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Influence of roughness on surface instability of medical grade cobalt–chromium alloy (CoCrMo) during contact corrosion–fatigue
Applied Surface Science 273 (2013) 536–541
Contents lists available at SciVerse ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Influence of roughness on surface instability of medical grade cobalt–chromium alloy (CoCrMo) during contact corrosion–fatigue Jae Joong Ryu a,∗ , Pranav Shrotriya b a b
Department of Mechanical Engineering, The University of Texas at Tyler, TX 75799, USA Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
a r t i c l e
i n f o
Article history: Received 15 July 2011 Received in revised form 8 January 2013 Accepted 11 February 2013 Available online 4 March 2013 Keywords: Surface roughness Contact corrosion–fatigue Stress-assisted dissolution Bio-implant
a b s t r a c t Surface roughness and contact load play a major role in contact corrosion–fatigue phenomena that accelerates corrosion pits on the stressed surface area. The local yielding and stress concentration will be produced when the rough surface is brought into cyclic contact. Subsequently, the selective electrochemical attacks on the stressed surface will lead to the roughness evolution during environmental corrosion. The continuous roughness evolution by the stress-assisted dissolution will ultimately nucleate microcracks on the surface. In this article, a new evaluation method was introduced to identify the thermodynamic driving forces responsible for the stress-assisted dissolution. In order for complete understanding of the mechanical and electrochemical response of materials surface during contact corrosion–fatigue, finite element calculations and contact corrosion–fatigue experiments were performed on textured medical grade cobalt–chromium–molybdenum (CoCrMo) specimen surfaces. Consequently, the quantitative model of roughness evolution was developed to predict contact corrosion–fatigue damage of CoCrMo surface. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Cobalt–chromium alloys have been widely used for implants and prosthetic devices such as Total Hip Joint Replacement (THR) due to their resistive property in corrosion and fatigue. Although the alloys are specially designed to withstand fatigue loading and corrosion, the synergistic degradation by fatigue and corrosion is being a major issue to be solved in orthopedic implant failure and its biocompatibility problem [1–3]. In the numerous corrosion–fatigue studies, the fundamental mechanism of corrosion–fatigue is defined as a progressive sequence of surface damage due to the combination of cyclic mechanical loads with electrochemical reactions [4–8]. The process generally includes four successive stages: localized plastic strains; microcrack nucleation; crack growth; and coalescence and crack propagation in the following cyclic loads. The detailed damage mechanism has been described focusing on mechanical loads such as number of cycles and magnitude of loads [9–13]. The mechanical load opens and shears the crack produced by corrosion pit and the oxidation prohibits from reversibility of slip bands in small plastic strains near crack tips. This synergistic effect results in increase in stress level and crack growth rate. Mitchell and Shrotriya’s work was to
∗ Corresponding author. Tel.: +1 903 565 5914; fax: +1 903 565 5907. E-mail address: [email protected] (J.J. Ryu). 0169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2013.02.076
investigate fretting corrosion behavior of implant material surface while this experimental work investigated multi-asperity contact without fretting motion at the interface [8]. Their purpose was to identify the influence of reciprocal sliding contact (fretting) of nanoscale single asperity in corrosive environment. The fretting motion of nanoscale single was experimentally simulated utilizing AFM probe in aqueous environment. In this manuscript, however, authors emphasized the influence of residual stress induced by cyclic contact of multi-asperity surface on environmental corrosion. In contact corrosion–fatigue, the roughness of materials surface significantly affects surface instability that ultimately initiates microcracks on the contacting surface. Many investigations of surface instability have been performed to understand surface damage mechanism and identify the driving forces of the surface modification. Applied stress and surface roughness have been focused to predict surface instability of solids in liquid [14–17]. Asaro demonstrated the stress corrosion cracking process that is caused by selective growth of harmonic component of crack surface when there exist incorporating effects of applied stress and chemical free energy [14]. The morphological instability of corrugating surface was explained by the competition of surface energy and elastic energy at solid-liquid interface [15]. The strong relevance between surface morphology modification and dilatation stress was provided by presenting critical wavelength of surface instability. A new mechanism of elastic strain energy-driven instability was introduced to describe the effect of stress on the mobility
J.J. Ryu, P. Shrotriya / Applied Surface Science 273 (2013) 536–541
on film-substrate interface [16]. In the comparison of theory and experiment, Barvosa-Cater illustrated increase in perturbation at corrugating Si(001) interface with compressive stress. Roughness evolution of stressed surface during chemical reaction was monitored by using FFT spectrum of Atomic Force Microscopy measurement [17]. This experimental result demonstrated that the surface stress state significantly affects roughness domains that are subjected to roughening and flattening during nanoetching. In spite of the abundant studies on corrosion of stressed surfaces, the direct influence of the contact stress of rough surface on corrosion damage has not been fully understood. In this paper, the central hypothesis of “the surface roughness affects onset of surface crack nucleation during contact corrosion–fatigue” was investigated. The machining process creates corrugating texture on the manufactured surface, and when the surface is brought into contact, only the protruding asperities undergo microcontacts. The small contact areas plastically deform and generate nonuniform residual stress over the contacting surface. As a result, the residual stress deviations on the material surface drive roughness instability during corrosion i.e. the degrees of roughness and magnitudes of contact loading determine the material dissolution rate during aeration period in chemical solution. The preferential dissolution results in continuous roughness evolution and ultimately creates microcracks on the contacting surface. In the previous investigation, the Finite Element (FE) method was used to illustrate the augmented residual stress field established during head-stem interaction in total joint replacement. It presented that the superposition of residual stress in between two neighboring contact asperities leads to stress concentration at the surface troughs [18]. In the current investigation, the previous approach was employed and extended to identify thermodynamic driving forces of CoCrMo in contact corrosion–fatigue. A series of finite element models of rough surface contact were created to calculate residual stress fields in a wide range of surface roughness. Accordingly, the thermodynamic driving forces were utilized to predict roughness evolution of contact stressed surfaces during electrochemical dissolution.
