Volume 23 Preprint 14
Fatigue Crack Arrest in Mild Steel via Iron Electroplating
J. Huang and H. Cardenas
Keywords: Fatigue, Crack Closure, Crack Propagation, Iron Plating, Electrochemical Treatment, Galvanic Corrosion
In this work, electrochemical plating treatments were applied to ASTM A36 steel specimens to study the efficiency and limitations of this method for arresting fatigue crack propagation. Electroplated iron was deposited onto the crack surfaces using a circuit in which Swedish Iron served as the anode in a solution of Ammonium Iron (II) Sulfate Hexahydrate. The iron ions were driven into fatigue cracks that were formed within ASTM E399 compact tension specimens. This work showed that an iron-plating treatment operated at 20â„ƒ can arrest fatigue crack propagation for a significant period of cycles. The propagation re-initiation lives that resulted ranged from 11,000 to 230,000 cycles. As observed in prior work, the propagation re-initiation life correlated strongly to the magnitude of the stress intensity factor range that was applied during cycling. As this stress intensity increased, the propagation re-initiation life decreased. Repeated treatments on the same crack provided extended service lives by as much as 370,000 cycles or 60% of the entire fatigue life of the component. Future work may show that re-application of the treatment, when conducted prior to crack re-initiation, could further extend the service life indefinitely. The Correia crack closure model was modified to provide an empirical expression for predicting the crack re-initiation life of the treated component. Interestingly, highly effective arrest behavior was still observed for cracks that were loaded to stress intensity factors of only 3-6 MPaâˆšm during the treatment but then subjected to 20 MPaâˆšm during cyclic loading. Galvanic corrosion of the plated material exposed to simulated seawater was estimated to be 3 mpy. Future work will examine the use of less active plating alloys and the possibility of applying effective treatments into cracks that are in an unloaded state.
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Fatigue Crack Arrest in Mild Steel via Iron Electroplating
Louisiana Tech University, 201 Mayfield Ave, Ruston, LA 71270, USA
Henry E. Cardenas
Department of Mechanical Engineering, Louisiana Tech University
In this work, electrochemical plating treatments were applied to ASTM A36 steel specimens
to study the efficiency and limitations of this method for arresting fatigue crack
propagation. Electroplated iron was deposited onto the crack surfaces using a circuit in
which Swedish Iron served as the anode in a solution of Ammonium Iron (II) Sulfate
Hexahydrate. The iron ions were driven into fatigue cracks that were formed within ASTM
E399 compact tension specimens. This work showed that an iron-plating treatment
operated at 20℃ can arrest fatigue crack propagation for a significant period of cycles. The
propagation re-initiation lives that resulted ranged from 11,000 to 230,000 cycles. As
observed in prior work, the propagation re-initiation life correlated strongly to the
magnitude of the stress intensity factor range that was applied during cycling. As this
stress intensity increased, the propagation re-initiation life decreased. Repeated
treatments on the same crack provided extended service lives by as much as 370,000
cycles or 60% of the entire fatigue life of the component. Future work may show that reapplication of the treatment, when conducted prior to crack re-initiation, could further
extend the service life indefinitely. The Correia crack closure model was modified to
provide an empirical expression for predicting the crack re-initiation life of the treated
component. Interestingly, highly effective arrest behavior was still observed for cracks that
were loaded to stress intensity factors of only 3-6 MPa√m during the treatment but then
subjected to 20 MPa√m during cyclic loading. Galvanic corrosion of the plated material
exposed to simulated seawater was estimated to be 3 mpy. Future work will examine the
use of less active plating alloys and the possibility of applying effective treatments into
cracks that are in an unloaded state.
Keywords: Fatigue, Crack Closure, Crack Propagation, Iron Plating, Electrochemical
Treatment, Galvanic Corrosion
Metal fatigue is a progressive damage process which leads to crack formation and growth
caused by cyclic loading [1,2]. It tends to begin at surface irregularities and stress
concentration points. It is a complicated metallurgical process which is difficult to
accurately describe and model on a microscopic level. Under cyclic loading, cracks can
initiate at stress levels that are much lower than the yield strength of the material. Once
initiated, a crack will continue to grow during each loading cycle until it reaches a critical
size that results in failure . Crack initiation and propagation are largely controlled by the
tensile component of the applied stress but can be greatly influenced by environmental
factors that impact the crack surfaces, especially in the vicinity of the crack tip. In this
study, an electrochemical treatment was developed to stop fatigue crack propagation in
A36 mild steel. This work specifically focused on the electro-deposition of iron onto the
surfaces of open cracks.
