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A numerical study on the effect of particle shape on the erosion of ductile materials
Wear 313 (2014) 135–142
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A numerical study on the effect of particle shape on the erosion of ductile materials Z.G. Liu a,n, S. Wan b, V.B. Nguyen a, Y.W. Zhang a a b
Engineering Mechanics Department, Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore Fluid Dynamics Department, Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore
art ic l e i nf o
a b s t r a c t
Article history: Received 4 December 2013 Received in revised form 10 March 2014 Accepted 11 March 2014 Available online 18 March 2014
Although extensive studies have been performed to establish the relationship between material erosion rate and system parameters, how to accurately predict the erosion rate of engineering materials is still a challenge. Recent experiments have shown that particle shape cannot only affect erosion rate but also change material erosion mechanisms, thus casting doubts on existing models based on the erosion mechanisms incurred by ideal rigid spherical particles. In this study, finite element simulations with the Johnson–Cook constitutive and failure models are used to study the erosion mechanism and erosion rate of different materials under the impact of solid particles with different shapes. The simulations not only reveal distinct mechanisms under the impact of particles with different shapes, but also establish the relationship between the erosion rate and particle shape. Importantly, the established relationship is in good agreement with existing experimental observations. The present work not only gains interesting insights into the effect of particle shape on material erosion, but also provides useful guideline for developing anti-erosion strategies. & 2014 Elsevier B.V. All rights reserved.
Keywords: Erosion rate Shape effect Ductile material Finite element analysis
1. Introduction Erosion is one of the major failure modes that can cause fatal damage to components in offshore equipment, such as gas turbine, oil and gas pipeline, drilling platforms, etc. In an erosion process, solid particles are entrained into fluid flow in an operating process, and impact on a component surface to cause local damage. This damage mode affects not only operating productivity, but also operating safety as well. Therefore, it is highly desirable to find out a robust and accurate method to predict the erosion for offshore equipment. To analyze the erosion damage and estimate the lifetime of equipment in service, great efforts have been made to understand the effect of operating parameters, such as shot impact angle and velocity on erosion processes [1–9]. For example, Yerramareddy and Bahadur [5] studied the erosion behavior of Ti–6Al–4V alloy under ambient conditions using a sand-blast type test rig and silicon carbide particles. Their experiment exhibited a typical ductile erosion pattern with the maximum erosion occurring at an impact angle of 301. Oka et al. [6–9] performed systematic experimental tests to study the erosion damage caused by the impact of solid particles and the effect of the ratio of cutting action
n
Corresponding author. Tel.: þ 65 6419 1544; fax: þ65 6463 0200. E-mail address: [email protected] (Z.G. Liu).
http://dx.doi.org/10.1016/j.wear.2014.03.005 0043-1648/& 2014 Elsevier B.V. All rights reserved.
vs. repeated plastic deformation on material removal. Their experiment work revealed the importance of both material properties and particle impact angle. Undoubtedly, those previous experiments provided important guidance for developing empirical or semi-empirical models to describe erosion processes. Two of the most widely used models are the Finnie and Bitter's models [1–3]. However, these models can only match with experiment for ductile materials under low impact angles, where material cutting is the dominant mechanism [4]. Many researchers tried to improve the Finnie and Bitter's models, or propose new models. But all these models are only applicable to specific materials, erosion particles and operating conditions. So far only limited success was achieved to develop a generalized model for material erosion [4–9]. In general, it is both time consuming and labor intensive to study the erosion process experimentally. Since the 1990s, computational methods, such as a finite element (FE) method, have been used to study materials erosion behavior. Initially, twodimensional (2D) models were used to investigate system parameters that affect material erosion [10,11]. However, since 2D models cannot correctly consider the effects of multiple impacts and impact area overlapping, therefore three-dimensional (3D) FE models have been used subsequently for erosion modeling. For example, Alman et al. [12] studied erosion behavior of both brittle and ductile materials, and concluded that the impact angle was an important factor that affects erosion rate. They also showed that
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the ductile material exhibits the maximum erosion rate at an impact angle of about 20–401. ElTobgy et al. [13] studied the erosion process using multiple impacts, and reported that a single particle impact is insufficient, and multiple particles are needed to create erosion damage. Wang and Yang [14,15] performed FE simulations on erosion with 100 spherical particles and analyzed the erosion rate of both ductile and brittle materials. It should be noted that all of these simulation models were based on the erosion mechanism incurred by ideal rigid spherical particles. However, recent experimental results revealed that the erosion mechanism can be different for different shapes of particles [6–9]. Hence, it is interesting to perform simulations with multiple impacts using different particle shapes to study the erosion mechanism and erosion rate. In this study, we perform 3D FE simulations using the Johnson– Cook material model and also Johnson–Cook failure model to study the effect of particle shape on the erosion rate and erosion mechanism. Three different ductile materials are tested by multiple impacts using both spherical and non-spherical particles. The obtained simulation results are also compared with published experimental data.
2. Simulation model and numerical method 2.1. Simulation settings In ductile materials, it is known that erosion can occur via the following two mechanisms, i.e., repeated plastic deformation and cutting action. Thus, the total erosion is a combined contribution from both mechanisms [16–19]. It was also shown that the particle angularity plays an important role in erosion. However, the underlying mechanism and its effect on erosion are still unclear. Previous numerical studies [13–15] have shown that models based on single particle impact are insufficient to describe erosion behavior. As a result, multiple particle impacts are required to consider overlapping and accumulative damage. Therefore, in the present work, we perform 3D FEM simulations to consider both multiple particle impacts and particle angularity effect. Schematic of the present model is shown in Fig. 1. Different particle parcels, for example, spherical particles, cubic particles, mixed spherical and cubic particles, etc., are used in order to study angularity effect. In each parcel, 100 particles are used. To save the simulation times, these 100 particles are divided into 10 groups. In each group, 10 particles are directed to impact the substrate surface simultaneously with random impact locations. Practically, the erosion process of a target material is often characterized by erosion rate. However, there are several ways to define erosion rate. Here, we follow the definition in [15], in which the erosion rate is defined as the ratio of the cumulative mass loss
of the target material to the total particle weight, that is, Erosion rate ¼
ð1Þ
2.2. Mechanical models A key issue in the simulations is the choice of material models to consider elasticity, plasticity, damage initiation and propagation. In this study, the elastic response of the target material is assumed to be linear and is defined by elastic modulus and Poisson's ratio. The plasticity model and failure model are briefly described below.
2.2.1. Plasticity model The Johnson–Cook (J–C) visco-plastic model is used in this study [20,21]. In this model, the flow stress ε depends on the _ equivalent plastic strain rate (ε), and equivalent plastic strain (ε), temperature. The model can be expressed as follows: ε ð1 T nm Þ s ¼ ðA þ Bεn Þ 1 þC ln _ ð2Þ ε0 where A, B, C and m are material constants, n is strain hardening _ ε_ 0 is the normalized equivalent plastic strain rate exponent, ε= (typically normalized by a strain rate of 1.0 s-1), and T n is the homologous temperature, which is defined as follows: Tn ¼
T T r Tm Tr
ð3Þ
where T is the current temperature, T r is the reference temperature, T m is the melting temperature of material. It is assumed that the strength is isotropic.
