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Numerical model for prediction of tool wear and worn-out pin profile during friction stir welding
Author’s Accepted Manuscript Numerical model for prediction of tool wear and worn-out pin profile during friction stir welding Pankaj Sahlot, Amit Arora
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PII: DOI: Reference:
S0043-1648(17)31731-3 https://doi.org/10.1016/j.wear.2018.05.007 WEA102418
To appear in: Wear Received date: 3 December 2017 Revised date: 23 March 2018 Accepted date: 9 May 2018 Cite this article as: Pankaj Sahlot and Amit Arora, Numerical model for prediction of tool wear and worn-out pin profile during friction stir welding, Wear, https://doi.org/10.1016/j.wear.2018.05.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Numerical model for prediction of tool wear and worn-out pin profile during friction stir welding Pankaj Sahlot, Amit Arora* Advanced Materials Processing Research Group, Materials Science and Engineering, Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar - 382355, India *Corresponding author: [email protected]
Abstract Understanding tool wear during friction stir welding (FSW) is important for joining of high melting point metallic (HMPM) materials. Heat transfer and material flow based models developed in past have improved understanding of the FSW process. However, numerical models to predict tool wear and pin profile during FSW of HMPM materials are not available. Thus, the current research has focused on developing a heat transfer and material flow based model to predict tool wear and worn-out tool pin profile of H13 steel during FSW of Cu-0.8Cr-0.1Zr (CuCrZr) alloy. Temperature evolution and material flow are computed by solving conservation equations of mass, momentum and energy. The model thus developed is validated for thermal cycles and tool pin profile for various process parameters. Tool wear is predicted based on forces and stresses acting on the tool. Modified Archard’s wear theory is applied to compute tool wear and worn-out tool pin profile. The wear model successfully predicts the worn-out tool pin profile and self-optimized phenomena for various process parameters. The model is also applied to understand the changes in worn-out pin profile during FSW process.
Keywords: Friction Stir Welding; Numerical modelling; Thermal cycle; Stresses; Wear depth; Tool pin profile
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1. Introduction Friction stir welding (FSW) tool is the primary source for heat generation and material flow during the joining process. Several researchers have related tool design with heat generation rate, material flow and weld properties [1–3]. Some investigators also proposed and patented new non-trivial tool shoulder and pin shapes to improve weld properties such as tensile strength and hardness [3–5]. A change in tool shape due to wear results in unexpected weld joint properties [6–8]. Tool wear is not an issue during FSW of low melting point metallic materials such as aluminium and magnesium alloys, because not enough resistance to tool rotation occurs during FSW of these materials [9]. However, high melting point metallic materials such as steel, copper and titanium alloys lead to faster and more severe wear of FSW tools [10,11]. Tool wear not only affects weld properties but also increases processing costs and reduces tool life [12,13]. Tool wear during FSW of high melting point metallic materials is an important factor affecting tool life and usability. So, studying and understanding tool wear to obtain reliable weld properties and improve tool life for such materials are important. Several experimental tool wear studies were investigated to understand and reduce tool wear during FSW for various tool and workpiece material combinations. Jasthi et al. [14] observed less wear in pcBN tool as compared to W-25%Re during FSW of Invar (Fe-36%Ni), due to high strength of pcBN at elevated temperature. Miles et al. [15] compared 60% pcBN with 40%W-Re tool (Q60) and 70% pcBN with 30% W-Re tool (Q70) for friction stir spot welding (FSSW) of DP 980 steel. They reported that the Q60 tool survived lower welding distance due to low hardness at high temperature. Surekha et al. [16] used cryotreatment to improve wear resistance of H13 and powder metallurgically (P/M)- produced steel tool during FSW of copper. Wear resistance improved due to the formation of fine eta-carbide particles and transformation of retained austenite to martensite. These experimental studies have increased understanding of the tool wear during FSW. However, numerical studies to understand and predict tool wear during FSW of high melting point metallic materials are limited. An experimentally validated numerical model can provide a suitable explanation of the actual process, significant insight into the process, and reduce experimental cost [2,17–19]. Heat transfer and material flow (HTMF) based models can predict properties such as temperature distribution, material velocity, strain, torque, forces, and stress during FSW [20–24]. Nandan et al. [20] developed a three-dimensional model to compute temperature, material flow and 2