The study of electrochemical crack treatment involving the plating of metal was examined
by earlier studies conducted by Dolgan, Shrestha and Cardenas [3,4]. Dolgan and Cardenas
found that the deposition of nickel (Ni) onto the surfaces of the cracks in mild steel caused
the arrest of fatigue crack propagation . Later, to minimize the impact of galvanic
corrosion resulting from the dissimilarity of Ni and Fe, Aawaz and Cardenas studied the
galvanic corrosion behavior that resulted when iron was plated onto mild steel . This
work found that the plated iron sacrificially protected the mild steel from corrosion. In
contrast, the nickel-plating from the earlier work was tending to drive the corrosion of the
steel. Dolgan and Cardenas observed that nickel-plating achieved significant periods of
crack arrest in ASTM A36 . The re-initiation of crack propagation was well correlated to
the stress intensity factor range that was applied during loading cycling. A model based on
a crack surface adhesion theory also exhibited a reasonably useful prediction of crack reinitiation but was highly empirical. As noted earlier, the nickel-plating approach exhibited
the potential for galvanic corrosion to cause damage to the base metal. The current work
examined the alternative of plating iron into the fatigue crack and using a semi-empirical
crack closure model to assist in the prediction of crack re-initiation.
The following sections examine several key elements that motivate and guide the approach
used in this study. The primary background element is the modeling and prediction of
fatigue crack growth and the highly influential concept of crack closure. This section also
includes concepts on electroplating and dissimilar metal corrosion.
Fatigue Crack Growth
The most widely accepted equation used to characterize the crack growth behavior was
obtained by Paris . The Paris Law has the form,
where a is the crack length, N is the number of loading cycles, C and m are empirical
material constants and ∆K is the stress intensity factor range, ∆K = K max - Kmin. The
fundamental crack growth behavior of metals can be divided into three distinct regions:
Slow crack growth, Power law growth, and final failure [1,5]. Slow crack growth is a crack
propagation phenomenon that is difficult to predict since it is highly dependent on
microstructure, environment, and material properties whose interplay are not well
understood. At low stress intensity factors, fatigue crack behavior is bounded by a
threshold value ΔKth, below which there is no crack growth. The ΔKth value for steels found
in the literature is typically between 5 and 15 MPa√m . For larger magnitudes of ∆K, the
crack growth is governed by the Paris Law. Near the end of the service life, the crack
propagation can become unstable and extremely rapid [6,7]. Crack growth of this nature is
largely controlled by the fracture toughness of the material, K c. Forman’s equation is a
modification of the Paris Law that incorporates this fracture toughness as well as the mean
stress [8,9]. It governs the rapid crack growth behavior observed near the end of service
life and has the form,
where R is the stress ratio (R =
), and Kc is the critical fracture toughness value at which
catastrophic fracture can occur.
Crack closure is a phenomenon characterized by the surfaces of fatigue cracks remaining
closed even as a tensile load is being applied [10,11]. It was first described by Elber in
1970. Elber found that significant contact between the fracture surfaces was occurring due
to the plastic deformation. He proposed that this contact of crack surfaces was the result
of permanent deformation occurring within a plastic zone that forms at the crack tip where
the yield stress of the material is being exceeded. This yielded region of material causes
the fatigue crack to remain closed when the applied load is still in tension. The crack will
not open again until a sufficiently high stress is applied. Related to this concept, Elber also
introduced the idea of a crack-opening stress . Crack-opening stress is the value of
the applied stress at which the crack just becomes fully open. He demonstrated that to
make fatigue crack growth occur, the crack must become fully open via an applied stress
that is greater than the crack-opening stress. That work introduced the concept of an
effective ΔK value that defined the stress intensity factor range during which a crack
remained open. For the determination of the effective ΔK, the stress intensity factors at
maximum load (Kmax) and at crack opening (Kopen) need to be known [10,11,12]. These
parameters were used to define an effective stress intensity factor range that is given by,
Revisiting the Paris Law (Equation 1), the fatigue crack growth rate, da/dN, according to
Elber, was now a function of the effective stress intensity factor range, ΔK eff. The crack
closure concept has often been used to explain the stress ratio effect. This is also known
as the R ratio, where R =
. Crack closure has also been used to explain temperature and
corrosion effects on ΔKth . Elber also suggested that ∆K
is dependent on the R ratio.
In general, a higher R ratio value often results in less crack closure and a higher ΔK eff value.
Elber’s empirical relationship between R ratio and the effective stress intensity factor range
is given by ,
= 0.5 + 0.4R .
Note this equation is only valid for R > 0. Another crack closure model of more expanded
applicability was introduced by Schijve in 2004 . It has the form,
U = 0.55 + 0.33R + 0.12R , (−1 ≤ R < 1).
