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Debonding between coating and substrate due to rolling–sliding contact
Materials and Design 23 (2002) 571–576
Debonding between coating and substrate due to rolling–sliding contact K. Aslantas*, S. Tasgetiren University of Afyon Kocatepe, Technical Education Faculty, Afyon, Turkey Received 2 January 2002; accepted 19 March 2002
Abstract Rolling–sliding contact of layered elastic solid is an important technical issue, since surfaces are often subjected to contact stresses. Generally, elastic surfaces are coated to increase wear resistance of the materials. However, coating materials sometimes debonds from substrate due to tangential and normal forces acting on the surface. Because of these forces, or existing bonding faults, cracks form between coating and substrate. If these forces are applied continuously, the crack propagates resulting in debonding. In this study, a numerical solution is applied to interface cracking. The variations of the stress intensity factors (KI, KII) with load position are obtained for various cases such as different combinations material of coating layer and substrate and changes in the coefficient of friction on the surface. Effects of the combination of the materials and the coefficient of friction on the stress intensity factors are discussed. The direction of the propagation of interface crack is also examined. 䊚 2002 Elsevier Science Ltd. All rights reserved. Keywords: Rolling–sliding contact; Debonding; Stress intensity factor; Finite element method
1. Introduction Coating is widely used for wear resistance of materials. On the other hand, materials are usually stressed under cyclic loading conditions. Loadings may contain rolling andyor sliding forms. Cracks are usually encountered between coating and substrate due to bonding discontinuities or may be formed due to the dissimilar material properties such as linear thermal expansion or elastic modulus. Under cyclic loading conditions, the preformed cracks propagate, or new cracks are formed faster than monolithic materials. A large number of papers concerning propagation of subsurface cracks in an elastically deforming homogeneous material have been published since Suh w1–3x who introduced the delamination theory of wear w3–7x. Fleming and Suh w8x obtained the stress intensity factors for subsurface cracks under a moving compressive load without considering friction on the crack surface. Debonding, on the other hand, is a relatively novel study area w8–12x. The solutions presented in the above *Corresponding author. E-mail address: [email protected] (K. Aslantas).
references can be applied to the subsurface crack in a homogeneous elastic material and a rigorous method of solution is still required for the analysis of subsurface cracks on the interface between dissimilar materials. In the present study, two different coating–substrate conditions were studied. An existing bonding discontinuity (crack) is considered for the analyses. The variations of the stress intensity factors (KI and KII) with load position were obtained. The effects of material, combination on the propagation of direction of interface crack and the coefficient of friction on the stress intensity factor were also obtained. 2. Finite element analysis 2.1. Method Numerical modeling is done by the ANSYS 54 finite element program. Fig. 1 depicts the configuration of a subsurface crack on the interface between coating layer and substrate. Eight nodes of isoparametric finite element elements were used for the solution model domain, except those contacting the crack tip. These elements
0261-3069/02/$ - see front matter 䊚 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 1 - 3 0 6 9 Ž 0 2 . 0 0 0 2 0 - 1
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
572
Fig. 1. Finite element mesh for interface crack. Table 1 Elastic constant for the material combinations in the problem solutions
1 2 3
Modulus of elasticity E (GPa)
Poisson’s ratio n
Substrate
Coating
Substrate
Coating
210 210 210
210 324 548
0.3 0.3 0.3
0.3 0.27 0.23
friction (m) was 0, 0.3 and 0.5. The properties of coating and substrate material are given in Table 1. 2.2. Calculation of stress intensity factors
were six nodes triangular quarter point elements. The element and node numbers were 2400 and 7401, respectively. The same assumptions are employed for the solution. The size of the solution domain is sufficient for a half space problem, the materials are isotropic and linear elastic, the coating is well bonded throughout the interface, except the crack and the loading is elliptical according to the Hertz Contact Theory. The nodes at the bottom boundary of the mesh were constrained against displacement in the vertical direction whereas the left corner node was also constrained against displacement in the horizontal direction. Four coating thicknesses and three friction coefficients were considered. The ratios of (tyc), the crack length to the thickness of the coating layer were 0.5, 1.0, 1.5 and 2 and the coefficient of
In this analysis, displacement correlation was used. This method is appropriate for numerical solutions based on finite element methods. Definitions are given in Fig. 2 for the application of the method. Displacement correlation is one of the most popular methods to calculate stress intensity factors by numerical techniques. After the finite element or boundary element solution for a cracked structure is obtained, nodal displacement values of nodes a, b, c, d and e (Fig. 2) are determined. Opening mode KI and shear mode KII are defined as w12x,
y 2pL D wn y4n q3n xyD wn y4n q3n x 2p K sy D wn y4n q3n xyD wn y4n q3n x L KIs
II
e
1
e
1
Ž1qg.l0
d
d
a
a
G1 , coshŽp´. k1e qgeyp´ Ž1qg.l0 G2 D 2s Ø p´ coshŽp´. k2e qgeyp´ D 1s
Ø
2
2
c
c
b
b
a
a
(1) (2)
p´
(3)
Fig. 2. (a) Coordinate system around the interface crack tip; (b) six-node quarter point triangular elements at crack tip used in finite element model.