Fig. 1. The roughness evolution of harmonic surface of h(x) is determined by the relative dissolution rate of solid at asperity summits and surface troughs, ıR = (hs − ht ) /t = vs − vt , where hs and ht are surface height changes at asperity summits and troughs, respectively.
exposure period may not be able to detect significant role of chemical potential on the roughness evolution. R=
Ho h = M (g − USE − K) = Mg + M (−USE − K) + t t
The driving forces stimulating the surface roughness changes in contact corrosion–fatigue were identified by utilizing thermodynamic quantities of liquid-solid interface. Previous researches from Kim [17] and Yu [19] illustrated the total reaction of solid surface in liquid as; R = MF,
(1)
where R is reaction rate, M is proportionality constant known as the mobility of surface and F is driving force. Only when the reaction process is thermally activated the mobility M will affect the surface reaction following Arrhenius relation. However, the liquid – solid system is not thermally activated in this investigation that is, assumed to be constant. The electrochemical reaction rate was characterized by linear superposition of thermodynamic driving forces [20]; F = g − USE − K,
(2)
where g is chemical potential, USE is strain energy, and and K are interfacial energy and local surface curvature, respectively. This kinetic law illustrated that the electrochemical potential g is independent and constant over the surface during the chemical reactions. In this article, authors focused on the impact of strain energy and surface curvature on differential dissolution. The microetching experiment conducted during the short
(3)
This total material dissolution rate (R) includes uniform dissolution by consistent chemical potential over the surface (Mg), and nonuniform dissolution by local deviations of elastic strain energy and surface curvature (M(–USE –K)). The uniform dissolution is responsible for the average height changes (Ho /t, where the Ho is average surface height) over the surface during chemical exposure while the nonuniform dissolutions (h/t, where the h is local surface heights at surface locations) lead to roughness changes. In this analysis, the rough surface was simplified as a sinusoidal configuration with a unique amplitude (a) and period () such that the surface height function is h(x) = a cos(2/). Accordingly, nonuniform dissolution measures the roughness evolution that implies the relative height changes between asperities and surface troughs during aeration period as shown in Fig. 1. Therefore, the only the relative height change (ıR) contributes roughness evolutions driven by elastic strain energy variation and surface roughness as in Eq. (2). ıR =
2. Thermodynamic forces of contact corrosion–fatigue
537
hs − ht ≈ M (−USE − 2K) t
(2)
The local surface curvature (K) was evaluated by the second order differentiation of the surface function of h such that the local solid surface curvature is K = ∂2 h(x)/∂x2 . The strain energy (USE ) was evaluated based on the residual stress developed during cyclic contacts of the solid surface. The complex mechanism of roughness instability due to contact corrosion–fatigue will be summarized by the factors of Eq. (3). The relative height changes in between asperity summits and surface troughs are determined by contact residual stress and surface curvature. ıR =
hs − ht h(0) h(/2) ≈ − t t t
=M
s 2 − t 2 ∂2 h − 2 2 − 2E ∂x
(3)
In the presence of significant surface stress, the stress-assisted dissolution establishes roughening of the material surface while in the absence of surface stress, the surface undulation will decay. 3. Finite element model of rough surface contact In order to complete the roughness evolution model illustrated in Eq. (3), surface residual stress generated by cyclic contact was predicted by Finite Element Method. Finite element models of rough surface were created to be a sinusoidal surface with amplitude and period as illustrated in Fig. 2. Groups of surface roughness
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contact simulations was performed in a sequence of contact loading and complete unloading for each group of surfaces to identify influences of roughness and contact loading on the residual stress development. The predicted stress was employed to calculate strain energy required in the thermodynamic driving force equation. 4. Experimental design
Fig. 2. Finite element models of rough surface contact with periodic boundary conditions were created to predict residual stress development during fatigue contact.