torque on tool. Arora et al. [25] computed strains and strain rates from a coupled heat transfer and visco-plastic material flow model during FSW. Gan et al. [26] presented a numerical model for selection of tool material for FSW of L80 steel to avoid tool degradation. Their investigation of tool degradation of both commercial pure tungsten (CPW) and W–25%Re revealed that latter produced less degradation due to high temperature strength as compared to CPW. Arora et al. [27] developed a numerical model to compute the load-bearing capacity of the tool pin to improve pin geometry and selection of tool material to avoid tool degradation. These models have successfully predicted experimental observations during FSW of various alloys [20–22,24,28]. However, numerical models are not available to predict tool wear and a worn-out tool pin profile during the FSW process. Thus, a numerical model to predict tool wear and worn-out tool pin profile during FSW will be of great importance. Here we present a three-dimensional HTMF based numerical model to predict tool wear and tool pin profile during FSW of CuCrZr alloy. Numerically computed and experimentally measured thermal cycles are compared to validate HTMF-based model for FSW of CuCrZr alloy. These temperature values are used to compute the forces and stresses acting on the tool. Regression analysis is used to modify Archard’s wear model for FSW of CuCrZr alloy. Modified Archard’s wear hypothesis is applied to predict tool wear based on stresses acting on tool pin surfaces. Predictions of tool pin profiles from the modified Archard’s model are compared with experimentally observed tool pin profiles for various parameters. The wear model successfully predicts post-wear tool pin profile for various process parameters. The model is also applied to explain the effect of various process parameters on predicted worn-out tool pin profiles and also computed self-optimized phenomena. An HTMF-based numerical model would provide a broader picture to understand tool wear during FSW of various materials without performing experiments.
2. Numerical Model 2.1 HTMF-based model for FSW of CuCrZr alloy A three-dimensional heat transfer and material flow (HTMF) based numerical model is developed to predict tool wear and tool pin profile during FSW of CuCrZr alloy. The model is developed in two stages; first, the HTMF based model is used to compute temperature distribution, material flow, forces and stresses acting on the tool pin are computed using solid mechanics approach. Finally, these computed parameters are used with modified Archard’s wear model to predict tool wear and tool pin profile during FSW of CuCrZr alloy.
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An existing three dimensional HTMF based model is adapted where conservation equations of mass, momentum and energy are solved to compute the temperature evolution and material velocity [29–31]. The three conservation equations solved are as follows [20].
u i =0 x i
ρ
u i u j x i
ρCp
[1]
=-
P + x j x i
u j u j u +μ i -ρU μ x j x1 x i
[2]
(u i T) T T = +Sin +Sb k -ρCp U x i x i x i x1
[3]
Where i= 1, 2 and 3 represent the index notation for x, y and z direction respectively, ρ, µ, CP and k are density, non-Newtonian viscosity, specific heat at constant pressure, thermal conductivity of material. P is the pressure and U is the constant traverse speed. T is the temperature, Sin is the heat generation rate per unit volume due to both friction and plastic deformation at pin interface, and Sb is the heat generation rate per unit volume due to viscous dissipation. The details of the HTMF model are available in the previous literature [30]. Experimentally measured thermo-physical properties (k, Cp and yield strength) of CuCrZr alloy are used to adapt this model to estimate accurate and reliable temperature and material flow during FSW of this alloy [32]. The forces, stresses and torque acting on the tool pin lead to change in pin profile due to wear. In this study, Archard’s model is adapted to compute the tool wear and pin profile [33]. As per the adapted Archard’s wear model, the wear depth depends on the normal stresses acting on the tool, relative velocity between tool and workpiece, and temperature dependent hardness of the tool material. These variables can be computed using the numerical model. Arora et al. [27] proposed calculations to compute stresses acting on the simple cylindrical vertical pin surface leading to tool pin fracture. However, the stress calculations on pin bottom surface were not considered in that study. Wear occurs on both vertical and bottom surfaces, leading to change in the overall pin profile due to material removal [34]. So, it is also important to perform stress calculations on both the surfaces to compute tool wear and tool pin profile. In this study, stress calculations are carried out on both tapered cylindrical and flat pin bottom surfaces to predict the overall pin profile during the FSW process.