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
573
Fig. 3. The influence of KII on the direction of crack propagation w7x.
´s
1 G1qk1G2 lng gs 2p G2qk2G1
B1 E1y2 l0sC q´2F D4 G
(4)
where ´ is the bimaterial constant, and G1, G2, n1 and n2 are shear modulus and Poisson’s ratios for respective material. k is defined for plane strain or plane stress conditions as, ks3y4ni
Fig. 6. Variation of KII at left crack tip with respect to load positions and friction coefficients (as0.4).
(5)
For problems of the crack on the interface between dissimilar materials, the combination of materials can be characterized with two Dundur parameters, which are defined in state of plane strain as w5x,
as bs
G1Ž1yn2.yG2Ž1yn1.
, G1Ž1yn2.qG2Ž1yn1. 1 G1Ž1y2n2.yG2Ž1y2n1. 2 G1Ž1yn2.yG2Ž1yn1.
(6)
where G and n are shear modulus and Poisson’s ratio,
Fig. 4. Variation of KII at left crack tip with respect to load positions and friction coefficients (as0.2).
Fig. 5. Variation of KII at right crack tip with respect to load positions and friction coefficients (as0.2).
Fig. 7. Variation of KII at right crack tip with respect to load positions and friction coefficients (as0.4).
Fig. 8. Variation of KI at left crack tip with respect to load positions and material combinations.
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
574
where Ks and Kt are functions of u and xm yc since KI and KII depend on load position w6x. KII affects the trajectory of the path of propagation of crack. Erdogan and Sih w14x have shown that a crack continues to advance in its own plane when it is subjected to pure mode I. The presence of positive KII deflects the crack away from the free surface, and negative KII causes the crack to deviate toward the surface as indicated in Fig. 3. 3. Results and discussion 3.1. Variation of the stress intensity factor Fig. 9. Variation of KI at right crack tip with respect to load positions and material combinations.
