Residual Ultimate Buckling Strength of Steel Stiffened Panels Subjected

RESIDUAL ULTIMATE BUCKLING STRENGTH OF STEEL STIFFENED PANELS SUBJECTED

TO CORROSION DAMAGE

A Thesis Presented to The Graduate Faculty of The University of Akron

In Partial Fulfillment Of the Requirements for the Degree Master of Science

Elijah Fox May, 2017

RESIDUAL ULTIMATE BUCKLING STRENGTH OF STEEL STIFFENED PANELS SUBJECTED

TO CORROSION DAMAGE

Elijah Fox

Thesis

Approved: Accepted:

Advisor Department Chair Dr. Anil Patnaik Dr. Wieslaw K. Binienda

Committee Member Interim Dean of the College Dr. Craig Menzemer Dr. Donald J. Visco

Committee Member Dean of the Graduate School Dr. Ping Yi Dr. Chand Midha

Date

ACKNOWLEDGEMENTS

I would like to thank my mother, Janice, and my siblings, Kivie and Nakita. Without

my families support over all of these years, I would not have been able to complete my degree. My mother has always been strong and has taught me so many fundamentals which

I live by; I just want to thank her for making me the man I am today. My family has always

been so supportive, loving, and has done anything they could to help me succeed and because

of this, I am forever grateful.

I owe a special thank you to my amazing life partner, Marisa. She has been in my life

since my first day of college and I would not have been able to make it without her love and

support throughout these years. She is still by my side through all of the trials and

tribulations life has thrown at me over the past seven years and words could not express

how appreciative I am of all of her help.

Lastly, I would like to thank Dr. Anil Patnaik for the opportunity to pursue my

master’s degree at The University of Akron. Over the last few years, his help and guidance

has been invaluable and I will forever be appreciative for that. Dr. Patnaik has allowed me to explore worlds beyond structural engineering and has allowed me to broaden my knowledge beyond my focus of study. In addition, I would like to thank all of my colleagues at The

University of Akron who have helped me over the process of my research.

ABSTRACT

Corrosion is a naturally occurring electro-chemical process that causes damage in the form of surface material deterioration on metal structures. In many industries, particularly naval ships, it is common to assess the corrosion damage of structural components primarily based on visual inspection with limited or no structural stress analysis. Premature replacement of such components can prove expensive over time while delayed replacement of these components might be a safety concern. The overall goal in the assessment of remaining life is to relate thickness loss in the system to the performance of individual structural elements in order to better predict the remaining life of the structure. This methodology will be applied to some of the structural steel configurations that are of importance in naval applications. Corrosion damages on naval ships are mainly categorized as: uniform (general) corrosion, pitting corrosion, non-uniform, and grooving corrosion.

This proposed study will investigate the effects of various intensities of uniform corrosion on the remaining ultimate buckling strength of stiffened panel under combined loading.

While visual inspection of uniform (general) corrosion may be used industry wide, without qualitative research to support the quantitative data collected during visual inspection, this technique can prove un-reliable. This is due to the inability to accurately measure the thickness loss of the corroded surface. The objective of this study is to understand the relationship between increased levels of uniform corrosion and the decrease in remaining ultimate buckling strength of stiffened panel while being subjected to combined axial compression and lateral pressure. As a continuing effort to understand the various other forms of corrosion, we are tasked with developing a method to produce pitting and grooving

4 corrosion in a laboratory setting. In order to achieve this objective, a series of finite element analysis (FEA) models are conducted for stiffened panels subjected to combined loading with and without uniform corrosion damage. The FEA software package called ABAQUS is used to conduct these analyses. ASTM A572 grade 50 structural steel is the material used for the experimental testing and FEA models. Accelerated corrosion was performed on fabricated stiffened panels using the B117 method outlined in American Society for Testing and

Materials (ASTM). The non-corroded and corroded stiffened panel specimens are mechanically tested under axial compression and the result are compared with the FEA results and industry guidelines. The FEA results and the experimental panel test data will provide a basis for developing a preliminary method to predict the remaining ultimate buckling strength of stiffened panels exposed to uniform corrosion under combined loading conditions. Based on the correlation between increased corrosion damage and the load of ultimate strength, the goal of this researched is to also act as a precursor to future works and help aid in the development of a visual inspection rating tool supported by qualitative data and/or modify preexisting design codes to include corrosion damage.

Table of Contents

CHAPTER 1. INTRODUCTION ...... 14 1.1 Problem Statement ...... 15 1.2 Objectives ...... 17

CHAPTER 2. CORROSION BACKGROUND RESEARCH ...... 19 2.1 Corrosion Definition and Chemistry ...... 19 2.2 Types of Corrosion ...... 24 2.2.1 Uniform (General) Corrosion ...... 24 2.2.2 Non-Uniform (Localized) Corrosion ...... 27 2.2.3 Pitting Corrosion ...... 28 2.2.4 Grooving Corrosion ...... 29 2.2.5 Galvanic Corrosion ...... 30 2.3 Effects of Corrosion on Steel Structures and Members ...... 32 2.4 Inspection and Controlling Corrosion Damage ...... 35 2.4.1 Inspections ...... 35 2.4.2 Visual Rating System ...... 39 2.5.3 Corrosion Prevention and Mitigation Methods ...... 41

CHAPTER 3. LITERATURE REVIEW ...... 48 3.1 Structural Steel ...... 48 3.2 Stiffened Panels ...... 50 3.2.1 Stiffener ...... 55 3.3 Basic Ship Hull Structures ...... 56 3.4 Load Distribution ...... 58 3.5 Stiffened Panel Failure Mode ...... 61 3.6 Factors that Affect the Ultimate Buckling Strength ...... 67 3.7 Stiffened Panel Finite Element Analysis (FEA) modeling...... 72 3.8 Design Equation ...... 74

CHAPTER 4. UNIFORM CORROSION PROCEDURE FOR STIFFENED PANEL ...... 79 4.1 Introduction ...... 79 4.2 ATSM B117 Laboratory Corrosion Test ...... 80 4.2.1 Salt Solution Preparation ...... 82 4.3 Test Specimen Cleaning Preparation ...... 83 4.4 Determining Environmental Corrosion Rate ...... 84 4.4.1 Corrosion Rate ...... 88 4.5 Stiffened Panel Test Specimen ...... 90 4.6 ASTM B117 Procedure ...... 93

4.7 Post corrosion cleaning ...... 98 4.8 Mechanical Testing ...... 102 4.9 Methods to Produce Grooving and Pitting Corrosion ...... 106

CHAPTER 5. UNIFORM CORROSION ON STIFFENED PANEL FINITE ELEMENT MODEL ...... 113 5.1 Introduction ...... 113 5.2 Material and Geometry ...... 114 5.2.1 Corrosion Geometry ...... 116 5.3 Element type and Meshing ...... 118 5.4 Boundary Conditions and Load Arrangement ...... 119 5.5 Imperfections...... 122 5.6 Non-linear Post-Buckling Analysis ...... 122

CHAPTER 6. RESULTS AND DISCUSSION ...... 125 6.1 Introduction ...... 125 6.2 Non-Corroded Stiffened Panel Control Samples ...... 126 6.2.1 Non-Corroded Stiffened Panel Control Samples Discussion ...... 127 6.3 Corroded Stiffened Panel Control Samples ...... 128 6.3.1 Discussion of the Corroded Stiffened Panel Control Samples ...... 142 6.4 Stiffened Panels Under Combined In-plane Compression and Lateral Loading ...... 142 6.4.1 Combined Loading Discussion ...... 145 6.5 Pitting and Grooving Corrosion Labortory Production Results ...... 146 6.5.1 Pitting and Grooving Corrosion Labortory Production Discussion ...... 153

CHAPTER 7. CONCLUSION ...... 154 7.1 Other Conclusions ...... 155

CHAPTER 8. FURTURE CONTINUING WORKS ...... 156

CHAPTER 9. REFERENCES ...... 15

7 Table of Figures

Figure 1: (a) shows the steel life cycle, and (b) is a diagram of a simplified corrosion process. [8] ...... 21 Figure 2: Effect of pH on the Corrosion Rate of Iron in Water [9]...... 23 Figure 3: Uniform Thickness Loss Model [11] ...... 25 Figure 4: Pitting intensity diagrams (a) DOP=10%; (b) DOP=20%; (c) DOP=30%; (d) DOP=50% [16] ...... 29 Figure 5: The grooving corrosion mechanism [67] ...... 30 Figure 6: galvanic corrosion around a screw connection [68] ...... 32 Figure 7: Assumptions about remaining strength and recommended course of action to need to accompany the visual rating guide [25]...... 40 Figure 8: Cross-section through a typical hot-dip galvanized coating [28] ...... 43 Figure 9: Cross-section through a thermally sprayed aluminum coating [28] ...... 44 Figure 10: (a) simple ICCP system and (b) is a simple SCP system [29] ...... 46 Figure 11: Conventional vs True Stress-Strain Curve for Steel [31] ...... 49 Figure 12: typical stiffened panel section with a flange ...... 51 Figure 13: Typical stiffened panel arrangement in ship hull structures...... 52 Figure 14: Uniaxial (longitudinal) stiffened panel ...... 53 Figure 15: Orthogonal stiffened panel ...... 53 Figure 16: Stiffened Panel terminology [35] ...... 54 Figure 17: Nomenclature for a stiffened plate structure [36] ...... 55 Figure 18: Illustrates the typical stiffener types ...... 56 Figure 19: Basic construction of a ship hull [37] ...... 57 Figure 20: Illustration of a ship bulkhead [39] ...... 58 Figure 21: Diagram of a ship hull subjected the (1) sagging and (2) hogging [40]...... 59 Figure 22: (a) Model I. Overall buckling of the plating and stiffeners as a unit ...... 62 Figure 23: (b) Model II. Yielding at plate edges between the stiffeners due to transverse compression ...... 62 Figure 24: (c) Model III. Yielding at the plate-stiffener combination (Beam-column type collapse) at mid-span ...... 63

Figure 25: (d) Model IV. Local buckling of the stiffener web ...... 63 Figure 26: (e) Model V. Lateral-torsional buckling (or “tripping”) of the stiffeners ...... 64 Figure 27: Failure modes of stiffened plates [43]...... 67 Figure 28: Sectional view of the experimental setup...... 68 Figure 29: Distribution of the corrosion pits...... 69 Figure 30: Deformation and the stress distribution mid-surface at the ultimate state...... 70 Figure 31: ABAQUS model for three-bay grillages ...... 72

Figure 32: (a) Details of the Test Rig (b) Cross Section View ((i) Section X1-X1 and (ii)

Section X2-X2) [32]...... 74 Figure 33: The (a) front and (b) inside view of the test chamber used to induce accelerated corrosion on all A572 test speicmens...... 81 Figure 34: The AutoCAD draft rendering (a) and actually (b) ASTM E8 test specimens...... 85 Figure 35: (a) The corrosion by-product build-up after 2 weeks of exposure on the un-clean dog-bone specimens, (b) the condition after two of the dog-bones are cleaned, while the remaining two are left un-clean, (c) the corrosion build-up after 7 weeks of exposure on the un-clean dog-bone specimens, (d) this is the condition after two of the dog-bone are clean, while the remaining two are left un-clean...... 87 Figure 36: Corrosion rate of specimen #1 and specimen #4 over the duration of the corrosion process...... 90 Figure 37: (a) an AutoCAD draft of the idealized steel stiffened panel, and (b) the actual experimental steel stiffened panel...... 91 Figure 38: (a) Show the overview of the fabricated A572 Gr. 50 test stiffened panels, and (b) provides a profile view of the stiffener and welded connection to the plate element. ... 94 Figure 39: 24-hour cycle of ASTM B117 salt spray ...... 95 Figure 40: Weekly cleaning of stiffened panel test speciman after 90 days of exposure to the ASTM B117 inside the enviromental chamber. (a) the intial state of corrosion on the test specimans immediatly after stopping the enviromental chamber,(b) the specimans are rinsed with de-ionzed water, (c) followed by a light scrubing of the entire surface on the test specimans with an nylon brush and re-rinsed with de-ionzed water...... 98 Figure 41: Shows the stiffened panel sample before the cleaning process at various viewpoints...... 100

Figure 42: The stiffened panel sample after the cleaning process at various viewpoints. .. 101 Figure 43: axial compression mechanical testing load set-up ...... 104 Figure 44: prototype combined loading load set-up...... 106 Figure 45: Sample placement in the corrosion chamber ...... 107 Figure 46: Shows the three arrangement in which the coating was applied. In the above figures, the surface preparation for the samples is arranged as sand blasted (left) and wet- polish (right) surface preparation. The figures are described as follows; (a) pitting corrosion using small pieces of adhesive, (b) grooving corrosion, and (c) pitting corrosion using a small tool...... 110 Figure 47: Rectangle specimens after the 12-week corrosion process. (a) Shows the samples that were wet-polished to remove the mill-scale, (b) samples that were sandblasted to remove mill-scale...... 112 Figure 48: Auto CAD rendering of typical cross-sectional details of one of the test panels. *the purple dotted line represents the neutral axis for each component of the stiffened panel...... 116 Figure 49: Uniform Thickness Loss Model [11]...... 118 Figure 50: shows the boundary conditions of the stiffened panel model...... 121 Figure 51: Load Displacement Diagram comparing the results from the mechanical testing and the FEAs...... 126 Figure 52: Load displacement diagram for the mechanically tested corroded samples ..... 128 Figure 53: Load displacement diagram for the FEAs on the corroded samples ...... 129 Figure 54: (a) Load displacement diagram for corroded Sample A – comparing the FEA results to the mechanically tested results...... 130 Figure 55: (a) FEA predicted failure shape for Sample A ...... 131 Figure 56: (a) Shows the failure behavior of Sample A during mechanical testing from various prospectives...... 132 Figure 54: (b) Load displacement diagram for corroded Sample B – comparing the FEA results to the mechanically tested results...... 133 Figure 55: (b) FEA predicted failure shape for Sample B ...... 133 Figure 56: (b) Shows the failure behavior of Sample B during mechanical testing from various prospectives...... 134

Figure 54: (c) Load displacement diagram for corroded Sample C – comparing the FEA results to the mechanical test results...... 135 Figure 55: (c) FEA predicted failure shape for Sample C ...... 135 Figure 56: (c) Shows the failure behavior of Sample C during mechanical testing from various prospectives...... 136 Figure 54: (d) Load displacement diagram for corroded Sample A5 – comparing the FEA results to the mechanically tested results...... 137 Figure 55: (d) FEA predicted failure shape for Sample A5 ...... 137 Figure 56: (d) Shows the failure behavior of Sample A5 during mechanical testing from various prospectives...... 138 Figure 54: (e) Load displacement diagram for corroded Sample B5 – comparing the FEA results to the mechanically tested results...... 139 Figure 55: (e) FEA predicted failure shape for Sample B5 ...... 139 Figure 56: (e) Shows the failure behavior of Sample B5 during mechanical testing from various prospectives...... 140 Figure 57: Residual Ultimate Strength Comparison ...... 141 Figure 58: Shows the relationship bewteen axial loading and lateral loading on stiffened panels subjected to various degrees of corrosion...... 143 Figure 59: Shows the residual ultimate capacity of the independent loading axis for increased degrees of uniform corrosion...... 144 Figure 60: Residual Ultimate Strength Capacity under combined loading...... 145 Figure 61: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface...... 147 Figure 62: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface...... 148 Figure 63: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface...... 149 Figure 64: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface...... 150 Figure 65: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface...... 151

Figure 66: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface...... 152

Table of Tables

Table 1: Average Values for Corrosion Parameters A and B, for Carbon and Weathering Steel ...... 26 Table 2: Values of K for use in the ASTM corrosion rate equation ...... 89 Table 3: Geometric Properties of Stiffened Panel ...... 92 Table 4: Experimental stiffened panels’ thickness and mass loss data ...... 94 Table 5: Chemical cleaning procedure for removal of corrosion products ...... 101 Table 6: Input for material properties in ABAQUS* ...... 115 Table 7: Experimental stiffened panels’ thickness and mass loss data ...... 117 Table 8: Mechanical Testing Results and Predicted Results from FEA, API and ABS design codes ...... 127 Table 9: Shows the percent error of the the predicted values compared to the mechanical testing...... 127 Table 10: Mechanically tested stiffened panel results ...... 129 Table 11: FEAs stiffened panel results...... 129 Table 12: Remaining axial capacity results and percentage error...... 141 Table 13: Residual Ultimate Capacity with respect to independent axis...... 144

CHAPTER 1

INTRODUCTION

Damage from corrosion is widely considered the most common problem facing steel structures. The National Association of Corrosion Engineer (NACE) International [1] estimates that in the U.S, approximately $276 billion is spent annually on corrosion related damages and repairs. Due to the chemical make-up of steel, corrosion is more aggressive on steel structures in the presence of electrolytes such as offshore structures and ship structures. The damage from corrosion may result as increased local stress, change in geometric properties, and/or the reduction in member cross section properties such as section modulus or increase in slenderness ratio [2]. The risk of failure and residual strength a corroded member has depends on the type of corrosion and the environment in which a structure is exposed to. The reduction in cross sectional properties due to the thickness loss on the steel structural members will result in a reduction in the load carrying capacity of the member [5].

To reduce to financial and safety impact of corrosion damage, a greater knowledge of the different forms of corrosion and their effect of steel structures is needed. The lack of understanding regarding the effects of corrosion damage particularly on ship hull and bulkhead structures has had major finical and safety impact. In 2002, the U.S Navy contracted the production of a new small surface vessel, ideal for close to shore operations. The ship named USS Independence (LCS 2) and it suffered extensive corrosion damage less than a

14 year after being built. The Navy also discovered another ship, the USS Freedom suffering major corrosion damage, which led to a crack through its hull [3]. The corrosion damage resulted in extensive repairs and led to changes in maintenance procedures for similar ship types.

In order to assess the damage from corrosion, visual inspection is a widely used method. Visual inspection on steel structures suffering from corrosion damage can be categorized based on level of deterioration. Members that fall in the severest categories are subject to design checks using section properties based on the measured section size [4].

Although this procedure is useful for categorizing the type of corrosion damage on steel structures and the members affected by corrosion damage, it does not include the critical properties to accurately assess remaining strength. The preliminary solution is to replace the damaged structural component or the entire structure itself. But premature replacement of ship components (or other steel structure) can prove to be expensive and takes an immense amount of time for larger structure repairs. These procedures can be problematic since they usually are not specific to the form of corrosion damage. Hence, the need of a procedure supported by qualitative data or a more accurate methods for evaluating the residual load capacity of corroded steel structures is needed.

1.1 Problem Statement

Steel is one of the most used construction material due to its high strength to weight ratio, but the chemical make-up is highly susceptible to corrosion damage. Corrosion can be defined as the gradual degradation of a metal due to chemical or electrochemical reactions with its environment. As the level of corrosion increases, the load carrying capacity

15 decreases. This decrease will eventually lead to failure of the steel structure. Corrosion damages on ship structures is a major issue; in the U.S, there is an estimation of 3.15 billion dollars spent annually on corrosion related damages and repairs [6]. To combat this problem, visual inspections are used to assess the damage and the overall effectiveness. This method, while simple and quick, is not effective as it cannot accurately determine residual load capacity. The ships structure which is typically effected by corrosion is the bulkhead areas, which is made up of a system of stiffened panel members. Although stiffened panels are attacked by various forms of corrosion, they are most commonly effected by uniform corrosion.

Since stiffened panel members are used to make up the bulkhead and hull itself, they usually are subject to combined loading. Numerous researchers have developed methods to predict the residual strength in corroded stiffened panels through means of mathematical and analytical methods but few presented the result in a manner to aid in visual inspections.