were created in the range of 0.003 ≤ ˛/ ≤ 0.01 and the applied loads ( appl ) were approximated by nominally elastic contact pressure in the range of 0.3 y ≤ appl ≤ 0.7 y with rigid plate, where y is yield strength of the CoCrMo. The surface elements were characterized as the elastic-perfectly plastic isotropic solid with the mechanical properties of CoCrMo. The Young’s modulus of 230 GPa, yield strength of 450 MPa, and Poisson’s ratio of 0.3 were applied to the surface elements and the periodic boundary conditions were implemented. Plane strain, triangular quadratic elements were meshed and refined to achieve numerical convergence. A series of
Surface roughness evolution driven by contact fatigue and corrosion were monitored by combined experiments of normal indentation and microetching. Rough surfaces were created by milling process on the cobalt–chromium–Molybdenum (CoCrMo, cast ASTM F-75) specimens. The milled surfaces presented the regularly undulating configurations as illustrated in Fig. 3(a). The rough surfaces were brought into cyclic contacts with the mirror finished CoCrMo surface as shown in Fig. 3(b). The nominally elastic contact loads were applied 10 times in the range of 40–70% of specimen yield strength ( y = 450 MPa). Then the stressed surface was exposed to strong acidic solution of 20 ml HCl, 10 ml HNO3 and 3 g FeCl3 [21]. This alternating procedure was repeated with different magnitudes of contact loads and aerated in the aggressive etchant for 3 min. Table 1 summarized the experimental scheme. The surface profilometry measurement was conducted after each contact and corrosion experiment to observe surface roughness changes. The Fast Fourier Transform (FFT) calculation of the measured roughness data was used to identify the roughness modes that involved in the most significant amplitude changes during the alternating test in contacts and microetching. 5. Results and discussion Before and after each normal contact experiment, surface roughness was measured and compared to verify plastic strain
Fig. 3. (a) The surface profile presents regularly undulating surface. (b) The undulating surface was subjected to normal indentation with mirror-finished CoCrMo surface and polymeric substrate was utilized to ensure the normal motion of indentation and to develop contact stress only on the contacting side.
Table 1 The contact corrosion–fatigue test was performed on 12 specimens in each test group by the alternating sequence of cyclic elastic contacts and exposure to chemical etchant for 3 min. After incremental test of contact and etching the surface roughness has been measured by using optical profilometer. Test group
Nominal contact stress ( y : yield strength)
10 cycles of fatigue contact loading with
Micro-etching
No. of specimen
1 2 3 4
0.4 y 0.5 y 0.6 y 0.7 y
91 kN 114 kN 137 kN 160 kN
3-min aeration in solution of HCl, HNO3 and FeCl3
12 12 12 12
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Fig. 4. (a) The FFT spectrum shows roughness amplitude changes by alternation of normal contact loading with 70% of yield strength of CoCrMo and etching test. (b) The FFT spectrum presents that the most dominant surface roughness modes collapsed after normal contact and then the suppressed roughness modes increased after etching experiment.
539
development. Subsequently, the residually stressed surface was aerated in strong acidic etchant for 3 min. The surface roughness amplitude change by preferential corrosion on stressed surface was quantified by Fast Fourier Transform (FFT) calculations of the surface data. As a result, the FFT spectrum indicated the significant decrease in roughness amplitudes at some harmonic components of the rough surface after contact loadings. This result implies the plastic strain develops residual stress after contact loading and unloading procedure. In the successive microetching test, FFT spectrum illustrated the growth of roughness amplitudes that have collapsed during the normal contact experiment. The repeating motions of decrease and increase in roughness amplitudes were found in some dominant roughness modes which mainly involve the real contact during normal indentations. The roughness evolution procedure was summarized by superimposed FFT spectrum. The three most dominant surface roughness components were observed in the series of contact and corrosion experiment as highlighted in Fig. 4. Among three dominant surface components, the roughness component at the longest surface wavelength of = 36 m experienced the most significant amplitude changes during the contact loading and microetching experiments. The roughness amplitudes at = 36 m were selected to quantify the relative dissolution rate (ıR) in Eq. (3). The selected roughness component (˛/ = 0.003) was employed to create finite element model of the undulating surface contact. The FE simulation results illustrated high stress variations established on the undulating surface due to the misfitting between plastically deformed materials under the contacting asperities and surrounding elastically deformed materials during contact loading. This misffiting resulted in local stress concentration at the surface troughs after complete unloading as shown in Fig. 5. The average stress level at surface asperities was order of 10% of the stress concentration at surface troughs. The series of contact simulations of the undulating surfaces described the higher contact load induced the greater stress concentrations at the surface troughs while the stress at the summits remains 10% of maximum stress at troughs. Fig. 6 presents the residual stress developed at surface roughs after 10 complete cycles of contact loading and unloading. The normalized stress as a function of normalized load describes a clear relevance of surface roughness parameter (˛/). The relative dissolution rates measured by the contact and microetching experiments were plotted with stress values at the surface troughs obtained from finite element simulations. Fig. 7 demonstrated that the higher stress concentration induced by higher contact loads on the rough surface accelerates
Fig. 5. Lateral stress (S11) illustrated nonuniform distribution on the undulating surface (a/ = 0.003) by 70% of yield strength of nominal contact load. High stress concentration was found at the surface troughs in all other contact loads of 40, 50 and 60% of yield strength of CoCrMo material.