respectively. It should be noted that both a and b change sign when materials are interchanged. When the mode I and II stress intensity factors are known, the predicted crack propagation angle can be estimated under mixed mode loading. Fatigue crack growth is assumed to occur either in the plane of maximum shear stress intensity factor range or that of the maximum tensile stress intensity range w6x. Erdogan and Sih w14x developed the theory of maximum tangential stress method. According to the theory, the stresses in the tip vicinity of a plane crack in two-dimensional elastic solid subjected to mixed mode I and II loading are given sus trus
1
y2pr
cos
z uw u 3 xKIcos2 y KIIsinu| ~ 2y 2 2
u cos wKIsinuqKIIŽ3cosuy1.x y2pr 2 1
(7) (8)
Denoting the tensile and shear stress intensity factor by Ks vs. Kt, respectively, KsŽu,xmyc.ssuy2pr
(9)
KtŽu,xmyc.struy2pr
(10)
The mode I and II stress intensity factors are computed by Eqs. (1)–(5). Figs. 4–9 give the results of these analyses. In Fig. 4 and Fig. 7, the variations of KII at both crack tip are given material combinations as0.2 and as0.4, respectively. The variations of KI at both crack tips are given in Figs. 8 and 9 for the same material combinations. KII has both negative and positive values and this affects both the propagation direction and the propagation rate. Increase of the friction coefficient also increases the KII values. On the other hand, the higher elastic modulus of coating decreases the positive values and increases the negative values. The values of right crack tip are higher. This indicates that the movement direction of the loading affects the crack propagation direction. As a result, this crack is likely to grow from the right end. In such subsurface crack problems, KI is negative, as expected for all load positions. Because loadings applied on the surface are always compressive, KI may take positive values as in a previous study w13x. In that study, KI is positive before xm ycsy2 and after xm ycs2, i.e. KII values are nearly zero. When the modulus of elasticity of coated material is increased, the maximum absolute value of KI decrease slightly. The reason for this decrease is the decrease of elastic deformation at the crack tip with increasing modulus of elasticity of the
Fig. 10. Variation of the extreme values of KII vs. coating thickness and material combination.
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
Fig. 11. Variation of crack growing directions vs. load position of as 0.2.
coating material. According to Figs. 8 and 9, the maximum stress intensity factor arises at different load positions. While the absolute value of KI at the left crack tip arises at xm ycsy0.25, it is 0.25 for the right tip. Fig. 10 shows the variation of the extreme values with respect to coating thickness and material combination. Increasing coating thickness decrease the absolute KII values for both crack tips. On the other hand, increasing elasticity modulus decreases the KII for the left tip while the condition is vice versa for the right tip. For both crack tips, the difference between the maximum and minimum values are nearly equal. In this study, the direction of crack propagation with respect to load position is obtained. Fatigue crack growth is assumed to occur either in the plane of maximum shear stress intensity factor or that of the maximum tensile stress intensity range w6x. In this study, tensile stress intensity factor is not taken into consideration because of its negative value. According to this theory, crack propagates in the direction in which Kt is maximum. For this reason, a basic computer code was written for calculation of Kt at every angle
575
Fig. 12. Variation of crack growing directions vs. load position of as 0.4.
from y180 to 1808 for all load positions. The direction of crack propagation is shown in Figs. 11 and 12 with respect to load position. The results in Figs. 11 and 12 verify the expression in Fig. 3. The value of u is negative, as load is approached toward the left crack tip and the crack is forced to grow into the substrate. However, the crack is forced to growth towards the coating at xm ycGy0.25 for the left crack. For xm yc-y0.25, the right crack tip grows into the substrate However, at xm ycG0.25, u takes positive values and the crack tip tends to grow towards the free surface. Another result obtained from this analysis is that xm y csy0.25 and xm ycs0.25 is the most critical position. At these load positions, values of Kt of both crack tips are very close to each other. This means that crack tips are forced to grow at the interface. If there are some bonding faults or weakness, coating material debonds from the substrate. The possible crack propagation directions obtained with load positions are given schematically in Fig. 13.
Fig. 13. Schematic representation of possible crack propagation direction.
576
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
4. Conclusions The behavior of an interface crack between coating and substrate was analyzed by the finite element method under linear elastic fracture mechanics conditions. The load is considered as a Hertz contact. The problem is a mixed mode fracture problem, so the stress intensity factors (KI and KII) are calculated. Four material combinations and three friction coefficients were investigated for nine load positions. Mode II is the effective mode for the propagation of the crack. Increasing rigidity decreases the possibility of debonding. For crack propagation, the right crack tip has more possibility than the left crack tip. The friction coefficient has little effect on the propagation direction. Maximum tangential stress theory was used to determine the direction of crack propagation. It was determined that the most critical load positions are xm ycsy0.25 and xm ycs0.25 for left and right crack tips, respectively. Both left crack tip and right crack tip may propagate at the interface at these load positions and then debonding between coating and substrate may be unavoidable. References w1x Suh NP. The delamination theory of wear. Wear 1973;25(2):111 –124. w2x Fleming JR, Suh NP. The relationship between crack propagation rates and wear rates. Wear 1977;44:57 –64.