The purpose of this research is to investigate the effects of various levels of uniform corrosion on the remaining ultimate buckling strength of steel stiffened panels made from

ASTM A572 steel, which is a commonly used high-strength steel. The panels will be analyzed under combined axial compression loading and lateral pressure with appropriate boundary conditions. In order to accomplish the objective of this research, a series of non-linear finite element analyses using ABAQUS was performed along with experimental testing. The experimental test specimens are mechanically tested under axially only compression. The percent error when comparing the FEA result to the experimental result will be used to validate the modeling technique used for the stiffened plates under combined loads. As an additional form of validating the results obtained in specific potions of this research,

16 analytical calculations based on American Bureau of Shipping (ABS) and American

Petroleum Institute (API) guidelines will be used. These methods will be discussed in further detail later in this thesis.

1.2 Objectives

Many studies have investigated the effect of corroded and un-corroded stiffened panels under combined loaded, but few detail the correlation between various degrees of general corrosion damage and the remaining buckling strength. Furthermore, corrosion damage that occurs on steel structures is commonly accessed based on visual inspection, using a numerical rating systems that are not supported using qualitative data to approximate the remaining strength or failure type. While this may be effective for structures that are not susceptible to rapid corrosion, for structures such as naval ships, this may not be the case. Pitting and grooving corrosion are other forms of corrosion that warrant further investigation but producing these forms of corrosion to a specific limit in a laboratory setting is difficult.

The primary objectives of this research is as follow:

1. Develop a greater understanding of the correlation between the effects of various degrees of uniform corrosion damage on stiffened panels under combined axial compression and lateral pressure.

2. Develop a load setup that truly represents the loading conditions a stiffened panel experiences under normal operation.

3. Use percent error between axial compression, mechanical testing, and FEAs to verify

modeling techniques for combined loading FEA of stiffened plates.

4. Produce a FEA model capable of predicting the remaining ultimate buckling

strength of steel stiffened panels under combined loading subjected to various

degrees of uniform corrosion damage.

5. Create a technique capable of producing pitting corrosion and grooving corrosion

in a laboratory setting.

6. Using the results obtained in the research, aid in the future development of a quantitative rating system for evaluation of the remaining ultimate bucking strength of steel stiffened panels under combined loading,

7. Based on the results obtained in this research, aid in the modification of preexisting industry design codes to incorporate corrosion damage.

CHAPTER 2

CORROSION BACKGROUND RESEARCH

2.1 Corrosion Definition and Chemistry

Corrosion may be defined as the electrochemical reaction that causes the degradation

of a material. This electrochemical reaction occurs in the presence of water, oxygen, and ions.

The process of corrosion is a time dependent, meaning the longer the exposure time, the

more corrosion will occur.

Steel is an alloy composed primarily of iron and a small percentage of carbon. Due to

its composition, iron is not chemically stable and wants to return to a stable state. Chemical

stability is achieved through an oxidation reduction reaction or ‘redox’ reaction. In the case

of the corrosion of steel, the iron in the steel readily “oxidizes”, or gives off negatively charged

electrons and positively charged iron ions. Then, oxygen in the water picks up the electrons

to form negatively charged hydroxyl ions. The positively charged iron ions combine with the

negative hydroxyl ions to form the corrosion product iron oxide, which is commonly known as “rust”. Figure 1 (a) shows the steel corrosion cycle as metal is the transformed from metal to it oxide through the electrochemical reaction. The chemical reaction equation can be shown in the following steps:

Oxidation of Iron:

Fe(s)  Fe2+ + 2e-

Reduction of Oxygen:

O2 + 4e- +4H+  2H2O

(H20 contains H+ and OH- ions)

Then, combination of iron and hydroxide ions:

Fe2+ + 2OH-  Fe(OH)2 (dries to become rust) Fe(OH)3 [7]

Corrosion Ore (Rust)

Enviroment (water, salt, Steel wet/dry cycle)

(a)*arrows indicate flow of process

(b)

Figure 1: (a) shows the steel life cycle, and (b) is a diagram of a simplified corrosion process. [8]

When exposed to a corrosive environment, the loss of steel material will occur over

time. This loss of material over time is called the “corrosion rate”. Corrosions rate is

expressed in various units; in./year, mm/year, mils per year or g/m2h are among the most common units used. Among many other factors, the rate of corrosion can also be affected by environmental effects such as temperature and humidity. High temperature will cause an increases in the rate of corrosion. In regions/areas where water is plentiful and/or humidity is high, the corrosion rate is higher compared to regions with average or below average precipitation. The amount of exposure a structure receives is important in assessing corrosion on a single structure. Regions/areas exposed to wind or sun that can dry quickly are less prone to corrosion than areas where water can remain in contact with the metalwork

21 for extended periods of time. This is evident especially in the bulk head on naval ships, where, due to the compact geometry of stiffened panels, stagnant standing water is common.

Locations where the electrolyte oxygen concentration is low (such as stagnant standing water) are anodic and prone to corrosion, an example of this is shown in figure 1 (b). The condition shown in figure 1 (b), is known as a “corrosion cell”. When oxygen concentration in an electrolyte determine the anode and cathode location, the process is considered an oxygen cell. Concentration of salt and other ions play a role in the corrosion rate. Higher concentrations of salts can increase corrosion rates significantly because of this, structures in coastal areas or naval vessels will corrode faster than structures not exposed to salt.

Studies have shown corrosion rates around 2.75 times higher due to the exposure of salts.

Finally, what may be the most over looked factor is the pH. The pH of the solution that the steel is exposed to will have a critical effect on the rate at with electrons can be exchanged. As shown in figure xx, the pH at either extreme of the pH scale with have a significant impact on the rate of corrosion. In the range of pH 4 to pH 10, the corrosion rate is relatively independent of the pH of the solution. In this pH range, the corrosion rate is governed by the rate at which oxygen reacts with absorbed atomic hydrogen, thereby depolarizing the surface and allowing the reduction reaction to continue. When the pH values are below 4.0, ferrous oxide (FeO) is soluble and therefore, the oxide dissolves as it is formed rather than depositing on the metal surface. Ferrous oxide trends to act as a protective film, but since it dissolves the metal surface it is in direct contact with the acid solution, and the corrosion reaction proceeds at a greater rate. When the pH values are almost above 10, the corrosion rate falls as pH is increased. This is due to an increase in the rate of the reaction of oxygen with Fe(OH)2 in the oxide layer to form a protective film

(Fe2O3) [9]. The results shown in Figure 2 are based on the effects of temperature and pH

on an iron surface. Since steel is composed primarily of iron, the results shown in the figures

can at least give an idea of the effect on steel.

Figure 2: Effect of pH on the Corrosion Rate of Iron in Water [9].

The rate of corrosion on steel in not constant, and fluctuate over the duration of

exposure to a corrosive environment. The behavior of corrosion rate can be describe in three

phases; (1) no corrosion, (2) corrosion accelerating, and (3) corrosion decelerating [10]. The

new or un-damage (from corrosion) structural member is represented by phase (1). Phase

(2) describe when the surface of new or un-damage steel members are left unprotected, the

initial corrosion rate is high due to minimum hindrance on the corrosion process. However,

as the corrosion product builds up the corrosion rate decrease, this behavior explains phase

(3).

2.2 Types of Corrosion

There are many types of corrosion that may affect metal materials. Common types of corrosion that affect steel structures include the following; uniform corrosion (known as general surface corrosion), pitting corrosion, galvanic corrosion, crevice corrosion and stress corrosion cracking. There are many protective systems in place to prevent the occurrence of these various forms of corrosion, but due to the ever increasing service life of steel structures, corrosion is an inevitable result. Although some corrosion formed, such as uniform corrosion, can be identified visually, others like stress corrosion cracking can prove to be difficult to identify and understand the severity of the corrosion.

In this study, although the main form of corrosion being studied focuses on uniform corrosion, other forms of corrosion such as pitting corrosion, galvanic corrosion, and grooving corrosion will be discussed. These are the common forms of corrosion that affect marine structures and naval ship structural members such as; beams, columns, hull, decking, and bulkheads. In the following sections, these forms of corrosion will be briefly discussed.

The discussion will include the formation of the corrosion, the frequency of observation, and a visual representation of the corresponding form of corrosion.

2.2.1 Uniform (General) Corrosion

Uniform corrosion (or general corrosion) is the most prevalent form of corrosion.

This form of corrosion attacks steel structures by general/overall surface material loss which eventually leads to gradual thinning of steel members. This type of corrosion accounts for the largest percentage of corrosion damage affecting steel structures. Due to the nature of the corrosion process, it is regarded as one of the easiest forms of corrosion to identify

without needing any special equipment. Since the loss of material occurs uniformly overall

(figure 3), the corrosion rate is also considered to be uniform. Since uniform corrosion is

easy to identify with the naked eye, it is considered to be the least dangerous form of

corrosion.

Figure 3: Uniform Thickness Loss Model [11]

Where,

TN= as-new thickness of flange

tN= as as-new thickness of web

B= flange width

D = depth of section

A ships structural components (such as bulkheads, hulls and decks) are typically constructed of steel stiffened panels which are generally exposed to corrosive environments throughout the life span of the structure. Due to the highly corrosion environment, it becomes imperative for the design and evaluation of marine infrastructure be done on a

continuous basis. A study was recently released that introduces a probabilistic model of

corrosion as a function of time for general corrosion [12-13]

From an article by Komp, M. E. [14], it is shown that the uniform corrosion can be

expressed as a function of time. The expression for the corrosion loss is linear equation is

represented as:

C = AtB

Where, C is the average corrosion penetration (in microns), t is the time in number of years and both A and B are parameters determined from the regression analysis of experimental data. A study by Albrecht and Naeemi [15] summarized the test results for both parameters

A and B (shown in table 1) for carbon and weathering steel.

Table 1: Average Values for Corrosion Parameters A and B, for Carbon and Weathering Steel

Environment Carbon Steel Weathering Steel

A B A B

Rural 34.0 0.65 33.3 0.5

Urban 80.2 0.59 50.7 0.57

Marine 70.6 0.79 40.2 0.56

2.2.2 Non-Uniform (Localized) Corrosion

When corrosion damage occurs on a limited or small portion of a steel structural

member, this is characterized as non-uniform (or localized) corrosion. This type of corrosion usually occurs at steel beam ends or the edges of stiffened panels. This form of corrosion

usually causes thinning of web/flange sections which lead to irregular pitting/holes. There

is another form of corrosion known as edge corrosion, which causes material loss along the

edge of a steel member. Edge corrosion is can also be seen as a form of non-uniform

corrosion.

Since deterioration of material only occurs on a limited section of the member, this

can cause stress concentration and localized buckling, which leads to overall strength

reduction in a stiffened panel. Those factors could critically affect the overall buckling

behavior and redistribution of stress in a steel member. The effect of localized deterioration

on the overall behavior of a steel member will depend on the type of member and the

location, nature, and severity of the corrosion. A local reduction in strength does not

necessarily mean that the overall strength of a member will share the same. For example,

localized corrosion on the plate element of a stiffened panel will have less of an effect on

residual buckling strength than localized corrosion that occurs on the web or flange element.

This is due to these elements having a higher concentration of compression stresses.

Extensive deterioration of a stiffened panel can affect the behavior of a bulkhead structure

as a whole. It can affect the load distribution characteristics of the structure and reduce the

load carrying capacity of the deteriorated member overall.

2.2.3 Pitting Corrosion

Pitting corrosion can be regarded as another form of non-uniform corrosion, but is unique in the manner in which is attacks the steel members. Pitting corrosion is characterized as a form of corrosion that cause material loss by creating deep, but small diameter holes in the surface of a steel member. Flaws in corrosion inhabiting coatings (or protective paint systems), deposits of foreign material, and fluids that contain abrasive material are ideal conditions for pitting corrosion to take place. Cracking due to stress concentration is the result of extensive pitting corrosion, leading to structural failure. Just like uniform corrosion, pitting corrosion can also be easily identifiable be the naked eye.

Unlike uniform corrosion, the severity of pitting corrosion is not as easy to determine because the loss of material is based on the depth and concentration of the pits, which is difficult to accurately measure. The severity of pitting corrosion in defined as the ratio of the pitted surface area to the original plate surface area. This ratio is called the degree of pitting

(DOP) and is shown in figure 4. Pits can form in many different shapes and sizes. Although shallow/small pits are not likely to immediately affect the structural integrity of the member, they can act as a point of stress concentration and cracks [16]. The form of cracking is a corrosion mechanism call stress corrosion cracking (SCC).

Figure 4: Pitting intensity diagrams (a) DOP=10%; (b) DOP=20%; (c) DOP=30%; (d) DOP=50% [16]

2.2.4 Grooving Corrosion

Stiffened panels and other steel members that have compact geometry that allow

water to collect are usually subjected to pitting corrosion and grooving corrosion. Grooving

corrosion affects the area near the welding of two plates. This form of corrosion is usually

caused by one of the following: extensive buildup of corrosive solution in the corners of the

web/flange section, improper welding techniques, or when welding of dissimilar materials

occur. Figure 5 shows the grooving corrosion mechanism and how it affects the stiffened panels. As shown below, this form of corrosion causes material loss around the welding area.

The length of the area were material loss occurs is called the groove breadth.

Figure 5: The grooving corrosion mechanism [67]

Grooving corrosion is regarded as another form of localized corrosion commonly found in confined locations where water is allow to collect for an extended period of time

[67]. When steel material is removed around the web/flange section, the overall bucking behavior of a stiffened panel is changed. This can cause localized web tipping or localized flange buckling, while global bucking of the stiffened panel is the ideal buckling behavior.

The severity of the corrosion is determined by length (and width) of the groove breadth.

When excessive deterioration is present, this will prevent the proper distribution of stresses and led to sudden failure of an overall member. Just as pitting corrosion and non-uniform corrosion, grooving corrosion and its severity is easy to identify with the naked eye.

2.2.5 Galvanic Corrosion

Galvanic corrosion refers to corrosion damage that occurs due to the difference in

electric potentials between dissimilar metals. When these dissimilar metals are in contact

30 with each other in the presence of an electrolyte (such as salt water), a galvanic couple is formed due to the flow of electrons. When a galvanic couple forms, one of the metals in the couple becomes the anode and corrodes faster than it would by itself, while the other becomes the cathode and corrodes slower than it would alone, figure 6 provides a clear example of this effect. The intensity of corrosion depends on the difference in potential between the metals and also on the ratio of the exposed area. This is an important factor to be taken into consideration when dealing with coupling of dissimilar metals such as titanium, aluminum and steel.

This problem is common in bridge structures in places such as structural connections

(where the gusset plates and bearing meet), handrail-support connections, and electrical conduits which are in contact with steel. In order to mediate this problem, American Society of Metals (ASM) have provided data of the material potential on commonly used metals. The table provides useful guidance with respect to selecting metals to be joined so that the coupled metals have minimal galvanic interaction. Unlike the other forms of corrosion discussed so far, galvanic corrosion also has a beneficial applications too. There are application where paints that contain zinc is painted on a steel surface to minimize corrosion.

Zinc (which is a less resistant metal) will be sacrificed in the corrosion process while the surface of the steel remains corrosion free, this process is known as galvanization [17]. As with the other forms of corrosion, galvanic corrosion can be easily identified visually.

Figure 6: galvanic corrosion around a screw connection [68]

2.3 Effects of Corrosion on Steel Structures and Members

The overall effect of corrosion on steel structures and members is loss of material

from the outer exposed surface of the steel member. As stated previously, corrosion attacks

steel members in a variety of ways, but they all lead to the loss of material. The loss of

material causes a reduction in the cross-section area which leads to a reduction in strength of the material. This is especially problematic for steel stiffened panels because their primary benefit is having a high strength to minimum weight ratio. Along with cross sectional area, sectional properties such as surface area, moment of inertia etc. are also affected due to the loss of material. The loss of material and the reduction in strength of structural members can have severe consequences in terms of finance, safety, and convenience. According to the U.S

Department of Defense, an estimated 7.36 billion U.S dollars is spent annually on corrosion maintenance on four main categories that are effected by corrosion; aviation, ships, ground vehicles and facilities [71]. Of the four primary categories, corrosion maintenance on the

ships makes up the large percentage at 43.5% or 3.2 billion U.S dollars [69]. Along with the

many consequences, the reduction of member cross section area is critical when it comes to

general corrosion due to this form of corrosion attacks a member approximately equal

overall. This effect of general corrosion has been studied for many decades. A study

conducted by S. Sultana el al. [70] investigated the effects of corrosion on steel plates’

ultimate compressive strength. They concluded that corrosion damage causes reduction in

cross sectional area and leads to an increase in the slenderness ratio. The change to the

slenderness ratio also caused a change in mode failure.

Unlike some forms of corrosion (such as general, groove, and galvanic), the severity

of pitting corrosion is more difficult to determine based on visual inspection alone. Over the

past decade, many studies have been conducted to determine to severity of damage to

remaining strength ratio. The effects of pitting corrosion on the reduction of strength and its

increase deformability on marine structural components has been studied by Nakai et al. and

Sumi [18][19]. Both of the studies found the degree of pitting (DOP) the critical factor in the

reduction of strength. A publication by Paik and Lee [20] studied the ultimate buckling strength of ship panels with pitting corrosion under axial compression loads. They used finite element software named ANSYS, and they concluded that plates subjected to small amounts of pitting showed no significant decrease in strength but larger amount of pitting had an adverse effect on strength due material volume loss. Studies carried out by Paik et al.

[20][21], produced an empirical formula derived to predict the ultimate compressive strength and shear strength of plates exposed to pitting corrosion. The study investigated the effects of pitting corrosion on steel plates subjected to in-plane shear and axial

compression using the ANSYS nonlinear finite element analyses software for plate elements.

Corrosion on steel structures that use rivet connections such as offshore structures and naval ships is extremely problematic. One largely overlooked factor that corrosion effects on naval ships and offshore structural is the effect of rust on steel members that have been connected using rivets. In riveted construction, one of the key areas of vulnerability is the plate seam corroding. This presents a common problem for ship shell plate elements such as ship outer haul and bulkheads subjected to moist conditions. The joints between these plates cannot be completely sealed from moisture. Even if the shell plates are caulked, moisture will not be completely absent from the joint. Overtime, corrosion will occur in the plate joints were moisture is present. The corrosion in the joint will result in the riveted plates being pushed apart due to the expanding rust scale. The action of the plates being pushed apart causes extreme force on the rivets and this causes shearing of rivets or even pulling the heads though the plate. Diagnosing this problem can be an issue for visual inspection due to it is often difficult to determine whether the rivets are still attached or not.

In some cases, removing the rust scale from the joint and sealing off the joint is done but this method is usually ineffective and a waste of time. The most effective method is to completely remove the old rivets, clean out and coat the seams of the plates and re-rivet the joint.

Although this method has proved to be very effective, it is also costly and time consuming.

When corrosion damage is not monitored correctly and material degradation goes unchecked, repairs and replacement are generally much more finically demanding and time consuming.

2.4 Inspection and Controlling Corrosion Damage

The effect of corrosion damage on steel structures have been thoroughly discussed over the course of the chapter. Failure to properly access corrosion damage maybe result in catastrophic failure. Due to this vital aspect of corrosion damages, inspection for corrosion is conducted annually, semi-annually or in some events even multiple times a year.

Depending on the length in between inspections, various forms of inspection may be carried out. Along with inspections, additional efforts are made to minimize the effect of corrosion damage by using coatings and cathodic protection systems. The U.S Department of Defense estimates 1.5 billion U.S dollars is spent annually toward corrosion prevention (such as inspection, painting, and coating) for naval ships alone [69].

