Finite Element Modelling Of Surface Stresses In Coatings Under Single Particle Impact

Finite Element Modelling Of Surface Stresses In Coatings Under Single Particle Impact

Ashutosh Dubey , Francis John

Department of Mechanical Engineering and Applied Mechanics Sam Higginbottom Institute of Agriculture, Technology and Sciences

Allahabad, U.P. INDIA

Abstract – In the present work finite element model was developed to investigate tensile stresses in the surface of coatings under single particle impact, simulating particulate erosion conditions. Modelling was done using ABAQUS/ Explicit Student Edition 6.5-3. Erosion resistant ability of coating was measured in terms of peak value of surface stress (tensile stress) in the coating. Lower the peak value of tensile stress better is the erosion resistant of the coating. Nine different coating architectures were analysed with different layer thickness and material properties. It may be suggested that the top layer of coating should be thin and bond layer should be thick to minimize tensile stress on coating surface which, in turn, improves erosion resistance ability of coating. It is also suggested to keep lesser value of youngs modulus of coating to minimize tensile stress on surface thus improving its erosion resistance.

Keywords: Tensile stress; Radial stress distributions; Finite element method; coating thickness; Youngs modulus; Modelling; Simulation.

1. Introduction

Erosive wear is defined as Material damage caused by the attack of particles entrained in a

subject, such as those by Hutchings [4], Finnie [5], Bitter [6], and Sundarajan [7] just to name a few.

Objective of the present work is to find optimum coating architecture to maximize the reduction in the surface tensile stress generated in the coating under single particle impact. 3-D model of the system is developed. Four types of material (substrate, coating, bond layer and erodent) were created and implemented in the model. Coating response to an impact was quantified as the amplitude of the tensile peak in the surface of the coating. Stress field was tensile at the surface of the coating and compressive at the site of impact and also at the coating- substrate. These results were in accordance with the experimental results [8], [11].The coating internal structure (coating thickness, bond layer role thickness) and Youngs modulus of coating is optimized from the point of view of maximum reduction in the tensile stresses in the surface. The approach used in this work is based on the modelling of stress distribution. In this context, minimum erosion rate will be obtained by minimizing tensile stresses that are responsible for crack initiation and propagation in the coating and the coating/substrate interface [8].

2 .Governing equation

The momentum equation below is governing equation [1]

fluid system impacting the surface at high speed

MU

F ext F int

(1)

[1]. Solid particle erosion is a serious problem in gas turbines, rocket nozzles, cyclone separators, valves, pumps and boiler tubes. Also, it causes troubles in steam and jet turbines, pipelines used in slurry transportation of matter, and fluidized bed system [2]. Variables affecting the erosion process are particle velocity, particle size and angle of impact, particle shape, and particle density. Also, material property, its youngs modulus, Poissons ratio and failure behaviour also affects the erosion process [3].

There are many extensive reviews on this

Where M is the lumped mass matrix, U is the nodal acceleration at each time step, Fext is the externally applied load for each node and Fint is the internal force. This set of equations was solved using explicit time integration with the central difference method employing a lumped mass matrix, which improves the computational efficiency considerably. In our model, external force (Fext) is zero while internal force (Fint) is generated due to impact of particle on coating surface.

1. Methodology of finite element analysis

   3D model of a single particle impacting a monolayer coating with a bond layer on a steel substrate was developed using finite element method.

   ABAQUS/CAE Student Edition 6.5-3 was used for model preparation whereas ABAQUS/Explicit Student Edition 6.5-3 was used for calculations. The processing of the results was done using ABAQUS/Viewer Student Edition 6.5-3.

   1. Materials modelled

      Four types of materials were implemented in the models. They are Substrate, Coating, bond layer and eroding particle.

   2. The Substrate was PH-17 Stainless Steel modelled as deformable elastic- plastic strain hardening material [10]. Its chemical composition (weight %) is Fe 73.7, Cr 17.5, Ni 3.8, Cu 2.9, Si 1.2, Mn 0.6and C 0.3. Its mechanical properties are Density 7810 kg/m3, Youngs modulus 196 GPa, Poissons ratio 0.27, Yield strength 1208 MPa.

      ,

      ,

   3. The coating was assumed to be hard ceramic coating of TiN [10]. To deposit the coating CVD methodology is used. It was modelled as elastic material with properties as Density 5220 kg/m3 Youngs modulus 200- 600GPa, Poissons ratio 0.25.

   4. The bond layer, located between the coating and the substrate, was modelled as a Titanium (Ti) layer with deformable elastic-plastic properties. Properties of bond layer of TI are as density 5000 kg/m3, Youngs modulus 100 GPa, Poissons ratio 0.27 [19].