2.2.2. Failure model The Johnson–Cook failure model is used for the ductile failure criterion [20,21] in which the equivalent plastic strain at the onset of damage, εpl D , is assumed to be a function of stress triaxiality (η), strain rate (εn ) and temperature. The Johnson–Cook failure model is expressed in term of the failure strain as follows: n n εpl D ¼ ½d1 þd2 expð d3 ηÞð1 þd4 ln ε Þð1 þ d5 T Þ; η ¼
∑h ; ∑e
ð4Þ
where, d1 – d5 are material constants, Σh is the hydrostatic stress (positive in tension), Σe is the von-Mises stress, and T n is the homologous temperature. In the explicit FE method, the overall damage variable D captures the combined effects of all active damage mechanisms, and is computed in terms of the individual damage variables. The damage parameter D is defined as follows: D¼
Fig. 1. Side view of particle parcel. The particles are simulated by l0 layers.
cumulative mass loss of substrate material impact particles weight
∑Δεpl εpl D
ð5Þ
In each increment, ðΔεpl Þi is calculated for finite element i, and the damage parameter D for element i is subsequently calculated. When the damage parameter D reaches 1, the element i is deemed to have lost its loading capacity and thus removed from the model instantly [15]. In this study, three different materials, that is, stainless steel, aluminum alloy Al6061-T6 and titanium alloy Ti–6Al–4V, are used in the simulations, and the simulation results are compared with published experimental data. Summary of their material properties is presented in Table 1 [5–9,20,21].
Z.G. Liu et al. / Wear 313 (2014) 135–142
0.20
Table 1 Summary of material properties for the three materials used in the present study [5–9,20,21]. Symbol
Steel
Al6061-T6
Ti–6Al–4V
Density Elastic modulus Poisson's ratio J–C yield strength J–C hardening coefficient J–C strain hardening exponent J–C strain rate constant J–C softening exponent J–C damage constant J–C damage constant J–C damage constant J–C damage constant J–C damage constant
ρ (kg/m3) E (GPa) ν A (MPa) B (MPa) N C M d1 d2 d3 d4 d5
7800 200 0.3 175 380 0.32 0.06 0.55 2.2 5.43 0.47 0.016 0.63
2800 69 0.3 164 211 0.465 0.00197 1.419 0.77 1.45 0.47 0 1.60
4428 113.8 0.31 1098 1092 0.93 0.014 1.1 0.09 0.27 0.48 0.014 3.87
1st impact 2nd impact 3rd impact 4th impact 5th impact 6th impact 7th impact 8th impact 9th impact 10th impact
Particles: SiC (120 m) Substrate: Ti-6Al-4V Velocity: 55m/s
0.18 0.16
Erosion rate (mg/g)
Material properties
137
0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0
10
20
30
40
50
60
70
80
90
100
Impact angle ( )
2.3. FE model The erosion process is simulated using a commercial finite element solver, ABAQUS/Explicit (Version 6.12-2). To examine the particle shape effect, both spherical and non-spherical particles, are used in the present simulation study. In the FE model, the impact particles are modeled as a rigid body. 3-node and 4-node bilinear quadrilateral rigid elements (R3D3 and R3D4) are used for the particles. The substrate is modeled by the J–C models, and eight-node brick hexahedral elements with reduced integration and hourglass control (C3D8R) are used to mesh the substrate. The calculation accuracy is tested with different mesh grid sizes, and the final mesh is chosen to ensure neither time-consuming nor leading to unreasonable error. The “general contact” is defined between the impact particles and target material. In this definition, the contact property is assumed to follow the Coulomb friction, and the friction coefficient between impact particle and the target material is assumed to be 0.2 [15]. The boundary condition for the target material is prescribed by fixing its bottom plane. The erosion simulations are conducted by using different particle parcels. According to Woytowitz and Richman [22], the distance between two particles in the same group should not be less than 0.6r in order to avoid the damage interaction (r is the radius of the spherical impact particle). It is well-known that impact angle is an important parameter that greatly influences particle erosion [23]. Therefore, in the present study, the impact angle is chosen to vary from 101 to 901 with interval of 101.
3. Results and discussion 3.1. Spherical particles In this section, multiple impacts of spherical particles on two different ductile materials are studied and the simulation results are compared with the corresponding experimental measurements. At first, we perform FE modeling to simulate the Yerramareddy and Bahadur’s experiment [5]. In their experiment, the titanium alloy Ti–6Al–4V was used as target material, and spherical particles were silicon carbide (SiC) with a density of 3200 kg/m3. The target material was eroded with a total of 120 g of silicon carbide particles. The mass loss was measured after each impact of 20 g of the particles. In the present simulation, we use the same target, particles, and boundary condition as in the real erosion test. It was shown that the variation in erosion rate is insignificant with particle size when their size is larger than 50 μm [5]. In the
Fig. 2. Erosion rate vs. impact angle by multiple particles impact (V ¼ 55 m/s) after each layer of spherical particles impacts.
present work, we choose the particles of a diameter of 120 mm in our simulations. Fig. 2 shows the variation of erosion rate with each layer of spherical particle impacts. It is seen that for low angle impacts (that is, o101), the erosion is nearly negligible. The severe erosion occurs at the impact angle between 251 and 601. The erosion mainly occurs in the first layer impacts and subsequent layer impacts contribute steadily to the total erosion. For each layer impact, the pattern of the curves is the similar, with the maximum erosion occurring at an impact angle of 401. Fig. 3(A)–(C) shows the Von Mises equivalent stress distributions of the example case after 1st layer, 5th layer and 10th layer particle impacts, respectively. It is seen that plastic deformation and material removal (erosion) do occur at the surface of target material, and the effect of impact area overlapping and cumulative damage is obvious after multiple particle impacts. Fig. 4 shows the variation of the normalized erosion rate with impact angle for titanium alloy at the room temperature for both the experiment result from [5] and the present simulation results. Here, the normalized erosion rate is defined as ERðαÞ=ERm , where ERðαÞ is the erosion at impact angle of α and ERm is the maximum erosion rate at the impact angle of 401. It is seen that the experimental erosion rate follows the familiar trend of typical ductile target materials [1] with the maximum erosion rate at the angle of about 301. Although the simulation erosion rate also shows a similar trend as the experiment, the erosion rates between them at low impact angles are significantly different, with the simulation erosion rate being much lower than the experimental one. In addition, the impact angle corresponding to the maximum erosion rate in the simulation is higher, at about 401. This value, however, is in good agreement with the simulation result [13]. Next, we perform FE modeling to simulate Oka and Nagahashi’s experiment [8]. The substrate material used in their experiment was aluminum alloy Al6061-T6 (Hv ¼0.4 GPa), and zirconia spherical particles with the average diameter of 211 mm were used (ρ¼3700 kg m-3, Hv ¼15 GPa). In the present simulation, the velocity of 106 m/s is chosen as the same as in the experiment. Fig. 5 shows the variation of the erosion rate with impact angle for the aluminum alloy. It is seen that both the experimental and simulation erosion rates also follow the typical erosion behavior of ductile materials, consistent with the observation in [13–15]. Similar to Ti–6Al–4V, the erosion rates at low impact angles between experiment and simulation results are significantly different, and the simulation maximum erosion rate also occurs at a higher angle of 401.
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Fig. 3. Material removal by sequential impacts of 100 spherical particles with impact velocity ¼ 55 m/s, angle ¼301. The substrate is Ti–6Al–4V, impact particles are spherical silicon carbide. (A) 1st layer impact; (B) 5th layer impact; (C) 10th layer impact.