2.4.1 Inspections

The first step to prevent corrosion damage is to conduct inspections of all in-service members or structures. Most inspections are conducted annually or bi-annually, depending on the type of structure and the risk of failure of the structure. An example of this is bridges, they are built with many safety factors in place and are considered less of a failure risk to corrosion then thin-walled structures and offshore structures such as naval ships and ocean drilling rigs.

The U.S Department of Transportation (U.S DOT) Federal Highway Administration

(FHWA) inspection guidelines are based on the age of the bridge, the amount of previously inspected damages, and the amount of traffic the bridge encounters. The frequency of inspection is divided into 3 major inspection procedures; routine inspection, underwater

inspection, and fracture critical member (FCM) inspection. The inspection guideline states

for routine inspection, which is the basic inspection, is as follows [22]:

• Inspect each bridge at regular intervals not to exceed twenty-four months.

• Certain bridges require inspection sat less than twenty-four-month intervals.

Establish criteria to determine the level and frequency to which these bridges

are inspected considering such factors as age, traffic characteristics, and

known deficiencies.

• Certain bridges may be inspected at greater than twenty-four month intervals,

not to exceed forty-eight months, with written FHWA approval. This may be

appropriate when past inspection findings and analysis justifies the increased

inspection interval.

Underwater inspections:

• Inspect underwater structural elements at regular intervals not to exceed sixty

months.

• Certain underwater structural elements require inspection at less than sixty-

month intervals. Establish criteria to determine the level and frequency to

which these members are inspected considering such factors as construction

material, environment, age, scour characteristics, condition rating from past

inspections and known deficiencies.

• Certain underwater structural elements may be inspected at greater than

sixty-month intervals, not to exceed seventy-two months, with written FHWA

approval. This may be appropriate when past inspection findings and analysis

justifies the increased inspection interval.

Fracture critical member (FCM) inspections:

• Inspect FCMs at intervals not to exceed twenty-four months.

• Certain FCMs require inspection at less than twenty-four-month intervals.

Establish criteria to determine the level and frequency to which these

members are inspected considering such factors as age, traffic characteristics,

and known deficiencies.

The routine inspection is considered the basic or general requirement while the two other procedures outline special circumstances and have an appropriate inspection schedule. Even in the most critical situation, the U.S DOT inspection guidelines allow a maximum time between inspections of twenty-four months. Although the procedure does state that the severity of the damage will influence inspection schedule [22].

The U.S DOT allows for such a variation of time for bridge inspections because it is extremely rare for a bridge failure to occur due to the effect of corrosion alone without multiple years of prior indication unless the original design was structurally inadequate. It is very unlikely that a bridge that is considered safe during an annual inspection will fail due to corrosion within a year. Even bridges that are considered structurally deficient continue to operate relatively safe. In the U.S, 58,495 bridges out of the 609,539 bridges are currently rated as structurally deficient. That equates to 9.6 percent of the bridge stock in the nation

[23].

Unlike bridges, corrosion damage that occurs to offshore structural and naval ships can quickly escalate into a serious problem within a year due to the corrosive environment of the ocean. The presence of electrolytes such as salt water and the constant movement of water are some of the key contributors for the rapid nature of corrosion. In order minimize

37 the chances of failure from structural defects and corrosion, the American Bureau of

Shipping (ABS) developed a ship inspection program. The program, titled Hull Inspection and Maintenance Program (HIMP), is a guide for ship owners to use for inspection and to have a maintenance schedule. The program clearly illustrates the time frame necessary between various inspection types and the maintenance which is needed. The ABS guide categorizes the inspection into three main time frames; annual inspection, intermediate inspection, and five year inspection. The guidelines states the following for each inspection time frame [24]:

• Annual inspections are required to be completed prior to ABS Surveyor

attendance for the Annual Survey of Hull. Annual Survey of Hull cannot be credited

by ABS until all due annual inspections are completed by a qualified inspector and

reported in ABS NS5 HIM software, when installed, or in the ABS approved HIMP

manual if software is unavailable. In general, the frequency of the annual

inspection is to be 12 months. In no case is this frequency to be extended beyond

18 months from the date the last such inspection was completed.

• Intermediate inspections are required to be completed prior to ABS Surveyor

attendance for the Drydocking Survey (or UWILD if agreed by ABS). Drydocking

Survey cannot be credited by ABS until all due intermediate inspections are

completed by a qualified inspector and reported in ABS NS5 HIM software, when

installed, or in the ABS approved HIMP manual if software is unavailable. In

general, the frequency of the intermediate inspection is to be between 24 to 36

months. In no case is this frequency to be extended beyond 36 months from the

date the last such inspection was completed.

• Five year inspections are required to be completed prior to ABS Surveyor

attendance for the Special Survey of Hull. Special Survey of Hull cannot be credited

by ABS until all due five year inspections are completed by a qualified inspector

and reported in ABS NS5 HIM software, when installed, or in the ABS approved

HIMP manual if software is unavailable. The frequency of the five year inspection

is not to exceed 60 months from the anniversary date or completion of the last

such inspection.

The ABS HIMP program also details the type of maintenance that should be done within each inspection time frame. Also, it includes notes such as areas were special attention should be paid to during inspection and different common areas of maintenance.

The glaring difference between the ABS HIMP and U.S DOT inspection guideline is the time allowed between inspections. ABS pushes to have ship/offshore structures checked annually but under no circumstance allow time between inspections to exceed 18 months.

2.4.2 Visual Rating System

The common factor among bridges, naval ships, offshore structures, transportation, etc. is the need for inspection. One of the key areas of focus for this project is to aide in the development of a visual rating system that helps inspectors to better understand the strength of structures after being corroded. This would also reduce the need for frequent inspection for corrosion on structures that use stiffened panel and plate elements. The rating system should be able to give an approximate remaining buckling strength depending on various levels and forms of corrosion. Since the vast majorities of inspection are visually based, a rating system that gives an approximate strength is very beneficial. This rating

39 systems would help inspectors understand just how critical the damage on a structure is and then allow them to development personalized inspection procedures and decide the proper course of action. Application of the rating system would minimize the risk of failure do to corrosion on stiffened panel and plate elements.

The system would help prioritize inspection scheduling allowing structures that show minimal corrosion damage to operate longer between inspections and visa verse for heavy damaged structures. Properly scheduling corrosion maintenance and inspections could reduce the time a structure is out of service due to repair by preventing extensive corrosion damage from occurring. Figure 7 is an example of how the visual rating system should look. Depending on the form of corrosion (general, pitting, etc.) and the severity of the corrosion, the chart would be able to give an approximate remaining bucking strength.

Knowing the environmental corrosion rate or the loss of thickness could aide in approximation of the corrosion damage severity.

Figure 7: Assumptions about remaining strength and recommended course of action to need to accompany the visual rating guide [25].

Based on the visual ratings guide, as-new members or members that show no sign of corrosion damage would be considered safe and receive a rating of 1. If a member falls within the range of 2-4 from corrosion damage, the member may continue to function properly but

more investigation or possibly even repair would be recommended in order to prevent

extensive damage and keep repair cost down depending on the level of damage. Any member

that is rated as a 5 is recommended to be repaired immediately, but the goal of this visual

rate guide is to prevent ratings of 5. While a visual rating guide may not be enough to

determine if a member or system is fully adequate, it may provide an inexpensive and less

time consuming method to understand the corrosion damage and plan the correct steps for

action.

2.5.3 Corrosion Prevention and Mitigation Methods

Structural steel such as A572 or A36 is commonly used, but when left unprotected is

very susceptible to corrosion. The best way to minimize to risk of failure or extensive damage

from corrosion is to prevent substantial corrosion from ever occurring from the start. There

is a large variety of protection methods throughout the industries, but for naval ships and

other offshore structures, the use of coatings and cathodic protection systems are common.

The term coating may be misleading because there is no one single used coating.

There is a large variety of coatings available and the use of each depends on the application

and the environment. Coatings may represent the largest market of corrosion prevention.

The common types of coatings are organic coatings, metallic coating, and paints.

Organic coatings are usually one of the common forms of corrosion protection on

offshore structures and naval ships. An organic coating is defined as non-metallic

compounds that contain carbon bonds in which at least one carbon atom is covalently linked

to an atom of another type such as hydrogen, oxygen, or nitrogen [26]. Organic coatings are

considered barrier coatings, a coating made with a fluoropolymer based resin.

Fluoropolymers are multiple carbon–fluorine bonds and are characterized as high

resistance to solvents, acids, and bases. The properties of the resin makes them ideal for

corrosion protection. The down side to using this coating is once the barrier is broken, protection of the substrate and the coating may begin to flake off. When using this type of coating, the consulting of a corrosion engineer is recommended and information on the environment plays a critical role. Since many companies to not publish details on corrosion failures for their products, it is also important to obtain information on ships and structures that have previously used the product. Organic coatings provide some of the best corrosion protection on the market, but costs are high and it requires more time for application.

Metallic coatings are considered a favorable second opinion to organic coatings.

Galvanized surfaces on naval ships may have a service lifetime of 10 to 15 years before the zinc loses its protective properties [27]. This type of coating is described as using a metal that is resistance to corrosion, to coating a metal that is not so resistance to corrosion. The two common forms of this application is hot-dip galvanizing and thermal spraying. Hot-dip

galvanizing is a process that involves immersing the steel component to be coated in a bath

of molten zinc (at about 450°C) after pickling and fluxing and then withdrawing it [xx]. The

surface that is immersed in the bath is uniformly coated with layers of zinc alloys and then a

layer with just zinc as shown is figure 8. The final product is a tough, durable, abrasion

resistant coating that also provides cathodic protection.

Figure 8: Cross-section through a typical hot-dip galvanized coating [28]

Thermally sprayed coatings follow the same principle as the hot-dip galvanized coating, but instead of dipping the steel in a molten zinc, the molten metal coating is sprayed onto the surface of the raw steel with a compressed air jet as shown in figure 9. Zinc,

aluminum, and zinc-aluminum alloys are the most commonly used metals in this process.

The metal is in either powder or wire form and is fed through a heated spray gun. The heating

element consists of either an oxygen flame or an electric arc. The benefit of this technique is

that there is no drying time required, the coating does not run or sag, and there is no size

limitation on the work piece that can be coated. Since the surface of the steel remains cool,

distortion of the steel surface is minimum. A down side to this method is that thermal

spraying is much more expensive and time consuming then hot-dip galvanizing.

Figure 9: Cross-section through a thermally sprayed aluminum coating [28]

The use of corrosion inhibiting paints are considered a good choice for short term use. These paints, while effective, are very susceptible to external damage and are not as durable of some of the other coatings. The effectiveness of this coating relies mostly on the surface preparation, if even a small amount of oil or debris is present, it will cause failure of the coating. In the industry, paints are usually combined with another forms of corrosion protection. The paint acts as an added corrosion protection or is used to protect the other corrosion protection system used.

Coatings provide good protection against corrosion but may be problematic due to surface preparation being critical to the success of the coatings. An ideal alternative to coatings is a cathodic protective system. This system is comprised of a cathode, an anode, a reference electrolyte and a conducting pathway between the cathode and the anode. The system works on the same principle as galvanic corrosion by makes the surface of the metal

that needs to be protected act as an electrochemical cell. The galvanic surface re-direct

current away from the anode and sends it to protecting structural (cathode). There are two

types of cathodic protection systems; a sacrificial (galvanic) cathodic protection (SCP) and

an Impressed Current Cathodic Protection (ICCP). The primary difference between the two

systems is that the galvanic cathodic protection is a passive system and functions by coupled

steel (cathode) with a more active anode. The driving voltage is caused by the potential

difference between the steel to be protected and a second metal in the same electrolyte.

Common anodes used in this system are zinc and aluminum; the anode will need to be

eventually replaced.

Unlike the sacrificial cathodic protection, the ICCP utilizes a DC power source, such as a cathodic protection rectifier, connected to an anode to provide corrosion protection as illustrated in Figure 10. The usual anodes is this system are high silicon cast iron, graphite,

mixed metal oxide, platinum coated titanium or niobium coated rods and wires. The rectifier

is used to provide positive current to the anode, which is then delivered to the structure to

be protected. The reference electrodes track the protection level and the controlling unit

regulates the produced current accordingly. Eventually, the metal structure becomes

negatively charged, which ultimately leads to decrease of potential below a certain threshold

value [29]. The anode is this system is not sacrificial, meaning it will not dissolve or need

replacing.

(a)

(b)

Figure 10: (a) simple ICCP system and (b) is a simple SCP system [29]

With each system, there are pros and cons; factors such as time, cost, and structure size should be carefully considered. SCP systems are simple to maintain and use but for long time operation, it is more expensive than the ICCP system. Since the only current in the system is supplied by material potential difference, the SCP system has size limitations and is not effective on large structures/ships. The ICCP system provides good corrosion

46 protection regardless of structure size, but since the system is more complex than a SCP system, a skilled worker is needed for maintenance. The ICCP is more fragile with corrosion protection then SCP, such that if a continuous power supply is not maintained or the current is connected in the wrong direction, corrosion protection will stop. The amount of current needed for either system to prevent corrosion is a function of temperature, environment corrosiveness, and the amount surface area that needs to be protected.

CHAPTER 3

LITERATURE REVIEW

This chapter is meant to give background knowledge on steel properties, stiffened panel structural theory, factors that affect steel member strength, industry design codes, and finite element analysis practices used to simulate corrosion. The combined knowledge will be used to model and quantify the remaining ultimate buckling strength on corroded A572 grade 50 steel stiffened panels. There has been numerous studies previously that investigated this topic, but most are directed at developing a specific equation for predicting the remaining ultimate buckling strength. The goal of this project, along with aiding in the development of a visual rate system, is to be a precursor in modifying existing design codes such as American Bureau of Shipping (ABS) and American Petroleum Institute (API).

3.1 Structural Steel

Steel is defined as an alloy of iron and carbon containing less than 1% of carbon and manganese, along with small amounts of silicon, phosphorus, sulfur and oxygen. Steel is one of the most widely used engineering and construction material in the world with an estimated 1,621 million tons produced in 2015 [30]. The popularity of steel stems from its high strength to weight ratio. Steel has the ability to carry extreme loads without adding extreme weight to structures. Materials like wood and concrete also have the ability to carries heavy loads but are very brittle unlike steel, so once cracking occurs, the load carrying capacity drops or ceases completely. The property that really separates steel from other

building materials is its ductility. Steel is unique in its capability to yield and continue to

carry loads and function properly. This property can be illustrated with a stress-strain

diagram. The ideal stress-strain diagram for steel is shown in figure 11. The figure shows

that steel has two distinctive behavior patterns; elastic behavior and plastic behavior. Elastic

behavior represents the limit of where a load can be applied and removed and the steel will

return to its original shape. Once the limits of elastic behavior are reached, steel begins to

display plastic behavior. At this point, yielding will occur and once the load is removed from

the steel, it will not return to its original shape.

Figure 11: Conventional vs True Stress-Strain Curve for Steel [31]

The behavior of steel can be broken down even further into four behavior sub- regions; elastic, yielding, strain hardening, and necking. The elastic region is characterized the same as elastic behavior. In this region, steel exhibits a linear stress line; this line is call the Young’s modulus. This region is followed by yielding; this is where the strain in the steel increases while the stress remains the same. During strain hardening, the strain in steel will

continue to increase but the steel will also be able to take on more stress until failure (or

ultimate stress) is reached. Following failure, extensive strain will occur in the steel cause

large deformation but it will be unable to handle any stress; this behavior is characterized as

necking.

In reality, high strength steel often does not have such a clearly defined transition

between the yield point and strain hardening. This is due to high strength steel being less

ductile then mild structural steel. To define the yield strength, a stress at the point of unloading that corresponds to a strain of 0.002 is used. This method of determining the yield strength is called the 0.2% offset method. High or mild strength steel is commonly used to construct naval ships, where the type of steel used depends on the size of the ship and the environment it will navigate through.

3.2 Stiffened Panels

Stiffened panels are defined as a stiffener (plate element) connected to the face of

another plate element usually in an orthogonal arrangement. A typical stiffened panel consist

of a plate element, a web element, and depending on the stiffener type, a flange element as

illustrated in figure 12. Stiffened panels are commonly used as wall plating for ship decks

(figure 13), hulls, bulkheads, box girder bridges, bridge decks, and superstructures of

offshore oil platforms [32]. The stiffened panels are commonly made of high or mild strength

steel. Stiffened panels are commonly arranged as either uniaxial stiffened panels or

orthogonal stiffened panels. Both styles of stiffened panels provide resistance to lateral loads

but are used situational depending on other load combination.

Figure 12: typical stiffened panel section with a flange

Where,

B ‐ Width of plate

bf ‐Width of stiffener

hw ‐Height of stiffener web

tw ‐Thickness of stiffener web

tf ‐Thickness of stiffener flange

t‐Thickness of plate

d‐Clear depth of stiffened panel

Uniaxial stiffened panels consist of stiffeners running in one direction connected to a plate element face. The stiffener for this style is usually arranged in a longitudinal direction to the structure as shown in figure 14. The use of this style stiffener is ideal for structures subjected to loads in a uniaxial in-plane fashion or structures with a short length compared to its width. Ship decks and bottom structure panels are reinforced mainly in the longitudinal direction with widely spaced heavier transverse stiffeners, as seen in figure xx for illustration. These stiffeners are typically placed at the boundary end of the longitudinal

stiffeners and usually has significantly greater stiffness in the panel of a lateral load. For a

uniaxial stiffened panel, the transverse stiffeners are primary used to provide resistance to

the load at the bottom and side shell element caused by water pressure [33].

Figure 13: Typical stiffened panel arrangement in ship hull structures.

Orthogonal stiffened panels are similar to uniaxial stiffened panels in the sense that they comprise of a thin plate reinforced with stiffeners in both longitudinal and transverse directions (as shown in figure 15). The difference is that the orthogonal stiffened plate’s transverse stiffeners are placed much closer to one another. The transverse stiffeners on the plate not only carry a portion of the compressive load, but also subdivide the plate into smaller panels. This drastically increases the critical stress at which the plate will buckle and also increase the ultimate load carrying capacity of all of the panels. The use of transverse

52 stiffened panels also allows this style of panel to be subjected to biaxial loading [34].

Orthogonal stiffened panels are more commonly used for large ships (such as naval ship and cargo ships) because of its ability to handle larger loads and load combinations.

Figure 14: Uniaxial (longitudinal) stiffened panel

Figure 15: Orthogonal stiffened panel

53 The overall large plate in which stiffeners are attached to is considered the gross

panel. When the gross panel is comprised of longitudinal stiffeners and transverse frames

(stiffeners) it is call a gross stiffened panel or grillage as shown in figure 16. The plate constitutes for the majority of the cross-sectional area of the plate/stiffener combination and carries most of the in-plane compressive load [35]. The longitudinal stiffener provides stability to the plate allowing it to absorb the in-plane load and also help with absorbing lateral loads. The transverse frames have deeper webs and are more rigid than longitudinal stiffeners, providing greater stiffness in bending. They are used to help support the longitudinal stiffeners and also by absorbing lateral loads. Figure 17 shows the basic nomenclature associated with stiffened panels. The full length of a stiffened plate structure is represented by L; and the spacing of longitudinal girders, transverse frames and longitudinal stiffeners are B, a, and b, respectively.