w3x Salehizadeh H, Saka N. Crack propagation in rolling line contact. J Tribol 1992;114:690 –697. w4x Evans AG, Hutchinson JW. On the mechanics of delamination and spalling in the compressed films. Int J Solid Struct 1984;20:455 –466. w5x Lee KS, Jinn JT, Earmme YY. Finite element analysis of a subsurface crack on the interface of a coated material under a moving compressive load. Wear 1992;155(1):117 –136. w6x Komvopoulos K, Cho SS. Finite element analysis of subsurface crack propagation in a half-space due to moving asperity contact. Wear 1997;209:57 –68. w7x Dally JM, Chen YM, Jahanmir S. Analysis of subsurface crack propagation and implications for wear of elastically deforming materials. Wear 1990;141:95 –114. w8x Djabella H, Arnell RD. Finite element analysis of the contact stresses in elastic coatingysubstrate under normal and tangential load. Thin Solid Films 1993;223:87 –97. w9x Komvopoulos K. Subsurface crack mechanisms under indentation loading. Wear 1996;199:9 –23. w10x Tasgetiren S. Thermomechanical analysis of bimaterials with ¨ ¨ Universitesi, an interfacial crack. Ph. D. Thesis, Dokuz Eylul Izmir, 1997. w11x Lewicki DG, Ballarini R. Effect of rim thickness on gear crack propagation path. NASA technical report ARL-TR-1110. w12x Tan CL, Gao YL. Treatment of bimaterial interface crack problems using the boundary element method. Eng Fracture Mech 1990;36(6):919 –932. w13x Aslantas K, Tasgetiren S. Analysis of propagation behaviour of a subsurface crack by using finite element method. Tubitak, J Eng Environ Sci (in press). w14x Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear. J Basic Eng 1963;85:519 – 527.
Debonding between coating and substrate due to rolling–sliding contact K. Aslantas*, S. Tasgetiren University of Afyon Kocatepe, Technical Education Faculty, Afyon, Turkey Received 2 January 2002; accepted 19 March 2002
Abstract Rolling–sliding contact of layered elastic solid is an important technical issue, since surfaces are often subjected to contact stresses. Generally, elastic surfaces are coated to increase wear resistance of the materials. However, coating materials sometimes debonds from substrate due to tangential and normal forces acting on the surface. Because of these forces, or existing bonding faults, cracks form between coating and substrate. If these forces are applied continuously, the crack propagates resulting in debonding. In this study, a numerical solution is applied to interface cracking. The variations of the stress intensity factors (KI, KII) with load position are obtained for various cases such as different combinations material of coating layer and substrate and changes in the coefficient of friction on the surface. Effects of the combination of the materials and the coefficient of friction on the stress intensity factors are discussed. The direction of the propagation of interface crack is also examined. 䊚 2002 Elsevier Science Ltd. All rights reserved. Keywords: Rolling–sliding contact; Debonding; Stress intensity factor; Finite element method
1. Introduction Coating is widely used for wear resistance of materials. On the other hand, materials are usually stressed under cyclic loading conditions. Loadings may contain rolling andyor sliding forms. Cracks are usually encountered between coating and substrate due to bonding discontinuities or may be formed due to the dissimilar material properties such as linear thermal expansion or elastic modulus. Under cyclic loading conditions, the preformed cracks propagate, or new cracks are formed faster than monolithic materials. A large number of papers concerning propagation of subsurface cracks in an elastically deforming homogeneous material have been published since Suh w1–3x who introduced the delamination theory of wear w3–7x. Fleming and Suh w8x obtained the stress intensity factors for subsurface cracks under a moving compressive load without considering friction on the crack surface. Debonding, on the other hand, is a relatively novel study area w8–12x. The solutions presented in the above *Corresponding author. E-mail address: [email protected] (K. Aslantas).
