia en Ingenierıa Quımica, A.C.

Volumen 12, Numero 1, Abril 2013

ISSN 1665-2738

1Vol. 12, No. 1 (2013) 65-72

FRACTAL QUANTIFICATION OF ALUMINUM PITTING CORROSION INDUCEDBY HUMID TROPICAL CLIMATE

CUANTIFICACION FRACTAL DE LA CORROSION DE ALUMINIO PORPICADURAS INDUCIDA POR EL CLIMA TROPICAL HUMEDO

L. Veleva, A. Garcıa-Gonzalez∗, and G. Perez

Departamento de Fısica Aplicada, Centro de Investigacion y Estudios Avanzados del Instituto PolitecnicoNacional, Unidad-Merida, Antigua carretera Merida-Progreso Km.6, C.P. 97310, Merida, Yucatan, Mexico.

Received 4 of February 2012; Accepted 11 of November 2012

AbstractDuring three annual exposure periods, aluminum samples of wire, used for transmission of high voltage electricity, were exposedat outdoor atmospheric marine-coastal and rural environments, located in the humid tropical climate of Yucatan Peninsula, inthe Mexican gulf. In atmospheric conditions the naturally formed aluminum oxide layer can be destroyed by the presence ofchlorides, causing pitting localized corrosion attack, difficult for evaluation. The concepts of fractal geometry and self-similaritywere used in this study for evaluation of the pitting corrosion as a function of time, making a statistics of the frequency ofappearance of pits versus the area occupied by them. The data showed that the distribution of the pits follows a power law. Theexponent of self-similarity varied between 1.7-1.9 and it is relatively stable with the progress of corrosion progress. The progressof pits in area and frequency is more pronounced in time in the marine-coastal atmosphere, compared to pitting developed inrural- urban one. The concepts of fractal geometry and self-similarity can quantify the extent of localized corrosion with time, asnondestructive form and rapid method.

Keywords: aluminum, fractal quantification, atmospheric corrosion, pitting corrosion, self-similarity.

ResumenDurante tres anos, se expusieron muestras de alambre de aluminio (usadas para el transporte de electricidad de alto voltaje), endos diferentes atmosferas, en una marina-costera y la otra rural-urbana, en el clima tropical humedo de la penınsula de Yucatan,en el golfo de Mexico. En estas condiciones de exposicion, la capa de oxido natural del aluminio puede ser destruida en presenciade cloruros, causando picaduras localizadas por el ataque corrosivo, lo que dificulta su analisis. Los conceptos de geometrıa defractales y auto-similaridad se utilizaron para la evaluacion de la corrosion por picadura en funcion del tiempo, haciendo unaestadıstica de la frecuencia de aparicion de picaduras contra el area superficial ocupada por estas. Los datos muestran que ladistribucion de picaduras sigue una ley de potencias. El exponente de auto-similaridad vario entre 1.7-1.9 y es relativamenteestable con el avance de la corrosion. El aumento del tamano del area de las picaduras y en frecuencia, es mas pronunciadocon el tiempo en la atmosfera marina-costera, en comparacion con la rural-urbana. Los conceptos de geometrıa de fractales yauto-similaridad pueden predecir la extension de la corrosion localizada de aluminio con el tiempo, de una forma no destructivay rapida.

Palabras clave: aluminio, cuantificacion fractal, corrosion atmosferica, corrosion por picadura, auto-similaridad.

1 Introduction

Aluminum is widely used metal for transmission ofhigh voltage electricity and in construction industry.

Thermodynamically it is very active and immediatelycorrodes when is produced (high level of free energyand high negative potential value -1.67 V) (Evans,1965; Szklarska-Smialowska, 1971; Foley, 1986;

∗Corresponding author. E-mail: [email protected]

Publicado por la Academia Mexicana de Investigacion y Docencia en Ingenierıa Quımica A.C. 65

Veleva et al./ Revista Mexicana de Ingenierıa Quımica Vol. 12, No. 1 (2013) 65-72Veleva et al./ Revista Mexicana de Ingenierıa Quımica Vol. 12, No. 1 (2013) XXX-XXX

Table 1. Coefficients of σ for different time of Aluminum corrosion progress and aggressivity of environment: Rural urban (RU) and Marine coastal (MC) test sites, located in humid tropical climate.

Environment Exposition time RU σ (µm-2)

MC σ (µm-2)

3 months 0.0422 0.0170

9 months 0.0259 0.0336

12 months 0.0243 0.0289

Figure 1. Schematic presentation of cross-sections of non uniform (localized) forms of corrosion attacks.

Figure 2. Pourbaix diagram (potential vs pH) for Aluminum in water at 25ºC [Veleva L., Kane R. (2003)].

43

Fig. 1. Pourbaix diagram (potential vs pH) for44

Aluminum in water at 25oC [Veleva L., Kane R.45

(2003)].46



MC σ (µm-2)