Figure 16: Stiffened Panel terminology [35]

Figure 17: Nomenclature for a stiffened plate structure [36]

3.2.1 Stiffener

Stiffeners are a very important structural component to any stiffened panel. The

stiffeners are the critical element on stiffened panels to strengthen the plate element and to

increase their load carrying capacity for lateral and in-plane loads. Stiffeners are usually

orientated in a longitudinal or transverse arrangement. Based on the arrangement, this will

determine what type of increased strength the plate element will receive. Due to the

simplistic nature of using stiffeners, they are ideal for naval ships due to their ability to add

strength to the plate structure without add excessive weight. Stiffeners come in varies types,

see figure 18 for illustration. The stiffeners used in the longitudinal direction are commonly

T-bar, angle bar, or flat bar while transverse stiffeners are typically T-bar sections [33]. The type of stiffener used is determined based on the size of the ship, the combination of loads, the magnitude of the loads, and the location of where the stiffened panel will be located.

I‐Section Angled/L bar Tee Angle

Figure 18: Illustrates the typical stiffener types

Where,

b‐ Width of plate

bf ‐Width of stiffener

hw ‐Height of stiffener web

tw ‐Thickness of stiffener web

tf ‐Thickness of stiffener flange

tp ‐Thickness of plate

d ‐Clear depth of stiffened panel

3.3 Basic Ship Hull Structures

The use of stiffened panels varies widely from aircrafts to offshore structures to bridge decks, but the focus of this study is the use of stiffened panels on naval ships, specifically bulkheads in the ship hull. The hull of the ship is the main body of the ship that is below the main outside deck. The hull is made primary of a system of stiffeners to create

56 the framework and plates to create the skin (outer plating) of the ship (shown in figure 19).

The framework and skin of the ship are commonly secured with the use of welds or rivets.

Other than the framing and plating, the keel is the critical component in the make-up of the hull. The keel runs from the stem of the bow to the stern of the ship. The keel is consider the backbone of the ship, giving the ship its shape and also strength to the hull. Strake is a component of the hull where a plate is overlapped with other ship plates to create a water tight seal. The deck of the ship is supported by deck beams (which are stiffeners that attached to the deck plating) and the bulkhead.

Figure 19: Basic construction of a ship hull [37]

The bulkhead is defined as the vertical walls which form partitions within the ship’s structure, starting from the ships double bottom top until the upper main deck as shown in figure 20. Stiffeners are a major element in the bulkhead; by running the length of the wall, they stabilize the walls and give them strength. The vertical partition divides the hull into

57 separate compartments. Bulkheads are typically used to carry cargo, to prevent the passage of air and/or water, and to compartmentalize the hull. Bulkheads provide structural stability and rigidity to the ship [38]. They also help absorb the impact of the sheer force caused by waves. Due to the nature of bulkheads, they are extremely susceptible to corrosion damage.

Figure 20: Illustration of a ship bulkhead [39]

3.4 Load Distribution

Ship structures are subject to a numerous variety of loads, but for our studies, we are concerned with the load acting the on ship hull girder where the bulkheads are located. The primary structural load acting on the bulkhead comes from the ships own weight, cargo, buoyancy, waves, and operation in an environment such as the sea. The loads acting on the ship hull girder are categorized as either still-water loads, wave loads, or dynamic loads. The

58 loads affect the deck and bottom shell hulls by subjecting them to flexural compressive stress due to the sagging and hogging bending moments. Sagging is defined as the ship structure bending downward in the center of the ship in the longitudinal direction as shown in figure

21, while hogging is the opposite when the ship structure bends upward at the center.

Figure 21: Diagram of a ship hull subjected the (1) sagging and (2) hogging [40].

Factors such as cargo, ship weight distribution, and buoyancy all factor into determining the still-water loads. The wave load is defined as the impact load a wave has on the outer hull of the ship, where factors like wave height have a significant effect on the wave strength. Dynamic loading is a combination of both load types. The frequency of the waves and how they affect the movement of the ship/cargo all factor into determining the dynamic loading.

In ship structures, these loads produce three types of loading; negative bending moments, positive bending moments, and in-plane compression. The negative bending moment is from the lateral pressure. The lateral pressure acting on the stiffened panels is due to still-water loads, wave loads, dynamic loading, and liquids in tanks. The lateral pressure causes the plate to be in tension and the stiffeners flange to be in compression. The positive bending moment occurs when the plate is in compression and the stiffener flange is in tension. The final type of loading is uniform in-plane compression, this type of loading stems from the bending of the hull girder. This is the dominant type of loading acting on the hull girder. The bending comes from a combination of weight and buoyancy distribution of the hull girder and cargo load perpendicular to the ship. These three types of loading may occur individually or in a combination with one another.

When vertical bending occurs, the deck panel is subjected to longitudinal axial compression, if sagging, or longitudinal axial tension, if hogging. The bottom panel of the ship is subjected to combined longitudinal axial compression/tension and lateral pressure. Since stiffened panels are used to make-up the walls of the bulkhead in the ship hull, they are primary subjected to fluid lateral pressure (negative bending moment) and in-plane compression/tension. Although stiffened panels experience various other loads, our focus for this study will be stiffened panels subjected to combined loading of lateral pressure and longitudinal in-plane compression. The in-plane loads in a stiffened panel is distributed as a truss patter meaning the applied load is felt at the ends of component. The load acted along the axis and placed the end in compression or tension. The welding connection between stiffened panel components allows the member to act as one (a whole).

3.5 Stiffened Panel Failure Mode

The failure of stiffened panels is contributed to the loading condition in which it’s exposed to and the geometry of the stiffener and plates. There has been countless studies conducted on the buckling behavior of stiffened panels, but the benchmark study by Paik and

Kim [42] may be the most profound. Paik characterized the bucking of stiffened panels under predominantly in-plane loading as having six types of buckling modes (as shown in figure 22 through figure 26) [42].

buckling of the plating and stiffeners as a unit

• Mode I: overall

• Mode II: collapseyielding due at tothe predominant plate-stiffener transverse combination compression (Beam-column type

•collapse) Mode III: at mid-span

local buckling of the stiffener web

• Mode IV:lateral -torsional buckling (or “tripping”) of the stiffeners

• Mode V: Gross yielding

These modes• Mode are VI: neither mutually exclusive nor independent; they can occur together and they can interact [35]. This is because stiffened panels are rarely subjected to one single type but rather, they are generally subjected to combined in-plane and lateral pressure loads.

Figure 22: (a) Model I. Overall buckling of the plating and stiffeners as a unit

Figure 23: (b) Model II. Yielding at plate edges between the stiffeners due to transverse compression

Figure 24: (c) Model III. Yielding at the plate-stiffener combination (Beam-column type collapse) at mid-span

Figure 25: (d) Model IV. Local buckling of the stiffener web

Figure 26: (e) Model V. Lateral-torsional buckling (or “tripping”) of the stiffeners

Mode I typically occur when the stiffeners are weak. In this failure mode, the stiffeners and plating buckle together but the overall buckling behavior remains elastic. Stiffened panels typically are able to sustain more loading even after overall bucking has occur in the elastic region. Ultimate strength is reached once a large yielding region form inside the panel and/or along the panel edges. When Mode I is the bucking mode of a stiffened panel, the panel is behaving as an ‘orthotropic plate’.

Modes II-VI typically occur when the stiffeners are strong enough that they remain straight until the plating between the stiffeners buckles or collapse locally. Stiffened panel that experience this mode reach the ultimate limit state by failure of the stiffeners along with the associated plating. Mode II is a plate induced failure at the ends, where the collapse is due to yielding at the corner of the plating region between the stiffeners. When stiffened panels are subjected to predominantly biaxial compression loads, Mode II collapse may also

occur. Mode III usually occurs when yielding located at the plating-stiffener combination at

mid span takes place; this is considered a plate-induced failure at mid-span. The ultimate strength is determined once column or beam-column type failure happens at the plate- stiffener combination with the associated plating.

Failure Mode IV and V usually occur when the stiffener flange is not adequate enough to remain straight so the stiffener web twists/buckles or when the ratio of web height to web thickness is too large on the stiffened panel. Failure for Mode IV occurs due to local buckling of the stiffener web. For Mode V, failure is reached once lateral-torsional buckling (tipping) occurs in the stiffener. Unlike Modes I-V, Mode VI is not related to the web but instead the plate. This type of failure typically occurs when the plate slenderness ratio is very large and/or when the stiffened panel is subjected to predominantly axial compressive loading so neither local nor overall buckling can occur before the panel cross section yields entirely

[42].

The direction in which a load is applied to a stiffened panel has a critical impact on the buckling behavior. A study by G.Y. Grondin el al. [43] investigated stiffened panels under combined in-plane compression and lateral pressure. They concluded that stiffened panels subjected to this type of loading condition has three forms of buckling; plate buckling figure

27(a), tripping of the stiffener figure 27(b), or overall “Euler” buckling figure 27(c). In the first form, failure occurs when the plating between the stiffener buckles. This failure behavior usually occurs when the stiffener web slenderness ratio is too low and the plate fails before the stiffener. Lateral torsional buckling is the cause of failure for the second form of buckling; this is due to rotation occurring at mid-span were the stiffener and plate connect.

Also in the study, cases where a bending moment was applied to induce initial compressive

65 stresses in the stiffener flange was shown to initiate tipping behavior. A study by D.A

Danielson et al. [44], determined that tipping of stiffened panels under axial compression is directly related to the torsional stiffness of the stiffeners and determined whether the panel fails from local plate bucking and tipping of the stiffener. The behavior of a steel stiffened panel depends on a variety of factors such as: geometric/material properties, loading characteristics, initial imperfections, boundary conditions and/or corrosion damage. For the purpose of this study, the focus is steel stiffened panels subjected to combined in-plane compression and lateral loading with initial geometric imperfections and corrosion damage considered.

(a) Plate Buckling

(b) Tripping of the Stiffeners

Figure 27: Failure modes of stiffened plates [43].

3.6 Factors that Affect the Ultimate Buckling Strength

The ultimate buckling strength of a stiffened plate depends on the plate geometry, material properties (plate slenderness ratio and column slenderness ratio), initial geometric imperfections, residual stresses, and boundary conditions. The type of corrosion (such as general, pitting, etc.) in which the panel is exposed to also contributes to the type of failure mode the plate encounters. A number of studies that determine the ultimate buckling

strength for stiffened panels have been undertaken experimentally, numerically and

theoretically.

To understand which factors, affect the ultimate strength of a stiffened panel, a study

was undertaken by N.E Shanmugam et al. [45]. Experimental work and finite element

analyses (done with ABAQUS) were conducted to study un-corroded stiffened panels that

were subjected to in-plane compression and lateral pressure. The relationship between in- plane compression and lateral pressure was studied as well. To apply the in-plane

compression and lateral pressure, a load set similar to that shown in figure 28 was used. The

in-plane load was applied in the horizontal direction with an actuator on the frame. The

lateral pressure was applied with an air bag. The air bag was placed between the stiffened

panel and a flat steel plate and filled with air. The vertical actuator is used to act as a load cell

and resist to lateral displacement. The in-plane load and lateral pressure was applied

simultaneous, but once the predetermined axial load limit was reached, the specimen is

laterally loaded until failure occurs.

Figure 28: Sectional view of the experimental setup.

N.E Shanmugam concluded that when lateral pressure is increased, the ability to

resist axial compression is reduced sustainably and vice versa. He also determined that the

plate slenderness ratio has a major influence on the ultimate load of stiffened panels

68 subjected to in-plane compression and lateral pressure. An increase in the plate slenderness ratio resulted in a decrease of the ultimate load capacity.

A study published by Y. Huang et al. [46] investigated hull structural plates subjected to pitting corrosion under biaxial compression loading. FEM analysis was performed to study the effects of volume loss (with respect to plate slenderness and the ratio between the transverse and longitudinal in-plane stresses), as well as the effect of scattered pit distribution (figure 29) on the panel surface and various pit shapes (figure 30). Based on Y.

Huang’s study, he found that the ultimate strength reduction of the plates under biaxial compression loads with respect to the corroded volume loss was not affected by the plate slenderness and linear factor at the plate’s edge, but it is affected by the ratio between the transverse and longitudinal in-plane stresses.

Figure 29: Distribution of the corrosion pits.

Figure 30: Deformation and the stress distribution mid-surface at the ultimate state.

He also determined that ultimate strength reduction was not affected by pit distribution or pit shape as long as the volume loss is kept consent between the models. Y.

Huang concluded that the ultimate strength reduction limit factor is volume loss and developed a formula based on volume loss to determine reliability or risk assessment of the actual hull structure with pitting corrosion damage.

A publication by Paik and Thayamballi [20] studied the ultimate strength of ship panels subjected to pitting corrosion under axial compression using the finite element software ANSYS. From the study they concluded, the small presence of pitting corrosion anywhere on the surface of the plate had no significant reduction on ultimate compression

70 strength, but extensive pitting would impact the ultimate compressive strength. X. Jiang and G. Soares [47] investigated the ultimate strength of rectangle plates exposed to pitting corrosion under in-plane compression. That study showed that pits on one side of the plate had more of an influence then on both sides. D. Ok et al. [48] conducted over 256 non-linear finite element analyses on unstiffened panels under uniaxial compression. They studied the effects of localized corrosion on the ultimate strength of panels with pitting corrosion over various locations on the plate surface and intensity. Both studies concluded that the degree of pitting (DOP) intensity had a significate influence on the ultimate strength due to the volume loss being more influential than the plate slenderness on compression capacity. X.

Jiang developed an empirical formula to predict the ultimate capacity of plates under axial compression as a function of volume loss and plate slenderness.

Compared to uniform corrosion, determining the load carrying capacity of members exposed to large amounts of pitting corrosion is challenging due to the random scattering of pits. Based on numerous experimental and analytical studies conducted on steel plates subjected to pitting corrosion, Tanker Structure Co-operative Forum (TSCF) [49] recommended the use of a formula based on equivalent plate thickness to predict the bending capacity of steel panels with pitting damage. The equation includes factors such as plate geometry, bending stiffness, mass loss, and boundary conditions. J. C. Daidola et al [50] developed a model to estimate the residual thickness of pitted plates based on the number of pits and the average/maximum depth of the pits. They studied the effect of reduction in thickness on local yielding based on using the probabilistic approach. They work aided in the development of tools to assess the residual strength in plates subjected to pitting corrosion.

3.7 Stiffened Panel Finite Element Analysis (FEA) modeling

This section is to summarize the different modeling techniques used the produce the

stiffened panel FEA (principle) model used to characterize the effect uniform (general)

corrosion has on the ultimate buckling strength. The principle model was developed based

on the combination of two studies. Y. Chen [35] investigated the ultimate strength of un- corroded stiffened panels under in-plane longitudinal compression. In his publication, he detailed a method to model an orthotropic stiffened panel model using the FEA software

ABAQUS. The stiffened panel modeled in ABAQUS was half of a three-bay grillage (as shown in figure 31).

Figure 31: ABAQUS model for three-bay grillages

Y. Chen performed a nonlinear buckling analysis followed by a post-buckling analysis to ultimate buckling strength. The material used in the study was steel with the following material properties:

Yield stress: 352.8 MPa

Young’s modulus: 205800 N/mm2

Poisson’s ratio: 0.3

The stiffened panels were modeled using shell elements and incorporated the initial

geometrical imperfections of the stiffener based on the scaling factor, wo = 0.0025a, where a is the length of one bay. The stiffened panels were simply supported and loaded with in- plane compression in the longitudinal direction. Over the course of the study, Chen modeled

107 panels with various panel geometries. When the ABAQUS results were compared to the beam-column method, the average percent error was 3.32%. Based on the percent error of the ABAQUS models, it can be concluded that the method used to determine the ultimate buckling strength of stiffened panels is completed with respectable accuracy. Based on experimental data and FEA using ANSYS, M. Kumar et al. [34] was able to estimate the

ultimate buckling strength and buckling shape of stiffened panels under combined axial

compression and lateral pressure. In the study, the load set-up (shown in figure 32) was used

to apply the combined loading conditions. The axial compression was done using a hydraulic

jack and the lateral pressure was applied using an inflated air bag. The panels were initially

loaded laterally to a deserved limit, then axially loaded until failure. Nonlinear finite element

analysis was carried out on the FEA model. The FEA model was done using shell elements,

but neither initial imperfections nor residual stress were included in the model.

Figure 32: (a) Details of the Test Rig (b) Cross Section View ((i) Section X1-X1 and (ii) Section X2-X2) [32]

The buckling behavior of the stiffened panel was accurately predicted as well using the method described in the study. M. Kumar and their colleagues concluded that although the estimated ultimate buckling strength is comparable to the experiment data, factors such as initial imperfections and residual stress should be considered for best results.

3.8 Design Equation

This section summarizes a few design guidelines used in the industry to estimate the limiting state. The guidelines are used due to their suitable due the literature review and the nature of this current study. The following design guidelines are used specifically for longitudinally stiffened panels subjected to uniaxial compression. Although the focus of this study is stiffened panels subjected to combined loading, the guidelines will be used to validate our stiffened panel FEA models at certain stages and the experimental specimens.

The design guidelines are conducted using Microsoft Excel spreadsheet program. The

guidelines of the American Petroleum Institute (API) [51] and the American Bureau of

Shipping (ABS) [52] are used to calculate the limiting states of a longitudinally stiffened panels under uniaxial compression. The process of calculating the limit states is described as followed:

• Ultimate Limit State (API)

This guideline is for stiffened panels subjected to in-plane uniaxial compression that is acting in the same direction of the stiffener. The ultimate limiting state is reached when the applied in-plane compressive stress, f, equals fu. The allowable in-plane compressive

stress is obtained by dividing the limit state, fu, by the appropriate factor of safety:

= , < 0.5

𝑢𝑢 𝑦𝑦 ̅ =𝑓𝑓 1𝐹𝐹.5 , 0.5𝜆𝜆< < 1.0

𝑓𝑓𝑢𝑢 𝐹𝐹𝑦𝑦� 0−.5𝜆𝜆̅� 𝜆𝜆̅ = , > 1.0

𝑓𝑓𝑢𝑢 𝐹𝐹𝑦𝑦 � � 𝜆𝜆̅ Where, 𝜆𝜆̅

1 12(1 ) = 2 𝐵𝐵 𝐹𝐹𝑦𝑦 − 𝑣𝑣 𝜆𝜆̅ � � � 𝑡𝑡= 𝜋𝜋 𝐸𝐸. ( , 𝑘𝑘)

𝑘𝑘 𝑚𝑚𝑚𝑚𝑚𝑚= 4𝑘𝑘𝑅𝑅 𝑘𝑘𝐹𝐹 2 Where, n= number of sub-panels𝑘𝑘𝑅𝑅 (individual𝑛𝑛 plates)

(1 + ) + = , , (1 + ) 2 2 (1 + ) 1 𝛼𝛼 𝑛𝑛Ƴ �4 𝑘𝑘𝐹𝐹 2 𝑖𝑖𝑖𝑖 𝛼𝛼 ≤ 𝑛𝑛Ƴ 2(𝛼𝛼1 + 1 +𝑛𝑛𝑛𝑛 ) = , , (1 + ) 1 + 1 √ 𝑛𝑛Ƴ �4 𝑘𝑘𝐹𝐹 𝑖𝑖𝑖𝑖 𝛼𝛼 ≥ 𝑛𝑛Ƴ Where, 𝑛𝑛𝑛𝑛

= 𝐴𝐴𝑠𝑠 𝛿𝛿 and, 𝐵𝐵𝐵𝐵

12(1 ) = 2 − Ƴ 𝐼𝐼𝑠𝑠 Ƴ 3 � � = aspect ratio of whole panel, 𝑡𝑡 𝑑𝑑

I𝛼𝛼 = Moment of inertia of one stiffener about the axis parallel

s to the plate surfaceat the base of the stiffener t = plate thickness d = spacing between stiffeners

• Overall Buckling Limit State (ABS)

The overall buckling strength of the entire stiffened panel is to satisfy the following

equations with respect to the biaxial compression:

2 1 σx � gx� ≤ η σ if P = σex1 P (1 P ) if σex ≤ Prσ0 gx 0 σ � 0 r r σ ex r 0 σ � − − ex σ ≥ σ K (DσD ) / = 2 t b 1 2 xπ x y σex 2 ( +x ) = 𝑆𝑆𝑥𝑥𝑡𝑡 𝐴𝐴𝑠𝑠𝑠𝑠 𝑡𝑡𝑥𝑥 = 𝑆𝑆𝑥𝑥

𝑥𝑥 𝑔𝑔𝑔𝑔 Critical buckling load 𝜎𝜎 𝜂𝜂𝜎𝜎

P = A

x sxσx 76

• Nomenclature

- American Petroleum Institute (API)

fu = ultimate limit state, psi

FY = minimum specified yield stress of material, psi

B = plate width, in

t = plate thickness, in

E = modulus of elasticity, psi

= Poisson’s ratio, 0.3 for steel

υFor more information, refer API Bulletin 2V [51]

- American Bureau of Shipping (ABS)

= Calculated average compressive stress in longitudinal direction,

σpsi𝑥𝑥

= Critical buckling stress for uniaxial compression in the

𝑔𝑔𝑔𝑔 longitudinalσ direction, psi

Pr = proportional linear elastic limit of the structure, which may be

taken as 0.6 for steel

= elastic buckling stress in the longitudinal direction, psi

kσ𝐸𝐸𝐸𝐸 = 4 for l/b>1

D𝑥𝑥 = Flexural Rigidity in the longitudinal direction of the entire panel

D𝑥𝑥 = Flexural Rigidity in the transverse direction for plate only

𝑌𝑌

I = Moment of inertia of the stiffener with the effective plate in the longitudinal𝑋𝑋 direction

= aspect ratio of the whole plate = 2

Eα = modulus of elasticity, psi

= specified minimum yield point of plate = 50ksi for ASTM A572 plateσ0 t = Equivalent thickness of the plate and stiffener in the longitudinal𝑥𝑥 direction

S = Spacing of stiffeners t 𝑥𝑥 = Thickness of plate, in

A = Sectional area of stiffeners excluding the plate

𝑠𝑠𝑠𝑠 For more information, refer ABS (2004) [52]

CHAPTER 4

UNIFORM CORROSION PROCEDURE FOR STIFFENED PANEL

4.1 Introduction

Since steel stiffened panels are used to make-up the outer shell structure and inner

bulkhead structure of a ship’s hull girder [53], these structural elements are highly

susceptible to corrosion in forms such as uniform (general), pitting, and grooving corrosion.