A more recent empirical model that also incorporates the ΔKth was proposed by Correia in
2016 . To obtain ΔKeff, the parameter U provided by Correia was presented as,
U = (1 −
)(1 − R)
is the threshold value of stress intensity range at R = 0, and 𝛾 is a material
parameter obtained from crack propagation experiments and viewed as dependent on
“measurements location and measurements sensitivity”. By its association with crack tip
plasticity, it is conceivable that 𝛾 may also carry some level of material plasticity impact.
Electrochemical Deposition and Layer Interactions
Electrochemical deposition is a process by which a metal layer is deposited onto the
surface of a conductive substrate by reducing the dissolved metal ions out from the
electrolytic solution [16,17,18]. Plating treatments require a ready source of metal ions
that are in solution. A sacrificial metal can serve as a source of ions. It thus serves as an
anode. A substrate metal can serve as a cathode that receives the plated layer. The primary
application of electrochemical deposition is to change the surface properties of the
component. This may typically include changes to corrosion resistance, wear resistance,
and aesthetic quality.
According to Faraday’s law of electrolysis, the amount of material deposited onto a
substrate is proportional to the amount of electric current applied . Faraday’s law has
where W is the weight of the plated metal in grams, I is the current in amperes, t is time in
seconds, n is the valence of the dissolved metal in solution, A is the atomic weight and F is
Faraday’s constant (F=96,485.309 coulombs/equivalent). The electrodeposition process
can be affected by temperature, pH level, current density, and the presence of other ions
present in the plating solution .
When metals are plated onto dissimilar metallic substrates, galvanic corrosion can arise
from the new arrangement . Under these circumstances, one of the metals behaves
more actively (or anodic) and will corrode sacrificially, while the other metal behaves in a
more noble (or cathodic) manner that effectively protects it from corrosion. The driving
force for the accelerated corrosion of the anodic metal is the galvanic potential difference
which is a voltage reading that can be measured between these two metals. In general, a
smaller galvanic potential reading would tend to indicate a lower likelihood of a significant
corrosion rate being suffered by the anodic metal.
Methodology and Procedures
The fatigue tests were conducted using compact tension (CT) specimens as defined in
ASTM E399 . (see Figure 1) The specimens consisted of ASTM A36 mild (low carbon)
steel. Fatigue cycling was conducted using an MTS servo-hydraulic testing machine. The
machine was controlled using TestStar™ IIs system (MTS Systems Corporation, MN, USA).
The cycling load was administered in a constant amplitude sinusoidal pattern at 2 Hz, with
a stress ratio (R) in the range of 0.1 – 0.3. The maximum stress intensity (K) and the ΔK
were permitted to increase as the cracks grew. The values used for the initial ΔK applied to
the uncracked notch ranged from 19 MPa√m to 29 MPa√m .
The crack treatments were conducted after cracks were formed as shown in Figure 1. A
static loading armature was used to apply a force (F) to achieve a crack mouth opening
displacement that correlated to a stress intensity factor of approximately 3 MPa√m. When
possible, repeat treatments were provided after crack propagation had resumed. These
repeat treatments were provided while the cracks were statically loaded at stress intensity
values in the range of 3 – 6.5 MPa√m. These K values constituted approximately 10 – 15%
of the ∆K values that were later applied during subsequent fatigue cycling. The bath
solution consisted of Ammonium Iron (II) Sulfate Hexahydrate ((NH 4)2Fe(SO4)2·6H2O) in deionized (DI) water . The dosage was close to the maximum solubility (of 300 gram/liter)
at 20℃. The pH in the bath started in the range of 5.0 - 5.5. After the 60-minute
treatment the ending pH was in the vicinity of 6.0. Each specimen was plated with a
constant D.C. current density of 0.02 A/cm 2 at 20℃. The voltage required to achieve this
current density was in the ranged of 1 - 2 V. The plating surface area was calculated using
the plated notch and fatigue crack length (that was covered by the treatment solution), and
the thickness of the specimen.
Figure 1. Schematic of electrochemical fatigue crack treatment.
Following treatment each specimen was fatigue cycled with the same magnitude and
frequency of loading as was applied during the crack initiation process. These specific ∆K
values are noted in Figure 4. Post-treatment, the load cycling was continued until crack
propagation resumed. In most cases, the re-initiated fatigue cracks were subjected to one
or more additional treatments in order to study the effectiveness of repeated treatments.