3 months 0.0422 0.0170

9 months 0.0259 0.0336

12 months 0.0243 0.0289



47

Fig. 2. Schematic presentation of cross-sections of non48

uniform (localized) forms of corrosion attacks.49

Graedel, 1989; Bockris and Khan, 1994; Wiersma50

and Hebert, 1991; Meakin et al., 1993; Szklarska-51

Smialowska, 1999; Pourbaix, 1974). According to the52

electrochemical Pourbaix Diagram (Fig. 1), aluminum53

could get three possible states known for this metal54

(and its alloys): passivity, immunity and corrosion55

(active state) (Pourbaix, 1974). There is a region of pH56

(from 4 to 9) and electrochemical potentials where the57

metal reach passivity, due to the formation of a very58

thin (transparent), hydrated oxide layer (Al2O3·H2O)59

with a low porosity, well adherent to the metal. The60

passive layer is the reason for aluminum very good61

corrosion resistance when exposed to atmospheric62

conditions, free of chloride ions. However, even63

in non- contaminated atmosphere, when aluminum64

it is in contact with humidity (water), after a long65

exposure time the passive layer can be destroyed and66

corrosion attack appears focused in small and specific67

locations on the metal surface, referred to as corrosion68

pits (up to 100 µm deep) (Fig. 2). This type of69

localized corrosion can be observed on aluminum and70

its alloys (Szklarska-Smialowska, 1971; Foley, 1986;71



Smialowska, 1999; McCafferty, 2003; Burstein et al.,74

2004). It is often induced by the presence of chloride75

ions (for example, airborne salinity in marine-coastal76

environments). The presence of metal impurities (Fe,77

Cu) increases the pitting process in depth and pit78

diameter, which is rate-controlled by the oxygen (O2)79

cathodic reduction on the metal inclusions.80

A variety of atmospheric factors, climatic81

conditions and air-chemical pollutants, determines the82

corrosiveness (i.e. aggressivity) of the atmosphere83

and contributes to the metal corrosion process in84

distinct ways (Evans, 1965; Bockris and Khan,85

1994; Lee and Baker, 1982; ISO 9223:92, 1992;86

Leygraf and Graedel, 2000). Climatic characteristics87

play a key role on the atmospheric electrochemical88

corrosion process and to be able to fully understand89

this corrosion phenomenon, it is very important to90

properly describe the environment that causes metal91

degradation. The most important factors related to the92

climate and its effect on that material are represented93

by a combination of (a) air temperature (T) and94

relative humidity (RH) values, often described as95

the temperature-humidity complex (THC), (b) annual96

values of pluvial precipitation, and (c) time of wetness97

(TOW), during which an electrolyte (moisture) exists98

on the metal surface and corrosion occurs. In recent99

years, the parameter TOW has received special100

attention, since it is the fundamental parameter that101

relates to the time during which the corrosion cell102

(anode-cathode) can operate (ISO 9223:92, 1992;103

Cole et al., 1995; Dean and Reiser, 1995; Veleva et104

al., 1997; Tidblad, 2000; Veleva and Alpuche-Aviles,105

2002; Veleva and Kane, 2003). Based on statistical106

analysis of the T-RH complex, it was previously107

shown that the tropical humid climate presents high108

annual values of TOW, from 4800 h to 8500 h per year,109

respectively for rural-urban and marine-coastal areas110

of Southeaster Mexico. Besides, the TOW occurs in111

temperature range of 20-25oC (Veleva et. al., 1997)112

and both factors contribute to a much accelerated113

corrosion process, especially in the marine coastal114

regions (Veleva and Alpuche-Aviles, 2002; Veleva115

and Kane, 2003; Corvo et al., 1997; Veleva and116

Maldonado, 1998; Santana-Rodriguez et al., 2003).117

The reports note that the humid tropical climate118

is extremely aggressive, according to ISO 9223:92119

(1992), for the widely used standard metals (zinc,120

copper, low carbon steel and aluminum), compared to121

the aggressivity of different temperate climates.122

Corrosion attack by pitting is difficult for123

evaluation. Different types of tests have been124

developed for pitting corrosion (ISO 11463-93, 1993;125

ASTM Guide G46-94, 2005; Kelly, 2005), based126

on physical and chemical methods. The exposures127

2 www.rmiq.org

Veleva et al./ Revista Mexicana de Ingenierıa Quımica Vol. 12, No. 1 (2013) XXX-XXX



MC σ (µm-2)

3 months 0.0422 0.0170

9 months 0.0259 0.0336

12 months 0.0243 0.0289



43

Fig. 1. Pourbaix diagram (potential vs pH) for44

Aluminum in water at 25oC [Veleva L., Kane R.45

(2003)].46



MC σ (µm-2)