Ships are commonly constructed using mild or high strength steel depending on the size and

intended use of the vessel. This chapter will detail the procedure for producing various

degrees of uniform corrosion on stiffened panels which are mechanically loaded to

determine the ultimate buckling strength under in-plane axial compression loading

conditions. Due to its commonalty, the high strength A572 Grade 50 steel (that follows ATSM

standards) is used to fabricate the stiffened panel test specimens, dog-bone test samples, and

non-uniform corrosion samples. The degree of uniform corrosion is defined based on

percentage mass loss when comparing the corroded test specimens to its original non-

corroded counterpart. A method developed by ASTM for a controlled corrosion process

using a fine spray (or fog) technique, is used to induce accelerated uniform corrosion on the

steel stiffened panel specimens. This ASTM method is known as the B117-11 (salt spray fog)

test. It is one of the most widely used corrosion processes to induce accelerated corrosion.

Although the effects of uniform corrosion on the steel stiffened panel is the primary focus,

the means and methods of producing pitting and grooving corrosion in a controlled

laboratory setting are detailed also in the chapter. The mechanical testing results obtained

from corroded test specimens will be compared with non-corroded (as-new) specimens tested under the same loading conditions. The percent error between the results of both the non-corroded and corroded stiffened panels will be used to verify the FEA process used to produce the finite element (FE) models in a later chapter. These FE models will be used to predict the residual ultimate buckling strength of corroded stiffened panels under combined in-plane axial compression and lateral pressure.

4.2 ATSM B117 Laboratory Corrosion Test

The ASTM B117 [54] is a standard test used to induce corrosion and to provide

corrosion resistance information on a particular metal. This method induces corrosion by

spraying a fine salt (fog) solution on a specimen housed in a closed controlled chamber.

ASTM B117 is commonly referred to as the salt spray test or the fog test. The test is

considered an accelerated form for atmospheric corrosion testing. Using the B117 test

allows more corrosion damage to occur in a much shorter time span than what would

naturally occur. This method is ideal to induce simulated uniform corrosion because

combined with the environmental chamber, it allows for uniform cover of the salt fog over

the entire specimen. For the purpose of this thesis, the target degrees of uniform corrosion

on steel stiffened panels are; 5 percent mass loss (5% corrosion), 10 percent mass loss (10%

corrosion), and 15 percent mass loss (15% corrosion). Concentration of the salt solution,

temperature, and acidity are the three key factors that have been carefully considered when

using this accelerated corrosion test. This procedure was conducted under cyclic conditions,

using an environmental chamber (shown in figure 33) [55]. The environmental chamber

80 used is a Q-Fog chamber model SPP-1100. This chamber allows the concentration of salt solution, temperature and the acidity of the solution to be controlled.

(a)

(b)

Figure 33: The (a) front and (b) inside view of the test chamber used to induce accelerated corrosion on all A572 test speicmens.

ASTM B117 is a simple, commonly used accelerated corrosion test but does have a

few drawbacks. The test is not intended for use on materials that contain chromium plating,

cadmium plating, and zinc die castings. This method is not meant to provide a direct

corrosion correlation between laboratory corrosion results and real-world corrosion

results; the reason being is that the high concentrations of the corrosive elements and the

high temperatures generally do not occur in the natural environment. The purpose of this

method is to provide a means to induce accelerated corrosion. The correlation between

corrosion damage and the reduction in ultimate buckling strength is based on percent mass

loss.

4.2.1 Salt Solution Preparation

The specification of salt spray solution used in ASTM B117 is detailed in the section.

The procedure on mixing the solution is outlined as well. The testing solution is prepared in

percent (%) by mass as follows:

• Sodium Chloride (NaCl): 0.05

• De-ionized Water (H2O): 0.95

The sodium chloride (NaCl) used in the solution adheres to the purity grade of the

Certified American Chemical Standards (ACS). The de-ionized water follows the requirements from ASTM D1193 Type IV. The acidity of the solution is to be kept in the pH range between 6.5 to 7.2 pH. After the solution is mixed, the pH is checked by using a sodium bicarbonate (CaCl2) reagent to adjust the pH accordingly. Once the solution meets the required specifications, the salt solution is poured into the solution reservoir in the

82 environmental chamber. inside the chamber. The temperature of the salt solution is maintained at 95 ͦF (35 ͦC)

4.3 Test Specimen Cleaning Preparation

The surface condition of exposed steel plays a vital role in the type of corrosion and the amount of corrosion damage that will occur. The presence of either oils, organic debris, or non-organic debris can cause non-uniform surface contact of the salt spray solution on the steel test specimens. To insure proper saturation of the salt solution on all specimens used in the corrosion process, the following surface preparation steps were followed:

• All A572 steel arrived in its factory condition; covered in mill scale. Mill scale is a thin

layer of iron oxide that forms on the surface of hot rolled steel. To remove the mill

scale, all steel test specimens were sandblasted. This step removes any initial oils and

debris on the surface also.

• The freshly sandblasted specimens are rinsed with de-ionized water to remove any

remaining dust of sand and then dried with a lint free towel. To insure the steel

surface is completely free of oil, the specimens are then rinsed with methanol

followed by de-ionized water.

• Oil free raw steel exposed to air is extremely susceptible to surface corrosion, in some

cases it has taken less the ten minutes to show corrosion on the surface in a laboratory

setting. Once clean, the steel specimens are dried using a hot air gun and placed

immediately inside of a desiccator until they are ready to be corroded.

4.4 Determining Environmental Corrosion Rate

The first step in the corrosion process was to determine the environmental corrosion rate of the Q-Fog chamber. The rate of corrosion on steel in not constant, it fluctuates over

the duration of exposure to a corrosive environment. The corrosion rate is a time dependent

process; the longer the expose time, the more corrosion will occur. As the corrosion product

builds up, the rate of corrosion decreases. In order to determine how much higher the

corrosion rate would be between removing the corrosion product and not removing the

corrosion product, four flat (rectangular dog-bone shaped) specimens (figure 34) were place in the Q-Fog chamber. The dog-bone specimens are numbered 1-4 as shown in figure 34(b).

Determining the rate of corrosion would also provide a window of completion for the various

degrees of corrosion.

(a)

(b)

Figure 34: The AutoCAD draft rendering (a) and actually (b) ASTM E8 test specimens.

Every few days, all specimens were rinsed with de-ionized water and then rotated

180 degrees. All specimens had the same exposure duration, but once every week, specimen

#1 and #4 had their respective corrosion by-product removed using a small nylon brush and

de-ionized water. The other two specimens’ (#2 and #4) corrosion by-product remained

untouched. Figure 35 shows the visual comparison of the clean (corrosion by-product removed using nylon brush) and un-clean (no nylon brush used) test specimen over various exposure durations. The cleaning process was repeated on the same two specimens for the duration of this test, while the un-clean specimens remained constant as well.

85 #1

(a)

(b)

(c)

(d)

Figure 35: (a) The corrosion by-product build-up after 2 weeks of exposure on the un-clean dog-bone specimens, (b) the condition after two of the dog-bones are cleaned, while the remaining two are left un-clean, (c) the corrosion build-up after 7 weeks of exposure on the un-clean dog-bone specimens, (d) this is the condition after two of the dog-bone are clean, while the remaining two are left un-clean.

The goal of testing the dog bones was to determine the highest achievable corrosion rate possible in the corrosion chamber and to determine if the corrosion process duration can be approximated. Each week, on the same day, the #1 and #4 test samples were scrubbed with a nylon brush; the test specimens were dried and weighed to determine mass loss. The thickness of the test specimens was measured as well using an ultrasonic thickness reader.

4.4.1 Corrosion Rate

Based on the reduction of thickness and mass loss, the average corrosion rate was determine using ASTM corrosion equation. In reality, the reduction of the thickness would have an impact on the surface area, but the impact is negligible, so the surface area and density are kept as a constant. The corrosion rate was obtained using the following equation:

= ASTM G1-03 [56] 𝐊𝐊∗𝐖𝐖 𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂𝐂 𝐑𝐑𝐑𝐑𝐑𝐑𝐑𝐑 𝐀𝐀∗𝐓𝐓∗𝐃𝐃 Where,

K = constant (Refer to Table X)

T = Time of exposure (hr)

A = Area (cm2)

W = Mass loss (g)

D = Density (g/cm3)

ASTM corrosion allows the use of many different units to express corrosion rates. The

desired corrosion rate units can be chosen by picking the corresponding K constant from

table 2. For the purpose of this study, the corrosion rate units will be presented in inches per year (ipy).

Table 2: Values of K for use in the ASTM corrosion rate equation

Corrosion Rate Units Desired Constant (K) in Corrosion Rate Equation

mils per year (mpy) 3.45 x 106

inches per year (ipy) 3.45 x 103

millimeters per year (mm/y) 2.87 x 102

micrometers per year (um/y) 8.76 x 104

picometers per second (pm/s) 8.76 x 107

The following is the corrosion rates of specimens #1 and #4 over a 7-week exposure period (shown in figure 36). The corrosion rate of the un-clean test dog-bone specimens indicate a constant rate of corrosion of .0198 ipy. This is due to the thickness loss on the un- clean coupons can only be taken once at the end of the corrosion process. In contrast, the data from the cleaned dog-bone specimens shows a varying rate of corrosion and the corrosion rate was higher than the specimens that did not have their corrosion product removed. Since the corrosion rate of test specimens #1 and #4 shows inconsistent corrosion rates, the ASTM G1-03 equation cannot be used the approximate the duration that the stiffened panel test samples must be exposed to the corrosive environment to produce the desired degree of corrosion.

Exposure Time vs. Corrosion Rate 0.0500

0.0444 0.0450 0.0417 0.0400 0.0390 0.0400 0.0384

Speciman #1 0.0350 0.0338 0.0332 0.0336 0.0318 Speciman #4 Corrosion (ipy) Rate Corrosion 0.0300 0.0287

0.0250 0 1 2 3 4 5 6 7 8 Exposure Time (wks)

Figure 36: Corrosion rate of specimen #1 and specimen #4 over the duration of the corrosion process.

4.5 Stiffened Panel Test Specimen

Prior to conducting any experimental test or FEA models on a stiffened panel, an idealized panel had to be designed. The steel stiffened panels used in this study, are shown in figure 37. They are designed based on the typical range of plate slenderness ratio, column slenderness ratio, and the stiffener to plate area ratio (Ast/Ap) of large-scale grillages commonly used on industry warships where the panels are subjected to combined loading.

- -0.900) and

AThest/A rangesp=(0.12 of-0.43) these [ 57various]. While parameters designing are the as stiffened followed; panel β=(1.0 specimen,4.5), λ=(0.15 size limitations

90 based on the environmental chamber was also kept in mind. The parameters used to design the panels are based on the following equations:

Plate slenderness ratio: = 𝑏𝑏 𝜎𝜎𝑦𝑦 𝛽𝛽 𝑡𝑡 � 𝐸𝐸

Column slenderness ratio: = 𝑎𝑎 𝜎𝜎𝑦𝑦 𝜆𝜆 𝜋𝜋𝜋𝜋 � 𝐸𝐸 Stiffener/plate area ratio: 𝐴𝐴𝑠𝑠𝑠𝑠 𝐴𝐴𝑝𝑝

(a) (b)

Figure 37: (a) an AutoCAD draft of the idealized steel stiffened panel, and (b) the actual experimental steel stiffened panel.

Table 3: Geometric Properties of Stiffened Panels

b a hw bf t (in) tw (in) tf (in) Ast/Ap (in) (in) (in) (in) Test 9 18 0.1875 1.5 0.1875 2 0.1875 1.993β 0.363λ 0.389 Specimen

Where,

b = width of plate

a = length of plate

t = thickness of plate

hw = height of web

tw = thickness of web

bf = width of flange

tf = thickness of flange

Based on the allowable parameter ranges and size restrictions; the geometric dimensions of the stiffened panel are presented in table 3 along with the test panel parameters. The parameters of the test specimen were kept constant over the course of both the experimental testing and the FEA modeling. The stiffener and plate elements of fabricated stiffened panels are both made using ASTM A572 steel. The ASTM A572 is characterized as a high strength carbon steel which incorporates small amounts columbium, vanadium, and titanium into the standard carbon steel chemical composition. The typical grades of A572 steel are Grades 42, 50, 55, 60, and 65; for this study A572 Grade 50 steel is used. From ASTM, the mechanical properties of the steel are as follows: Young’s modulus of elasticity (E)=29 x 106 y)=50 k stiffened panels, all spsi,haring yield the strength same (σ parameters,si, and were Poisson’s fabricated. ratio (υ)=0.3. The mechanical Eight steel properties are used in ABAQUS to model the stiffened panel. Once the fabrication of the

panels was complete, they were cleaned using the steps outlined in the previous section and

prepared for testing.

4.6 ASTM B117 Procedure

Eight un-corroded steel stiffened panel test specimens were prepared using the

method described in Section 4.3, five of the specimens were placed in the environmental

chamber (shown in figure 38). The environmental chamber used is a Q-Fog chamber model

SSP-1100. The remaining three sample will act as the un-corroded control test samples.

Before placing the test specimens in the chamber, the samples were weighed and recorded.

The five stiffened panels to be corroded were identified as A, B, C, A5, and B5. The percent

mass loss (or degree of uniform corrosion) for each experimental test panel is shown in table

4. The figure 39 shows the 24 hour cycle of the ASTM B117 salt spray procedure. Using a cyclic condition allows more wet-dry cycles to occur in a 24 hours period. The increase of

wet-dry allows for more corrosion to occur, because the process of corrosion take place as

water leaves the surface of a metal [58]. The 24 hours cycle is repeated continuously until the desired degree of uniform corrosion is concluded.

(a) (b)

Figure 38: (a) Show the overview of the fabricated A572 Gr. 50 test stiffened panels, and (b) provides a profile view of the stiffener and welded connection to the plate element.

Table 4: Experimental stiffened panels’ thickness and mass loss data

Model I.d Experimental As-new Original Mass *After Corrosion

(ideal percent Percentage thickness (in) (g) Corroded Test Duration

mass loss) mass loss Mass (g) (weeks)

A5 (5%) 7.56 % .1875 5597 5183 10

B5 (5%) 6.56 % - 5601 5176 10

A (10%) 11.29 % - 5537 4912 16

B (10%) 11.37% - 5540 4910 16

C (15%) 16.32 % - 5540 4639 32

* After corrosion mass reading was taken after the corrosion product was removed from the test specimens.

94 Fog 8 hours

Dwell Dry-off 2 Hours 2 hours

Dry-off Dwell 2 Hours 2 hours

Fog 8 Hours

Figure 39: 24-hour cycle of ASTM B117 salt spray

The initial stage in the cycle is the “fog”. This is where the B117 salt solution is uniformly misted over the specimen for an 8 hour period. To accelerate the evaporation of water from the surface of the test panel, the “fog” stage is followed by the “dry-off” stage.

Over the next 2 hour period, warm air is cycled through the environment chamber without any salt mist or added humility. The “dwell” stage is the final step before the process is repeated; during this stage the test specimen lay for a 2 hour period without any salt mist or moving air. The function of the “dwell” stage is to ensure the surface of the stiffened panel specimens are completely dry; this allows the highest achievable amount of corrosion to take place.

In addition to the continuous corrosion cycle, the environmental chamber is stopped momentarily every two days. During the brief intermission, the stiffened panel specimens

95 are rinsed with de-ionized water. This removes the built-up of salt on the test specimen and removes any loose corrosion by-product; these are both factors that can reduce the rate of corrosion. After the test specimens are rinsed thoroughly, they are rotated and then the corrosion process is resumed. Based on the results from an earlier portion of this thesis to determine the environmental corrosion rate, the rate of corrosion was shown to fluctuate from week to week. Since the corrosion rate is inconsistent, the window of completion for the various degrees of uniform corrosion cannot confidently be determined. To overcome this obstacle, at the end of every week, the test specimens were removed from the environmental chamber and cleaned. The process of the weekly cleaning is shown in figure

40. The test specimens were first rinsed with de-ionized water to remove any loose corrosion by-product, followed by the use of nylon brushes to scrub the entire surface of the samples. Finally, the samples were re-rinsed and allowed to dry with use of compressed air.

Once the specimens were dry, they were weighed to determine the exact mass loss. The process is repeated weekly until the desired percentage of mass loss was reached. When the test specimens completed the corrosion process, they were removed from the environmental chamber and stored in a desiccator until the corrosion process on all test specimens was completed.

(a)

(b)

(c)

Figure 40: Weekly cleaning of stiffened panel test speciman after 90 days of exposure to the ASTM B117 inside the enviromental chamber. (a) the intial state of corrosion on the test specimans immediatly after stopping the enviromental chamber,(b) the specimans are rinsed with de-ionzed water, (c) followed by a light scrubing of the entire surface on the test specimans with an nylon brush and re-rinsed with de-ionzed water.