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Fig. 6. Residual stress calculated by Finite Element modeling of multi-asperity contact. Surface roughness was characterized by amplitude-to-wavelength ratio in the range of 0.003 ≤ ˛/ ≤ 0.0125 and the contact loads were determine in nominally elastic regime 0.3 ≤ Appl/ Yield ≤ 0.7.
roughness evolution. This result indicates precipitations of local pitting attacks at surface troughs during stressed surface corrosion. The thermodynamic driving forces in Eq. (3) were compared to the combined results from experiment and finite element simulation to evaluate the solid surface mobility (M) and interfacial energy (). The least squares approach was employed to create a quadratic polynomial function of surface stress at troughs. The coefficient of the first degree term was forced to be zero as illustrated in Eq. (3). The surface curvature was approximated by the second order derivatives of the surface function at asperity tips and troughs. The Young’s modulus of Cobalt–chromium alloy was used. The interfacial energy of CoCrMo in the etchant was 0.578 J/m2 and the surface mobility was 1.255 × 105 m3 /N min. The approximated quantities were utilized to complete the predictive thermodynamic equation of contact corrosion–fatigue on CoCrMo surface. Additional FE simulations of rough surface contact were developed to identify residual stresses at the surface trough and the corresponding local surface curvatures were calculated from surface height function to characterize the local corrosion attacks with
Fig. 8. Predicted roughness amplitude changes: as the surface roughness and elastic contact load increase, roughness amplitude increases and then leads to early surface damage by contact corrosion–fatigue.
degrees of surface roughness (˛/) and levels of contact pressures ( appl ). Accordingly, the predictive thermodynamic characterization of surface instability presented that the contact pressures and surface roughness exponentially accelerate the localized damage by contact corrosion–fatigue (Fig. 7). 6. Conclusion The thermodynamic analysis of rough surface contact corrosion–fatigue was performed by combined experimental approach with finite element simulations to understand direct influence of surface roughness on corrosion damage phenomena. The experimental measurements of roughness changes after cyclic normal contacts and microetching of milled surface described the continuous motion of decrease and increase of roughness amplitudes due to stress-assisted dissolutions. The required thermodynamic properties were approximated and employed to identify surface characteristics in corrosion. In summary, a new approach of contact fatigue and corrosion was conducted to identify the influence of roughness condition and contact pressures on early stage of contact corrosion–fatigue damage mechanism. As a result, the predictive equation of roughness instability enabled to characterize the surface damage of rough surfaces during contact corrosion–fatigue (Fig. 8). References
Fig. 7. Roughness height difference (hs – ht ) in between summits and troughs during the aeration period presents a quadratic correlation with surface stress developed by normal fatigue contact.
[1] J.L. Gilbert, C.A. Buckley, J.J. Jacobs, In vivo corrosion of modular hip prosthesis components in mixed and similar metal combinations. The effect of crevice, stress, motion, and alloy coupling, Journal of Biomedical Materials Research 27 (1993) 1533–1544. [2] N.J. Hallab, J.J. Jacobs, Orthopedic implant fretting corrosion, Corrosion reviews 21 (2003) 183–213. [3] J.J. Jacobs, J.L. Gilbert, R.M. Urban, Corrosion of metal orthopaedic implants, Journal of Bone and Joint Surgery-American Volume 80A (1998) 268–282. [4] A. Mitchell, P. Shrotriya, Onset of nanoscale wear of metallic implant materials: Influence of surface residual stresses and contact loads, Wear 263 (2007) 1117–1123. [5] A. Scala, A. Squillace, D. Monetta, D.B. Mitton, D. Larson, F. Bellucci, Corrosion fatigue on 2024T3 and 6056T4 aluminum alloys, Surface and Interface Analysis 42 (2009) 194–198. [6] S. Suresh, R.O. Ritchie, Mechanistic dissimilarities between environmentallyinfluenced fatigue-crack propagation at near-threshold and higher growth rates in lower strength steels, Metal Science 16 (1982) 1627–1631. [7] F.E. Fujita, Oxidation and dislocation mechanisms in fatigue crack formation, in: D.C. Drucker, J.J. Gilman (Eds.), Fracture of Solids, 1963, pp. 657–670. [8] A. Mitchell, P. Shrotriya, Mechanical load-assisted dissolution of metallic implant surfaces: influence of contact loads and surface stress state, Acta Biomaterialia 4 (2008) 296–304.