1.4
1.4
1.0 0.8 0.6 0.4
10
20
30
40
50
60
0.8 0.6 0.4
0.0
0.0 0
1.0
0.2
FE Simulation Ref Experiment [5]
0.2
Substrate: Al6061-T6 Velocity: 106 m/s
1.2
Normalized erosion rate
1.2
Normalized erosion rate
Particles: ZrO (211 m)
Particles: SiC (120 m) Substrate: Ti-6Al-4V Velocity: 55 m/s
70
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100
Impact angle ( 0)
FE Simulation Ref Experiment [8] 0
10
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Impact angle ( )
Fig. 4. Comparison of the normalized erosion rate of Ti–6Al–4V under multiple SiC spherical particle impacts between the present simulation and experiment results [5].
Fig. 5. Comparison of the normalized erosion rate of Al6061-T6 under multiple ZrO2 spherical particle impacts between the present simulation and experiment results [8].
Although the variations of the erosion rate with impact angle obtained from the present simulations for both Ti alloy and Al alloy are qualitatively agreeable with that from experimental measurements, there are large discrepancies in the erosion rate at small impact angles and also the angle corresponding to the
maximum erosion rate. These discrepancies were also observed in previous studies [13–15]. Clearly, simulations using spherical particles fail to quantitatively reproduce the experimental results. Below, we would like to address these issues by considering the particle angularity effect.
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3.2. Cubic particles
0.40 0.35
Fig. 7. Material removal by sequential impacts of 100 cubic particles with impact velocity ¼100 m/s, angle ¼ 301. The substrate is stainless steel, impact particle is SiO2. (A) 1st layer impact; (B) 5th layer impact; (C) 10th layer impact.
1.4 1.2
Normalized erosion rate
The finite element simulations with multiple cubic particles are also performed on the two ductile materials, stainless steel and Al6061-T6, used in Oka et al.'s experiments [6,9]. For the stainless steel (Hv ¼4.46 GPa), impact particles are angular SiO2 (ρ¼2600 kg m 3, Hv ¼20 GPa). The impact velocity was 104 m/s, and the particle size was 326 mm [6]. The present simulations use the same substrate and particles. Fig. 6 shows the evolution of erosion rate with each layer of cubic particle impacts. It is seen that for low angle impacts, the erosion primarily occurs in the first layer impacts, subsequent layer impacts contribute little to the total erosion. For high impacts, however, subsequent layer impacts also contribute the total erosion. It is also seen that severe erosion occurs at high impact angles, suggesting that the plastic deformation is the dominant mechanism in angular particle impacts, consistent with ElTobgy et al.'s observation [13]. Fig. 7(A)–(C) shows the Von Mises equivalent stress distributions of the example case after 1st layer, 5th layer and 10th layer particle impacts, respectively. The effect of impact area overlapping and cumulative damage is obvious after multiple particle impacts. The material removal is also shown in cross section view, the erosion area and intensity are both increased after multiple particle impacts. Fig. 8 shows the comparison of the variation of normalized erosion rate with impact angle between the present finite element simulation and experiment by Oka et al. [6] under multiple angular particle impacts. Here, the normalized erosion rate is defined as ERðαÞ=ERð90Þ, where ERðαÞ is the erosion at impact angle of α and ERð90Þ is the maximum erosion rate at the impact angle of 901. The two results show an excellent agreement. Also for both experimental and simulation results, the erosion induced by angular particle impacts is high at high impact angles due to plastic deformation. The present simulations show that the maximum shear strain is at the side and forward rims of the craters, which is consistent with Oka's experimental observations. In addition, the simulations show that angular multiple particle impacts cause large plastic deformation due to angularity, which is consistent with Takaffoli and papini’s study [16–19]. We also perform finite element simulations on aluminum alloy Al6061-T6 (Hv ¼0.4 GPa) using angular SiO2 particles (ρ¼ 2600 kg m 3, Hv ¼ 20Gpa). In the experiment, the impact velocity was 100 m/s, and the particle size was 326 mm [9]. The present simulations use the same substrate, particles and initial
1.0 0.8
FE Simulation Ref Experiment [6]
0.6 0.4
Particles: SiO (326 m) 0.2
Erosion rate (mg/g)
0.30 0.25
Substrate: Stainless Steel Impact velocity: 104m/s
0.0
1st impact 2nd impact 3rd impact 4th impact 5th impact 6th impact 7th impact 8th impact 9th impact 10th impact
0.20 0.15 0.10 0.05
0
10
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30
40
20
30
40
50
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70
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90
100
Impact angle ( ) Fig. 8. Comparison of impact angle dependence of normalized erosion rate with simulation and experiment results [6] in stainless steel.
Particles: SiO (326 m) Substrate: Stainless steel Impact velocity: 104m/s
0.00 0
10
50
60
70
80
90
100
Impact angle ( ) Fig.6. Erosion rate vs. impact angle by multiple particles impact (V ¼ 104 m/s) after each layer of cubic particles impacts.
conditions. The normalized erosion rates are also compared between the simulation and experimental results. Fig. 9 shows the comparison of the variation of normalized erosion rate with impact angle for the aluminum alloy. It is seen that the simulation result is in good agreement with the experimental one. Despite the large difference in the mechanical behavior of the two materials used, the normalized erosion rates follow a very
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similar tendency, indicating that the present simulation model considering multiple impacts with angular particles can be used to study general erosion phenomena involved both cutting action and plastic deformation occurring in engineering materials.
Rm ¼ f Rs þ ð1 f ÞRc
3.3. Mixed spherical and cubic particles In reality, the shape of erosion particles is often not homogeneous, but a mixture of different shapes. In this section, we would like to study the effects of such mixture on the erosion rate. Here, we perform simulations using parcels with different mixtures of spherical and cubic particles. Fig. 10 shows the impact angle dependence of erosion rate under these parcels, together with the two individual parcels. It is seen clearly that the erosion 2.4
Particles: SiO (326 m) Substarte: Al6061-T6 Impact velocity: 100 m/s
Normalized erosion rate
2.0 1.6 1.2 0.8
FE Simulation Ref Experiment [9]
0.4 0.0
0
10
20
30
40
50
60
70
80
90
100
Impact angle ( ) Fig. 9. Comparison of impact angle dependence of normalized erosion rate with simulation and experiment results [9] in aluminum alloy.
0.8
Particles: SiC (120 m) Substrate: Ti-6AL-4V velocity: 55 m/s
Erosion rate (mg/g)
0.6
f=0
f=0.3
0.4
f=0.5 f=0.7
0.2
f=1.0
0.0 0
10
20
30
40
50
rates are dramatically different among purely spherical, purely cubic and mixed particles. These simulations demonstrate that with increasing the percentage of angular particles, the erosion rate increases. It appears that the erosion rate for the mixed parcel can be estimated by the rule of mixture, that is
60
70
80
90
100
Impact angle ( )
Fig. 10. Comparison of impact angle dependence of erosion rate using different parcels. The curves with solid markers depict the simulation results, while the curves with hollow markers depict the results from the analytical equation.