Galvanic corrosion potential and current measurements were conducted to assess the
corrosion compatibility of the plated material with respect to the base metal. The galvanic
potential was measured using a high impedance voltmeter [21,22]. Both electrodes were
submerged in 3.5 wt.% NaCl solution at 20℃. The Swedish iron electrode was a cylindrical
bar with a diameter of 1 cm and a length of 1.5 cm, while the bare A36 steel was a flat bar
with dimensions of 2.5 cm x 2 cm x 1.5 cm. These two electrodes were spaced 5 cm apart
in the simulated seawater solution. To avoid polarization error, the readings were recorded
immediately after completing the circuit. The galvanic current was measured using a zeroresistance ammeter [21,22]. The test setup consisted of a power supply, a voltmeter, an
ammeter, a plated iron electrode and an A36 steel electrode. The electrodes (as described
earlier) were immersed in simulated seawater solution (3.5 wt.% NaCl) at 20℃. To
overcome the inherent resistance of the ammeter, the power supply was adjusted until the
circuit resistance reading was zero. The current read from the ammeter at that (zeroreading) moment was recorded. 6 trials were conducted for all measurements.
Results and Discussion
In the following sections, the electrochemical treatment impact on extending the fatigue
crack propagation life of A36 steel specimens was examined. A modified Correia’s crack
closure model was developed and compared to the crack re-initiation life observed. The
corrosion behavior of the plated metal was also examined.
Fatigue Crack Treatment Response
To study the fatigue crack growth behavior after electrochemical treatment, compacttension specimens were tested using the MTS servo-hydraulic testing machine as
described earlier in accordance with ASTM E399. In most cases the treatments were
repeated after the crack propagation had reinitiated.
During this study, the fatigue crack initiation life from the notch exhibited a wide range of
behavior. For example, one crack initiated at 17,000 cycles under a ΔK value of 30 MPa√m.
Another crack initiated at 350,000 cycles under lower stress with a ΔK value of 19 MPa√m.
The R values for each specimen was within the range of 0.1 to 0.3. The cracks were initially
treated when crack lengths ranged from 2.13 to 4.22 cm. The corresponding ∆K values for
these cases ranged from 28 to 33 MPa√m. In each case, the first 1.9 cm of the crack length
consisted of the E399 notch. This meant that the actual length of the fatigue crack that
initially received treatment ranged from 0.22 to 2.3 cm.
An example of the fatigue crack behavior following electrochemical treatment is shown in
Figure 2. The crack started propagating at 145,000 cycles, and the first electrochemical
treatment was performed at 170,000 cycles at a crack length of 2.67 cm and a ΔK of
28 MPa√m. Following this treatment, the crack propagation halted for 230,000 cycles.
Another treatment was applied after the crack reached 2.84 cm at 440,000 cycles and a ΔK
value of 29 MPa√m . The crack propagation was arrested for 140,000 cycles after this 2 nd
treatment. After the 2nd crack re-initiation, failure occurred at 600,000 cycles and a ΔK
value of 37 MPa√m. The entire fatigue life of this specimen was approximately 600,000
Figure 2. Fatigue crack propagation of a typical E399 low carbon steel specimen with two
electrochemical treatments shown. Both treatments caused crack arrest for over 105 cycles.
The fracture surface of this specimen is presented in Figure 3. The dashed line A indicates
the location of the initial crack tip at the notch at the start of load cycling. Position B is
where Treatment 1 was performed at 170,000 cycles. The crack was arrested for 230,000
cycles. The area between A and B was the fatigue crack area that received this initial
treatment. This area exhibited iron oxide discoloration that developed during cyclic
loading. Location C is the crack tip location when Treatment 2 was applied at 440,000
cycles. Following this treatment, the crack was arrested for 140,000 cycles. The area
between B and C is the surface of the treated iron that was partially covered with iron
oxide. Location D is the surface of the fracture that was observed at failure at 600,000
cycles when the ΔK reached 37 MPa√m .
Figure 3. Fracture surface of the treated specimen from Figure 2. (A: Initial Crack Tip Location;
B: Crack Tip Location where Treatment 1 was performed; C: Crack Tip Location where
Treatment 2 was performed; D: Location of the start of fracture instability).
As noted above, the total fatigue life of this specimen was 600,000 cycles. The crack
started propagating at 145,000 cycles. The total fatigue life was extended by 370,000
cycles or approximately 60% due to the two plating crack treatments. The two treatments
succeeded in arresting the crack propagation for 230,000 cycles and 140,000 cycles
respectively. Based on these observations, it appears that this treatment can extend the
fatigue service life of low carbon steel both significantly and repeatedly.
The fracture surface shown in Figure 3 exhibited two major areas of particular interest.