J.J. Ryu, P. Shrotriya / Applied Surface Science 273 (2013) 536–541 [9] D.J. Duquette, Environmental effects on general fatigue resistance and crack nucleation in metals and alloys, Fatigue and Microstructure American Society for Metals (1979) 335–363. [10] D.J. Duquette, H.H. Uhlig, Effect of dissolved oxygen and NaCl on corrosion fatigue of 0.18% carbon steel, Transaction of the American Society for Metals 61 (1968) 449–456. [11] A.J. McEvily, R.P. Wei, Fracture mechanics and corrsion fatigue, Corrosion Fatigue: Chemistry, Mechanics and Microstructure NACE-2 (1972) 381–395. [12] S.I. Rokhlin, J.-Y. Kim, H.Z.B. Nagy, Effect of pitting corrosion on fatigue crack initiation and fatigue life, Engineering Fracture Mechanics 62 (1999) 425–444. [13] J. Xie, A.T. Alpas, D.O. Northwood, A mechanism for the crack initiation of corrosion fatigue of Type 316L stainless steel in Hank’s solution, Material Characteristics 48 (2002) 271–277. [14] R. Asaro, W. Tiller, Interface morphology development during stress corrosion cracking: Part I. Via surface diffusion, Metallurgical Transactions 3 (1972) 1789–1796.
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[15] D.J. Srolovitz, On the stability of surfaces of stressed solids, Acta Metallurgica 37 (1989) 621–625. [16] W. Barvosa-Carter, M.J. Aziz, L.J. Gray, T. Kaplan, Kinetically driven growth instability in stressed solids, Physical Review Letters 81 (1998) 1445–1448. [17] K.S. Kim, J.A. Hurtado, H. Tan, Evolution of a surface-roughness spectrum caused by stress in nanometer-scale chemical etching, Physical Review Letters 83 (1999) 3872–3875. [18] J. Ryu, V. Dayal, P. Shrotriya, Onset of surface damage in modular orthopedic implants: influence of normal contact loading and stress-assisted dissolution, Experimental Mechanics 47 (2007) 395. [19] H.H. Yu, P. Shrotriya, J. Wang, K.S. Kim, Dislocation nucleation and segregation in nano-scale contact of stepped surfaces, in: MRS Winter Meeting, Boston, 2003. [20] C. Herring, in: W.E. Kingston (Ed.), The Physics of Powder Metallurgy, McGrawHill, 1951, pp. 143–179. [21] A.C. Fraker, ASM handbook, in: A.C. Fraker (Ed.), Corrosion of Metallic Implants and Prosthetic Device, pp. 1324–1335.
Contents lists available at SciVerse ScienceDirect
Applied Surface Science journal homepage: www.elsevier.com/locate/apsusc
Influence of roughness on surface instability of medical grade cobalt–chromium alloy (CoCrMo) during contact corrosion–fatigue Jae Joong Ryu a,∗ , Pranav Shrotriya b a b
Department of Mechanical Engineering, The University of Texas at Tyler, TX 75799, USA Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, USA
a r t i c l e
i n f o
Article history: Received 15 July 2011 Received in revised form 8 January 2013 Accepted 11 February 2013 Available online 4 March 2013 Keywords: Surface roughness Contact corrosion–fatigue Stress-assisted dissolution Bio-implant
a b s t r a c t Surface roughness and contact load play a major role in contact corrosion–fatigue phenomena that accelerates corrosion pits on the stressed surface area. The local yielding and stress concentration will be produced when the rough surface is brought into cyclic contact. Subsequently, the selective electrochemical attacks on the stressed surface will lead to the roughness evolution during environmental corrosion. The continuous roughness evolution by the stress-assisted dissolution will ultimately nucleate microcracks on the surface. In this article, a new evaluation method was introduced to identify the thermodynamic driving forces responsible for the stress-assisted dissolution. In order for complete understanding of the mechanical and electrochemical response of materials surface during contact corrosion–fatigue, finite element calculations and contact corrosion–fatigue experiments were performed on textured medical grade cobalt–chromium–molybdenum (CoCrMo) specimen surfaces. Consequently, the quantitative model of roughness evolution was developed to predict contact corrosion–fatigue damage of CoCrMo surface. © 2013 Elsevier B.V. All rights reserved.