3 months 0.0422 0.0170

9 months 0.0259 0.0336

12 months 0.0243 0.0289



47

Fig. 2. Schematic presentation of cross-sections of non48

uniform (localized) forms of corrosion attacks.49



Smialowska, 1999; Pourbaix, 1974). According to the52

electrochemical Pourbaix Diagram (Fig. 1), aluminum53

could get three possible states known for this metal54

(and its alloys): passivity, immunity and corrosion55

(active state) (Pourbaix, 1974). There is a region of pH56

(from 4 to 9) and electrochemical potentials where the57

metal reach passivity, due to the formation of a very58

thin (transparent), hydrated oxide layer (Al2O3·H2O)59

with a low porosity, well adherent to the metal. The60

passive layer is the reason for aluminum very good61

corrosion resistance when exposed to atmospheric62

conditions, free of chloride ions. However, even63

in non- contaminated atmosphere, when aluminum64

it is in contact with humidity (water), after a long65

exposure time the passive layer can be destroyed and66

corrosion attack appears focused in small and specific67

locations on the metal surface, referred to as corrosion68

pits (up to 100 µm deep) (Fig. 2). This type of69

localized corrosion can be observed on aluminum and70

its alloys (Szklarska-Smialowska, 1971; Foley, 1986;71



Smialowska, 1999; McCafferty, 2003; Burstein et al.,74

2004). It is often induced by the presence of chloride75

ions (for example, airborne salinity in marine-coastal76

environments). The presence of metal impurities (Fe,77

Cu) increases the pitting process in depth and pit78

diameter, which is rate-controlled by the oxygen (O2)79

cathodic reduction on the metal inclusions.80

A variety of atmospheric factors, climatic81

conditions and air-chemical pollutants, determines the82

corrosiveness (i.e. aggressivity) of the atmosphere83

and contributes to the metal corrosion process in84

distinct ways (Evans, 1965; Bockris and Khan,85

1994; Lee and Baker, 1982; ISO 9223:92, 1992;86

Leygraf and Graedel, 2000). Climatic characteristics87

play a key role on the atmospheric electrochemical88

corrosion process and to be able to fully understand89

this corrosion phenomenon, it is very important to90

properly describe the environment that causes metal91

degradation. The most important factors related to the92

climate and its effect on that material are represented93

by a combination of (a) air temperature (T) and94

relative humidity (RH) values, often described as95

the temperature-humidity complex (THC), (b) annual96

values of pluvial precipitation, and (c) time of wetness97

(TOW), during which an electrolyte (moisture) exists98

on the metal surface and corrosion occurs. In recent99

years, the parameter TOW has received special100

attention, since it is the fundamental parameter that101

relates to the time during which the corrosion cell102

(anode-cathode) can operate (ISO 9223:92, 1992;103

Cole et al., 1995; Dean and Reiser, 1995; Veleva et104

al., 1997; Tidblad, 2000; Veleva and Alpuche-Aviles,105

2002; Veleva and Kane, 2003). Based on statistical106

analysis of the T-RH complex, it was previously107

shown that the tropical humid climate presents high108

annual values of TOW, from 4800 h to 8500 h per year,109

respectively for rural-urban and marine-coastal areas110

of Southeaster Mexico. Besides, the TOW occurs in111

temperature range of 20-25oC (Veleva et. al., 1997)112

and both factors contribute to a much accelerated113

corrosion process, especially in the marine coastal114

regions (Veleva and Alpuche-Aviles, 2002; Veleva115

and Kane, 2003; Corvo et al., 1997; Veleva and116

Maldonado, 1998; Santana-Rodriguez et al., 2003).117

The reports note that the humid tropical climate118

is extremely aggressive, according to ISO 9223:92119

(1992), for the widely used standard metals (zinc,120

copper, low carbon steel and aluminum), compared to121

the aggressivity of different temperate climates.122

Corrosion attack by pitting is difficult for123

evaluation. Different types of tests have been124

developed for pitting corrosion (ISO 11463-93, 1993;125

ASTM Guide G46-94, 2005; Kelly, 2005), based126

on physical and chemical methods. The exposures127

2 www.rmiq.org66 www.rmiq.org


of coupons to natural environments or solutions that128

simulate service conditions are extremely valuable129

tests, due to their direct applicability. However, mass130

loss measurement, which characterizes the rate of131

uniform metal corrosion, can be extremely misleading132

for pitting localized corrosion. Badly pitted specimens133

can exhibit negligible mass loss if the attack is134

extremely localized. There are several ways in135

which pitting can be described, giving a quantitative136

expression to indicate its significance, to predict the137

life of material. Some of the more commonly used138

methods for examination and evaluation of pitting139

corrosion are described in ISO 1146-93 (1993) and140

ASTM G 46 (1998) (Kelly, 2005), although for most141

cases no single method is sufficient by itself: (a)142

standard rating charts for pits in terms of density, size,143

and depth; (b) metal penetration expressed in terms144

of the maximum pit depth; (c) application of statistics145

to the analysis of corrosion pitting data; (d) loss in146

mechanical properties (tensile strength, elongation,147

fatigue strength, impact resistance and burst pressure),148

if pitting is the predominant form of corrosion and149

the density of pitting is relatively high. It should be150

stressed that some of the mentioned above methods are151

destructive as procedures.152

While prediction of localized penetration rate153

remains a goal of electrochemical testing, recent154

applications of statistics to the corrosion process155

appear promising. Another technique which does not156

appear to have received much attention is the use157

of nondestructive image analysis of corroded metal158

surface morphology. Although the method is more159

time consuming than mass change measurements, this160

one has the potential of allowing the required data161

to be easily gathered and combined with statistical162

analysis of a sufficient number of images (sample163

area), deriving the progress of pit-size distribution in164

corrosion patterns or pitting penetration.165

Nowadays fractal concepts have become166

increasingly popular when trying to quantitatively167

characterize apparently irregular or disordered objects168

(Mandelbrot, 1983; Vicsek, 1989; Gordon et al.,169

2001). Fractal geometry is finding many applications170

in material science. A preliminary account of fractal171

properties of steel corrosion pitting has been reported172

by Costa et al. (1991) and later the authors use173

a Monte Carlo simulation of localized corrosion174

(Reigada et al., 1994). An attempt is made to correlate175

the fractal dimensions of surface profiles measured on176

corroded aluminum specimens immersed in 3% NaCl,177

with results obtained with electrochemical impedance178

spectroscopy (EIS) (Roberge and Trethewey,179

1995). Fractal characterization of two-dimensional180

aluminum foils corrosion fronts (in pH=12, 1M181

NaCl electrolyte), controlled pontentiostatically, was182

reported (Holten et al., 1994). The results show that183

the fronts (at the metal-electrolyte interface) can be184

described in terms of self-affine fractal geometry over185

a significant range of length scales.186

In our study we present the progress of pitting187

corrosion attach on aluminum after exposure to humid188