ð6Þ
where Rm denotes the erosion rate of the mixed parcel, Rs is the erosion rate of spherical parcel, Rc is the erosion rate of cubic particles, f is the number percent of spherical particles. The prediction from the rule of mixture is in good agreement with the simulation results (see Fig. 10). 3.4. Other particle shapes In reality, the erosion particles are never perfectly spherical, but always angular to a certain degree. For a comparative study, we pick two more shapes, dodecahedron and icosahedron in addition sphere and cube, as impact particles shown in Fig. 11 to further illuminate the shape effect. Fig. 12 shows the topographic images of the craters on Ti–6Al– 4V substrate caused by SiC particles with four different shapes. In order to clearly illustrate a material removal mechanism, only toplayer elements are shown. The crater shapes are different in these four cases. These simulation results evidently show that the effect of angularity can have a significant effect on the erosion patterns on the material surface. The surface topography of craters arising from particle impacts was experimentally measured before [8,18,24]. To compare with these experimental measurements, we have extracted the surface topography from our simulations with both angular and spherical particle impacts. Fig. 13 shows the typical crater topographic images formed on the surface from both our simulation and the experiment [18]. It is seen that the formation of pile-ups and lips at the crater edges is clearly visible in both simulation and experimental images. Fig. 14 shows the crater topographic images formed on the iron surface under spherical WC particle impacts. It is seen that the simulated crater topography shows very similar features (size and shape) compared with that from experiment [8]. We also calculate the erosion rates from the simulation using the four different particle geometries. The simulation results are compared with Yerramareddy and Bahadur's experiment [5]. In the simulations, the same target material, boundary conditions and average equivalent particle size 120 mm as the real erosion test are used. The same mass loss method used in experiment [5] is also used in the simulations. Similar to the normalization used before, the normalized erosion rate is defined as ERðαÞ=ERm , where ERðαÞ is the erosion at impact angle of α and ERm is the maximum erosion rate. Fig. 15 shows the variation erosion rate with impact angle under different particle shapes. It is seen that on the one hand, the simulations using spherical particles reasonably predict the experimental results at high impact angles but severely underestimate the experimental results at low impact angles; on the other hand, the simulations using cubic particles reasonably predict the experimental results at low impact angles but severely
Fig. 11. Particles with different angularities to test shape effect. (a) Cube; (b) dodecahedron; (c) icosahedron; (d) sphere.
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Fig. 12. Surface topography of crater by single SiC particle impact, the substrate is Ti–6Al–4V (velocity ¼ 55 m/s, angle ¼ 301). (a) Cubic particle; (b) dodecahedral particle; (c) icosahedral particle; (d) spherical particle.
Fig. 13. Crater topography formed on the substrate surface resulting from particle impact test at α ¼ 301 and V ¼117 m/s. The substrate is Al6061-T6 and the particles are angular SiC. (a) Experiment from [18] and (b) Simulation. Source: reprinted with permission from Elsevier B.V. © 2012.
Fig. 14. Typical surface topography of crater obtained by particle impact test impact velocity at α ¼ 301 and V ¼100 m/s. The substrate is iron and the particles are round WC balls. (a) Experiment from [8] and (b) Simulation. Source: reprinted with permission from Elsevier B.V. © 2003.
overestimate the experimental results at high impact angles. For icosahedral particles, the erosion rate is in excellent agreement for the full range of impact angle. Therefore, the difference between simulation and real experiment can be well explained by particle shape effect.
4. Conclusion In this work, we have proposed a new numerical method to predict the erosion behavior of ductile materials. We show that
multiple impacts considering particle shape effect are more effective for erosion simulation. Compared with experiment, this new simulation method provides a useful and economical tool to study the erosion rate and erosion mechanism. Using this method, we studied the particle angularity effect on erosion rates under different particle parcels. The simulation results were extensively compared with the existing experiments. For the multiple spherical particle impacts on two ductile materials, the predicted impact angle dependence of erosion rate shows a typical erosion curve. But there is a large discrepancy in the erosion rate at low impact angles with experiment results. To address this
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1.4 Particles: SiC (120 m) Substrate: Ti-6Al-4V Velocity: 55 m/s
1.2
Nomalized erosion rate
Cubic
1.0
Dodecahedron Icosahedron
0.8 0.6 0.4 0.2
Ref Experiment [5]
Pure sphere
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Impact angle ( ) Fig. 15. Normalized erosion rate under multiple particle impacts with different particle shapes. The simulations using angular particles give a good prediction for erosion rate at low impact angles, while the simulations using spherical and icosahedral particles give a good prediction for erosion rate at high impact angles. The erosion rate using icosahedral particles is in excellent agreement with experimental results for the whole range of impact angle.
discrepancy, we performed impact simulations using multiple cubic particles, and a good agreement is obtained between the simulation and experimental results, suggesting that the simulation with cubic particles is able to consider the dominance of cutting mechanism at low impact angles. We further investigated that for mixed spherical and cubic impact particles, the erosion rate can be approximated by the rule of mixture of the individual particles. We also find that the erosion rate by the impacts of icosahedral particles is in excellent agreement than that in experimental results for the whole range of impact angles. Combined with computational fluid dynamics simulations, the present work can be used to predict the erosion behavior in real equipment. It is expected that this study provides useful guidelines for antierosion design strategies in offshore industry. Acknowledgment The support for this work through Grant WBS no. R-265-000412-305 from Agency for Science, Technology and Research, Singapore (AnSTAR) is gratefully acknowledged. References [1] I. Finnie, Erosion of surfaces by solid particles, Wear 3 (1960) 87–103. [2] J.G.A Bitter, A study of erosion phenomena. part I, Wear 6 (1963) 5–21.