1. Introduction Cobalt–chromium alloys have been widely used for implants and prosthetic devices such as Total Hip Joint Replacement (THR) due to their resistive property in corrosion and fatigue. Although the alloys are specially designed to withstand fatigue loading and corrosion, the synergistic degradation by fatigue and corrosion is being a major issue to be solved in orthopedic implant failure and its biocompatibility problem [1–3]. In the numerous corrosion–fatigue studies, the fundamental mechanism of corrosion–fatigue is defined as a progressive sequence of surface damage due to the combination of cyclic mechanical loads with electrochemical reactions [4–8]. The process generally includes four successive stages: localized plastic strains; microcrack nucleation; crack growth; and coalescence and crack propagation in the following cyclic loads. The detailed damage mechanism has been described focusing on mechanical loads such as number of cycles and magnitude of loads [9–13]. The mechanical load opens and shears the crack produced by corrosion pit and the oxidation prohibits from reversibility of slip bands in small plastic strains near crack tips. This synergistic effect results in increase in stress level and crack growth rate. Mitchell and Shrotriya’s work was to
∗ Corresponding author. Tel.: +1 903 565 5914; fax: +1 903 565 5907. E-mail address: [email protected] (J.J. Ryu). 0169-4332/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.apsusc.2013.02.076
investigate fretting corrosion behavior of implant material surface while this experimental work investigated multi-asperity contact without fretting motion at the interface [8]. Their purpose was to identify the influence of reciprocal sliding contact (fretting) of nanoscale single asperity in corrosive environment. The fretting motion of nanoscale single was experimentally simulated utilizing AFM probe in aqueous environment. In this manuscript, however, authors emphasized the influence of residual stress induced by cyclic contact of multi-asperity surface on environmental corrosion. In contact corrosion–fatigue, the roughness of materials surface significantly affects surface instability that ultimately initiates microcracks on the contacting surface. Many investigations of surface instability have been performed to understand surface damage mechanism and identify the driving forces of the surface modification. Applied stress and surface roughness have been focused to predict surface instability of solids in liquid [14–17]. Asaro demonstrated the stress corrosion cracking process that is caused by selective growth of harmonic component of crack surface when there exist incorporating effects of applied stress and chemical free energy [14]. The morphological instability of corrugating surface was explained by the competition of surface energy and elastic energy at solid-liquid interface [15]. The strong relevance between surface morphology modification and dilatation stress was provided by presenting critical wavelength of surface instability. A new mechanism of elastic strain energy-driven instability was introduced to describe the effect of stress on the mobility
J.J. Ryu, P. Shrotriya / Applied Surface Science 273 (2013) 536–541
on film-substrate interface [16]. In the comparison of theory and experiment, Barvosa-Cater illustrated increase in perturbation at corrugating Si(001) interface with compressive stress. Roughness evolution of stressed surface during chemical reaction was monitored by using FFT spectrum of Atomic Force Microscopy measurement [17]. This experimental result demonstrated that the surface stress state significantly affects roughness domains that are subjected to roughening and flattening during nanoetching. In spite of the abundant studies on corrosion of stressed surfaces, the direct influence of the contact stress of rough surface on corrosion damage has not been fully understood. In this paper, the central hypothesis of “the surface roughness affects onset of surface crack nucleation during contact corrosion–fatigue” was investigated. The machining process creates corrugating texture on the manufactured surface, and when the surface is brought into contact, only the protruding asperities undergo microcontacts. The small contact areas plastically deform and generate nonuniform residual stress over the contacting surface. As a result, the residual stress deviations on the material surface drive roughness instability during corrosion i.e. the degrees of roughness and magnitudes of contact loading determine the material dissolution rate during aeration period in chemical solution. The preferential dissolution results in continuous roughness evolution and ultimately creates microcracks on the contacting surface. In the previous investigation, the Finite Element (FE) method was used to illustrate the augmented residual stress field established during head-stem interaction in total joint replacement. It presented that the superposition of residual stress in between two neighboring contact asperities leads to stress concentration at the surface troughs [18]. In the current investigation, the previous approach was employed and extended to identify thermodynamic driving forces of CoCrMo in contact corrosion–fatigue. A series of finite element models of rough surface contact were created to calculate residual stress fields in a wide range of surface roughness. Accordingly, the thermodynamic driving forces were utilized to predict roughness evolution of contact stressed surfaces during electrochemical dissolution.
Fig. 1. The roughness evolution of harmonic surface of h(x) is determined by the relative dissolution rate of solid at asperity summits and surface troughs, ıR = (hs − ht ) /t = vs − vt , where hs and ht are surface height changes at asperity summits and troughs, respectively.
exposure period may not be able to detect significant role of chemical potential on the roughness evolution. R=
Ho h = M (g − USE − K) = Mg + M (−USE − K) + t t
The driving forces stimulating the surface roughness changes in contact corrosion–fatigue were identified by utilizing thermodynamic quantities of liquid-solid interface. Previous researches from Kim [17] and Yu [19] illustrated the total reaction of solid surface in liquid as; R = MF,
(1)
where R is reaction rate, M is proportionality constant known as the mobility of surface and F is driving force. Only when the reaction process is thermally activated the mobility M will affect the surface reaction following Arrhenius relation. However, the liquid – solid system is not thermally activated in this investigation that is, assumed to be constant. The electrochemical reaction rate was characterized by linear superposition of thermodynamic driving forces [20]; F = g − USE − K,