references can be applied to the subsurface crack in a homogeneous elastic material and a rigorous method of solution is still required for the analysis of subsurface cracks on the interface between dissimilar materials. In the present study, two different coating–substrate conditions were studied. An existing bonding discontinuity (crack) is considered for the analyses. The variations of the stress intensity factors (KI and KII) with load position were obtained. The effects of material, combination on the propagation of direction of interface crack and the coefficient of friction on the stress intensity factor were also obtained. 2. Finite element analysis 2.1. Method Numerical modeling is done by the ANSYS 54 finite element program. Fig. 1 depicts the configuration of a subsurface crack on the interface between coating layer and substrate. Eight nodes of isoparametric finite element elements were used for the solution model domain, except those contacting the crack tip. These elements
0261-3069/02/$ - see front matter 䊚 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 1 - 3 0 6 9 Ž 0 2 . 0 0 0 2 0 - 1
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
572
Fig. 1. Finite element mesh for interface crack. Table 1 Elastic constant for the material combinations in the problem solutions
1 2 3
Modulus of elasticity E (GPa)
Poisson’s ratio n
Substrate
Coating
Substrate
Coating
210 210 210
210 324 548
0.3 0.3 0.3
0.3 0.27 0.23
friction (m) was 0, 0.3 and 0.5. The properties of coating and substrate material are given in Table 1. 2.2. Calculation of stress intensity factors
were six nodes triangular quarter point elements. The element and node numbers were 2400 and 7401, respectively. The same assumptions are employed for the solution. The size of the solution domain is sufficient for a half space problem, the materials are isotropic and linear elastic, the coating is well bonded throughout the interface, except the crack and the loading is elliptical according to the Hertz Contact Theory. The nodes at the bottom boundary of the mesh were constrained against displacement in the vertical direction whereas the left corner node was also constrained against displacement in the horizontal direction. Four coating thicknesses and three friction coefficients were considered. The ratios of (tyc), the crack length to the thickness of the coating layer were 0.5, 1.0, 1.5 and 2 and the coefficient of
In this analysis, displacement correlation was used. This method is appropriate for numerical solutions based on finite element methods. Definitions are given in Fig. 2 for the application of the method. Displacement correlation is one of the most popular methods to calculate stress intensity factors by numerical techniques. After the finite element or boundary element solution for a cracked structure is obtained, nodal displacement values of nodes a, b, c, d and e (Fig. 2) are determined. Opening mode KI and shear mode KII are defined as w12x,
y 2pL D wn y4n q3n xyD wn y4n q3n x 2p K sy D wn y4n q3n xyD wn y4n q3n x L KIs
II
e
1
e
1
Ž1qg.l0
d
d
a
a
G1 , coshŽp´. k1e qgeyp´ Ž1qg.l0 G2 D 2s Ø p´ coshŽp´. k2e qgeyp´ D 1s
Ø
2
2
c
c
b
b
a
a
(1) (2)
p´
(3)
Fig. 2. (a) Coordinate system around the interface crack tip; (b) six-node quarter point triangular elements at crack tip used in finite element model.
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
573
Fig. 3. The influence of KII on the direction of crack propagation w7x.
´s
1 G1qk1G2 lng gs 2p G2qk2G1
B1 E1y2 l0sC q´2F D4 G
(4)
where ´ is the bimaterial constant, and G1, G2, n1 and n2 are shear modulus and Poisson’s ratios for respective material. k is defined for plane strain or plane stress conditions as, ks3y4ni
Fig. 6. Variation of KII at left crack tip with respect to load positions and friction coefficients (as0.4).
(5)
For problems of the crack on the interface between dissimilar materials, the combination of materials can be characterized with two Dundur parameters, which are defined in state of plane strain as w5x,
as bs
G1Ž1yn2.yG2Ž1yn1.
, G1Ž1yn2.qG2Ž1yn1. 1 G1Ž1y2n2.yG2Ž1y2n1. 2 G1Ž1yn2.yG2Ž1yn1.