tropical climate (marine and rural environments)189

during one year, as a function of time, making a190

statistics of the frequency of appearance of pits versus191

the area occupied by them. The degree of corrosion192

damage manifests itself in the severity of corrosion193

and aggressivity of the environment. Since corrosion194

results in texture changes of a metal surface, it changes195

its fractal dimension as well. The concept of fractals196

and self-similarity were applied for the study of the197

phenomena of localized corrosion of aluminum.198

2 Materials and methods199

2.1 Sampling and field exposure200

Wire samples (1 m and 3.1 mm of diameter) of201

electrolytic aluminum (99, 999%), used for electricity202

transmission of high voltage, were prepared as203

open helix specimens (exposed vertically). Their204

surface encompasses all exposure angles and is205

oriented equal1y with respect to al1 wind directions,206

which usual1y determine the principal pollutants (ISO207

9223:92, 1992). Therefore it is recommended that208

preference be given to the comparison of metal209

corrosion rates obtained with open helix specimens210

when exposures are conducted in different climates211

and at different geographical latitudes (ISO 9223:92,212

1992; Veleva and Maldonado, 1998). After exposure213

at tropical climate, the samples where chemically214

treated according to ISO 8407 (1993), removing the215

corrosion products on the aluminum surface.216

2.2 Test site characterization217

During three annual exposure periods, aluminum open218

helix specimens were exposed in accordance with ISO219

9226 (1992) at outdoor atmospheric corrosion in two220

test sites located in the humid tropical climate of221

the Yucatan Peninsula (Southeastern Mexico, in the222

Caribbean area): marine-coastal (MC) environment223

(at Progreso Port, 21o18’N, 89o39’W), 30 m from the224

seashore and a rural-urban (RU) site at Merida, 30 km225

far from the sea (Fig. 3).226

www.rmiq.org 3


of coupons to natural environments or solutions that128

simulate service conditions are extremely valuable129

tests, due to their direct applicability. However, mass130

loss measurement, which characterizes the rate of131

uniform metal corrosion, can be extremely misleading132

for pitting localized corrosion. Badly pitted specimens133

can exhibit negligible mass loss if the attack is134

extremely localized. There are several ways in135

which pitting can be described, giving a quantitative136

expression to indicate its significance, to predict the137

life of material. Some of the more commonly used138

methods for examination and evaluation of pitting139

corrosion are described in ISO 1146-93 (1993) and140

ASTM G 46 (1998) (Kelly, 2005), although for most141

cases no single method is sufficient by itself: (a)142

standard rating charts for pits in terms of density, size,143

and depth; (b) metal penetration expressed in terms144

of the maximum pit depth; (c) application of statistics145

to the analysis of corrosion pitting data; (d) loss in146

mechanical properties (tensile strength, elongation,147

fatigue strength, impact resistance and burst pressure),148

if pitting is the predominant form of corrosion and149

the density of pitting is relatively high. It should be150

stressed that some of the mentioned above methods are151

destructive as procedures.152

While prediction of localized penetration rate153

remains a goal of electrochemical testing, recent154

applications of statistics to the corrosion process155

appear promising. Another technique which does not156

appear to have received much attention is the use157

of nondestructive image analysis of corroded metal158

surface morphology. Although the method is more159

time consuming than mass change measurements, this160

one has the potential of allowing the required data161

to be easily gathered and combined with statistical162

analysis of a sufficient number of images (sample163

area), deriving the progress of pit-size distribution in164

corrosion patterns or pitting penetration.165

Nowadays fractal concepts have become166

increasingly popular when trying to quantitatively167

characterize apparently irregular or disordered objects168

(Mandelbrot, 1983; Vicsek, 1989; Gordon et al.,169

2001). Fractal geometry is finding many applications170

in material science. A preliminary account of fractal171

properties of steel corrosion pitting has been reported172

by Costa et al. (1991) and later the authors use173

a Monte Carlo simulation of localized corrosion174

(Reigada et al., 1994). An attempt is made to correlate175

the fractal dimensions of surface profiles measured on176

corroded aluminum specimens immersed in 3% NaCl,177

with results obtained with electrochemical impedance178

spectroscopy (EIS) (Roberge and Trethewey,179

1995). Fractal characterization of two-dimensional180

aluminum foils corrosion fronts (in pH=12, 1M181

NaCl electrolyte), controlled pontentiostatically, was182

reported (Holten et al., 1994). The results show that183

the fronts (at the metal-electrolyte interface) can be184

described in terms of self-affine fractal geometry over185

a significant range of length scales.186

In our study we present the progress of pitting187

corrosion attach on aluminum after exposure to humid188

tropical climate (marine and rural environments)189

during one year, as a function of time, making a190

statistics of the frequency of appearance of pits versus191

the area occupied by them. The degree of corrosion192

damage manifests itself in the severity of corrosion193

and aggressivity of the environment. Since corrosion194

results in texture changes of a metal surface, it changes195

its fractal dimension as well. The concept of fractals196

and self-similarity were applied for the study of the197

phenomena of localized corrosion of aluminum.198

2 Materials and methods199

2.1 Sampling and field exposure200

Wire samples (1 m and 3.1 mm of diameter) of201

electrolytic aluminum (99, 999%), used for electricity202

transmission of high voltage, were prepared as203

open helix specimens (exposed vertically). Their204

surface encompasses all exposure angles and is205

oriented equal1y with respect to al1 wind directions,206

which usual1y determine the principal pollutants (ISO207

9223:92, 1992). Therefore it is recommended that208

preference be given to the comparison of metal209

corrosion rates obtained with open helix specimens210

when exposures are conducted in different climates211

and at different geographical latitudes (ISO 9223:92,212

1992; Veleva and Maldonado, 1998). After exposure213

at tropical climate, the samples where chemically214

treated according to ISO 8407 (1993), removing the215

corrosion products on the aluminum surface.216

2.2 Test site characterization217

During three annual exposure periods, aluminum open218

helix specimens were exposed in accordance with ISO219

9226 (1992) at outdoor atmospheric corrosion in two220

test sites located in the humid tropical climate of221

the Yucatan Peninsula (Southeastern Mexico, in the222

Caribbean area): marine-coastal (MC) environment223

(at Progreso Port, 21o18’N, 89o39’W), 30 m from the224

seashore and a rural-urban (RU) site at Merida, 30 km225

far from the sea (Fig. 3).226

www.rmiq.org 3www.rmiq.org 67


Figure 3. Map of Yucatan Peninsula (Southeastern Mexico, Caribbean area).

Figure 4. Menger sponge to tree iterations with DF = 1.8927, [Bunde Armin, Havlin Shlomo. (1995)].