(2)
where g is chemical potential, USE is strain energy, and and K are interfacial energy and local surface curvature, respectively. This kinetic law illustrated that the electrochemical potential g is independent and constant over the surface during the chemical reactions. In this article, authors focused on the impact of strain energy and surface curvature on differential dissolution. The microetching experiment conducted during the short
(3)
This total material dissolution rate (R) includes uniform dissolution by consistent chemical potential over the surface (Mg), and nonuniform dissolution by local deviations of elastic strain energy and surface curvature (M(–USE –K)). The uniform dissolution is responsible for the average height changes (Ho /t, where the Ho is average surface height) over the surface during chemical exposure while the nonuniform dissolutions (h/t, where the h is local surface heights at surface locations) lead to roughness changes. In this analysis, the rough surface was simplified as a sinusoidal configuration with a unique amplitude (a) and period () such that the surface height function is h(x) = a cos(2/). Accordingly, nonuniform dissolution measures the roughness evolution that implies the relative height changes between asperities and surface troughs during aeration period as shown in Fig. 1. Therefore, the only the relative height change (ıR) contributes roughness evolutions driven by elastic strain energy variation and surface roughness as in Eq. (2). ıR =
2. Thermodynamic forces of contact corrosion–fatigue
537
hs − ht ≈ M (−USE − 2K) t
(2)
The local surface curvature (K) was evaluated by the second order differentiation of the surface function of h such that the local solid surface curvature is K = ∂2 h(x)/∂x2 . The strain energy (USE ) was evaluated based on the residual stress developed during cyclic contacts of the solid surface. The complex mechanism of roughness instability due to contact corrosion–fatigue will be summarized by the factors of Eq. (3). The relative height changes in between asperity summits and surface troughs are determined by contact residual stress and surface curvature. ıR =
hs − ht h(0) h(/2) ≈ − t t t
=M
s 2 − t 2 ∂2 h − 2 2 − 2E ∂x
(3)
In the presence of significant surface stress, the stress-assisted dissolution establishes roughening of the material surface while in the absence of surface stress, the surface undulation will decay. 3. Finite element model of rough surface contact In order to complete the roughness evolution model illustrated in Eq. (3), surface residual stress generated by cyclic contact was predicted by Finite Element Method. Finite element models of rough surface were created to be a sinusoidal surface with amplitude and period as illustrated in Fig. 2. Groups of surface roughness
538
J.J. Ryu, P. Shrotriya / Applied Surface Science 273 (2013) 536–541
contact simulations was performed in a sequence of contact loading and complete unloading for each group of surfaces to identify influences of roughness and contact loading on the residual stress development. The predicted stress was employed to calculate strain energy required in the thermodynamic driving force equation. 4. Experimental design
Fig. 2. Finite element models of rough surface contact with periodic boundary conditions were created to predict residual stress development during fatigue contact.
were created in the range of 0.003 ≤ ˛/ ≤ 0.01 and the applied loads ( appl ) were approximated by nominally elastic contact pressure in the range of 0.3 y ≤ appl ≤ 0.7 y with rigid plate, where y is yield strength of the CoCrMo. The surface elements were characterized as the elastic-perfectly plastic isotropic solid with the mechanical properties of CoCrMo. The Young’s modulus of 230 GPa, yield strength of 450 MPa, and Poisson’s ratio of 0.3 were applied to the surface elements and the periodic boundary conditions were implemented. Plane strain, triangular quadratic elements were meshed and refined to achieve numerical convergence. A series of
Surface roughness evolution driven by contact fatigue and corrosion were monitored by combined experiments of normal indentation and microetching. Rough surfaces were created by milling process on the cobalt–chromium–Molybdenum (CoCrMo, cast ASTM F-75) specimens. The milled surfaces presented the regularly undulating configurations as illustrated in Fig. 3(a). The rough surfaces were brought into cyclic contacts with the mirror finished CoCrMo surface as shown in Fig. 3(b). The nominally elastic contact loads were applied 10 times in the range of 40–70% of specimen yield strength ( y = 450 MPa). Then the stressed surface was exposed to strong acidic solution of 20 ml HCl, 10 ml HNO3 and 3 g FeCl3 [21]. This alternating procedure was repeated with different magnitudes of contact loads and aerated in the aggressive etchant for 3 min. Table 1 summarized the experimental scheme. The surface profilometry measurement was conducted after each contact and corrosion experiment to observe surface roughness changes. The Fast Fourier Transform (FFT) calculation of the measured roughness data was used to identify the roughness modes that involved in the most significant amplitude changes during the alternating test in contacts and microetching. 5. Results and discussion Before and after each normal contact experiment, surface roughness was measured and compared to verify plastic strain
Fig. 3. (a) The surface profile presents regularly undulating surface. (b) The undulating surface was subjected to normal indentation with mirror-finished CoCrMo surface and polymeric substrate was utilized to ensure the normal motion of indentation and to develop contact stress only on the contacting side.
Table 1 The contact corrosion–fatigue test was performed on 12 specimens in each test group by the alternating sequence of cyclic elastic contacts and exposure to chemical etchant for 3 min. After incremental test of contact and etching the surface roughness has been measured by using optical profilometer. Test group
Nominal contact stress ( y : yield strength)
10 cycles of fatigue contact loading with
Micro-etching
No. of specimen
1 2 3 4
0.4 y 0.5 y 0.6 y 0.7 y
91 kN 114 kN 137 kN 160 kN
3-min aeration in solution of HCl, HNO3 and FeCl3
12 12 12 12
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Fig. 4. (a) The FFT spectrum shows roughness amplitude changes by alternation of normal contact loading with 70% of yield strength of CoCrMo and etching test. (b) The FFT spectrum presents that the most dominant surface roughness modes collapsed after normal contact and then the suppressed roughness modes increased after etching experiment.