(6)
where G and n are shear modulus and Poisson’s ratio,
Fig. 4. Variation of KII at left crack tip with respect to load positions and friction coefficients (as0.2).
Fig. 5. Variation of KII at right crack tip with respect to load positions and friction coefficients (as0.2).
Fig. 7. Variation of KII at right crack tip with respect to load positions and friction coefficients (as0.4).
Fig. 8. Variation of KI at left crack tip with respect to load positions and material combinations.
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
574
where Ks and Kt are functions of u and xm yc since KI and KII depend on load position w6x. KII affects the trajectory of the path of propagation of crack. Erdogan and Sih w14x have shown that a crack continues to advance in its own plane when it is subjected to pure mode I. The presence of positive KII deflects the crack away from the free surface, and negative KII causes the crack to deviate toward the surface as indicated in Fig. 3. 3. Results and discussion 3.1. Variation of the stress intensity factor Fig. 9. Variation of KI at right crack tip with respect to load positions and material combinations.
respectively. It should be noted that both a and b change sign when materials are interchanged. When the mode I and II stress intensity factors are known, the predicted crack propagation angle can be estimated under mixed mode loading. Fatigue crack growth is assumed to occur either in the plane of maximum shear stress intensity factor range or that of the maximum tensile stress intensity range w6x. Erdogan and Sih w14x developed the theory of maximum tangential stress method. According to the theory, the stresses in the tip vicinity of a plane crack in two-dimensional elastic solid subjected to mixed mode I and II loading are given sus trus
1
y2pr
cos
z uw u 3 xKIcos2 y KIIsinu| ~ 2y 2 2
u cos wKIsinuqKIIŽ3cosuy1.x y2pr 2 1
(7) (8)
Denoting the tensile and shear stress intensity factor by Ks vs. Kt, respectively, KsŽu,xmyc.ssuy2pr
(9)
KtŽu,xmyc.struy2pr
(10)
The mode I and II stress intensity factors are computed by Eqs. (1)–(5). Figs. 4–9 give the results of these analyses. In Fig. 4 and Fig. 7, the variations of KII at both crack tip are given material combinations as0.2 and as0.4, respectively. The variations of KI at both crack tips are given in Figs. 8 and 9 for the same material combinations. KII has both negative and positive values and this affects both the propagation direction and the propagation rate. Increase of the friction coefficient also increases the KII values. On the other hand, the higher elastic modulus of coating decreases the positive values and increases the negative values. The values of right crack tip are higher. This indicates that the movement direction of the loading affects the crack propagation direction. As a result, this crack is likely to grow from the right end. In such subsurface crack problems, KI is negative, as expected for all load positions. Because loadings applied on the surface are always compressive, KI may take positive values as in a previous study w13x. In that study, KI is positive before xm ycsy2 and after xm ycs2, i.e. KII values are nearly zero. When the modulus of elasticity of coated material is increased, the maximum absolute value of KI decrease slightly. The reason for this decrease is the decrease of elastic deformation at the crack tip with increasing modulus of elasticity of the
Fig. 10. Variation of the extreme values of KII vs. coating thickness and material combination.
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
Fig. 11. Variation of crack growing directions vs. load position of as 0.2.
coating material. According to Figs. 8 and 9, the maximum stress intensity factor arises at different load positions. While the absolute value of KI at the left crack tip arises at xm ycsy0.25, it is 0.25 for the right tip. Fig. 10 shows the variation of the extreme values with respect to coating thickness and material combination. Increasing coating thickness decrease the absolute KII values for both crack tips. On the other hand, increasing elasticity modulus decreases the KII for the left tip while the condition is vice versa for the right tip. For both crack tips, the difference between the maximum and minimum values are nearly equal. In this study, the direction of crack propagation with respect to load position is obtained. Fatigue crack growth is assumed to occur either in the plane of maximum shear stress intensity factor or that of the maximum tensile stress intensity range w6x. In this study, tensile stress intensity factor is not taken into consideration because of its negative value. According to this theory, crack propagates in the direction in which Kt is maximum. For this reason, a basic computer code was written for calculation of Kt at every angle
575
Fig. 12. Variation of crack growing directions vs. load position of as 0.4.