227

Fig. 3. Map of Yucatan Peninsula (Southeastern228

Mexico, Caribbean area).229

Periodically, at 1, 3, 6, 9, and 12 months, three230

replicate open helix specimens were evaluated. Time231

of wetness (TOW) values was calculated using a232

statistical analysis of temperature-relative humidity233

(T-RH) complex. Despite the close distance between234

both test sites, the difference in their daily T-RH235

complex makes them interesting to study, because they236

show how variable the tropical climate can be [18].237

For example, the RU zone is hotter that the MC one,238

however, the MC zone is more humid than the RU239

environment, but the MC shows less fluctuation in240

T-RH values during the year. We believe that the241

described differences are due to the influence of the242

permanent thermodynamic buffering effect of the sea243

on T and RH for the MC atmosphere. On RU zones,244

this effect is not present and T and RH show much245

larger fluctuation during the night and day, interrupting246

corrosion process and introducing internal stress in247

corrosion metal products. Besides, the annual TOW248

values (4,800 h in RU-site and 8,400 h in MC one)249

have very different distribution of TOW in temperature250

regions. In the RU site a larger percentage of TOW251

(54-66%) occurs in the 20-25oC range, but in the MC252

site 64-73% of TOW is in the 25-30oC.253

The airborne salinity (chlorides) and SO2 were254

monitored monthly, according to ISO 9225 (1992),255

using the wet candle and sulphation plate methods,256

respectively. The MC site presents high concentration257

of airborne salinity (annual average of chlorides ≈ 362258

mg m−2 d−1), while the RU atmosphere salinity is259

very low (10.21 mg m−2 d−1) and insignificant from260

the point of view of corrosive attack. Both test sites261

present low and very low annual categories of SO2262

aggressiveness, according to ISO 9223 (1992).263

2.3 Fractal quantification of pitting264

corrosion265

A fractal is defined as “a set for which the Hausdorff266

dimension strictly exceeds the topological dimension”267

and is less than the embedding dimension (Vicsek,268

1999; Gordon et al., 2001; Costa et al., 1991;269

Bunde and Havlin, 1991). The fact that the pits270

cover a finite area on the metal surface, give the271

reason to study their distribution using the concept272

of fat fractal (Mandelbrot, 1983; Vicsek, 1999).273

The characterization analysis consists in obtaining274

black and white images of pitted regions on the275

metal surface. This is done in order to obtain276

data on pit density and pit size, during the time of277

corrosion progress, distinguishing the influence of278

atmosphere corrosive aggressively (pollution) of both279

test sites. After elimination of corrosion products,280

33 samples were cut (1 cm of length of wire) from281

helix specimens that have been exposed at different282

period to corrosion in MC and RU test sites. Scanning283

Electron Microscope (SEM), Phillips XL-30 ESEM284

(at 0.3 Torr and work distance of 7.7-12.5 mm), was285

used for morphology analysis of aluminum corroded286

surface.287

The collected 174 images where characterized288

with the Image J program, defining conversion factor289

of pixels to area (µm2) and running the program290

for statistical analysis of pitted areas for one base291

threshold and for thresholds moved to ±5%.292

The cumulative frequency for pit area was293

calculated for each time and site of exposure.294

The analyzed data show power-law decay, whose295

coefficient and exponent can be finding from log-log296

graphs. Therefore, it is clear that we can use the297

Korcak’s exponent of self-similarity (s), as exponent298

of fat fractal (β) (Vicsek, 1999).299

The fractal characteristic more important is that300

the fractal has a d lower dimension value than need301

include the object. However, there is structures that302

DF = d, but show a fractal behavior [ Mandelbrot303

Benoit B., (2004)]. In these cases, when the volume304

V(l) was compute, usually called fat fractal, using305

spheres the decrease size l, this converge a finite value306

whit a exponent no whole. In fat fractal V0 = V(0), but307

V(l) = f (l), show a power law with a exponent, which308

is just a rescale structure value. This can be expressed309

in Farmer (1986) form in the Eq. (1):310

V(L) ≈ V0 + Alβ (1)

where A is a constant and β is an exponent that311

quantify the fractal properties.312

4 www.rmiq.org




227

Fig. 3. Map of Yucatan Peninsula (Southeastern228

Mexico, Caribbean area).229

Periodically, at 1, 3, 6, 9, and 12 months, three230

replicate open helix specimens were evaluated. Time231

of wetness (TOW) values was calculated using a232

statistical analysis of temperature-relative humidity233

(T-RH) complex. Despite the close distance between234

both test sites, the difference in their daily T-RH235

complex makes them interesting to study, because they236

show how variable the tropical climate can be [18].237

For example, the RU zone is hotter that the MC one,238

however, the MC zone is more humid than the RU239

environment, but the MC shows less fluctuation in240

T-RH values during the year. We believe that the241

described differences are due to the influence of the242

permanent thermodynamic buffering effect of the sea243

on T and RH for the MC atmosphere. On RU zones,244

this effect is not present and T and RH show much245

larger fluctuation during the night and day, interrupting246

corrosion process and introducing internal stress in247

corrosion metal products. Besides, the annual TOW248

values (4,800 h in RU-site and 8,400 h in MC one)249

have very different distribution of TOW in temperature250

regions. In the RU site a larger percentage of TOW251

(54-66%) occurs in the 20-25oC range, but in the MC252

site 64-73% of TOW is in the 25-30oC.253

The airborne salinity (chlorides) and SO2 were254

monitored monthly, according to ISO 9225 (1992),255

using the wet candle and sulphation plate methods,256

respectively. The MC site presents high concentration257

of airborne salinity (annual average of chlorides ≈ 362258

mg m−2 d−1), while the RU atmosphere salinity is259

very low (10.21 mg m−2 d−1) and insignificant from260

the point of view of corrosive attack. Both test sites261

present low and very low annual categories of SO2262

aggressiveness, according to ISO 9223 (1992).263

2.3 Fractal quantification of pitting264

corrosion265

A fractal is defined as “a set for which the Hausdorff266

dimension strictly exceeds the topological dimension”267

and is less than the embedding dimension (Vicsek,268

1999; Gordon et al., 2001; Costa et al., 1991;269

Bunde and Havlin, 1991). The fact that the pits270

cover a finite area on the metal surface, give the271

reason to study their distribution using the concept272

of fat fractal (Mandelbrot, 1983; Vicsek, 1999).273

The characterization analysis consists in obtaining274

black and white images of pitted regions on the275

metal surface. This is done in order to obtain276

data on pit density and pit size, during the time of277

corrosion progress, distinguishing the influence of278

atmosphere corrosive aggressively (pollution) of both279

test sites. After elimination of corrosion products,280

33 samples were cut (1 cm of length of wire) from281

helix specimens that have been exposed at different282

period to corrosion in MC and RU test sites. Scanning283

Electron Microscope (SEM), Phillips XL-30 ESEM284

(at 0.3 Torr and work distance of 7.7-12.5 mm), was285

used for morphology analysis of aluminum corroded286

surface.287

The collected 174 images where characterized288

with the Image J program, defining conversion factor289

of pixels to area (µm2) and running the program290

for statistical analysis of pitted areas for one base291

threshold and for thresholds moved to ±5%.292

The cumulative frequency for pit area was293

calculated for each time and site of exposure.294

The analyzed data show power-law decay, whose295

coefficient and exponent can be finding from log-log296

graphs. Therefore, it is clear that we can use the297

Korcak’s exponent of self-similarity (s), as exponent298

of fat fractal (β) (Vicsek, 1999).299

The fractal characteristic more important is that300

the fractal has a d lower dimension value than need301

include the object. However, there is structures that302

DF = d, but show a fractal behavior [ Mandelbrot303

Benoit B., (2004)]. In these cases, when the volume304

V(l) was compute, usually called fat fractal, using305

spheres the decrease size l, this converge a finite value306

whit a exponent no whole. In fat fractal V0 = V(0), but307

V(l) = f (l), show a power law with a exponent, which308

is just a rescale structure value. This can be expressed309

in Farmer (1986) form in the Eq. (1):310

V(L) ≈ V0 + Alβ (1)

where A is a constant and β is an exponent that311

quantify the fractal properties.312





313

Fig. 4. Menger sponge to tree iterations with DF =314

1.8927, [Bunde Armin, Havlin Shlomo. (1995)].315

An example for these fractals is the Menger sponge316

(Bunde and Havlin, 1991), as shown in Fig. 4.317

3 Results and discussion318

Figures (5a)-(5b) present SEM images of aluminum319

surface of samples, corroded in MC and RU320

environments during different exposure times. It can321

be seen that the intensity of pits formed in the marine322

atmosphere (Fig. 5b) is more pronounced than in the323

rural-urban test site (Fig. 5a), because of the more324

accelerated corrosion progress, due to the very high325

salinity (chloride) contamination. After 6 months of326

corrosion, the pitting attack is more extended on the327

surface and the pits penetrate deeper into the metal328

structure. However, the formed corrosion products329

also can act as physical barrier between the metal330

surface and the environment, and due to this fact the331

corrosion progress goes slowly. This effect is observed332

in the MC zone, where the corrosion progress is more333

accelerated, compared to that in the RU one, and334

the samples show less pitting formation in 9 months,335

compared to that in 6 months, for example.336

After analyzing all collected SEM images of337

pitting attack, graphs presenting the frequency of338

pitting events as a function of their area (µc2) were339

constructed, following the methodology described340

above in the experimental part of this study. The341

graphs exhibited a good fitting to the power law,342

therefore can be presented the log-log form of these343

graphs (Fig. 6). The graphs show only the central part344

of the respective curves. For very small pits there are345

difficulties with the resolution limit of the images. On346

the other hand, the frequency for very large pits is quite347

low, giving rise to large statistical fluctuations. The348

accumulated frequency had be show in the Eq. (2):349

σ(a) =number of pits with area larger than a

total area of the sample(2)