One is the plated iron area (from Location A to C) which exhibited corrosion from exposure
to moisture for an extended period during cyclic loading. The corrosion products covered
a significant portion of the crack surface. Currently, it is indeterminate if the corrosion
product formation was helping the crack re-initiation life or reducing it. This question is
addressed further in the corrosion susceptibility section that follows and will be further
examined in future work. A feasible approach for this future work could involve both
treating and cycling in an anaerobic environment, such as a nitrogen atmosphere. In
general, there is need to study the impact of corrosion on a treated crack by comparing the
behavior of crack re-initiation and propagation under various corrosive environments, ΔK
values, and R ratios.
The crack re-initiation life of each specimen as related to the applied ΔK（as opposed to
ΔKeff）is presented in Figure 4. The correlation coefficient (R 2 value) of the exponential
trend line was 0.82. This indicated a strong relationship between the crack arrest life and
the corresponding ΔK level at the time of treatment. It was interesting to find that at a
lower ΔK level the treatment tended to provide a relatively higher crack re-initiation life.
According to Elber’s crack closure theory, a lower ΔK level (for the same R value) would
generally help the crack to remain closed during more of a given load cycle [10,11]. This
observation bears a significant implication for getting optimal treatment benefit. It appears
that treating cracks at relatively low ΔK levels may result in higher crack re-initiation lives.
This trend implies a time/cycle-dependent degradation of the treatment and its impact on
crack closure, i.e. ΔKeff. Possible reasons for this trend are discussed in a later section.
Figure 4. Fatigue crack re-initiation life for treatments conducted at various ΔK values.
During cyclic loading, it was observed that a treated crack restarted propagation even
when ΔKeff was relatively close to the fatigue threshold value of 15 Mpa√m . The crack
closure obtained in this work only temporarily caused cracks to remain closed. It is
possible that threshold values of ΔKth present in the current study may differ from
literature-reported values ranging from 5 to 15 Mpa√m . It is conceivable that localized
dislocation formation along fatigue crack surfaces during cycling could deteriorate the
impact of crack closure. This notion is further explored in the modeling section of this
Figure 5 shows the crack behavior of a specimen that was treated on three separate
occasions during cyclic loading. The stress ratio R for this specimen was approximately
0.23. The average crack growth rate for the entire test was about 10 -7 m/cycle. The three
treatments collectively provided a fatigue crack propagation life extension of 63,000
cycles, which was approximately 15% of the entire life of the specimen.
Figure 5. Fatigue crack propagation of a specimen that was treated on three occasions during
cyclic loading. The dashed line represents the fatigue crack behavior predicted by the Paris
Paris’ Law (Equation 1) was used to compare the current findings with anticipated crack
growth behavior from the literature. The coefficients of the Paris Law, obtained from the
literature, were specific to ASTM A36 steel. These values were C ≈ 7x10 -10 and m ≈ 3 .
The average crack growth rate before Treatment 1 was 3.2 x10-7 m/cycle. This agreed well
with the Paris Law model as shown in Figure 5. The first electrochemical treatment was
performed at 390,000 cycles when the crack had reached 3.33 cm and the stress intensity
factor range, ΔK, was equal to 32 MPa√m. After Treatment 1, there was no crack growth
observed for 48,000 cycles. The crack growth rate after the crack had re-initiated was
approximately 1.9 x10-7 m/cycle. The second treatment was applied at 471,000 cycles
when the crack was 4.22 cm and ΔK was 43 MPa√m. After this treatment, the crack was
arrested for 18,000 cycles. The crack started growing again at 489,000 cycles and the
third treatment was performed at 490,000 cycles at ΔK = 59 MPa√m. This time, the crack
propagation was not arrested by the third treatment. The specimen proceeded to fail at
498,000 cycles at ΔK = 75 MPa√m.
Based on observations from Figure 5, the third treatment was ineffective. The crack kept
growing rapidly and failed within 8000 cycles. The value of the plain strain fracture
toughness (KIc) for ASTM A36 steel reported in the literature ranges from 45 MPa√m to 67
MPa√m . When the third treatment was applied, the ΔK value (59 MPa√m) was in this
range, thus making it reasonable for fracture to be imminent. This last treatment was
attempted in the final fracture region of crack growth, when the ΔK value was in the range
of possible KIC values for this material. According to the Forman model (Equation 2) this
region of crack growth is not governed by ΔKeff. This suggests that crack closure is not
playing a significant role in crack growth. These observations appear to indicate that
relatively low plating treatment dosages may be ineffective in cases where ΔK is in the
vicinity of KIC and crack closure effects generally have little influence.
As calculated using the Paris Law, Specimen 3 from Figure 5 was expected to fail within
430,000 cycles. Following two treatments, the fatigue life of this specimen was extended
by 68,200 cycles, which constituted approximately 13% of the entire propagation life.
Table 1 lists the fatigue life extension and the number of treatments applied to each
specimen of the current study. It was observed that for E399 low carbon steel, applying the
iron plating treatment repeatedly could significantly extend the crack propagation life and
delay final failure.