4.7 Post corrosion cleaning

According to the ASTM [54], the methods used to remove the corrosion product from

the undamaged surface can be categorized as: mechanical, chemical and electrolytic. The

various cleaning procedures are grouped based on the specific metal that is being exposed

to the corrosive environment. Certain methods used to remove corrosion residue can cause

additional removal of un-corroded surface material along with corrosion by-product which provides an inaccurate percentage mass loss calculation. To correct this mass loss error, the un-corroded control sample should be cleaning using the same method used to clean to corroded samples. During this process, the un-corroded control sample must be weighed before and after the cleaning process to determine the mass loss from cleaning. Some of the

other methods are only suitable for use on small applications or required special equipment.

Therefore the post corrosion cleaning method is just as vital as the sample surface

preparation procedure done at the beginning of the corrosion process.

For the scope of this research, the cleaning process consists of a combination of

chemical and mechanical methods used to remove the corrosion by-product. ASTM C 3.2

corrosion removal procedure is used in this study for the cleaning process on all corroded stiffened panel specimens. This method is used due to the large size of the stiffened panel and this method does not require any heating of the solution or constant stirring of the solution. The details of the cleaning procedures are shown in table 5. The chemical aspect of

the procedure consists of immersing the corroded test specimens in a solution specifically

designed for removing corrosion from steel with minimal removal of the base metal. While

the sample is submerged in the solution, a brush is used to remove the softened corrosion

by-product from the surface of the specimen. Once the specimens are free of corrosion by-

product, they are immediately raised with de-ionized water and dried. The effectiveness of

the cleaning process is shown in figures 41 and figure 42. Figure 41(a) – 41(c) shows various viewpoints of the corroded stiffened panel before the cleaning process. Figure 42(d) – 42(f) shows the same specimens at various viewpoints after the cleaning process. The cleaning method proved to be efficient at removing the corrosion product without damaging the un- corroded steel surface. The cleaning samples are stored in a desiccator until the samples are ready to be prepared and tested.

(a) overview of the corroded stiffened panel

(b) profile view of corroded panel (c) under view of corroded stiffened panel

Figure 41: Shows the stiffened panel sample before the cleaning process at various viewpoints.

100

(d) overview of corroded stiffened panel

(e) profile view of corroded (f) under view of corroded stiffened panels

Figure 42: The stiffened panel sample after the cleaning process at various viewpoints.

Table 5: Chemical cleaning procedure for removal of corrosion products

Designation Material Solution Time Temperature

C 3.1 Iron and Steel • 1000 ml Hydrochloric Acid 1-25min 20 to 25oC

• 20 g antimony trioxide

• 50 g stannous chloride

101

4.8 Mechanical Testing

As stated previously, stiffened panels are subjected to a large variety of forces and

loading conditions based on the location of the panel on a navel vessel. For the purpose of

this research, the focus is on stiffened panels located in the bulkhead. These stiffened panels

are usually subjected to combined loading with in-plane compression and lateral hydraulic

compression. For this study, stiffened panel spicemans are mechanically tested under in-

plane compression loading conditions with the primary objective being the determination of

the ultimate buckling strength. The results obtained during this testing will be used to

validate FE model techniques used in a later chapter. Although the focus of this study is

combined loading, the load setup prototype for this form of loading is currently still being devoloped and will be completed in upcoming future works. The mechanical testing for both loading conditions will be detailed in the following section.

Once the corrosion process is complete, the stiffened panel specimans are placed in a

load set-up and axial compression is applied until failure (or until the panel no longer has

the ability to accepted addition loads). Figure 43 shows the loading setup for the in-plane compression mechnical testing. To apply the in-plane compression and provide stability, steel caps were fabericated and placed at both ends of the test spicemans. The caps consist of a thick steel plate with a channel that has a gap distance approximatly the same as the non-corroded stiffened panel height. To ensure the axial loading is equally distributed along the loaded edges, high-strength expoy is used at the end of the test specimans to fill voids.

The expoy also provides as an additional safety factor by minimizing the risk of the speicmans flying out of the load setup. During testing, displacement at the loading edge is

102 measured along with the applied load. The data is used to produce a load displacement diagram, which will be used to determine the residual ultimate buckling strength.

(a) stiffened panel in load set-up

(b) load set-up overview

103

(d) bottom end cap

Figure 43: axial compression mechanical testing load set-up

104

The second loading condition is combined in-plane compression and lataral pressure.

This mechincal testing will be completed in a future study, but a brief description of the

testing will be provided in this section. The panel specimens will be initially axially loaded to a predetermined load. Once the predetermined load is met, the panel will be laterally loaded until failure occurs. This loading style is used because in real world conditions, the axial loads are relatively constant on a fully loaded/operating ship while the lateral pressure is continuously fluccuating due to the nature of water. This loading condition will be conducted to all corroded specimans and one un-corroded control stiffened panel. Figure 44 shows the

load setup used to conduct the combined loading. The load setup for combined loading will

be comprised of five components: the base, end caps, a kevlar air bag, load cells, and a

hydraulic jack. The base and end caps are constructed from A572 Gr. 50 structural steel. The

base is comprised of a series of stiffeners and 0.5 in. thick steel plates connected using 1/8

in. fillet welds. The end caps are used to secure the stiffened panel specimens to the setup

and also to prevent the samples from flying out while being subjected to lateral loading. The

end caps also have a steel bar welded to them to allow the end of the panel to rotate out of

plane while still being loaded. The axial load will be applied manually using the hydraulic

jack. To apply the lateral load, a kevlar air bag will be used to simulate hydaulic fluid pressure

and will be inflated until failure occurs. Two load cells are used to record the loads on the

stiffend panels. One of the load cells will be placed in the center of the hydulic jack and the

second placed centered directly under the air bag. The data from the experiment will be

compared to the FEA model and will be used to vaildate the results of the corrosion models.

105

(a) load set-up overview

(b) front view of end cap (c) back view of end cap that shows the roller

Figure 44: prototype combined loading load set-up.

4.9 Methods to Produce Grooving and Pitting Corrosion

The research done over the course of this study is intended to serve as a precursor to future studies. The reduction of ultimate buckling strength due to the effects of pitting and grooving corrosion damage on stiffened panels is a situation that needs to be studied further but producing these forms of corrosion in a laboratory setting is difficult. This section will detail the experimental technique used to attempt to produce a re-creatable form of pitting

106 and grooving corrosion in a laboratory setting. The technique is based on using a corrosion inhibiting coating to coat a structural steel specimen while intentionally leaving a small amounts of steel surface exposed to a corrosive environment. The technique uses six (6 in. x

3 in. x 0.185 in.) rectangle samples made from A572 Gr. 50 steel. The samples are placed in a corrosion protected rack (shown in figures 45) in the vertical position to provide stagnant water build-up in the corrosion chamber. The specimens are subjected to the same ASTM

B117 corrosion inducing method used on the stiffened panel test specimens.

(a) corrosion protected rack with sample

(b) corrosion rack placement overview

Figure 45: Sample placement in the corrosion chamber

107

Surface preparation is critical to the success of a corrosion inhibiting coating (CIC). In

addition to using the same before and after preparation techniques outlined in previous sections; two methods of removing the steel mill scale is used. Three of the samples were

sandblasted while the remaining three samples were wet polished. The polished surface is

ideal for surface preparation in terms of removing all surface debris and contaminates but

in real world applications, it is not practical to expect workers in the field or on larger

members to wet polish the steel surfaces. Sandblasting the surface of raw steel is probably a

better means of removing mill scale in mobile and larger application but does it remove

enough debris/contaminates to allow the corrosion inhibiting coating to withstand a hostile

corrosive environment for extended periods of time? This is the purpose for comparing the

two methods of surface preparation and also to determine if either has an advantage over

the other at protecting the coated surfaces and the boundaries between the coated and un-

coated surfaces. Once the sample has undergone the full corrosion process, the boundaries

between the corrosion product and the costed surface will be closely examined to verify the

coatings ability to protect the coating surfaces.

Once the samples are properly prepared, the small steel samples are coated with a CIC.

Two coats of the CIC are applied to each sample and allowed 48 hours to dry to ensure the

coating fully sets up. The corrosion inhibiting coating is applied to the steel samples in three

different arrangements (shown in figure 46) to simulate the exposed surface area for pitting

and grooving forms of corrosion. The three arrangements are detailed as followed:

• Before samples A.1 and A.2 are fully coated with the CIC, they first have small

irregular shaped pieces of adhesive applied to their surface. Once fully coated and

108

allowed to dry, the pieces of adhesive are removed. This leaves small exposed

surface areas, resembling larger pits.

• Sample B.1 and B.2 are fully coated with the CIC while leaving a small exposed stripe

down the center of the sample to simulate grooving corrosion.

• Sample C.1 and C.2 are fully coated with CIC and allowed to fully dry. Once

completely dry, a small milling tool (approximately .5mm in diameter at the tip) is

used to mill small hole into the surface of the coating. The holes are only deep

enough to remove the coating and not to damage the surface of the steel sample.

A1 A2 (a)

109

B1 B2 (b)

C1 C2 (c)

Figure 46: Shows the three arrangement in which the coating was applied. In the above figures, the surface preparation for the samples is arranged as sand blasted (left) and wet- polish (right) surface preparation. The figures are described as follows; (a) pitting corrosion using small pieces of adhesive, (b) grooving corrosion, and (c) pitting corrosion using a small tool.

110

After the coating arrangement process is complete on all samples, they are then placed in the environmental chamber. The same ASTM B117 accelerated corrosion process used on the stiffened panels is used to induce corrosion on these samples. The samples are subjected to the extreme corrosive environment for 12 weeks in the environmental chamber.

Once the corrosion process is completed, the sample are stored in a desiccator to allow the samples to fully dry. Figure 47 shows the corrosion on the samples after the corrosion process is complete. Once the samples dry, the coating surface will be investigated and the result will be presented in a later chapter.

B1 A1 C1 (a)

111

B2 A2 C2

(b)

Figure 47: Rectangle specimens after the 12-week corrosion process. (a) Shows the samples that were wet-polished to remove the mill-scale, (b) samples that were sandblasted to remove mill-scale.

112

CHAPTER 5

UNIFORM CORROSION ON STIFFENED PANEL FINITE ELEMENT MODEL

5.1 Introduction

The damage and danger associated with corrosion damage is evident across all major industrial categories ranging for transportation municipals to offshore oil rigs. Having the ability to reduce the financial impact of corrosion damage while reducing the risk of structural member failure is an ideal situation for all industrials dealing with corrosion damage. For structures utilizing stiffened panels to make-up structural components in

environments that are susceptible to corrosion (such as naval ships, bridges, etc.) are very

prone to structural failure do to corrosion. This is due to stiffened panels being complex in

geometry which leads to members retaining stagnate water containing electrolytes and this

initiates the corrosion process. Along with complex geometries, the loading conditions that

stiffened panels are subjected to only exacerbate the risk of member/structural failure due

to corrosion damage.

Having the ability to predict the ultimate buckling strength and/or model the member

failure due to corrosion damage would allow for a reduction in inspection costs, to mitigate

unnecessary repairs, and eliminate failures due to corrosion. In this chapter, the procedure

to model various degrees of uniform corrosion damage on stiffened panels using a finite

element analysis (FEA) software called ABAQUS is detailed. The stiffened panel were

modeled under three loading conditions: (a) axial compression (b) combined loading using

axial compression and lateral pressure, and (c) lateral pressure. Using the three loading

113 conditions, a series of non-linear post buckling analyses were conducted to determine the

residual ultimate buckling strength from the various degrees of uniform corrosion.

Conducting the analysis under the three loading conditions provide a better representation

of the effects of various degrees of uniform corrosion on the ultimate buckling strength. This

also provides a progressive breakdown of the effects of initial axial compression on the

lateral load. Having the ability to determine the ultimate buckling strength and failure modes

of different degrees of corrosion allows the risk of failure to be determined. The design codes,

ABS and API, will be used to compare the result for the FEA modeling.

5.2 Material and Geometry

The stiffened panel FEA model presented in this chapter was developed according the similar guidelines used in the laboratory experimental test. The material used to develop the

FEA models was the same ASTM A-572 Grade 50 steel properties. The material properties used in the FEA model (shown in Table 6) are approximate values obtained from ASTM

Material Standards [59]. The material used in this paper is a high tensile strength steel. Steel material usually has a strain-hardening tangent modulus (Et) that ranges between 5-15% of

the Young’s modulus [60]. In a study by J.K Paik et al. it was stated that due to the effect of

strain-hardening, the ultimate strength obtained for steel plates is larger than when strain-

hardening is not considered [61]. For a more conservative assessment of the ultimate

strength of thin-walled steel structures such as stiffened panels, an elastic-perfectly plastic steel material model is sufficient and adequate. With this in mind, the material behavior used

114

in the stiffened panel FEA models will be analyzed and the effects of strain-hardening will

not be considered [61].

Table 6: Input for material properties in ABAQUS*

Material Parameter Values

Compressive Yield Stress (fy) 50 ksi

Poisson’s ratio (µ) 0.30 A-572 Grade 50 Steel Modulus of Elasticity (E) 29,000 ksi

Since the material properties used are according to ASTM standards, the actual

experimental yield stress may be higher. This is due to the fact that ASTM standards provides

the minimum associated yield strength. This means the residual ultimate buckling strength

values obtained using ABAQUS may be on the conservative side. The components (such as

the web, flange and plate) used to construct the non-corroded (“as-new”) stiffened panel is made up of 3D shell elements with an assigned thickness of 0.1875 inches. The overall stiffened panel dimensions (shown in figure 48) are slightly smaller than those of the experimental stiffened panel. This is due to the shell element models having to be constructed about the neutral axis of each component. The width and length dimensions are the same as the experimental sample used and the thickness of each will vary depending on the desired level of uniform corrosion.

115

Figure 48: Auto CAD rendering of typical cross-sectional details of one of the test panels. *the purple dotted line represents the neutral axis for each component of the stiffened panel.

5.2.1 Corrosion Geometry

In addition to creating a FEA model to simulate an un-corroded stiffened panels’ failure, FEA models to simulate uniform corrosion are developed. Two sets of FEA models were developed to investigate the effect of uniform corrosion on stiffened panels. The two categories of models can be described as the ideal degrees of uniform corrosion and the experimental degrees of uniform corrosion. The ideal degrees of uniform corrosion is defined as the actual target degree of uniform corrosion in which the goal is to obtain these in a controlled laboratory setting. The ideal degrees of uniform corrosion in this study are

5%, 10% and 15% percentage mass loss. Producing the exact amount of percentage mass loss is extremely difficult in a laboratory setting, even with constant monitoring. Knowing this, a second category of FEA models were developed using the actual amount of percentage mass loss obtained for the steel stiffened panels during the corrosion process. These

116 percentage mass loss values from the laboratory corrosion process is what defines the experimental degrees of uniform corrosion FEA models.

To simulate uniform corrosion according to specific degrees of percentage mass loss, the original thickness (0.1875 in.) is reduced to equate to the desired percentage mass loss.

The mass loss percentage and the corresponding thickness is shown in table 7. The reduction in thickness is calculated as a function of density, volume, and mass. A study conducted by

Sharfi et al. [62][11] used a similar approached when investigating the effect of corrosion on the remaining lateral torsional buckling capacity and shear capacity of I-shaped steel members. In the study, the degree of corrosion was measured by thickness loss and equated to percentage mass loss (shown in figure 49). Along with developing five model sets based on the percent mass loss obtained from the stiffened panel from the laboratory experiments, three FEA model sets were developed based on the ideal percentage of mass loss. All corrosion FEA models share the same overall dimension as the un-corroded stiffened panel

FEA model except for thickness.

Table 7: Experimental stiffened panels’ thickness and mass loss data

Model I.d (ideal Experimental As-new Corroded (actual) Ideal thickness percent mass Percentage thickness (in) thickness (in) (in) loss) mass loss A5 (5%) 7.56 % .1875 .1752 .1781

B5 (5%) 6.56 % - .1733 .1781

A (10%) 11.29 % - .16632 .16875

B (10%) 11.37% - .16618 .16875

C (15%) 16.32 % - .1569 .1594

117

Figure 49: Uniform Thickness Loss Model [11]

Where,

TN= as-new thickness of flange

tN= as-new thickness of web

B= flange width

D = depth of section

5.3 Element type and Meshing

Using the finite element code ABAQUS, the residual ultimate buckling strength of stiffened panels exposed to uniform corrosion is investigated. The components that are used to form the stiffened panels are all comprised of shell mesh elements denoted as “S4” elements. The “4” in “S4” described the numbers of nodes each element has. This element type allows for six degrees of freedom at each node; translations in the x, y, and z directions, and rotations about the x, y, and z-axes. These elements are well-suited for the modeling of

118 thin shell structures due to its ability to account for the changes in the thickness of the element because of deformation caused by an acting load [63]. S4 elements are often used in linear, large strain and/or large rotation nonlinear applications FEA studies where in-plane and/or out-of-plane bending is expected; as is our case in this study. When preforming FE analysis, a balance between accuracy and computational time needs to be established. Mesh density (or the number of elements) is a key factor for determining this balance. Using a finer mesh would provide greater accuracy but at the same time, that means more computational efforts is required, meaning longer time is needed to complete the analysis. Also, too fine of a mesh may result in computational issues and led to errors during the analysis. A mesh convergence study was undertaken to determine the mesh capable of provide accurate results for a nonlinear FE analysis without extensive computational time and/or errors. A global mesh of .25 is the mesh increment applied to the final analysis.

5.4 Boundary Conditions and Load Arrangement

The boundary conditions and load arrangement used to perform the FEA are supposed to simulate the experimental testing procedure as close as possible. When it comes to boundary conditions, it is common practice to use either simply supported or clamped boundaries along the longitudinal edges when assessing the ultimate limits. According to a studying conducted by J.K Paik [64] the difference between the two boundary conditions is marginal when the predominant loads is longitudinal compression. The study also indicated that using simply supported boundary conditions provide more conservative results. For the current study, the ultimate bucking strength of stiffened panels are analyzed under three

119 loading arrangements; (a) in-plane compression, (c) lateral pressure and (b) combined axial

compression and lateral compression. For these loading arrangements, the longitudinal

compression is the predominant load. Thus, simply supported boundary conditions would

be sufficient for all FEA models, but this doesn’t represent the mechanical testing conditions.

The longitudinal edge are left free of constraints as this is the case when mechanical testing

of the stiffened panel test specimens is performed.

When studying the FEA models where the loading condition is either in-plane

compression or lateral pressure, the stiffened panels are axially (or laterally) loaded until failure in the loading direction. For the combined loading FEA models, the procedure is slightly different. Based on the ultimate strength results obtained from the single directional loading, increments of axial (and lateral) loads that are to be initially applied are determined.

For FE models that are analyzed under combined loading, the predetermined axial load is applied in the first step followed by a lateral load until failure in the second step. The process is repeated for each increment of predetermined axial load for each simulated degree of uniform corrosion (including the non-corroded model). The predetermined axial loads for the combined loading arrangement is shown in the Results Chapter.

In addition to not using simply supported boundary conditions along the longitudinal edges of the stiffened panel and leaving them constraint free, it is essential to use boundary conditions at the loaded and un-loaded edges that allow the stiffened panel to buckle out of plane while not allowing displacement along those edges. Figure 50 shows the boundary conditions of the stiffened panel model. The applied boundary conditions used for these analyses are described as the following:

120

– Unloaded transverse edge BB'(Includes all plate's and stiffener's nodes): simply

supported with T [0,1,1], R [1,0,0].

– Loaded transverse edge AA'(Includes all plate's and stiffener's nodes): simply

supported with T [0,0,1], R [1,1,0]. B

B A

Figure 50: shows the boundary conditions of the stiffened panel model.