(a)

(b) Figure 5. SEM images of localized corrosion (pitting) formed on aluminum surface after 1, 3 and 6 months of exposure in rural-urban (a) and marine-coastal tropical climate.

Figure 6. Log of accumulated frequency of pits vs. Log of their area, observed on corroded surface of aluminum samples, after exposure in different periods, in urban-rural (Merida, 6, 9 and 12 months, from left to right) and marine-coastal (Progreso 6, 9 and 12 months, from left to right) environments of humid tropical climate.

350

Fig. 5. SEM images of localized corrosion (pitting) formed on aluminum surface after 1, 3 and 6 months of exposure351

in rural-urban (a) and marine-coastal (b) tropical climate.352

www.rmiq.org 5




313







































(a)



350



www.rmiq.org 5




313







































(a)



350





(a)



353

Fig. 6. Log of accumulated frequency of pits vs. Log of their area, observed on corroded surface of aluminum354

samples, after exposure in different periods, in urban-rural (Merida, 6, 9 and 12 months, from left to right) and355

marine-coastal (Progreso 6, 9 and 12 months, from left to right) environments of humid tropical climate.356

shows well defined power law scaling and a similarity357

to Eq. (1), that is:358

σ(a) = σ0a−s (3)

for any length of exposure, in both environments. Here359

s is the exponent of self-similarity andσ0 is a constant.360

The parameters σ0 and s can be obtained using the361

logarithmic form of Eq. (3):362

logσ(a) = logσ0 − s log a (4)

The value of σ0 can represent and reflect the corrosive363

aggressivity of test site and the changes of the density364

of pits with corrosion progress (see Eq. 4). The results365

show that the values of exponent of self-similarity366

vary between 1.7 and 1.9 during the annual corrosion367

period of aluminum exposed in both test sites, part368

of tropical humid climate: some values for σ are369

shown in Table 1. These results indicate that σ change370

(dependency) is a function of time of metal corrosion371

progress and aggressively of environments.372

Table 1. Coefficients of σ for different time ofAluminum corrosion progress and aggressivityof environment: Rural urban (RU) and Marine

coastal (MC) test sites, located in humid tropicalclimate.

Exposition Environmenttime RU σ(µ m−2) MC σ(µ m−2)

3 months 0.0422 0.1709 months 0.0259 0.033612 months 0.0243 0.0289

373

Conclusions374

The development of pitting has been studied as a375

function of time, making a statistics of the frequency376

of appearance of pits versus the area occupied by377

them. The data show that the distribution of the378

pits follows a power law. Even the corrosion pitting379

appears chaotically (depending of the anodic sites380

location, excess of Gibbs energy, etc. factors, the381

nature of aluminum obeys all the time the principal382

corrosion law - a power law. Therefore, the concept383

of self-similarity can be applied for the study of the384

phenomenon of localized corrosion, describing their385

development with time.386

The exponent of self-similarity varies between 1.7387

and 1.9 and it is relatively stable with the progress388

of corrosion progress on aluminum surface. The389

corrosion progress is more accelerated in marine-390

coastal environment, due to its high salinity (chloride)391

contamination. Due to this fact the progress of392

pits in area and frequency is more pronounced393

in time, compared to pitting developed in rural-394

urban atmosphere. The humid tropical climate395

induces accelerated progress of pitting, that affect396

the aluminum surface in very short period of time397

(months), extending the attack to the dept of the metal.398

Acknowledgements399

The authors wish to acknowledge Mexican400

CONACYT for its financial support of this study and401

6 www.rmiq.org


(a)



353






σ(a) = σ0a−s (3)




















373

Conclusions374

























Acknowledgements399



6 www.rmiq.org


(a)



353






σ(a) = σ0a−s (3)




















