Modelling of marine immersion corrosion for copper-bearing steels
Introduction
A phenomenological model for representing corrosion loss as a function of time and average seawater temperature was proposed previously for general corrosion of mild and low alloy steels under near-surface immersion conditions ‘at-sea’ [1]. The model consists of an expected (or mean-value) corrosion function and a zero-mean uncertainty function where is a vector of environmental and material conditions, t is time of exposure and is a bias function, assumed unity in the discussion below. For many practical purposes, the mean-value function is of most interest. The present paper is concerned only with calibrating this function to field data for copper-bearing steels. For these some older literature data exist but the main source of data is the ASTM-sponsored ‘round-robin’ program conducted during the mid-1980s and reported by Phull et al. [2] Some 14 sites world-wide were involved, covering a range of seawater temperatures and mainly coastal and harbour conditions.
By limiting attention to near-surface (shallow) ‘at-sea’ conditions the number of factors that need to be included in is substantially reduced. Of these, salinity, pH, carbonate balance, water velocity and marine growth and bacteria are all remarkably consistent for most ‘at-sea’ conditions [3]. Moreover, wave action and water velocity are likely to ensure full aeration and therefore oxygen availability for the corrosion process. Coupon surface condition and steel composition were controlled by considering only copper-bearing steel coupons prepared to accepted corrosion testing specifications. The main independent variable that was not controlled was seawater temperature.
Seawater temperature is known to influence corrosion loss [4], [5]. Since seawater temperature typically varies seasonally, the annual average seawater temperature has previously been used as the variable and this approach is also adopted here [1], [5]. As before, initial temperature and the season of first immersion are ignored owing to insufficient data. The net effect is that the environmental and other factors in vector are reduced to average seawater temperature T, so that, with good approximation, .
This paper is organized as follows. The next Section 2 reviews the model previously proposed and its parameterization. Section 3 reviews the data for copper-bearing steels and shows how the model may be used to interpret the data, with average seawater temperature being the variable of interest. Section 4 then employs the data to provide calibration of the model parameters, based on the concept that there must be consistency between various observations for the different sites and between the interpretations made for the parameters. This allows inferences about non-conforming site conditions to be made. Section 5 then employs the calibrated parameters to provide a consolidated overview of expected corrosion loss as a function of exposure period and average seawater temperature. A short discussion follows in Section 6.
Section snippets
Description of phenomenological model
The mean value function f(t,T) was proposed earlier [6] as consisting of several phases––kinetic, diffusion and anaerobic––each of which is assumed to control the corrosion process in turn. The model has since been refined [1] to include two anaerobic phases, as shown in Fig. 1. To make the present paper self-contained, a brief overview of the model is given below.
Phase 1 is the ‘kinetic’ phase, composed of a very short time period during which corrosion is under activation control followed by
Data sources and effect of seawater temperature
Not all data available in the literature for copper-bearing steels has sufficient detail for the present study. That which could be employed is summarized in Table 1. The principal data source was a major 1980s ASTM-sponsored testing program [2]. Some 14 sites around the world were involved but not all could be used in the present study, for reasons described below. The compositions of the steels are summarized in Table 2.
Fig. 2, Fig. 3, Fig. 4, Fig. 5 show the data reported in the ASTM study
Calibration of parameters
From the constructed corrosion loss–time curves shown in Fig. 2, Fig. 3, Fig. 4, Fig. 5 and others not shown, it was possible (in some cases iteratively, as noted above) to estimate the parameters r0, ta, ca, ra, cs and rs. They are summarized in Table 1. Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10, Fig. 11 show the data points as well as fitted smooth curves for each of parameter as a function of annual average seawater temperature. Because of data scarcity and limitations, it was not found
Some observations
In addition to the calibrated trend lines for copper-bearing steels, Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10, Fig. 11 also show, in light lines, the trends previously developed from data for mild and low alloy steels [1]. There are some interesting observations to be made.
For r0, the initial (phase 1) kinetic corrosion rate (Fig. 6) the trend line for the copper-bearing steel is closely similar to that obtained earlier for mild and low alloy steels [1], suggesting, contrary to the usual
Corrosion loss–time–temperature relationship
Using the trend lines in Fig. 6, Fig. 7, Fig. 8, Fig. 9, Fig. 10, Fig. 11 it is possible to construct a consolidated corrosion loss function for time of exposure (t) and temperature (T). This is shown in Fig. 12 as a series of corrosion contours in the range 0–25 °C. The non-linear nature of corrosion loss as a function of average seawater temperature is evident. The pattern is consistent with that derived directly from experimental field observations [5] but is smoother, presumably owing to
An application
The model of Fig. 1 can be used to clarify an apparent anomaly in observations of the corrosion of copper-bearing steel compared to that for mild steel. Blekkenhorst et al. [12] noted that for steels of various compositions exposed at around 10 °C for up to 7.2 years copper alloying may be beneficial (i.e. reducing corrosion). They noted that this was in conflict with the long-term observations of Forgeson et al. [18] who found that copper as an alloy was deleterious for exposures at around 28
Discussion
The present approach to modelling corrosion behaviour is based on using a plausible model having a corrosion-theoretical basis to interpret corrosion data. It is shown that the data that are not in doubt can be fitted to the model (adding confidence to its validity but not ‘proving’ it). This approach is rather different to convention, which usually consists of attempts to fit smooth curves through data points, with generally poor results, unable to account for inconsistencies in data and
Conclusion
Data points reported in the literature for the ‘at-sea’ near-surface immersion corrosion of copper-bearing steels have been interpreted in terms of a new non-linear phenomenological corrosion loss–time model. The model consists of four different corrosion phases, each described by one or more parameters. These relate to the main features of the model, including initial corrosion rate, the onset of anaerobic conditions and the longer-term anaerobic corrosion rate.
The parameters of the model were
Acknowledgements
This report has drawn on literature data as well as on information made available by a considerable number of people over a period of several years [5]. Particular appreciated is the help provided by Miller H. Peterson (formerly US Navy Research Labs), ‘Bob’ Phull (LaQue Laboratories, Wrightsville Beach, NC) and James F. Jenkins (formerly US Navy Civil Engineering Labs). This work was supported by the Australian Research Council under Large Grants A89801268 and A00104742.
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