[3] J.G.A. Bitter, A study of erosion phenomena. part II, Wear 6 (1963) 169–190. [4] I.M. Hutchings, Ductile-brittle transitions and wear maps for the erosion and abrasion of brittle materials, J. Phys. D 25 (1992) A212–A221. [5] S. Yerramareddy, S. Bahadur, Effect of operational variables, microstructure and mechanical properties on the erosion of Ti–6Al–4V, Wear 142 (1991) 253–263. [6] Y.I. Oka, K. Okamura, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact, part 1: effects of impact parameters on a predictive equation, Wear 259 (2005) 95–101. [7] Y.I. Oka, T. Yoshida, Practical estimation of erosion damage caused by solid particle impact, part 2: mechanical properties of materials directly associated with erosion damage, Wear 259 (2005) 102–109. [8] Y.I. Oka, Kazuo Nagahashi, Measurements of plastic strain around indentations caused by the impact of round and angular particles, and the origin of erosion, Wear 254 (2003) 1267–1275. [9] Y.I. Oka, H. Olmogi, T. Hosokawa, M. Matsumura, The impact angle dependence of erosion damage caused by solid particle impact, Wear203–204 (1997) 573–579. [10] K. Shimizu, T. Noguchi, H. Seitoh, E. Muranaka, FEM analysis of the dependency on impact angle during erosive wear, Wear 233–235 (1999) 157–159. [11] W.Y. Li, H.L Liao, Chang-Jiu Li, Bang Hee-SeonC. Coddet, Numerical simulation of deformation behavior of Al particles impacting on Al substrate and effect of surface oxide films on interfacial bonding in cold spraying, Appl. Surf. Sci. 253 (2007) 5084–5091. [12] D.E. Alman, J.H. Tylczak, J.A. Hawk, M.G. Hebsur, Solid particle erosion behavior of an Si3N4–MoSi2 composite at room and elevated temperatures, Mater. Sci. Eng. A 261 (1999) 245–251. [13] M.S. ElTobgy, E. Ng, M.A. Elbestawi, Finite element modeling of erosive wear, Int. J. Mach. Tools Manuf. 45 (2005) 1337–1346. [14] Yu-Fei Wang, Zhen-Guo Yang, A coupled finite element and meshfree analysis of erosive wear, Tribol. Int. 42 (2009) 373–377. [15] Yu-Fei Wang, Zhen-Guo Yang, Finite element model of erosive wear on ductile and brittle materials, Wear 265 (2008) 871–878. [16] M. Takaffoli, M. Papini, Finite element analysis of single impacts of angular particles on ductile targets, Wear 267 (2009) 144–151. [17] M. Takaffoli, M. Papini, Material deformation and removal due to single particle impacts on ductile materials using smoothed particle hydrodynamics, Wear 274–275 (2012) 50–59. [18] M. Takaffoli, M. Papini, Numerical simulation of solid particle impacts on Al6061-T6 part I: three-dimensional representation of angular particles, Wear 292–293 (2012) 100–110. [19] M. Takaffoli, M. Papini, Numerical simulation of solid particle impacts on Al6061-T6 part II: materials removal mechanisms for impact of multiple angular particles, Wear 296 (2012) 648–655. [20] G.R. Johnson, W.H. Cook, A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, in: Proceedings of the 7th International Symposium on Ballistics, The Hague, 1983, pp. 541–547. [21] G.R. Johnson, W.H. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fract. Mech. 21 (1) (1985) 31–48. [22] P.J. Woytowitz, R.H. Richman, Modeling of damage from multiple impacts by spherical particles, Wear 233–235 (1999) 120–133. [23] D. Aquaro, Erosion rate of stainless steel due to the impact of solid particles. AITC-AIT 2006, in: Proceedings of the International Conference on Tribology, Parma, Italy, 20–22 September, 2006. [24] L.E. Samuels, Metallographic Polishing by Mechanical Methods, ASM International, Materials Park, OH, 2003.
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Wear journal homepage: www.elsevier.com/locate/wear
A numerical study on the effect of particle shape on the erosion of ductile materials Z.G. Liu a,n, S. Wan b, V.B. Nguyen a, Y.W. Zhang a a b
Engineering Mechanics Department, Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore Fluid Dynamics Department, Institute of High Performance Computing, 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore
art ic l e i nf o
a b s t r a c t
Article history: Received 4 December 2013 Received in revised form 10 March 2014 Accepted 11 March 2014 Available online 18 March 2014
Although extensive studies have been performed to establish the relationship between material erosion rate and system parameters, how to accurately predict the erosion rate of engineering materials is still a challenge. Recent experiments have shown that particle shape cannot only affect erosion rate but also change material erosion mechanisms, thus casting doubts on existing models based on the erosion mechanisms incurred by ideal rigid spherical particles. In this study, finite element simulations with the Johnson–Cook constitutive and failure models are used to study the erosion mechanism and erosion rate of different materials under the impact of solid particles with different shapes. The simulations not only reveal distinct mechanisms under the impact of particles with different shapes, but also establish the relationship between the erosion rate and particle shape. Importantly, the established relationship is in good agreement with existing experimental observations. The present work not only gains interesting insights into the effect of particle shape on material erosion, but also provides useful guideline for developing anti-erosion strategies. & 2014 Elsevier B.V. All rights reserved.
Keywords: Erosion rate Shape effect Ductile material Finite element analysis
1. Introduction Erosion is one of the major failure modes that can cause fatal damage to components in offshore equipment, such as gas turbine, oil and gas pipeline, drilling platforms, etc. In an erosion process, solid particles are entrained into fluid flow in an operating process, and impact on a component surface to cause local damage. This damage mode affects not only operating productivity, but also operating safety as well. Therefore, it is highly desirable to find out a robust and accurate method to predict the erosion for offshore equipment. To analyze the erosion damage and estimate the lifetime of equipment in service, great efforts have been made to understand the effect of operating parameters, such as shot impact angle and velocity on erosion processes [1–9]. For example, Yerramareddy and Bahadur [5] studied the erosion behavior of Ti–6Al–4V alloy under ambient conditions using a sand-blast type test rig and silicon carbide particles. Their experiment exhibited a typical ductile erosion pattern with the maximum erosion occurring at an impact angle of 301. Oka et al. [6–9] performed systematic experimental tests to study the erosion damage caused by the impact of solid particles and the effect of the ratio of cutting action
n
Corresponding author. Tel.: þ 65 6419 1544; fax: þ65 6463 0200. E-mail address: [email protected] (Z.G. Liu).
http://dx.doi.org/10.1016/j.wear.2014.03.005 0043-1648/& 2014 Elsevier B.V. All rights reserved.
vs. repeated plastic deformation on material removal. Their experiment work revealed the importance of both material properties and particle impact angle. Undoubtedly, those previous experiments provided important guidance for developing empirical or semi-empirical models to describe erosion processes. Two of the most widely used models are the Finnie and Bitter's models [1–3]. However, these models can only match with experiment for ductile materials under low impact angles, where material cutting is the dominant mechanism [4]. Many researchers tried to improve the Finnie and Bitter's models, or propose new models. But all these models are only applicable to specific materials, erosion particles and operating conditions. So far only limited success was achieved to develop a generalized model for material erosion [4–9]. In general, it is both time consuming and labor intensive to study the erosion process experimentally. Since the 1990s, computational methods, such as a finite element (FE) method, have been used to study materials erosion behavior. Initially, twodimensional (2D) models were used to investigate system parameters that affect material erosion [10,11]. However, since 2D models cannot correctly consider the effects of multiple impacts and impact area overlapping, therefore three-dimensional (3D) FE models have been used subsequently for erosion modeling. For example, Alman et al. [12] studied erosion behavior of both brittle and ductile materials, and concluded that the impact angle was an important factor that affects erosion rate. They also showed that
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the ductile material exhibits the maximum erosion rate at an impact angle of about 20–401. ElTobgy et al. [13] studied the erosion process using multiple impacts, and reported that a single particle impact is insufficient, and multiple particles are needed to create erosion damage. Wang and Yang [14,15] performed FE simulations on erosion with 100 spherical particles and analyzed the erosion rate of both ductile and brittle materials. It should be noted that all of these simulation models were based on the erosion mechanism incurred by ideal rigid spherical particles. However, recent experimental results revealed that the erosion mechanism can be different for different shapes of particles [6–9]. Hence, it is interesting to perform simulations with multiple impacts using different particle shapes to study the erosion mechanism and erosion rate. In this study, we perform 3D FE simulations using the Johnson– Cook material model and also Johnson–Cook failure model to study the effect of particle shape on the erosion rate and erosion mechanism. Three different ductile materials are tested by multiple impacts using both spherical and non-spherical particles. The obtained simulation results are also compared with published experimental data.