      Fig. 1 Radial Stress Distribution with Coating thickness0.3mm, coating

      youngs modulus 200 GPa and bond layer thickness 0.1mm

      Figure 1 shows stress distribution on the surface

   5. The Eroding Particle was modelled as a rigid sphere of Alumina (Al2O3) with radius 250 m. Its mechanical properties are youngs modulus 380 GPa, density 3950 Kg/m3 and Poissons ratio 0.22 [7].

   6. Dimensions of the Model

      The dimension of the substrate was 30mm 30mm 3mm

      The coating is 30mm 30 mm with coating

      thickness varies from 0.3mm to 0.7 mm in steps of 0.2mm.

      The bond layer of thickness 0.1mm, 0.2mm and 0.3mm is used.

      The Al2O3 erodent was a spherical particle of 250 m radius.

      The dimensions of model parts and particle velocity were representative of the erosion conditions used in accelerated tests performed according to a standard procedure ASTM G76.

2. Results and discussion

Several 3-D FE models were prepared to perform calculations of the stresses in the coating. Simulations were performed with varied coating thickness, bond layer thickness and coating material properties. Substrate and eroding particle properties, dimensions and were kept constant in all simulations. A constant initial velocity of eroding particle of 100 m/s was used in all calculations.

1. RESULTS

   A tensile stress peak (radial component) in the coating surface was selected as an optimization (damage controlling) parameter.

   1. Effect of coating thickness

      of the coating after the impact of the spherical particle. Coating thickness is 0.3 mm, bond layer thickness 0.1mm and coatings youngs modulus was kept at 200 Gpa. Peak stress values as shown by the colour code are calculated. Also it can be seen that stress is compressive under impact and is tensile at away from impact point.

      Fig. 2 Radial Stress Distribution with Coating thickness 0.5 mm, coatings youngs modulus 200 GPa and bond layer thickness 01 mm

      Figure 2 shows stress distribution on the surface of the coating after the impact of the spherical particle. Coating thickness is 0.5 mm, bond layer thickness 0.1mm and coatings youngs modulus was kept at 20 GPa.

      Fig. 3 Radial Stress Distribution with Coating thickness 0.7mm, coatings youngs modulus 200 GPa and bond layer thickness 0.1mm

      Figure 3 shows stress distribution on the surface of the coating after the impact of the spherical particle. Coating thickness is 0.7 mm, bond layer thickness 0.1mm and coatings youngs modulus was kept at 200 GPa.

   2. Effect of coating modulus

      Fig. 4 Radial Stress Distribution with Coating thicknes0.3mm

      coatings younngs modulus 300 GPa and bond layer thickness 0.1 mm

      Figure 4 shows stress distribution on the surface of the coating after the impact of the spherical particle. Coating thickness was 0.3 mm, bond

      layer thickness 0.1mm and coatings youngs modulus was kept at 300 GPa.

      Fig. 5 Radial Stress Distribution with Coating thickness 3mm, Youngs modulus 600 GPa and bond layer thickness 0.1mm

      Figure 5 shows stress distribution on the surface of the coating after the impact of the spherical particle.

      4.1.2.2 Coating thickness 0.7 mm with variation in Youngs modulus

      Fig. 6 Radial Stress Distribution with Coating thickness 0.7mm, Coatings youngs modulus 400 GPa and bond layer thickness 0.1mm

      In figure 6 Coating thicknesses was 0.7 mm, bond layer thickness 0.1mm and coatings youngs modulus 400 Gpa. Maximum stress level increases.

      Fig. 7 Radial Stress Distribution with Coating thickness 0.7mm, coatings

      youngs modulus 600 GPa and bond layer thickness 0.1mm

      Figure 7 shows stress distribution on the surface of the coating after the impact of the spherical particle. Coating thickness is 0.7 mm, bond layer thickness 0.1mm and coatings youngs modulus

      was kept at 600 GPa.

   3. Bond layer thickness variation

Fig. 8

Fig. 9

Figure 8 and 9 shows effect of bond layer thickness variation on stress distribution.

In figure 8 coating thickness is 0.3 mm, bond layer thickness 0.2 mm and coatings youngs modulus was kept at 200 Gpa. In figure 9 coating thickness is reduced to 0.2 mm and bond layer thickness was kept 0.3 mm and coatings youngs modulus was 200 Gpa.