Table 1. Fatigue Life Extension due to Iron Plating
As shown in Table 1, the extended fatigue life achieved for each specimen ranged from
10-60%. It is interesting to note that the possibility that a treatment could be applied prior
to crack re-initiation. Doing so could further delay crack re-initiation. This approach could
be useful in the maintenance of fatigue sensitive systems. Timely re-application of iron
plating treatment could conceivably cause cracks to remain arrested indefinitely. Hence,
predicting the re-initiation life becomes a crucial precondition for implementing this
approach effectively. A theoretical model for crack re-initiation prediction is developed in
the following section.
Fatigue Crack Re-initiation Life Modeling
As illustrated in Figure 4, it was observed that the number of cycles required for reinitiating a fatigue crack decreased as ΔK increased. With this governing relationship in
hand, it is possible to obtain a useful correlation between the crack re-initiation cycles and
the effective stress intensity factor range (ΔKeff) at the time of treatment. A theoretical
model taking into account crack closure, mean stress, and the effects of a plating
treatment can be based on the Correia model (Equation 6). A modified version of the
Correia equation can have the form,
= (1 −
)(1 − R)(
is the effective stress intensity factor following treatment, ∆K
threshold value of the stress intensity range at R = 0, R is the stress ratio (
), 𝛾 is a
material parameter related to specific K value thresholds introduced by Correia . A
modification to address plating impact can be provided by the factor α. This α factor can
be related to the effect that the plating treatment has on the crack surfaces. To define a
quantitative value of α, the deposition of the plated iron in the crack was assumed to be a
uniformly thin layer as shown in Figure 6.
Figure 6. Conceptual schematic of a treated fatigue crack showing a representation of fatigue
striation topography that could be influenced by iron plating. The 𝛂 factor was conceived as
a parameter that influences this topography and thus the impact that a given treatment can
have on crack closure.
To start with, the model would be useful if it could relate to the relative height of fatigue
striations (See Figure 6). A relatively tall striation height would tend to cause cracks to be
closed for a greater portion of the load cycle. A key property of the striated material (and
the plating) would be the tendency for plasticity and hardening to influence the impact of
the striation height increase. Presumably, as striation height is gradually diminished, the
extent of crack closure (as conveyed by the magnitude of ∆K ) would also be diminished.
It is possible to quantify the treatment influence on striation height in terms of the volume
of material that is distributed via plating over the crack surface. The time-dependent
response of the newly deposited material to crack closure could then be tied to plasticity
and hardness. The influence of these factors may be estimated by the ultimate tensile
strength of the material. Changes to striation height are related to the volume of plated
iron (Vp) delivered by the treatment. A treatment effectiveness factor (α), may then be
estimated by calculating the decimal volume fraction of the plated material (V p) with
respect to the volume of the crack (Vc) and combining it with a similar ratio of the ultimate
tensile strengths of each material. An expression for α, could thus have the form,
where V is the volume of the plated material, V is the volume of the crack, σ
ultimate tensile strength of plated material and σ
is the ultimate tensile strength of base
Regarding Equations (8) and (9), a higher ratio of V /V would tend to cause the fatigue
crack to exhibit a more extended period of closure, since increasing α corresponds to a
relatively smaller ∆K . For a plated material that is softer than the base material, the
softness of the plasticity would tend to reduce the benefit from the ratio of V /V . This is
because localized yielding occurring at striation contact points would tend to reduce the
plated striation height. With these striation heights reducing over time, this would tend to
reduce the period of crack closure over time. This would be accompanied by ∆K
increasing over time until the crack finally resumes propagation.
The volume calculation of a fatigue crack was estimated by modeling it as a triangle wedge
(Figure 7). Utilizing the crack length (a), the crack mouth opening displacement (b), and
the thickness of the specimen (B), the crack volume (V ) was then found by,
Figure 7. Volume parameters of a fatigue crack.
The volume of plated material may be calculated using Faraday’s law (as introduced in the
background) and the material density. In this study, the ratio of V /V varied from 10 to
20%. The ultimate tensile strength of Swedish Iron and A36 Steel are 540 MPa and 550 MPa
respectively . From Equations (9) and (10), it was found that α ranged from 0.1 to 0.2.
From the literature, 𝛾 = 0.9 .
After obtaining the ∆K
from the modified Correia model, the number of cycles to re-
initiate fatigue crack propagation was estimated using an empirically derived curve of the
where Nre is the number of cycles for fatigue crack re-initiation, and the coefficients A and
B are empirical constants specific to the material system. From the re-initiation life data
presented in Table 1, A = 2x1012 and B = -6.1. The actual crack re-initiation values from
Table 1 and the predicted values for crack re-initiation as provided by the modified Correia
Model are compared in Figure 8.