from y180 to 1808 for all load positions. The direction of crack propagation is shown in Figs. 11 and 12 with respect to load position. The results in Figs. 11 and 12 verify the expression in Fig. 3. The value of u is negative, as load is approached toward the left crack tip and the crack is forced to grow into the substrate. However, the crack is forced to growth towards the coating at xm ycGy0.25 for the left crack. For xm yc-y0.25, the right crack tip grows into the substrate However, at xm ycG0.25, u takes positive values and the crack tip tends to grow towards the free surface. Another result obtained from this analysis is that xm y csy0.25 and xm ycs0.25 is the most critical position. At these load positions, values of Kt of both crack tips are very close to each other. This means that crack tips are forced to grow at the interface. If there are some bonding faults or weakness, coating material debonds from the substrate. The possible crack propagation directions obtained with load positions are given schematically in Fig. 13.
Fig. 13. Schematic representation of possible crack propagation direction.
576
K. Aslantas, S. Tasgetiren / Materials and Design 23 (2002) 571–576
4. Conclusions The behavior of an interface crack between coating and substrate was analyzed by the finite element method under linear elastic fracture mechanics conditions. The load is considered as a Hertz contact. The problem is a mixed mode fracture problem, so the stress intensity factors (KI and KII) are calculated. Four material combinations and three friction coefficients were investigated for nine load positions. Mode II is the effective mode for the propagation of the crack. Increasing rigidity decreases the possibility of debonding. For crack propagation, the right crack tip has more possibility than the left crack tip. The friction coefficient has little effect on the propagation direction. Maximum tangential stress theory was used to determine the direction of crack propagation. It was determined that the most critical load positions are xm ycsy0.25 and xm ycs0.25 for left and right crack tips, respectively. Both left crack tip and right crack tip may propagate at the interface at these load positions and then debonding between coating and substrate may be unavoidable. References w1x Suh NP. The delamination theory of wear. Wear 1973;25(2):111 –124. w2x Fleming JR, Suh NP. The relationship between crack propagation rates and wear rates. Wear 1977;44:57 –64.
w3x Salehizadeh H, Saka N. Crack propagation in rolling line contact. J Tribol 1992;114:690 –697. w4x Evans AG, Hutchinson JW. On the mechanics of delamination and spalling in the compressed films. Int J Solid Struct 1984;20:455 –466. w5x Lee KS, Jinn JT, Earmme YY. Finite element analysis of a subsurface crack on the interface of a coated material under a moving compressive load. Wear 1992;155(1):117 –136. w6x Komvopoulos K, Cho SS. Finite element analysis of subsurface crack propagation in a half-space due to moving asperity contact. Wear 1997;209:57 –68. w7x Dally JM, Chen YM, Jahanmir S. Analysis of subsurface crack propagation and implications for wear of elastically deforming materials. Wear 1990;141:95 –114. w8x Djabella H, Arnell RD. Finite element analysis of the contact stresses in elastic coatingysubstrate under normal and tangential load. Thin Solid Films 1993;223:87 –97. w9x Komvopoulos K. Subsurface crack mechanisms under indentation loading. Wear 1996;199:9 –23. w10x Tasgetiren S. Thermomechanical analysis of bimaterials with ¨ ¨ Universitesi, an interfacial crack. Ph. D. Thesis, Dokuz Eylul Izmir, 1997. w11x Lewicki DG, Ballarini R. Effect of rim thickness on gear crack propagation path. NASA technical report ARL-TR-1110. w12x Tan CL, Gao YL. Treatment of bimaterial interface crack problems using the boundary element method. Eng Fracture Mech 1990;36(6):919 –932. w13x Aslantas K, Tasgetiren S. Analysis of propagation behaviour of a subsurface crack by using finite element method. Tubitak, J Eng Environ Sci (in press). w14x Erdogan F, Sih GC. On the crack extension in plates under plane loading and transverse shear. J Basic Eng 1963;85:519 – 527.