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development. Subsequently, the residually stressed surface was aerated in strong acidic etchant for 3 min. The surface roughness amplitude change by preferential corrosion on stressed surface was quantified by Fast Fourier Transform (FFT) calculations of the surface data. As a result, the FFT spectrum indicated the significant decrease in roughness amplitudes at some harmonic components of the rough surface after contact loadings. This result implies the plastic strain develops residual stress after contact loading and unloading procedure. In the successive microetching test, FFT spectrum illustrated the growth of roughness amplitudes that have collapsed during the normal contact experiment. The repeating motions of decrease and increase in roughness amplitudes were found in some dominant roughness modes which mainly involve the real contact during normal indentations. The roughness evolution procedure was summarized by superimposed FFT spectrum. The three most dominant surface roughness components were observed in the series of contact and corrosion experiment as highlighted in Fig. 4. Among three dominant surface components, the roughness component at the longest surface wavelength of = 36 m experienced the most significant amplitude changes during the contact loading and microetching experiments. The roughness amplitudes at = 36 m were selected to quantify the relative dissolution rate (ıR) in Eq. (3). The selected roughness component (˛/ = 0.003) was employed to create finite element model of the undulating surface contact. The FE simulation results illustrated high stress variations established on the undulating surface due to the misfitting between plastically deformed materials under the contacting asperities and surrounding elastically deformed materials during contact loading. This misffiting resulted in local stress concentration at the surface troughs after complete unloading as shown in Fig. 5. The average stress level at surface asperities was order of 10% of the stress concentration at surface troughs. The series of contact simulations of the undulating surfaces described the higher contact load induced the greater stress concentrations at the surface troughs while the stress at the summits remains 10% of maximum stress at troughs. Fig. 6 presents the residual stress developed at surface roughs after 10 complete cycles of contact loading and unloading. The normalized stress as a function of normalized load describes a clear relevance of surface roughness parameter (˛/). The relative dissolution rates measured by the contact and microetching experiments were plotted with stress values at the surface troughs obtained from finite element simulations. Fig. 7 demonstrated that the higher stress concentration induced by higher contact loads on the rough surface accelerates
Fig. 5. Lateral stress (S11) illustrated nonuniform distribution on the undulating surface (a/ = 0.003) by 70% of yield strength of nominal contact load. High stress concentration was found at the surface troughs in all other contact loads of 40, 50 and 60% of yield strength of CoCrMo material.
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Fig. 6. Residual stress calculated by Finite Element modeling of multi-asperity contact. Surface roughness was characterized by amplitude-to-wavelength ratio in the range of 0.003 ≤ ˛/ ≤ 0.0125 and the contact loads were determine in nominally elastic regime 0.3 ≤ Appl/ Yield ≤ 0.7.
roughness evolution. This result indicates precipitations of local pitting attacks at surface troughs during stressed surface corrosion. The thermodynamic driving forces in Eq. (3) were compared to the combined results from experiment and finite element simulation to evaluate the solid surface mobility (M) and interfacial energy (). The least squares approach was employed to create a quadratic polynomial function of surface stress at troughs. The coefficient of the first degree term was forced to be zero as illustrated in Eq. (3). The surface curvature was approximated by the second order derivatives of the surface function at asperity tips and troughs. The Young’s modulus of Cobalt–chromium alloy was used. The interfacial energy of CoCrMo in the etchant was 0.578 J/m2 and the surface mobility was 1.255 × 105 m3 /N min. The approximated quantities were utilized to complete the predictive thermodynamic equation of contact corrosion–fatigue on CoCrMo surface. Additional FE simulations of rough surface contact were developed to identify residual stresses at the surface trough and the corresponding local surface curvatures were calculated from surface height function to characterize the local corrosion attacks with
Fig. 8. Predicted roughness amplitude changes: as the surface roughness and elastic contact load increase, roughness amplitude increases and then leads to early surface damage by contact corrosion–fatigue.
degrees of surface roughness (˛/) and levels of contact pressures ( appl ). Accordingly, the predictive thermodynamic characterization of surface instability presented that the contact pressures and surface roughness exponentially accelerate the localized damage by contact corrosion–fatigue (Fig. 7). 6. Conclusion The thermodynamic analysis of rough surface contact corrosion–fatigue was performed by combined experimental approach with finite element simulations to understand direct influence of surface roughness on corrosion damage phenomena. The experimental measurements of roughness changes after cyclic normal contacts and microetching of milled surface described the continuous motion of decrease and increase of roughness amplitudes due to stress-assisted dissolutions. The required thermodynamic properties were approximated and employed to identify surface characteristics in corrosion. In summary, a new approach of contact fatigue and corrosion was conducted to identify the influence of roughness condition and contact pressures on early stage of contact corrosion–fatigue damage mechanism. As a result, the predictive equation of roughness instability enabled to characterize the surface damage of rough surfaces during contact corrosion–fatigue (Fig. 8). References
Fig. 7. Roughness height difference (hs – ht ) in between summits and troughs during the aeration period presents a quadratic correlation with surface stress developed by normal fatigue contact.
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