U = 1, ∆Keff = ∆K
Nre = -6.3Log(∆Keff)
R² = 0.82
Nre = -6.1Log(∆Keff)
Figure 8. Log-log plot of the relationship between the effective stress intensity factor (ΔKeff)
and fatigue crack re-initiation life for modified Correia model and a special case when ΔKeff
equals to ΔK (U = 1).
Figure 8 also illustrates the comparison between the modified Correia model and a
correlation that crudely assumes ΔKeff = ΔK. Both correlations exhibit confidence intervals
in the vicinity of 95% . By taking into account crack closure, the modified Correia model
exhibited a correlation constant of 12.3 as opposed to a value of 14.2 for the other
correlation when crack closure was ignored. Based on these observations, it appears that
when incorporating crack closure, the constant required to achieve a predictive correlation
is reduced by approximately 13%. Figure 9 illustrates a similar comparison with three other
crack closure models for which the U values are not equal to 1. The re-initiation life
predicted by each model were all close to actual values.
Nre = -6.3Log(∆Keff) + 12.6
R² = 0.83
Nre = -6.3Log(∆Keff)
R² = 0.84
U=1, ∆Keff = ∆K
Nre = -6.3Log(∆Keff) +
R² = 0.82
Nre = -6.3Log(∆Keff)
R² = 0.84
Nre = -6.1Log(∆Keff)
R² = 0.85
Figure 9. Log-log plot of the relationship between the effective stress intensity factor (ΔKeff)
and fatigue crack re-initiation life for Modified Correia, Correia, Elber, Schijve and a special
case when ΔKeff = ΔK (U = 1).
In Figure 9, the slopes for each trend were very similar, ranging from -6.1 (for the
modified Correia model) to -6.3 (for all the others). The other constant in these curve fits
showed more significant differences in between each of the models. The biggest difference
was the large axis intercept value obtained in the curve fit that assumed no crack closure
behavior. This constant was equal to 14.2. The other curve fits that incorporated crack
closure models were exhibiting significantly lower axis intercept values (13, 12.8, 12.6,
12.3) clustered together. The Elber crack closure model exhibited an intercept value of
12.8 and required 2 empirical constants to calculate ΔK eff. The Schijve crack closure model
exhibited an intercept value of 13.0 and required 3 empirical constants. Both the Correia
and the modified Correia models exhibited lower intercept values of 12.6 and 12.3. Each
of these crack closure models required 1 adjustable empirical constant. It can be argued
that a lower number of empirical constants suggests evidence of a more rational predictive
model. Another possible indicator of a relatively rational predictive model can be seen by
examining the coefficients of the curve fit relationship between the crack re-initiation
cycles and ΔKeff of Figure 9. An interesting trend regarding these coefficients and empirical
constants is evident. It appears that a reduction in empirical constants needed for the
crack closure model (from 2 to 0) was accompanied by a reduction in the magnitude of the
crack re-initiation axis intercept (from 13 to 12.3). Based on these observations, the low
number of adjustable empirical constants in combination with the lowest magnitude of
curve fit constants appears to indicate that the modified Correia model may provide the
most rational basis for predicting the crack re-initiation behavior observed in this study.
In general, the localized induction of dislocation motion during fatigue cycling is believed
to be a primary reason for crack initiation . Similarly, the compressive stresses
associated with fatigue striations coming into contact during crack closure may also induce
localized dislocation motion. It is conceivable that this irreversible dislocation motion
could lead to the degradation of the effect of plating-induced crack closure. Dislocation
motion leading to the reduction of fatigue crack striation height could lead to the gradual
increase of ΔKeff to the point where crack propagation resumes.
Alternatively, it is conceivable that a treated crack may behave much as a notch, in which
the behavior of the treated crack may be predicted by a strain-life approach .
Unfortunately, the strain-life approach would require additional adjustable constants and a
value for Kt (stress concentration factor) that would be difficult to define in this case due to
the plated material influence. Hence, the fatigue crack re-initiation model based on crack
closure would appear to be a more convenient, rational and less empirical approach as
compared to using a strain life model to predict crack re-initiation.
In this study, it is notable that effective treatments were being applied even into crack
openings that correlated to Kmax values of only 3 – 6 MPa√m. These values were in the
vicinity of the ΔKth values (of 5 – 15 MPa√m ) that were reported in the literature . For
this steel, this treatment effectiveness suggests that these nearly closed cracks exhibited a
topography that permitted the transmission of Fe 2+ ions that were drifting in an electric
field. It would be interesting to see if a completely unloaded crack could exhibit a similar
topography, thus permit an effective crack arrest treatment. Based on these observations,
it is recommended that future studies examine the effectiveness of treating unloaded
The material plated onto a crack surface tends to exhibit a nonuniform distribution
because the electric field within a crack is nonuniform . This inherent discontinuity
allows for the dissimilar plated metal and the base metal to exhibit galvanic corrosion. This
galvanic corrosion could be significant enough to cause irreversible damage and strength
deterioration . In contrast, a small corrosion rate can actually cause crack arrest .