2. Simulation model and numerical method 2.1. Simulation settings In ductile materials, it is known that erosion can occur via the following two mechanisms, i.e., repeated plastic deformation and cutting action. Thus, the total erosion is a combined contribution from both mechanisms [16–19]. It was also shown that the particle angularity plays an important role in erosion. However, the underlying mechanism and its effect on erosion are still unclear. Previous numerical studies [13–15] have shown that models based on single particle impact are insufficient to describe erosion behavior. As a result, multiple particle impacts are required to consider overlapping and accumulative damage. Therefore, in the present work, we perform 3D FEM simulations to consider both multiple particle impacts and particle angularity effect. Schematic of the present model is shown in Fig. 1. Different particle parcels, for example, spherical particles, cubic particles, mixed spherical and cubic particles, etc., are used in order to study angularity effect. In each parcel, 100 particles are used. To save the simulation times, these 100 particles are divided into 10 groups. In each group, 10 particles are directed to impact the substrate surface simultaneously with random impact locations. Practically, the erosion process of a target material is often characterized by erosion rate. However, there are several ways to define erosion rate. Here, we follow the definition in [15], in which the erosion rate is defined as the ratio of the cumulative mass loss
of the target material to the total particle weight, that is, Erosion rate ¼
ð1Þ
2.2. Mechanical models A key issue in the simulations is the choice of material models to consider elasticity, plasticity, damage initiation and propagation. In this study, the elastic response of the target material is assumed to be linear and is defined by elastic modulus and Poisson's ratio. The plasticity model and failure model are briefly described below.
2.2.1. Plasticity model The Johnson–Cook (J–C) visco-plastic model is used in this study [20,21]. In this model, the flow stress ε depends on the _ equivalent plastic strain rate (ε), and equivalent plastic strain (ε), temperature. The model can be expressed as follows: ε ð1 T nm Þ s ¼ ðA þ Bεn Þ 1 þC ln _ ð2Þ ε0 where A, B, C and m are material constants, n is strain hardening _ ε_ 0 is the normalized equivalent plastic strain rate exponent, ε= (typically normalized by a strain rate of 1.0 s-1), and T n is the homologous temperature, which is defined as follows: Tn ¼
T T r Tm Tr
ð3Þ
where T is the current temperature, T r is the reference temperature, T m is the melting temperature of material. It is assumed that the strength is isotropic.
2.2.2. Failure model The Johnson–Cook failure model is used for the ductile failure criterion [20,21] in which the equivalent plastic strain at the onset of damage, εpl D , is assumed to be a function of stress triaxiality (η), strain rate (εn ) and temperature. The Johnson–Cook failure model is expressed in term of the failure strain as follows: n n εpl D ¼ ½d1 þd2 expð d3 ηÞð1 þd4 ln ε Þð1 þ d5 T Þ; η ¼
∑h ; ∑e
ð4Þ
where, d1 – d5 are material constants, Σh is the hydrostatic stress (positive in tension), Σe is the von-Mises stress, and T n is the homologous temperature. In the explicit FE method, the overall damage variable D captures the combined effects of all active damage mechanisms, and is computed in terms of the individual damage variables. The damage parameter D is defined as follows: D¼
Fig. 1. Side view of particle parcel. The particles are simulated by l0 layers.
cumulative mass loss of substrate material impact particles weight
∑Δεpl εpl D
ð5Þ
In each increment, ðΔεpl Þi is calculated for finite element i, and the damage parameter D for element i is subsequently calculated. When the damage parameter D reaches 1, the element i is deemed to have lost its loading capacity and thus removed from the model instantly [15]. In this study, three different materials, that is, stainless steel, aluminum alloy Al6061-T6 and titanium alloy Ti–6Al–4V, are used in the simulations, and the simulation results are compared with published experimental data. Summary of their material properties is presented in Table 1 [5–9,20,21].
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0.20
Table 1 Summary of material properties for the three materials used in the present study [5–9,20,21]. Symbol
Steel
Al6061-T6
Ti–6Al–4V
Density Elastic modulus Poisson's ratio J–C yield strength J–C hardening coefficient J–C strain hardening exponent J–C strain rate constant J–C softening exponent J–C damage constant J–C damage constant J–C damage constant J–C damage constant J–C damage constant
ρ (kg/m3) E (GPa) ν A (MPa) B (MPa) N C M d1 d2 d3 d4 d5
7800 200 0.3 175 380 0.32 0.06 0.55 2.2 5.43 0.47 0.016 0.63
2800 69 0.3 164 211 0.465 0.00197 1.419 0.77 1.45 0.47 0 1.60
4428 113.8 0.31 1098 1092 0.93 0.014 1.1 0.09 0.27 0.48 0.014 3.87
1st impact 2nd impact 3rd impact 4th impact 5th impact 6th impact 7th impact 8th impact 9th impact 10th impact
Particles: SiC (120 m) Substrate: Ti-6Al-4V Velocity: 55m/s
0.18 0.16
Erosion rate (mg/g)
Material properties
137
0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 0
10
20
30
40
50
60
70
80
90
100
Impact angle ( )
2.3. FE model The erosion process is simulated using a commercial finite element solver, ABAQUS/Explicit (Version 6.12-2). To examine the particle shape effect, both spherical and non-spherical particles, are used in the present simulation study. In the FE model, the impact particles are modeled as a rigid body. 3-node and 4-node bilinear quadrilateral rigid elements (R3D3 and R3D4) are used for the particles. The substrate is modeled by the J–C models, and eight-node brick hexahedral elements with reduced integration and hourglass control (C3D8R) are used to mesh the substrate. The calculation accuracy is tested with different mesh grid sizes, and the final mesh is chosen to ensure neither time-consuming nor leading to unreasonable error. The “general contact” is defined between the impact particles and target material. In this definition, the contact property is assumed to follow the Coulomb friction, and the friction coefficient between impact particle and the target material is assumed to be 0.2 [15]. The boundary condition for the target material is prescribed by fixing its bottom plane. The erosion simulations are conducted by using different particle parcels. According to Woytowitz and Richman [22], the distance between two particles in the same group should not be less than 0.6r in order to avoid the damage interaction (r is the radius of the spherical impact particle). It is well-known that impact angle is an important parameter that greatly influences particle erosion [23]. Therefore, in the present study, the impact angle is chosen to vary from 101 to 901 with interval of 101.
3. Results and discussion 3.1. Spherical particles In this section, multiple impacts of spherical particles on two different ductile materials are studied and the simulation results are compared with the corresponding experimental measurements. At first, we perform FE modeling to simulate the Yerramareddy and Bahadur’s experiment [5]. In their experiment, the titanium alloy Ti–6Al–4V was used as target material, and spherical particles were silicon carbide (SiC) with a density of 3200 kg/m3. The target material was eroded with a total of 120 g of silicon carbide particles. The mass loss was measured after each impact of 20 g of the particles. In the present simulation, we use the same target, particles, and boundary condition as in the real erosion test. It was shown that the variation in erosion rate is insignificant with particle size when their size is larger than 50 μm [5]. In the
Fig. 2. Erosion rate vs. impact angle by multiple particles impact (V ¼ 55 m/s) after each layer of spherical particles impacts.