373

Conclusions374

























Acknowledgements399





we also thank Eng. William Cauich for his technical402

assistance in SEM images.403

References404

40ISO 9225-92. (1992). Corrosion of metals405

and alloys, Corrosivity of atmospheres,406

Measurement of Pollution. ISO Int., Geneva.407

ASTM Guide G46-94. (2005). ‘Standard guide408

for examination and evaluation of pitting409

corrosion’. West Conshohoken. PA, ASTM Int.410

Bockris, J. O’M. and Khan S. U. M. (1994). Surface411

Electrochemistry: A Molecular Level Approach.412

Plenum Press, London.413

Bunde A. and Havlin S. Eds. (1995). Fractals and414

Disordered Systems. Springer. Second revised415

and Enlarged Edition.416

Burstein G.T., Liu C., Souto R.M. and Vines S.P.417

(2004). Origins of pitting corrosion. Corrosion418

Engineering, Science and Technology 39, 25-30.419

Cole I.S., Holgate R., Kao P. and Ganther W. (1995).420

The rate of drying of moisture from a metal421

surface and its implication for time of wetness.422

Corrosion Science 37, 455-465.423

Corvo F., Haces C., Betancourt N., Maldonado L.,424

Veleva L., Echeverria M., Rincon O. and Rincon425

A. (1997). Atmospheric corrosivity in the426

Caribbean area. Corrosion Science 39, 823-833.427

Costa J.M., Sagues F. and Vilarrasa M. (1991).428

Fractal patterns from corrosion pitting.429


Dean S.W. and Reiser D.B. (1995). In: Atmospheric431

Corrosion, (W. W. Kirk and H. H. Lawson Eds.),432

Pp. 3-10. ASTM STP 1239, ASTM Int. West433

Conshohocken, PA.434

Evans U. (1965). Electrochemical mechanism for435

atmospheric rusting. Nature 206, 980-982.436

Foley R.T. (1986). Localized Corrosion of437

Aluminum Alloys - a Review. Corrosion 42, 5,438

227-286.439

Gordon N.L., Rood W. and Edney R. (2001).440

Introducing Fractal Geometry. Appignanesi,441

Ed. Icon Books Ltd. Cambridge, UK.442

Graedel T.E. (1989). Corrosion mechanism for443

aluminum exposed to the atmosphere. Journal444

of The Electrochemical Society 136, 204C-445

211C.446

Holten T., Jossang T., Meakin P. and Feder J. (1994).447

Fractal characterization of two-dimensional448

aluminum corrosion fronts. Physical Review E449

50, 754-759.450

ISO 11463-93. (1993). Corrosion of metals and451

alloys, Evaluation of pitting corrosion. ISO Int.452

Geneva.453


alloys, Removal of corrosion products from455

corrosion test specimens. ISO Int. Geneva.456

ISO 9223:92. (1992). Corrosion of Metals457

and Alloys. Corrosivity of Atmospheres -458

Classification. ISO Int. Geneva.459


alloys, Corrosivity of atmospheres, Method461

of determination of corrosion rate of standard462

specimens for the evaluation of corrosivity. ISO463

Int. Geneva.464

Kelly R.G. (2005). Corrosion Tests and Standards,465

Application and Interpretation. In: ASTM Int.,466

(R. Baboian Ed.) 2nd Ed. Pp. 211-220. West467

Conshohoken, PA.468

Lee T.S., Baker E.A. (1982). Atmospheric Corrosion469

of Metals. In: ASTM STP 767, ASTM Int. (S.470

W. Dean Jr. and E. C. Rhea Eds.). Pp. 250-266.471

West Conshohocken, PA.472

Leygraf C., Graedel T. (2000). Atmospheric473

Corrosion. Wiley-Interscience. Pennington,474

NY.475

Mandelbrot B. B. (1983). The Geometry of Nature.476

W. H. Freeman and Company. New York.477

Mandelbrot B. B. (2004). The Fractal Geometry of478

nature, W. H. Freeman and Company New York.479

McCafferty E. (2003). Sequence of steps in the480

pitting of aluminum by chloride ions. Corrosion481

Science 45, 1421-1438.482

Meakin P., Jossand T. and Feder J. (1993). Simple483

passivation and depassivation model for pitting484

corrosion. Physical Review E 48, 2906-2916.485

www.rmiq.org 7


we also thank Eng. William Cauich for his technical402

assistance in SEM images.403

References404

40ISO 9225-92. (1992). Corrosion of metals405

and alloys, Corrosivity of atmospheres,406

Measurement of Pollution. ISO Int., Geneva.407

ASTM Guide G46-94. (2005). ‘Standard guide408

for examination and evaluation of pitting409

corrosion’. West Conshohoken. PA, ASTM Int.410

Bockris, J. O’M. and Khan S. U. M. (1994). Surface411

Electrochemistry: A Molecular Level Approach.412

Plenum Press, London.413

Bunde A. and Havlin S. Eds. (1995). Fractals and414

Disordered Systems. Springer. Second revised415

and Enlarged Edition.416

Burstein G.T., Liu C., Souto R.M. and Vines S.P.417

(2004). Origins of pitting corrosion. Corrosion418

Engineering, Science and Technology 39, 25-30.419

Cole I.S., Holgate R., Kao P. and Ganther W. (1995).420

The rate of drying of moisture from a metal421

surface and its implication for time of wetness.422


Corvo F., Haces C., Betancourt N., Maldonado L.,424

Veleva L., Echeverria M., Rincon O. and Rincon425

A. (1997). Atmospheric corrosivity in the426

Caribbean area. Corrosion Science 39, 823-833.427

Costa J.M., Sagues F. and Vilarrasa M. (1991).428

Fractal patterns from corrosion pitting.429


Dean S.W. and Reiser D.B. (1995). In: Atmospheric431

Corrosion, (W. W. Kirk and H. H. Lawson Eds.),432

Pp. 3-10. ASTM STP 1239, ASTM Int. West433

Conshohocken, PA.434

Evans U. (1965). Electrochemical mechanism for435

atmospheric rusting. Nature 206, 980-982.436

Foley R.T. (1986). Localized Corrosion of437

Aluminum Alloys - a Review. Corrosion 42, 5,438

227-286.439

Gordon N.L., Rood W. and Edney R. (2001).440

Introducing Fractal Geometry. Appignanesi,441

Ed. Icon Books Ltd. Cambridge, UK.442

Graedel T.E. (1989). Corrosion mechanism for443

aluminum exposed to the atmosphere. Journal444

of The Electrochemical Society 136, 204C-445

211C.446

Holten T., Jossang T., Meakin P. and Feder J. (1994).447

Fractal characterization of two-dimensional448

aluminum corrosion fronts. Physical Review E449

50, 754-759.450


alloys, Evaluation of pitting corrosion. ISO Int.452

Geneva.453


alloys, Removal of corrosion products from455

corrosion test specimens. ISO Int. Geneva.456

ISO 9223:92. (1992). Corrosion of Metals457

and Alloys. Corrosivity of Atmospheres -458

Classification. ISO Int. Geneva.459


alloys, Corrosivity of atmospheres, Method461

of determination of corrosion rate of standard462

specimens for the evaluation of corrosivity. ISO463

Int. Geneva.464

Kelly R.G. (2005). Corrosion Tests and Standards,465

Application and Interpretation. In: ASTM Int.,466