In the above boundary conditions, T[x,y,z] and R[x,y,z] represent translational constraints and rotational constraints related to x, y, and z axis, respectively. The values of x, y, and z are either “1” or “0”. A “1” means “constraint” and vice versa. When applying a load during a FE analysis, it is critical that the load is applied uniformly and the loading edges displace equally. Failure to keep the acting load uniform on the member could cause rotation about the axis perpendicular to the load and/or unnatural failure behavior. To achieve equal displacement along the loading edge the “EQUATION” constraint is applied to the center node, “c”, between the stiffener and plate at mid-span at the loaded edge. The center node

121

“c” is constrained to all other nodes along the loaded edge of the stiffened panel. This means

any displacement that occurs at the center node “c” in the z-direction will be applied on all other nodes along the loaded edge.

5.5 Imperfections

When using stiffened panels in real-world applications, it is highly unlikely to have stiffened members that are exactly straight or without imperfections. In order the obtain results that are concurrent with those that are closely representative of typical stiffened panels and of those used during the experimental process, an initial geometric imperfection is applied. This is achieved by using the “IMPERFECTION” option in ABAQUS; an overall buckling mode shape is obtained during the eigenvalue buckling analyses (which will be discussed further in an up-coming section). The imperfection is applied as a global imperfection meaning the imperfection is introduced to both the stiffener and plating elements. The scale factor used on the stiffened panel is: wo = a/400, where ‘a’ is the length

of one bay [35][65]. The imperfection is applied to all FEA including the non-corroded, ideal uniform corrosion, and experimental uniform corrosion models. Each FEA is also conducted without an imperfection to compare the effect of the initial imperfection.

5.6 Non-linear Post-Buckling Analysis

To determine the residual ultimate buckling strength of stiffened panels after

exposure to various degrees of uniform corrosion, a series of nonlinear post-buckling

analyses were conducted. This form of analysis was conducted on all FEA models. The

122

nonlinear analysis was used over the linear (eigenvalue) buckling analysis due to its

increased accuracy and allows for the use of geometric imperfections. Nonlinear buckling

analysis is a static method which accounts for nonlinear material behaviors, geometric

nonlinearities (P- - - displacement effectsΔ and [66]. P δ), The load “post perturbations,-buckling” term geometric indicates imperfections, analyses done and after large the initial

buckling has occurred based on the critical buckling load. The increased accuracy when

using a non-linear post-bucking analysis stems from the total load being applied

incrementally and that at each increment, the stiffness and response of the member are

evaluated. The following section will outline the process of conducting a non-linear post-

buckling analysis.

The analysis commences by first determining the critical buckling load of the

stiffened panel. This process is achieved by using the “BUCKLING” step function in ABAQUS,

and applying a unit load of 1 kip to the loaded edge of the stiffened panel. The “BUCKLING”

step function is a linear analysis and produces an eigenvalue and eigenvector. By

multiplying the initial load applied to the stiffened panel with the eigenvalue obtained

during the analysis, the critical buckling load is determined. The eigenvector obtained in

the first mode of failure is typically indicated to be the most likely means of failure and

failure shape. The second step is the applied post-bucking behavior to the FE model by

applying the critical buckling load to the initial FE model and inputting the initial geometric

imperfection in the KEYWORDS of the ABAQUS model. The final step is to conduct the

nonlinear post-bucking analysis with using the “STATIC general” step function in ABAQUS.

During this step, ABAQUS simultaneously solves for displacement and loads by finding a

single equilibrium path in space that is defined by the mesh variables and loading

123 parameter. A defined “arc length” along a static equilibrium path is used to measure the solutions progress since the load magnitude is unknown as well. The results of nonlinear static-RISK analyses are obtained by plotting of displacement against the load. The data obtained during the FEA will be compared with the result for the experimental corrosion process and the design codes ABS and API in the following chapter.

124 CHAPTER 6

RESULTS AND DISCUSSION

6.1 Introduction

In the following chapter, the results from the experimental chapter and the finite

element analysis (FEA) chapter will be presented and discussed. The residual ultimate

capacity, ultimate load, and percentage error will be the point of emphasis for all compared

results and discussions. The relationship of the ultimate load between the axial compression mechincally tested non-corroded stiffened panels and their FEA counter-part will be presented and discussed first. The uniformly corroded stiffened panel sample results from the axial compression mechincally tested stiffened panels and FEA models relatonship will follow. Wrapping up the stiffened panel results will be the FEA results for the stiffened panels under combined loading. For each degree of simulated uniform corrosion, various predetermined axial loads will be applied followed by being laterally loaded until failure.

These results will produce an “axial load vs. lateral load” diagram which will provide a closer understanding of the relationship between the residual ultimate strength and the increased

degrees of uniform corrosion. Based on the precentage of the FEA results for the stiffened panels under axial compression when comparing them to the mechanical testing done on an

actual corroded stiffened panel, the FE model techique used to produce the FEAs results for

the corroded stiffened panel under combined loading can be verified. In the final section of this chapter, the results of the procedure used to produce pitting corrosion and grooving

corrosion will be presented and discussed.

125

6.2 Non-Corroded Stiffened Panel Control Samples

In figure 51, the non-corroded (or control) sample results from the three mechanical

tests and the FE control sample are presented in a load displacement diagram. From the peak

of each sample line, the ultimate strength can be determined. Table 8 provides these values,

along with maximum displacement and predicted values from the FEA, the American

Patroium Insistuent (API) and the American Bearue of Shipping (ABS). The industry

guidelines, API and ABS, will be used to compare the ultimate strength and critical buckling strength (respectively) of the testing results.

LOAD DISPLACEMENT DIAGRAM FROM MECH. TESTING VS FEA RESULTS

120

100

80 Control A 60 Control B 40 Control C LOAD (KIPS) 20 Control FEA

0 0 0.1 0.2 0.3 0.4 0.5 0.6 -20 DISPLACEMENT (IN)

Figure 51: Load Displacement Diagram comparing the results from the mechanical testing and the FEAs.

126 Table 8: Mechanical Testing Results and Predicted Results from FEA, API and ABS design codes

Mech. Testing Results Predicted Value Sample Max I.D Max Load Displacement API ABS FEA (max load) Control A 101.846 0.531 Control 112.000 62.000 92.451 B 102.606 0.302 Control C 98.519 0.443 Average 100.991 0.425

6.2.1 Non-Corroded Stiffened Panel Control Samples Discussion

From figure 51 shown previously, the FE control samples’ ultimate load appears to

have a good coorelation with those of the three mechanically tested control samples. From

the average percentage error shown in table 9, the FEAs and mechanical test results have an

average error of 8.43% which is an acceptable amount of error. Even when comparing the

industry guildlines of API and ABS, the percent error is approximately 10% for API which is a acceptable error. The ABS percentge error on the other hand is much lower and provide an accurate comparisons. Figure 51 also indicates that the amount of displacement is not acturately determined from the FEA, but the focus of this study is the ultimate load obtained during testing.

Table 9: Shows the percent error of the the predicted values compared to the mechanical testing. Mech Testing % Error (compared to..) Sample I.D FEA API ABS Control A 9.225 9.782 1.057 Control B 9.897 8.969 0.309 Control C 6.159 13.490 4.470 Average 8.427 10.747 1.945

127 6.3 Corroded Stiffened Panel Control Samples

In the following section, the effect that unifrom corrosion has on the utimate strength of stiffened panels under axial compression will be presented. The first portion of this section

will show an overall perspective on the effects that uniform corrosion has on stiffened panels

for both mechanical analyses and FEAs. The second portion of this section will provide a

closer look at the effects that uniform corrosion has on the indivdual mechincally tested

samples and their FEA counterparts.

Figure 52 is an overview of load displacement for the actual corroded samples that

were mechanically tested. Figure 53 shows an overview of load displacement for the FEAs

where simulated corrosion is produced by reducing the overall component thicknesses; such

as the web, flange, and plate.

LOAD DISPLACEMENT DIAGRAM FROM MECH. TESTING ON CORRODED SAMPLES 100 90 80 70 60 Sample I.D A 50 Sample I.D B 40 Sample I.D C

LOAD (KIPS) 30 Sample I.D A5 20 Sample I.D B5 10 0 -0.05 -10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 DISPLACEMENT (IN)

Figure 52: Load displacement diagram for the mechanically tested corroded samples

128

Table 10: Mechanically tested stiffened panel results

Sample Mass Loss Max Load Max Displacement I.D (%) (kips) (in) A 11.29 81.33 0.3885 B 11.37 82.58 0.2835 C 16.32 75.86 0.2540 A5 6.56 88.02 0.2110 B5 7.56 80.36 0.2158

LOAD DISPLACEMENT DIAGRAM FOR FE MODELS 90 80 70 60 Sample I.D A (11.29% mass loss) 50 Sample I.D B (11.37% mass loss) 40 Sample I.D C (16.32% mass loss) LOAD (KIPS) 30 Sample I.D A5 (6.56% mass loss) 20 Sample I.D B5 (7.56% mass loss) 10 0 0 0.1 0.2 0.3 0.4 0.5 DISPLACEMENT (IN)

Figure 53: Load displacement diagram for the FEAs on the corroded samples

Table 11: FEAs stiffened panel results

Sample Mass Loss Max Load Max Displacement I.D (%) (kips) (in) A 11.29 78.23 0.406 B 11.37 78.15 0.407 C 16.32 72.72 0.415 A5 6.56 83.50 0.393 B5 7.56 82.36 0.396

129

In the following portion of this section, each uniformly corroded stiffened panel that

was mechanically tested will be closely compared to its’ FE modeled counterpart. The percentage error of the ultimate load bewteen these two forms of analyses will be presented.

Along with comparing the percentage error, the failure behavior between the mechanical testing and the FEA will be examined as well. Comparsions of the failure behavior is used as an additional form of verification of the FE model methods used to produce the FEA on the stiffened panel under combined loading. In figures 54(a) – 54(e), the load displacement diagrams will be shown comparing the mechanically tested samples and their FE counterpart results. Figures 55(a) – 55(e) shows the FEA predicted failure mode, followed by figures 56(a) – 56(e) which show the actual failure mode during mechanical loading.

SAMPLE A FEA VS MECH. TESTING RESULTS 90 80 70 60 50 40 Sample I.D A Sample I.D A FEA

LOAD (KIPS) 30 20 10 0 -0.1 0 0.1 0.2 0.3 0.4 0.5 -10 DISPLACEMENT (IN)

Figure 54: (a) Load displacement diagram for corroded Sample A – comparing the FEA results to the mechanically tested results.

130

FEA % error compared to Actual Mech Testing Sample Mech. Testing FEA Results Percent I.D Results Error (%) A 81.33 78.2331 3.80

Failure Behavior:

Figure 55: (a) FEA predicted failure shape for Sample A

131

Figure 56: (a) Shows the failure behavior of Sample A during mechanical testing from various prospectives.

132

SAMPLE B FEA VS MECH. TESTING RESULTS 90 80 70 60 50 40 Sample I.D B LOAD (KIPS) 30 Sample I.D B FEA 20 10 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 DISPLACEMENT (IN)

Figure 54: (b) Load displacement diagram for corroded Sample B – comparing the FEA results to the mechanically tested results.

FEA % error compared to Actual Mech Testing Sample Mech. Testing Results FEA Results Percent Error I.D (%) B 82.58 78.1475 5.37

Failure Behavior:

Figure 55: (b) FEA predicted failure shape for Sample B

133

Figure 56: (b) Shows the failure behavior of Sample B during mechanical testing from various prospectives.

134

SAMPLE C FEA VS MECH. TESTING RESULTS 80

40 Sample I.D C

LOAD (KIPS) 30 Sample I.D C FEA 20

0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 DISPLACEMENT (IN)

Figure 54: (c) Load displacement diagram for corroded Sample C – comparing the FEA results to the mechanical test results.

FEA % error compared to Actual Mech Testing Sample Mech. Testing Results FEA Results Percent Error I.D (%) C 75.86 72.72 4.14

Failure Behavior:

Figure 55: (c) FEA predicted failure shape for Sample C

135

Figure 56: (c) Shows the failure behavior of Sample C during mechanical testing from various prospectives.

136

SAMPLE A5 FEA VS MECH. TESTING RESULTS 100 90 80 70 60 50 Sample I.D A5 40 LOAD (KIPS) Sample I.D A5 FEA 30 20 10 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 DISPLACEMENT (IN)

Figure 54: (d) Load displacement diagram for corroded Sample A5 – comparing the FEA results to the mechanically tested results.

FEA % error compared to Actual Mech Testing Sample Mech. Testing Results FEA Results Percent Error I.D (%) A5 88.02 83.50 5.13

Failure Behavior:

Figure 55: (d) FEA predicted failure shape for Sample A5

137

Figure 56: (d) Shows the failure behavior of Sample A5 during mechanical testing from various prospectives.

138 SAMPLE B5 FEA VS MECH. TESTING RESULTS 90

40 Sample I.D B5 LOAD (KIPS) 30 Sample I.D B5 FEA

0 -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 DISPLACEMENT (IN)

Figure 54: (e) Load displacement diagram for corroded Sample B5 – comparing the FEA results to the mechanically tested results.

FEA % error compared to Actual Mech Testing Sample Mech. Testing FEA Results Percent Error I.D Results (%) B5 80.36 82.36 2.49

Failure Behavior:

Figure 55: (e) FEA predicted failure shape for Sample B5

139

Figure 56: (e) Shows the failure behavior of Sample B5 during mechanical testing from various prospectives.

140

RESIDUAL ULTIMATE STRENGTH CAPACITY REMAINING ULTIMATE CAPACITY (%)

SAMPLE A (11.29% SAMPLE B (11.37% SAMPLE C (16.32% SAMPLE A5 (6.56% SAMPLE B5 (7.56% MASS LOSS) MASS LOSS) MASS LOSS) MASS LOSS) MASS LOSS) SAMPLE I.D

Remaining Axial Capacity (Mech. Results) Remaining Axial Capacity (FEA Results)

Figure 57: Residual Ultimate Strength Comparison

Table 12: Remaining axial capacity results and percentage error.

Sample I.D Remaining Axial Capacity Remaining Axial Precentage (Mech. Results) Capacity (FEA Results) Error

Sample A 80.53 84.62 4.83 (11.29% mass loss) Sample B 81.77 84.53 3.27 (11.37% mass loss) Sample C (16.32% 75.12 78.66 4.50 mass loss) Sample A5 87.15 90.32 3.51 (6.56% mass loss) Sample B5 79.58 89.09 10.68 (7.56% mass loss) Average 5.36

141 6.3.1 Discussion of the Corroded Stiffened Panel Control Samples

When analyzing results of both the FEA and the mechanically tested results, the

percentage bewteen their ultimate loads across all degrees of uniform corrosions are less

than or approxmently equal to 5% error. The average percentage error among all five

comparisons is 4.18%. The buckling behavior bewteen the two forms of analyses also share similarities. The FEA indicated that the failure behavior would not change due to the loss of

mass and that the failure behavior would be a combination of plate buckling and flexural torsional buckling. As shown from the testing figures, this predicted failure behavior holds true. The stiffener (web and flange componets) remained straight while the plate failed and displaceed. The behavior is usually caused by having too low of a stiffener-web slenderness ratio causing the plate component to fail first. In figure 57, the residual ultimate strength capacity is shown for both the mechanical testing and FEAs. The data for the figure is presented in table 17 and the residual ultimate strength capacity is compared to the average ultimate strength results obtained from the mechanical testing on non-corroded samples.

The FEAs were capable of determining the residual ultimate strength with an aveage precent error of 5.36% when compared to the mechanical test results. Even when the outliner is removed, the error drops to 4.03%. The FEAs were not able to actually determine the displacement, but for this study, our focus is the residual ultimate strength.

6.4 Stiffened Panels Under Combined In-plane Compression and Lateral Loading

The section will present the results of the FEA on stiffened panels under combined

axial compression and lateral loading. The degrees of uniform corrosion used in this section

142 are ideal values of corrosion and not the degrees of corrosion from the experimental

corrosion process. The focus will be on the residual ultimate load and change of capacity with respect to increased combined loading and varying corrosion levels. Figure 58 presents an interactive diagram comparing the utlimate loads of both axial and lateral loading in regards to increased levels of uniform corrosion.

ULTIMATE AXIAL LOAD VS. ULTIMATE LATERAL LOAD

120

100

AXIAL FOAD FOAD (KIPS) AXIAL 40

0 0 5 10 15 20 25 30 35 ULTIMATE LATERAL LOAD (KIPS)

Original Sample (No Corrosion) 10 % Corrosion 20 % Corrosion 5 % Corrosion

Figure 58: Shows the relationship bewteen axial loading and lateral loading on stiffened panels subjected to various degrees of corrosion.

Figure 59 shows the change in both axial and lateral ultimate strength when

compared to the corresponding independent axis for ultimate strengths of the non-corroded

stiffened panels. The values for this figure is presented in table 18.

143 REMAINING ULTIMATE LOAD CAPACITY

Axial Capacity Lateral Capacity

120.00

100.00

80.00

60.00

40.00

REMAINING CAPACITY (%) 20.00

0.00 NON- CORRODED 5 % MASS LOSS 10 % MASS LOSS 20 % MASS LOSS CORROSION CORROSION CORROSION PERCENTAGE CORROSION

Figure 59: Shows the residual ultimate capacity of the independent loading axis for increased degrees of uniform corrosion.

Table 13: Residual Ultimate Capacity with respect to independent axis.

Sample I.D Axial Load Lateral Load Remaining Remaining Lateral Axial Capacity Capacity Non-corroded 92.58 33.75 100.00 100.00 5 % mass loss 86.28 31.43 93.20 93.13 corrosion 10 % mass loss 80 29.97 86.41 88.80 corrosion 20 % mass loss 74.56 25.67 80.54 76.06 corrosion

Figure 60 is similar to the interactive diagram shown previously in this section, but this figure takes a look at the residual ultimate strength capacity of the stiffened panel under combined loading simultaneously.

144

RESIDUAL ULTIMATE STRENGTH CAPACITY UNDER COMBINED LOADING

100.00

80.00

60.00

40.00

20.00

RESIDUAL UTIMATEAXIAL CAPACIITY (%) 0.00 0.00 20.00 40.00 60.00 80.00 100.00 RESIDUAL UTIMATE LATERAL CAPACITY (%)

Non-Corroded 5 % mass loss corrosion 10 % mass loss corrosion 20 % mass loss corrosion

Figure 60: Residual Ultimate Strength Capacity under combined loading.

6.4.1 Combined Loading Discussion

When using the interactive diagram shown in figure 58, the user could select a degree of uniform corrosion on an A572 Gr. 50 steel stiffened panel (with similar dimensions) and ideally determine the amount of residual ultimate strength in both directions of loading.

Figure 59 shows an average decrease of 6.48% in the axial loading direction bewteen the various degrees of corrosion. In the lateral loading direction, figure 59 shows an average loss of ultimate strength capacity of 7.98%. Figure 60 also allows a user to determine the residual ultimate strength with respect to the remaining capacity percentage. The results shown in the figures may not necessarily change due to changes in dimensions, but the material and loading conditions should be congruent with those of this study. This is due to the results reflecting capacity percentage and not actual ultimate strength values. When examining

145

results of figures 60, the non-corroded sample has an average decrease of 17.38% per 10 kips increased of axial load, where as a sample with 5% mass loss will have an expected average loss of ultimate lateral strength at a rate of 18.95% per 10 kips increased of axial load, a sample with 10% mass loss will have an expected average loss of 20.32% per 10 kips increased of axial load, and a 20% mass loss sample will have an expected loss of 24.01% per

10 kips increased of axial load. The change in capacity is presented as a change in lateral capacity per increase in axial load of 10 kips because during the FEA non-linear post buckling analysis, the stiffened panel samples were axially loaded until a determined load then laterally loaded until failure.