present work, we choose the particles of a diameter of 120 mm in our simulations. Fig. 2 shows the variation of erosion rate with each layer of spherical particle impacts. It is seen that for low angle impacts (that is, o101), the erosion is nearly negligible. The severe erosion occurs at the impact angle between 251 and 601. The erosion mainly occurs in the first layer impacts and subsequent layer impacts contribute steadily to the total erosion. For each layer impact, the pattern of the curves is the similar, with the maximum erosion occurring at an impact angle of 401. Fig. 3(A)–(C) shows the Von Mises equivalent stress distributions of the example case after 1st layer, 5th layer and 10th layer particle impacts, respectively. It is seen that plastic deformation and material removal (erosion) do occur at the surface of target material, and the effect of impact area overlapping and cumulative damage is obvious after multiple particle impacts. Fig. 4 shows the variation of the normalized erosion rate with impact angle for titanium alloy at the room temperature for both the experiment result from [5] and the present simulation results. Here, the normalized erosion rate is defined as ERðαÞ=ERm , where ERðαÞ is the erosion at impact angle of α and ERm is the maximum erosion rate at the impact angle of 401. It is seen that the experimental erosion rate follows the familiar trend of typical ductile target materials [1] with the maximum erosion rate at the angle of about 301. Although the simulation erosion rate also shows a similar trend as the experiment, the erosion rates between them at low impact angles are significantly different, with the simulation erosion rate being much lower than the experimental one. In addition, the impact angle corresponding to the maximum erosion rate in the simulation is higher, at about 401. This value, however, is in good agreement with the simulation result [13]. Next, we perform FE modeling to simulate Oka and Nagahashi’s experiment [8]. The substrate material used in their experiment was aluminum alloy Al6061-T6 (Hv ¼0.4 GPa), and zirconia spherical particles with the average diameter of 211 mm were used (ρ¼3700 kg m-3, Hv ¼15 GPa). In the present simulation, the velocity of 106 m/s is chosen as the same as in the experiment. Fig. 5 shows the variation of the erosion rate with impact angle for the aluminum alloy. It is seen that both the experimental and simulation erosion rates also follow the typical erosion behavior of ductile materials, consistent with the observation in [13–15]. Similar to Ti–6Al–4V, the erosion rates at low impact angles between experiment and simulation results are significantly different, and the simulation maximum erosion rate also occurs at a higher angle of 401.
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Fig. 3. Material removal by sequential impacts of 100 spherical particles with impact velocity ¼ 55 m/s, angle ¼301. The substrate is Ti–6Al–4V, impact particles are spherical silicon carbide. (A) 1st layer impact; (B) 5th layer impact; (C) 10th layer impact.
1.4
1.4
1.0 0.8 0.6 0.4
10
20
30
40
50
60
0.8 0.6 0.4
0.0
0.0 0
1.0
0.2
FE Simulation Ref Experiment [5]
0.2
Substrate: Al6061-T6 Velocity: 106 m/s
1.2
Normalized erosion rate
1.2
Normalized erosion rate
Particles: ZrO (211 m)
Particles: SiC (120 m) Substrate: Ti-6Al-4V Velocity: 55 m/s
70
80
90
100
Impact angle ( 0)
FE Simulation Ref Experiment [8] 0
10
20
30
40
50
60
70
80
90
100
Impact angle ( )
Fig. 4. Comparison of the normalized erosion rate of Ti–6Al–4V under multiple SiC spherical particle impacts between the present simulation and experiment results [5].
Fig. 5. Comparison of the normalized erosion rate of Al6061-T6 under multiple ZrO2 spherical particle impacts between the present simulation and experiment results [8].
Although the variations of the erosion rate with impact angle obtained from the present simulations for both Ti alloy and Al alloy are qualitatively agreeable with that from experimental measurements, there are large discrepancies in the erosion rate at small impact angles and also the angle corresponding to the
maximum erosion rate. These discrepancies were also observed in previous studies [13–15]. Clearly, simulations using spherical particles fail to quantitatively reproduce the experimental results. Below, we would like to address these issues by considering the particle angularity effect.
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3.2. Cubic particles
0.40 0.35
Fig. 7. Material removal by sequential impacts of 100 cubic particles with impact velocity ¼100 m/s, angle ¼ 301. The substrate is stainless steel, impact particle is SiO2. (A) 1st layer impact; (B) 5th layer impact; (C) 10th layer impact.
1.4 1.2
Normalized erosion rate
The finite element simulations with multiple cubic particles are also performed on the two ductile materials, stainless steel and Al6061-T6, used in Oka et al.'s experiments [6,9]. For the stainless steel (Hv ¼4.46 GPa), impact particles are angular SiO2 (ρ¼2600 kg m 3, Hv ¼20 GPa). The impact velocity was 104 m/s, and the particle size was 326 mm [6]. The present simulations use the same substrate and particles. Fig. 6 shows the evolution of erosion rate with each layer of cubic particle impacts. It is seen that for low angle impacts, the erosion primarily occurs in the first layer impacts, subsequent layer impacts contribute little to the total erosion. For high impacts, however, subsequent layer impacts also contribute the total erosion. It is also seen that severe erosion occurs at high impact angles, suggesting that the plastic deformation is the dominant mechanism in angular particle impacts, consistent with ElTobgy et al.'s observation [13]. Fig. 7(A)–(C) shows the Von Mises equivalent stress distributions of the example case after 1st layer, 5th layer and 10th layer particle impacts, respectively. The effect of impact area overlapping and cumulative damage is obvious after multiple particle impacts. The material removal is also shown in cross section view, the erosion area and intensity are both increased after multiple particle impacts. Fig. 8 shows the comparison of the variation of normalized erosion rate with impact angle between the present finite element simulation and experiment by Oka et al. [6] under multiple angular particle impacts. Here, the normalized erosion rate is defined as ERðαÞ=ERð90Þ, where ERðαÞ is the erosion at impact angle of α and ERð90Þ is the maximum erosion rate at the impact angle of 901. The two results show an excellent agreement. Also for both experimental and simulation results, the erosion induced by angular particle impacts is high at high impact angles due to plastic deformation. The present simulations show that the maximum shear strain is at the side and forward rims of the craters, which is consistent with Oka's experimental observations. In addition, the simulations show that angular multiple particle impacts cause large plastic deformation due to angularity, which is consistent with Takaffoli and papini’s study [16–19]. We also perform finite element simulations on aluminum alloy Al6061-T6 (Hv ¼0.4 GPa) using angular SiO2 particles (ρ¼ 2600 kg m 3, Hv ¼ 20Gpa). In the experiment, the impact velocity was 100 m/s, and the particle size was 326 mm [9]. The present simulations use the same substrate, particles and initial
1.0 0.8
FE Simulation Ref Experiment [6]
0.6 0.4
Particles: SiO (326 m) 0.2
Erosion rate (mg/g)
0.30 0.25
Substrate: Stainless Steel Impact velocity: 104m/s
0.0
1st impact 2nd impact 3rd impact 4th impact 5th impact 6th impact 7th impact 8th impact 9th impact 10th impact
0.20 0.15 0.10 0.05
0
10
20
30
40
20
30
40
50
60
70
80
90
100
Impact angle ( ) Fig. 8. Comparison of impact angle dependence of normalized erosion rate with simulation and experiment results [6] in stainless steel.
Particles: SiO (326 m) Substrate: Stainless steel Impact velocity: 104m/s
0.00 0
10
50
60
70
80
90
100
Impact angle ( ) Fig.6. Erosion rate vs. impact angle by multiple particles impact (V ¼ 104 m/s) after each layer of cubic particles impacts.
conditions. The normalized erosion rates are also compared between the simulation and experimental results. Fig. 9 shows the comparison of the variation of normalized erosion rate with impact angle for the aluminum alloy. It is seen that the simulation result is in good agreement with the experimental one. Despite the large difference in the mechanical behavior of the two materials used, the normalized erosion rates follow a very
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similar tendency, indicating that the present simulation model considering multiple impacts with angular particles can be used to study general erosion phenomena involved both cutting action and plastic deformation occurring in engineering materials.
