A simple model for long‐time degradation of magnesium under physiological conditions

Dahms, Michael; Höche, Daniel; Agha, Nezha Ahmad; Feyerabend, Frank; Willumeit‐Römer, Regine

doi:10.1002/maco.201709461

Cited by 17 publications

(11 citation statements)

References 30 publications

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“…Under static conditions degradation analysis is performed in the same medium during the whole immersion time [ 91 ] or by entirely or partially replacing it with fresh medium during the immersion time (semi-static) [ 7 , 100 , 102 ]. In these cases, mass transfer between the surface region and the bulk medium is controlled by the processes of migration, diffusion and a certain degree of convection generated by the H 2 evolution from the surface according to the cathodic reaction (Equation (2) ).…”

Section: To Flow or Not To Flow? The Question Of Experimental Setupsmentioning

confidence: 99%

Magnesium degradation under physiological conditions – Best practice

González

Hou

Nidadavolu

et al. 2018

Bioactive Materials

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202

130

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This review focusses on the application of physiological conditions for the mechanistic understanding of magnesium degradation. Despite the undisputed relevance of simplified laboratory setups for alloy screening purposes, realistic and predictive in vitro setups are needed. Due to the complexity of these systems, the review gives an overview about technical measures, defines some caveats and can be used as a guideline for the establishment of harmonized laboratory approaches.

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Section: To Flow or Not To Flow? The Question Of Experimental Setupsmentioning

confidence: 99%

Magnesium degradation under physiological conditions – Best practice

González

Hou

Nidadavolu

et al. 2018

Bioactive Materials

Self Cite

202

130

View full text Add to dashboard Cite

show abstract

“…The corrosion rate is given by

y_{GSG}^{true'} (t) = \frac{1}{τ} (d_{normal∞} - y_{GSG} (t)) = \frac{d_{\infty}}{τ} {normale}^{- t / τ} .

A similar expression is also used to model the influence of corrosion products on aluminum via FEM simulations Nidadavolu et al and Dahms et al,the empirical expression of the corrosion progress given by Nidadavolu et al and Dahms et al has the following implicit form

y_{normalN} (t) = y_{0} (1 - {normale}^{- y_{normalN} (t) / y_{0}}) + {\overset{y}{true}}_{normal∞} t .

y_{0}

is the corrosion depth on short time scales and

{\dot{y}}_{\infty}

is the long‐term corrosion rate. The implicit corrosion rate is given by

y_{normalN}^{true'} (t) = \frac{{\dot{y}}_{\infty}}{1 - {normale}^{- y_{normalN} (t) / {normaly}_{0}}}

where the parameter y 0 describes the initial period which is driven by electrode kinetics and

{\dot{y}}_{\infty}

the steady‐state situation which is determined by a limiting process again. Brown et al and Barnard et al,in this FEM simulation the corrosion rate hindered by corrosion products, for example zinc hydroxide, is given by

y_{BB}^{true'} (t) = a {(1 - p)}^{2} = a (1 - b y_{BB} (

…”

Section: Computational Modelingmentioning

confidence: 99%

“…Modeling of corrosion processes is a research subject of great interest and has applications among others in automotive industry, marine industry, and medical industry . There are various approaches to compute the corrosion progress.…”

Section: Introductionmentioning

confidence: 99%

Enhanced predictive corrosion modeling with implicit corrosion products

Gießgen

Mittelbach

Höche

et al. 2019

Materials & Corrosion

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An advanced mathematical approach to describe the influence of corrosion products on the corrosion rate is presented here. The related model can be used as input equation for numerical predictive corrosion simulations or simply as an empirical model, to extrapolate experimental data of corrosion tests to longer times and to interpret the physical parameters behind. This semiempirical model assumes that a constant share of the dissolved metal precipitates on the surface and hinders the diffusion processes. Hence, the effective corrosion rate decreases exponentially with increasing dissolution. The explicit corrosion progress over time is derived by time integration on a newly developed, time dependent corrosion rate equation. The derived expression can be effortlessly implemented in existing for example finite element method, which is demonstrated for the uniform corrosion of a zinc surface. Furthermore, this approach is qualitatively compared with other empirical models for corrosion products and the validity is demonstrated by fitting of experimental data. A very good agreement between experiment and theory can be achieved for various materials and environments considering no change of the driving corrosion mechanism.K E Y W O R D S corrosion products, corrosion simulation, finite element method, mixed potential theory, uniform corrosion

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“…There are numerous studies of similar problems for a range of metals that neglect the advective contribution to the corrosion dynamics, resulting in Stefan-like problems to describe corrosion in, for example, zirconium [ 20 ] and steel [ 21 ]. Magnesium corrosion has been the subject of a small number of modelling studies [ 22 , 23 , 24 ]. In [ 23 ], a simple two-phase bulk model of magnesium corrosion was proposed and parameter fitted to experimental data; however, the model is not explicit in the products of corrosion.…”

Section: Introductionmentioning

confidence: 99%

“…Magnesium corrosion has been the subject of a small number of modelling studies [ 22 , 23 , 24 ]. In [ 23 ], a simple two-phase bulk model of magnesium corrosion was proposed and parameter fitted to experimental data; however, the model is not explicit in the products of corrosion. A spatially explicit model of a galvanised magnesium was proposed in [ 24 ]; here, the magnesium block was a fixed domain and they showed that the thickness of the galvanised layer affected corrosion.…”

Section: Introductionmentioning

confidence: 99%

Numerical Modelling of Effects of Biphasic Layers of Corrosion Products to the Degradation of Magnesium Metal In Vitro

2017

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Magnesium (Mg) is becoming increasingly popular for orthopaedic implant materials. Its mechanical properties are closer to bone than other implant materials, allowing for more natural healing under stresses experienced during recovery. Being biodegradable, it also eliminates the requirement of further surgery to remove the hardware. However, Mg rapidly corrodes in clinically relevant aqueous environments, compromising its use. This problem can be addressed by alloying the Mg, but challenges remain at optimising the properties of the material for clinical use. In this paper, we present a mathematical model to provide a systematic means of quantitatively predicting Mg corrosion in aqueous environments, providing a means of informing standardisation of in vitro investigation of Mg alloy corrosion to determine implant design parameters. The model describes corrosion through reactions with water, to produce magnesium hydroxide Mg(OH)2, and subsequently with carbon dioxide to form magnesium carbonate MgCO3. The corrosion products produce distinct protective layers around the magnesium block that are modelled as porous media. The resulting model of advection–diffusion equations with multiple moving boundaries was solved numerically using asymptotic expansions to deal with singular cases. The model has few free parameters, and it is shown that these can be tuned to predict a full range of corrosion rates, reflecting differences between pure magnesium or magnesium alloys. Data from practicable in vitro experiments can be used to calibrate the model’s free parameters, from which model simulations using in vivo relevant geometries provide a cheap first step in optimising Mg-based implant materials.

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A simple model for long‐time degradation of magnesium under physiological conditions

Cited by 17 publications

References 30 publications

Magnesium degradation under physiological conditions – Best practice

Magnesium degradation under physiological conditions – Best practice

Enhanced predictive corrosion modeling with implicit corrosion products

Numerical Modelling of Effects of Biphasic Layers of Corrosion Products to the Degradation of Magnesium Metal In Vitro

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