6.5 Pitting and Grooving Corrosion Labortory Production Results

In the final section of the chapter, the results from the procudure used to induce

pitting corrosion and grooving corrosion will be discussed. The small coated rectangular

samples were subjected to an extremely corrosive environment for twelve weeks. Once the

corrosion process was completed, the samples were left to dry for two weeks. The samples

were analyzed based on the appearance of corrosion and the protection of the coating

surface immediately adjacent to the exposed corroded surface. The overall protection the

coating provided will be examined as well. Figures 61(a) – 66 (a) shows the sample once they

have completely dried and before the coating was removed. The figures 61 (b) -66 (b) inspect

the coated surfaces next to the exposed corroded surface and under the protected coated

surface. The result will be discussed at the conclusion of this section.

146

(a)

(b)

Figure 61: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface.

Surface Preparation Shown Above: Wet-Sand Polish Simulated Corrosion Type Shown Above: Grooving Corrosion

147

(a)

(b)

Figure 62: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface.

Surface Preparation Shown Above: Sand-blast Simulated Corrosion Type Shown Above: Grooving Corrosion

148

(a)

(b)

Figure 63: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface.

Surface Preparation Shown Above: Wet-Sand Polish Simulated Corrosion Type Shown Above: Large Diameter Pitting Corrosion

149

(a)

(b)

Figure 64: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface.

Surface Preparation Shown Above: Sand-blast Simulated Corrosion Type Shown Above: Large Diameter Pitting Corrosion

150

(a)

(b)

Figure 65: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface.

Surface PreparationShown Above : Wet-Sand Polish Simulated Corrosion Type Shown Above: Small Diameter Pitting Corrosion

151

(a)

(b)

Figure 66: (a) Shows before coating is removed and (b) after partial removal of the coating and shows the sample suface immediately adjacent to the corroded suface.

Surface Preparation Shown Above: Sand-blast Simulated Corrosion Type Shown Above: Small Diameter Pitting Corrosion

152

6.5.1 Pitting and Grooving Corrosion Labortory Production Discussion

When looking over the results shown is figures 61 (a) -66 (a) of the pitting corrosion and grooving corrosion procedure, all samples showed corrosion on the small exposed steel surfaces. The overall corrosion inhibiting coating (CIC) also showed that it is capable of withstanding a hostal corrosive environment. When taking a closer look at the protection of the surface under the CIC and immedialty next to the corroded exposed surfaces (shown in figures 61 (b) – 66 (b), the CIC is able to protect the surface under the coating and does not allows corrosive solution to penatrate the edges along the exposed surface areas. In the comparisons between the sand-blasted and wet-polish surface preparations, neither showed any major advantage in surface protection. They were both able to provide adequate surface protection.

153

CHAPTER 7

CONCLUSION

Stiffened panels used on naval ships and marine applications are extremely susceptible to uniform corrosion due to the hostile corrosive environment in which members are exposed to. That is exactly the reason why an understanding of the loss of ultimate strength as corrosion increases is needed. The effect that uniform corrosion has on the ultimate strength of steel members is widely known to cause a decrease in strength but the approximate amount of loss residual ultimate strength it not known. The effect that other forms of corrosion, such as (non-uniform corrosion) pitting corrosion and grooving corrosion, also need more understanding but producing these forms of corrosion in a laboratory setting is difficult. This chapter summarizes the research conclusions obtained from the different analyses and experiments performed on A572 Gr. 50 steel stiffened panels affected by uniform corrosion. The chapter will also summarize the conclusions of the procedure used to produce non-uniform corrosion in a laboratory setting. The analysis of data and charts developed in this thesis leads to the following conclusions:

• The FEA technique used to model stiffened panels under axial compression loading is

verified. The average percent error between the predicted ultimate strength for the

FEA and results of the mechanical testing is 4.18% and all five samples had an error

of less than or equal to 5%. Any error less than 10% is considered good results.

• The FEA technique used to model stiffened panels under combined loading is

applicable based on the success the techniques had for samples under axial

154

compression. When comparing the residual ultimate strength capacity results of the

FEA for axial compression to the mechanical testing, the average percent error is

5.36%. When removing the outliner, the percent error drops to 4.03%. As an

additional form of validation, the comparisons between the FEAs failure behavior and

the mechanical testing failure behavior were also identical.

• When a stiffened panel is subject to 5%, 10%, and 20% (mass loss) uniform corrosion,

the residual ultimate lateral strength capacity shows a decrease of: 18.95 %, 20.32%,

and 24.01%, respectively, per 10 kips increased of axial load.

• Using a corrosion inhibiting coating (CIC) to producing pitting corrosion and grooving

corrosion in a laboratory setting proved to be effective. The CIC is able to successfully

protect the steel surface under the coating and the edge along the exposed surface

while allowing the small exposed surfaces to corrode. The coating was able to

withstand twelve weeks in a hostile corrosive environment without showing signs of

failure.

7.1 Other Conclusions

The following conclusion presented in this section does not the focus on this research study, but are interesting observation obtained over the course of this study:

• Low levels of uniform corrosion has small to little effect of the failure behavior of

stiffened panels under axial compression. This behavior was observed during both

FEAs and mechanical testing.

• The method used to produce FE models under both single axial loading and combined

loading was not able to actually determine the excepted displacement during failure.

155

CHAPTER 8

FURTURE CONTINUING WORKS

In order to completely verify the results of the FEAs for stiffened panels under combined loading and to fully understand the effects that uniform corrosion and non- uniform corrosion has on the residual ultimate strength, more experimental study is needed.

At The University of Akron, a study of mechanically testing the stiffened panels is underway.

By mechanically testing the samples under combined loading, the results of the FEAs can be fully verified. In this study, additional factors such as slenderness, changes in overall geometry, and increased levels of uniform corrosion will be considered. This will also verify if the interactive residual ultimate strength capacity diagram shown in section 6.4 shows any changes in capacity. Another study at The University of Akron is underway to examine the effects of non-uniform corrosion such as pitting and grooving corrosion. This study will use the pitting and grooving procedure developed in this study to produce these forms of corrosion. Based on the results of these ongoing projects, these studies will produce a tool/method to determine the residual ultimate strength of steel stiffened panels outside a laboratory setting. The studies will also aid in the modification of industry guidelines to include the effects of corrosion.

156

CHAPTER 9 REFERENCES

(1) Koch, Gerhardus H, et al. (2002) Corrosion Costs and Preventive Strategies in the United States. McLean, Va, Federal Highway Administration, www.nace.org/uploadedFiles/Publications/ccsupp.pdf. Accessed 3 Nov. 2016.

(2) Czarnecki, A. A., & Nowak, A. S. (2008). Time-Variant Reliability Profiles for Steel Girder Bridges. Structural Safety, 30, 49-64.

(3) NACE. (2004). CORROSION FAILURE: LCS 2 USS Independence Naval Ship Engine Corrosion. NACE, NACE International, www.nace.org/CORROSION-FAILURE-LCS- 2-USS-Independence-Naval-Ship-Engine-Corrosion.aspx. Accessed 2 Dec. 2016.

(4) ICI Engineering, (1990). Procedure for: Condition categories for inspection of plant structures and pipe bridges. Standards & Technical Information Services, ICI Engineering, Cheshire, England.

(5) Jiang, X., & Soares, C. G. (2012). Ultimate capacity of rectangular plates with partial depth pits under uniaxial loads. Marine Structures, 26(1), 27-41.

(6) Herzberg, E., Chang, P., Daniels, M., & O’Meara, N. (2012). Estimate of the annual cost of corrosion for navy ships. Report DAC21T1.

(7) John Wiley and Sons. (2002). Redox Reactions. Retrieved October 25, 2016, from http://www.wiley.com/college/boyer/0470003790/reviews/redox/redox.htm

(8) Kulicki, J. M., Prucz, Z., Sorgenfrei, D. F., Mertz, D. R., & Young, W. T. (1990). Guidelines for evaluating corrosion effects in existing steel bridges (No. 333).

(9) Handbook, D. F. (1993). Chemistry. Volume, 1, DOE-HDBK-1015/1-93

(10) Qin, S., & Cui, W. (2002, July). A new corrosion model for the deterioration of steel structures in marine environments. In Proceedings of the 1st. ASRANet International Colloquium (pp. 8-10).

(11) Sharifi, Y., & Rahgozar, R. (2010). Remaining moment capacity of corroded steel beams. International Journal of Steel Structures, 10(2), 165-176.

(12) R. E. Melchers: Corrosion (NACE), 2004, 60, (9), 824–836.

(13) R. E. Melchers: Corrosion (NACE), 2004, 60, (10), 937–944

157

(14) Komp, M. E. (1987). "Atmospheric corrosion ratings of weathering steels— Calculations and significance." Materials Performance, 26(7), 42-44

(15) Albrecht, P., and Naeemi, A. H. (1984). "Performance of weathering steel in bridges." Report 272, Nat. Cooperative Highway Res. Program, July

(16) Caines, S., Khan, F., & Shirokoff, J. (2013). Analysis of pitting corrosion on steel under insulation in marine environments. Journal of loss prevention in the process industries, 26(6), 1466-1483.

(17) Corrosion Control Plan for Bridges – A NACE International White Paper, November 2012.

(18) Nakai, T., Matsushita, H., Yamamoto, N., & Arai, H. (2004). Effect of pitting corrosion on local strength of hold frames of bulk carriers (1st report). Marine structures, 17(5), 403-432.

(19) Sumi, Y. (2008). Strength and deformability of corroded steel plates estimated by replicated specimens. Journal of Ship Production, 24(3), 161-167.

(20) Paik, J. K., Lee, J. M., & Ko, M. J. (2003). Ultimate compressive strength of plate elements with pit corrosion wastage. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 217(4), 185-200.

(21) Paik, J. K., Lee, J. M., & Ko, M. J. (2004). Ultimate shear strength of plate elements with pit corrosion wastage. Thin-Walled Structures, 42(8), 1161-1176.

(22) U.S DOT (Dec 2004), National Bridge Inspection Standard Guidelines, https://www.gpo.gov/fdsys/pkg/FR-2004-12-14/pdf/04- 27355.pdf, Volume 69, No. 239, 74419-74439

(23) Cardno, Catherine A., PHD. "Analysis Reveals 58,495 U.S. Bridges Are Structurally Deficient." AMERICAN SOCIETY OF CIVIL ENGINEERS. THE MAGAZINE OF THE AMERICAN SOCIETY OF CIVIL ENGINEERS, 15 Mar. 2016. Web. 12 Jan. 2017. .

(24) Plaza, A. B. S. (2007). HULL INSPECTION AND MAINTENANCE PROGRAM.

(25) Le, H. J. (2015). Development of an Analytical Tool for the Estimation of Remaining Moment Capacity of Corroded Steel I-beams (Doctoral dissertation, University of Akron).

158

(26) Technologies, A., Ltd. (n.d.). Organic Coatings. Retrieved April 25, 2017, from https://www.anochrome.com/processes/organic-coatings/.

(27) Marchant, T. (2009). The feasibility of a corrosion resistant ship. BMT Defence Services, White Paper.

(28) Corrosion protection. (2015). Retrieved October 25, 2016, from http://www.steelconstruction.info/Corrosion_protection.

(29) Tezdogan, T., & Demirel, Y. K. (2014). An overview of marine corrosion protection with a focus on cathodic protection and coatings. Brodogradnja, 65(2), 49-59. (30) Association, W. (2016, May). WORLD STEEL IN FIGURES 2016. Retrieved October, 2016, from https://www.worldsteel.org/en/dam/jcr:1568363d-f735- 4c2c-a1da-e5172d8341dd/World Steel in Figures 2016.pdf

(31) Hibbeler, R. C. (2011). Mechanics of Materials. Upper Saddle River, NJ: Prentice Hall.

(32) Kumar, M. S., Alagusundaramoorthy, P., & Sundaravadivelu, R. (2009). A novel setup for testing of ship deck stiffened panels under axial and lateral loads. Journal of Testing and evaluation, 37(2), 1-15.

(33) Assakkaf, I. A., Ayyub, B. M., Hess, P. E., & Atua, K. (2002). Reliability‐Based Load and Resistance Factor Design (LRFD) Guidelines for Stiffened Panels and Grillages of Ship Structures. Naval engineers journal, 114(2), 89-112.

(34) Kumar, M. S., Kumar, C. L., Alagusundaramoorthy, P., & Sundaravadivelu, R. (2010). Ultimate strength of orthogonal stiffened plates subjected to axial and lateral loads. KSCE Journal of Civil Engineering, 14(2), 197-206.

(35) Chen, Y. (2003). Ultimate strength analysis of stiffened panels using a beam-column method (Doctoral dissertation, Virginia Tech).

(36) Paik, J. K. (2007). Empirical formulations for predicting the ultimate compressive strength of welded aluminum stiffened panels. Thin-Walled Structures, 45(2), 171-184.

(37) Pike, J. (Ed.). (2011, July 7). Military (The Hull). Retrieved November 2, 2016, from http://www.globalsecurity.org/military/systems/ship/hull.htm

159

(38) R. (2009, April 16). Ship Hull Designs in Naval Architecture - An Overview (L. Stonecypher, Ed.). Retrieved April 25, 2017, from http://www.brighthubengineering.com/naval-architecture/32007-basics-of- ship-hull-design/#imgn_0

(39) Chakraborty, S. (Ed.). (2016, February). Watertight Bulkheads: Construction and Regulations. Retrieved November 02, 2016, from http://www.marineinsight.com/naval-architecture/water-tight-bulkheads-on- ships-construction-and-arrangement/

(40) Herbert, G. W. (2016, October 31). Strength of ships. Retrieved April 25, 2017, from https://en.wikipedia.org/wiki/Strength_of_ships#/media/File:ShipSaggingHoggi ng.png (Photo Reference Only)

(41) Paik, J. K., & Kim, B. J. (2002). Ultimate strength formulations for stiffened panels under combined axial load, in-plane bending and lateral pressure: a benchmark study. Thin-Walled Structures, 40(1), 45-83.

(42) Paik, J. K., & Thayamballi, A. K. (2002). Ultimate strength of ageing ships. Proceedings of the Institution of Mechanical Engineers, Part M: Journal of Engineering for the Maritime Environment, 216(1), 57-77.

(43) Grondin, G. Y., Chen, Q., Elwi, A. E., & Cheng, J. J. (1998). Stiffened steel plates under compression and bending. Journal of Constructional Steel Research, 45(2), 125-148.

(44) Danielson, D. A., Kihl, D. P., & Hodges, D. H. (1990). Tripping of thin-walled plating stiffeners in axial compression. Thin-Walled Structures, 10(2), 121-142.

(45) Shanmugam, N. E., Dongqi, Z., Choo, Y. S., & Arockiaswamy, M. (2014). Experimental studies on stiffened plates under in-plane load and lateral pressure. Thin-Walled Structures, 80, 22-31.

(46) Huang, Y., Zhang, Y., Liu, G., & Zhang, Q. (2010). Ultimate strength assessment of hull structural plate with pitting corrosion damnification under biaxial compression. Ocean Engineering, 37(17), 1503-1512.

(47) Jiang, X., & Soares, C. G. (2012). Ultimate capacity of rectangular plates with partial depth pits under uniaxial loads. Marine Structures, 26(1), 27-41.

160

(48) Ok, D., Pu, Y., & Incecik, A. (2007). Computation of ultimate strength of locally corroded unstiffened plates under uniaxial compression. Marine Structures, 20(1), 100-114.

(49) TSCF. (1984). Experimental and theoretical investigation of the strength of corroded hull elements. Project 300, Report No. 84-3438, Tanker Structure Co- operative Forum.

(50) Daidola, J. C., Orisamolu, I. R., & Parente, J. (1996). Residual strength assessment of pitted plate panels. Ship Structure Committee, US Coast Guard.

(51) API BULLETIN 2V (2004), “Design of Flat Plate Structures” (Washington, D.C.: API Publishing Service)

(52) American Bureau of Shipping (2004), “Guide For Buckling and Ultimate Strength Assessment for Offshore Structures” (Houston, TX, American Bureau of Shipping)

(53) Naar, H. (2006). Ultimate strength of hull girder for passenger ships. Helsinki University of Technology.

(54) ASTM, B. (2003). 117. Standard Practice for Operating Salt Spray (Fog) Apparatus, 14.

(55) Corp, Q-Lab. (2004). Corrosion Chamber - Q-FOG. Q-Lab. Q-Lab Corporation,. Retrieved Web. 28 Oct. 2016. From . Westlake, OH

(56) ASTM Committee G-1 on Corrosion of Metals. (2011). Standard practice for preparing, cleaning, and evaluating corrosion test specimens. ASTM International.

(57) Smith, C. S. (1975). Compressive strength of welded steel ship grillages (No. NCRE/R611). NAVAL CONSTRUCTION RESEARCH ESTABLISHMENT DUNFERMLINE (SCOTLAND).

(58) Dunn, D. S., Bogart, M. B., Brossia, C. S., & Cragnolino, G. A. (2000). Corrosion of iron under alternating wet and dry conditions. Corrosion, 56(5), 470-481.

(59) ASTM A572/ A572M-12. (2012). Standard Specification for High-Strength Low-Alloy Columbium-Vanadium Structural Steel, ASTM International, West Conshohocken, PA.

161

(60) Cui, C., Yang, P., Li, C., & Xia, T. (2017). Ultimate strength characteristics of cracked stiffened plates subjected to uniaxial compression. Thin-Walled Structures, 113, 27-38.

(61) Paik, J. K., & Thayamballi, A. K. (2003). Ultimate limit state design of steel- plated structures. John Wiley & Sons.

(62) Sharifi, Y., & Rahgozar, R. (2010). Evaluation of the remaining lateral torsional buckling capacity in corroded steel members. Journal of Zhejiang University-SCIENCE A, 11(11), 887-897.

(63) ABAQUS. (2008). User's manual, version 6.8EF-2. Providence, RI, USA: Dassault Systèmes Simulia Corp.

(64) Paik, J. K., Kim, B. J., & Seo, J. K. (2008). Methods for ultimate limit state assessment of ships and ship-shaped offshore structures: Part II stiffened panels. Ocean Engineering, 35(2), 271-280.

(65) Tran, K. L., Douthe, C., Sab, K., Dallot, J., & Davaine, L. (2014). Buckling of stiffened curved panels under uniform axial compression. Journal of Constructional Steel Research, 103, 140-147.

(66) Kalny, O. (2014, March 30). Eigenvalue vs. Nonlinear buckling analysis - Technical Knowledge Base (J. Napier, Ed.). Retrieved March 12, 2017, from https://wiki.csiamerica.com/display/kb/Eigenvalue vs. nonlinear buckling analysis

(67) Veritas, D. N. (2010). Rules for classification of ships (Part 8). Det Norske Veritas Classification As.

(68) International, N. (n.d.). Galvanic Corrosion. Retrieved November 13, 2016, from https://www.nace.org/Corrosion-Central/Corrosion-101/Galvanic- Corrosion/

(69) Herzberg, E. (2011, May). DoD Estimates the Annual Cost of Corrosion for Navy Ships. Retrieved November 13, 2016, from http://corrdefense.nace.org/corrdefense_fall_2012/DoD_1.asp

(70) Sultana, S., Wang, Y., Sobey, A. J., Wharton, J. A., & Shenoi, R. A. (2015). Influence of corrosion on the ultimate compressive strength of steel plates and stiffened panels. Thin-Walled Structures, 96, 95-104.

162

(71) Needham, B. (2011, November 15). Navy Ships Corrosion Project Implementation. Retrieved October 13, 2016, from http://www.sae.org/events/dod/presentations/2011/Navy_Ships_Corrosion_Proje ct_Implementation.pdf

163