Using iron as plated metal over steel was considered a better choice than nickel since it
could create a lower galvanic potential that may result in a relatively low corrosion rate.
The following sections explore the galvanic driving potentials and corrosion rates observed
for this plating system. These evaluations were conducted using methods described
The galvanic potentials for the A36 steel observed with respect to the iron plated steel
ranged from 162 to 192 mV. In this measurement, the pH value of the 3.5 wt.% NaCl
solution was maintained at 6.8. The galvanic currents were measured by using a zero-
resistance ammeter (ZRA). Using Equation (12), these measured currents were converted
into corrosion rates expressed in mils per year (mpy).
where Icr is the corrosion current in amperes, K is a unit conversion constant equal to
1.288x105, EW is the equivalent weight in gram/equivalent, d is density in g/cm 3, and A is
the sample area in cm2. The anode to cathode surface area ratio was 1:4. The results of
both the galvanic potentials and the galvanic corrosion rates observed are shown in Figure
10. The error bars pertain to a 90% confidence interval.
Figure 10. Galvanic potential and corrosion rates between the ASTM A36 steel and plated
iron in 3.5 wt.% NaCl Solution. The listed corrosion potentials of the iron and plated iron
were negative with respect to the ASTM A36 steel base metal.
In this study, the galvanic corrosion rate of the plated iron with respect to the A36 steel
was 24 mpy for a 1:4 anode to cathode ratio. According to Aawaz’s study, this galvanic
corrosion rate could be reduced to 0.2 mpy for an anode to cathode ratio of 25:1 that
reflects a uniform plating layer that exhibits tensile cracks . The current system would
be expected to exhibit a higher rate due to the fact that the iron deposition would not
likely be uniform. Ideally, a low corrosion rate would be on the order of 1 mpy or below. In
order to reduce the corrosion rate further, it is conceivable that some degree of alloying of
the plated metal could reduce the galvanic corrosion potential as well as the corrosion
rate. Based on these observations, it is recommended that future work explore the
possibility of depositing a plated alloy with a small amount of nickel in order to further
reduce the galvanic corrosion potential of the system.
The corrosion of the plated iron (as indicated by Figure 10) is not likely to have direct
impact on the base metal. During cyclic loading, the corrosion products of the plated metal
would tend to build an oxide layer on the striation peaks (as shown in Figure 6). This thin
oxide layer on top of these striations could cause the crack surfaces to close relatively
sooner which could help extend the crack re-initiation life. The benefit obtained from this
oxide layer may be short-lived as it is weaker than the base metal and could easily be
broken up under this cyclic compression. Pitting and crevicing under the oxide could also
tend to reduce fatigue and corrosion resistance of the base metal. In contrast, a limited
oxygen availability within the crack tip would tend to inhibit such pitting and crevicing
behavior within the crack.
Conclusions and Recommendations
This study focused on developing an electrochemical treatment to arrest fatigue crack
propagation using iron plating. A modified crack closure model was also developed to
predict the resulting of crack re-initiation life. In this section, some conclusions and useful
recommendations are drawn.
1. The electrochemical treatment succeeded in arresting the propagation of fatigue
cracks for a useful period ranging from 11,000 to 370,000 cycles.
2. It was found possible to apply the treatment repeatedly and thus extend the fatigue
life of A36 steel from 10 - 60%.
3. Treating cracks that are cycling at relatively low ΔK levels tended to result in higher
crack re-initiation lives.
4. Relatively low plating treatment dosages may be ineffective in cases where K max is in
the vicinity of KIC and crack closure effects have little influence.
5. The low number of adjustable crack-closure constants and the low magnitude of reinitiation curve fit constants indicate that the modified Correia model may provide
the most rational version of the modeling options considered.
6. It is recommended that future studies examine the effectiveness of treating
7. Further work is recommended to determine when timely re-application of the
treatment (prior to crack re-initiation) could further cause crack propagation to
remain arrested indefinitely.
8. There is need to study the impact of corrosion on the plated metal of a treated
crack. Future work could involve both treating and cycling in various environments,
ΔK values, and R ratios.
9. It is recommended that future work explore the possibility of depositing a plated
iron alloy with a small amount of nickel in order to reduce the galvanic corrosion
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