(R. Baboian Ed.) 2nd Ed. Pp. 211-220. West467

Conshohoken, PA.468

Lee T.S., Baker E.A. (1982). Atmospheric Corrosion469

of Metals. In: ASTM STP 767, ASTM Int. (S.470

W. Dean Jr. and E. C. Rhea Eds.). Pp. 250-266.471

West Conshohocken, PA.472

Leygraf C., Graedel T. (2000). Atmospheric473

Corrosion. Wiley-Interscience. Pennington,474

NY.475

Mandelbrot B. B. (1983). The Geometry of Nature.476

W. H. Freeman and Company. New York.477

Mandelbrot B. B. (2004). The Fractal Geometry of478

nature, W. H. Freeman and Company New York.479

McCafferty E. (2003). Sequence of steps in the480

pitting of aluminum by chloride ions. Corrosion481

Science 45, 1421-1438.482

Meakin P., Jossand T. and Feder J. (1993). Simple483

passivation and depassivation model for pitting484

corrosion. Physical Review E 48, 2906-2916.485



Pourbaix M. (1974). Atlas of Electrochemical486

Equilibria in Aqueous Solutions. NACE487

Cebelcor. Houston, Tx.488

Reigada R., Sagues F. and Costa J.M. (1994).489

A Monte-Carlo Simulation of Localized490

Corrosion. Journal of Chemical Physics 101,491

2329-2337.492

Roberge P.R. and Trethewey K.R. (1995). The fractal493

dimension of corroded aluminium surfaces.494

Journal of Applied Electrochemistry 25, 962-495

966.496

Santana-Rodriguez J. J., Santana-Hernandez F. J. and497

Gonzalez-Gonzalez J.E. (2003). The effect of498

environmental and meteorological variables on499

atmospheric corrosion of carbon steel, copper,500

inc and aluminium in a limited geographic zone501

with different types of environment. Corrosion502

Science 45, 799-815.503

Shreir L.L., Jarman R.A., Burstein G.T. Eds. (1994).504

Metal/Environment reactions. In: Corrosion,505

Vol.1, 3rd Edition. Butterworth-Heinemann,506

Oxford, UK.507

Syrett B.C., Gorman J.A., Arey M.L., Koch G.H. and508

Jacobson G.A. (2002). Cost of corrosion in the509

Electric Power Industry. Materials Performance510

41, 8-22.511

Szklarska-Smialowska Z. (1999). Pitting corrosion512

of aluminum. Corrosion Science 41, 1743-513

1767.514

Szklarska-Smialowska Z. (1971). Effect of the ratio515

of Cl−/SO2−4 in solution on the pitting corrosion516

of Ni. Corrosion Science 11, 209-221.517

Tidblad J., Mikhailov A.A. and Kucera V. (2000).518

Model for the prediction of the time of519

wetness from average annual data on relative520

air humidity and air temperature. Protection of521

Metals 36, 533-540.522

Veleva L., Perez G. and Acosta M. (1997). Statistical523

analysis of the temperature-humidity complex524

and time of wetness of a tropical climate in525

the Yucatan Peninsula in Mexico. Atmospheric526

Environment 31, 773-776.527

Veleva L., Maldonado L. (1998). Classification of528

the atmosphere corrosivity in the humid tropical529

climate. British Corrosion Journal 33, 53-57.530

Veleva L. and Alpuche-Aviles M.A. (2002). Outdoor531

Atmospheric Corrosion. In: H. E. Townsend532

Ed. ASTM STP 1421. ASTM Int. West533

Conshohocken, PA, Pp. 48-58.534

Veleva L., Kane R. (2003). Atmospheric Corrosion:535

Fundamentals, Testing and Protection. In:536

Corrosion Vol.13A . Fundamentals, Testing537

and Protection (S.D. Cramer and B.S. Covinio538

Eds.). ASM Int. OH, Pp. 196-209.539

Vicsek T. (1999). Fractal Growth phenomena. World540

Scientific Publishing Co. Pte. Ltd. Singapore.541

Wiersma B. J., Hebert K.R. (1991). Observations542

of the early stages of the pitting corrosion543

of aluminum. Journal of the Electrochemical544

Society 138, 48-54.545

8 www.rmiq.org


Pourbaix M. (1974). Atlas of Electrochemical486

Equilibria in Aqueous Solutions. NACE487

Cebelcor. Houston, Tx.488

Reigada R., Sagues F. and Costa J.M. (1994).489

A Monte-Carlo Simulation of Localized490

Corrosion. Journal of Chemical Physics 101,491

2329-2337.492

Roberge P.R. and Trethewey K.R. (1995). The fractal493

dimension of corroded aluminium surfaces.494

Journal of Applied Electrochemistry 25, 962-495

966.496

Santana-Rodriguez J. J., Santana-Hernandez F. J. and497

Gonzalez-Gonzalez J.E. (2003). The effect of498

environmental and meteorological variables on499

atmospheric corrosion of carbon steel, copper,500

inc and aluminium in a limited geographic zone501

with different types of environment. Corrosion502

Science 45, 799-815.503

Shreir L.L., Jarman R.A., Burstein G.T. Eds. (1994).504

Metal/Environment reactions. In: Corrosion,505

Vol.1, 3rd Edition. Butterworth-Heinemann,506

Oxford, UK.507

Syrett B.C., Gorman J.A., Arey M.L., Koch G.H. and508

Jacobson G.A. (2002). Cost of corrosion in the509

Electric Power Industry. Materials Performance510

41, 8-22.511

Szklarska-Smialowska Z. (1999). Pitting corrosion512

of aluminum. Corrosion Science 41, 1743-513

1767.514

Szklarska-Smialowska Z. (1971). Effect of the ratio515

of Cl−/SO2−4 in solution on the pitting corrosion516

of Ni. Corrosion Science 11, 209-221.517

Tidblad J., Mikhailov A.A. and Kucera V. (2000).518

Model for the prediction of the time of519

wetness from average annual data on relative520

air humidity and air temperature. Protection of521

Metals 36, 533-540.522

Veleva L., Perez G. and Acosta M. (1997). Statistical523

analysis of the temperature-humidity complex524

and time of wetness of a tropical climate in525

the Yucatan Peninsula in Mexico. Atmospheric526

Environment 31, 773-776.527

Veleva L., Maldonado L. (1998). Classification of528

the atmosphere corrosivity in the humid tropical529

climate. British Corrosion Journal 33, 53-57.530

Veleva L. and Alpuche-Aviles M.A. (2002). Outdoor531

Atmospheric Corrosion. In: H. E. Townsend532

Ed. ASTM STP 1421. ASTM Int. West533

Conshohocken, PA, Pp. 48-58.534

Veleva L., Kane R. (2003). Atmospheric Corrosion:535

Fundamentals, Testing and Protection. In:536

Corrosion Vol.13A . Fundamentals, Testing537

and Protection (S.D. Cramer and B.S. Covinio538

Eds.). ASM Int. OH, Pp. 196-209.539

Vicsek T. (1999). Fractal Growth phenomena. World540

Scientific Publishing Co. Pte. Ltd. Singapore.541

Wiersma B. J., Hebert K.R. (1991). Observations542

of the early stages of the pitting corrosion543

of aluminum. Journal of the Electrochemical544

Society 138, 48-54.545


cuantificación fractal de la corrosión de aluminio por picaduras

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