1. tables of radial stress (S11) value

   Table 1 Effect of coating thickness variation on stress level with Ec = 200GPa

   Coating thickness varies from 0.3 mm to 0.7 mm with bond layer, substrate properties are constant
   Coating thickness (mm)	Radial stress (S11)		Max. Principle stress 10 3 GPa
   	Tensile (+ve) 10 3GPa	Compressive (-ve) 10 3GPa
   0.3	0.164	-0.0233	3.377
   0.5	0.0424	-0.03855	1.694
   0.7	0.00309	-0.1055	0.9366

   Table 2. Effect of coating Youngs Modulus variation on stress level with coating thickness fixed at 0.3mm

   Coating youngs modulus varies from 200GPa to 600GPa while all other parameters are kept constant with coating thickness0.3mm.
   Coating youngs modulu s(E) GPa	Radial stress (S11)		Max. Principle stress 1 03 GPa
   	Tensile (+ve) 10 3GPa	Compressive (-ve) 10 3GPa
   200	0.164	-0.0233	3.377
   300	1.321	-1.844	6.698
   600	4.666	-4.567	19.7

   Table 3. Effect of coating Youngs Modulus variation on stress level with coating thickness fixed at 0.7mm

   Coating youngs modulus varies from 200GPa to 600GPa while all other parameters are kept constant with coating thickness0.7mm.
   Coating youngs modulus( E) GPa	Radial stress (S11)		Max. Principle stress 103 GPa
   	Tensile (+ve) 10 3GPa	Compress ive(-ve) 10 3GPa
   200	0.00309	-0.1055	0.9366
   400	0.06476	-0.1606	4.597
   600	0.08469	-0.05064	3.70

   Radial Stress (S11), GPa

   Radial Stress (S11), GPa

2. Effect of coating thickness: Graph

   Titatinum Nitritde coating w ith young's modulus constant at 200 GPa and Tiatinum bond layer thickness 0.1mm

   180

   160

   140

   120

   100

   80

   60

   40

   20

   0

   0 0.2 0.4 0.6 0.8

   Coating thickness, mm

   Titatinum Nitritde coating w ith young's modulus constant at 200 GPa and Tiatinum bond layer thickness 0.1mm

   180

   160

   140

   120

   100

   80

   60

   40

   20

   0

   0 0.2 0.4 0.6 0.8

   Coating thickness, mm

   Fig. 10 Tensile Stress peak value vs. Coating Thickness

   Figure 10 shows that the thicker the coating the lower the stress in the surface.

   Bond layer thickness(mm)	Tensile stress S11(GPa)	Coating description
   0.2 0.3	1183 1034	TiN coating with E=200 GPa , (total coating thickness=0.4mm)

   Bond layer thickness(mm)	Tensile stress S11(GPa)	Coating description
   0.2 0.3	1183 1034	TiN coating with E=200 GPa , (total coating thickness=0.4mm)

   Table 8 Effect of bond layer thickness

   Radial Stress(S11), GPa

   Radial Stress(S11), GPa

3. Effect of Coating Modulus: Graph

   Coating thickness fixed at 0.3mm, bond layer thickness at 0.1 mm.Coating Young's Modulus varies

   5000

   4000

   3000

   2000

   1000

   0

   0 200 400 600 800

   Coating Young's Modulus, GPa

   Coating thickness fixed at 0.3mm, bond layer thickness at 0.1 mm.Coating Young's Modulus varies

   5000

   4000

   3000

   2000

   1000

   0

   0 200 400 600 800

   Coating Young's Modulus, GPa

   Radial Stress (S11), GPa

   Radial Stress (S11), GPa

   Fig. 11 Radial Stress (S11) vs. Coating Youngs Modulus

   Comparision of Radial Stress values of Coating thickness 0.3 mm and 0.7 mm varying Coating Young's Modulus

   Comparision of Radial Stress values of Coating thickness 0.3 mm and 0.7 mm varying Coating Young's Modulus

   coating thickness 0.3 mm coating thickness 0.7 mm

   coating thickness 0.3 mm coating thickness 0.7 mm

   5000

   4500

   4000

   3500

   3000

   2500

   2000

   1500

   1000

   500

   0

   5000

   4500

   4000

   3500

   3000

   2500

   2000

   1500

   1000

   500

   0

   0

   200 400 600 800

   0

   200 400 600 800

   Coating Young's Modulus, GPa

   Coating Young's Modulus, GPa

   Fig. 12 Amplitude of radial tensile stress (S11) vs. Coating Modulus

   Figure 11 shows that stress level on the surface of the coating is strongly dependent upon youngs modulus of the coating.

4. Effect of Bond Layer

In coating technology, a very thin metallic bond layer (often chromium (Cr) or titanium (Ti)) is used to improve coating adhesion to the substrate. Bond layer thikness is varied from

0.2 mm to 0.3 mm. total coating thickness was kept 0.4 mm. It can be seen from table 8 that thick bond layer reduces the stress level. However the reduction is not very much.

4.6 Validation of the FE Model

The results of the proposed finite element model are compared with the experimentally obtained results of Nicholls et al (2004)

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