Rm ¼ f Rs þ ð1 f ÞRc
3.3. Mixed spherical and cubic particles In reality, the shape of erosion particles is often not homogeneous, but a mixture of different shapes. In this section, we would like to study the effects of such mixture on the erosion rate. Here, we perform simulations using parcels with different mixtures of spherical and cubic particles. Fig. 10 shows the impact angle dependence of erosion rate under these parcels, together with the two individual parcels. It is seen clearly that the erosion 2.4
Particles: SiO (326 m) Substarte: Al6061-T6 Impact velocity: 100 m/s
Normalized erosion rate
2.0 1.6 1.2 0.8
FE Simulation Ref Experiment [9]
0.4 0.0
0
10
20
30
40
50
60
70
80
90
100
Impact angle ( ) Fig. 9. Comparison of impact angle dependence of normalized erosion rate with simulation and experiment results [9] in aluminum alloy.
0.8
Particles: SiC (120 m) Substrate: Ti-6AL-4V velocity: 55 m/s
Erosion rate (mg/g)
0.6
f=0
f=0.3
0.4
f=0.5 f=0.7
0.2
f=1.0
0.0 0
10
20
30
40
50
rates are dramatically different among purely spherical, purely cubic and mixed particles. These simulations demonstrate that with increasing the percentage of angular particles, the erosion rate increases. It appears that the erosion rate for the mixed parcel can be estimated by the rule of mixture, that is
60
70
80
90
100
Impact angle ( )
Fig. 10. Comparison of impact angle dependence of erosion rate using different parcels. The curves with solid markers depict the simulation results, while the curves with hollow markers depict the results from the analytical equation.
ð6Þ
where Rm denotes the erosion rate of the mixed parcel, Rs is the erosion rate of spherical parcel, Rc is the erosion rate of cubic particles, f is the number percent of spherical particles. The prediction from the rule of mixture is in good agreement with the simulation results (see Fig. 10). 3.4. Other particle shapes In reality, the erosion particles are never perfectly spherical, but always angular to a certain degree. For a comparative study, we pick two more shapes, dodecahedron and icosahedron in addition sphere and cube, as impact particles shown in Fig. 11 to further illuminate the shape effect. Fig. 12 shows the topographic images of the craters on Ti–6Al– 4V substrate caused by SiC particles with four different shapes. In order to clearly illustrate a material removal mechanism, only toplayer elements are shown. The crater shapes are different in these four cases. These simulation results evidently show that the effect of angularity can have a significant effect on the erosion patterns on the material surface. The surface topography of craters arising from particle impacts was experimentally measured before [8,18,24]. To compare with these experimental measurements, we have extracted the surface topography from our simulations with both angular and spherical particle impacts. Fig. 13 shows the typical crater topographic images formed on the surface from both our simulation and the experiment [18]. It is seen that the formation of pile-ups and lips at the crater edges is clearly visible in both simulation and experimental images. Fig. 14 shows the crater topographic images formed on the iron surface under spherical WC particle impacts. It is seen that the simulated crater topography shows very similar features (size and shape) compared with that from experiment [8]. We also calculate the erosion rates from the simulation using the four different particle geometries. The simulation results are compared with Yerramareddy and Bahadur's experiment [5]. In the simulations, the same target material, boundary conditions and average equivalent particle size 120 mm as the real erosion test are used. The same mass loss method used in experiment [5] is also used in the simulations. Similar to the normalization used before, the normalized erosion rate is defined as ERðαÞ=ERm , where ERðαÞ is the erosion at impact angle of α and ERm is the maximum erosion rate. Fig. 15 shows the variation erosion rate with impact angle under different particle shapes. It is seen that on the one hand, the simulations using spherical particles reasonably predict the experimental results at high impact angles but severely underestimate the experimental results at low impact angles; on the other hand, the simulations using cubic particles reasonably predict the experimental results at low impact angles but severely
Fig. 11. Particles with different angularities to test shape effect. (a) Cube; (b) dodecahedron; (c) icosahedron; (d) sphere.
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Fig. 12. Surface topography of crater by single SiC particle impact, the substrate is Ti–6Al–4V (velocity ¼ 55 m/s, angle ¼ 301). (a) Cubic particle; (b) dodecahedral particle; (c) icosahedral particle; (d) spherical particle.
Fig. 13. Crater topography formed on the substrate surface resulting from particle impact test at α ¼ 301 and V ¼117 m/s. The substrate is Al6061-T6 and the particles are angular SiC. (a) Experiment from [18] and (b) Simulation. Source: reprinted with permission from Elsevier B.V. © 2012.
Fig. 14. Typical surface topography of crater obtained by particle impact test impact velocity at α ¼ 301 and V ¼100 m/s. The substrate is iron and the particles are round WC balls. (a) Experiment from [8] and (b) Simulation. Source: reprinted with permission from Elsevier B.V. © 2003.
overestimate the experimental results at high impact angles. For icosahedral particles, the erosion rate is in excellent agreement for the full range of impact angle. Therefore, the difference between simulation and real experiment can be well explained by particle shape effect.
4. Conclusion In this work, we have proposed a new numerical method to predict the erosion behavior of ductile materials. We show that
multiple impacts considering particle shape effect are more effective for erosion simulation. Compared with experiment, this new simulation method provides a useful and economical tool to study the erosion rate and erosion mechanism. Using this method, we studied the particle angularity effect on erosion rates under different particle parcels. The simulation results were extensively compared with the existing experiments. For the multiple spherical particle impacts on two ductile materials, the predicted impact angle dependence of erosion rate shows a typical erosion curve. But there is a large discrepancy in the erosion rate at low impact angles with experiment results. To address this
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1.4 Particles: SiC (120 m) Substrate: Ti-6Al-4V Velocity: 55 m/s
1.2
Nomalized erosion rate
Cubic
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Ref Experiment [5]
Pure sphere
0.0 0
10
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40
50
60
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Impact angle ( ) Fig. 15. Normalized erosion rate under multiple particle impacts with different particle shapes. The simulations using angular particles give a good prediction for erosion rate at low impact angles, while the simulations using spherical and icosahedral particles give a good prediction for erosion rate at high impact angles. The erosion rate using icosahedral particles is in excellent agreement with experimental results for the whole range of impact angle.
discrepancy, we performed impact simulations using multiple cubic particles, and a good agreement is obtained between the simulation and experimental results, suggesting that the simulation with cubic particles is able to consider the dominance of cutting mechanism at low impact angles. We further investigated that for mixed spherical and cubic impact particles, the erosion rate can be approximated by the rule of mixture of the individual particles. We also find that the erosion rate by the impacts of icosahedral particles is in excellent agreement than that in experimental results for the whole range of impact angles. Combined with computational fluid dynamics simulations, the present work can be used to predict the erosion behavior in real equipment. It is expected that this study provides useful guidelines for antierosion design strategies in offshore industry. Acknowledgment The support for this work through Grant WBS no. R-265-000412-305 from Agency for Science, Technology and Research, Singapore (AnSTAR) is gratefully acknowledged. References [1] I. Finnie, Erosion of surfaces by solid particles, Wear 3 (1960) 87–103. [2] J.G.A Bitter, A study of erosion phenomena. part I, Wear 6 (1963) 5–21.
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