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2.2 Stresses acting on tapered pin surface Rotational and translational motion of the tool during FSW results in bending and torsional stresses on the tool pin, respectively. At the tapered pin surface, translational motion generates normal and shear stresses due to bending. However, rotational motion generates torsional shear stress. Following equations are used for calculation of the stresses on tapered cylindrical pin as adapted from literature available for straight cylindrical pin [27]. The normal bending stress can be calculated as
b =
M y .x I yy
=
M y (r.cosθ) πr 4 /4
[4]
4cosθ L z.Fp (z) dz πr 3 z1
Where, σb , My, Fp(z) and Iyy are normal stress due to bending, bending moment at point y, axial force acting on the pin, and second area moment, respectively. The normal distance of the cord from the neutral axis of the pin is x, r is the radius of pin, and θ is the angle from the welding direction. The shear stress due to bending can be calculated as
Fshear .Q 4 sin 2 τb = I yy .n 3 r2
L
z1
Fp ( z ) dz
[5]
and the shear stress, τt, due to torsion can be calculated as
τt =
MT r MT r 2.MT = = J zz πr 3 /2 πr 2
[6]
Where, MT is the sticking torque experienced at a point and Jzz is the polar moment of area. The maximum normal stresses σ, at a point due to combined bending and torsional loading can be expressed as
σ=
σb σ ( b ) 2 +(τ b +τ t sinθ) 2 +(τ t cosθ) 2 2 2 5
[7]
2.3 Stresses on pin bottom surface Tool wear also occurs at the pin bottom surface due to severe stresses during FSW [27,34]. These stresses are mainly due to rotational and translational motion of the tool. The rotational motion produces torsional shear stresses on the pin bottom surface. The tool pin is also subjected to shear stresses due to shear force present on the pin bottom surface. Figure 1 is a schematic diagram sectional view of tapered tool pin and circular bottom surface of pin with distribution of shear stresses. Constant axial pressure on the tool also generates stresses on the pin bottom surface. The rotational motion of tool results in torsional shear stress, τt, at pin bottom surface and can be calculated as [35]
τt =
Tb r Tb r 2 Tb r = = J zz πrtip 4 /2 πrtip 4
[8]
Where r is the radius of a particular point at bottom surface, Tb is torque acting on tool pin bottom surface and rtip is radius of pin tip at bottom.
Figure 1 (a) Schematic diagram of FSW tool and (b) distribution of torsional shear stress at pin bottom surface The shear stress, τf at bottom surface due to frictional force and plastic deformation of material is defined by the following expression:
f [(1 ) f PN ]
[9]
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where τ is temperature-dependent shear strength of workpiece material, PN is normal axial pressure acting on the tool, and δ and µf are spatially varying fractional slip and coefficient of friction, respectively, at tool and workpiece interface [30]. Maximum normal stress, σb, due to both shear stress and axial pressure on tool pin bottom surface is expressed as
P σb = N 2
2
2 PN + τ +τ f t 2
[10]
The relative velocity, Vr between tool pin bottom surface and workpiece material can be computed as
Vr =δ(ωr-Usinθ)
[11]
Where, ω is angular speed, r is radial distance from center, U is traverse speed and θ is the angle in the anticlockwise direction from the traverse direction [20]. Temperature-dependent hardness of H13 tool steel material is expressed as [36]
H (MPa)=6.3e10 T5 + 2.3e 6 T 4 +3.4e 3T 3 -2.4T 2 + 8.7e 2 T- 1.2e5 ,
for 300K T 1000K
H (MPa)= - 0.8T + 1.4e3 ,
for T 1000K
[12]
Where H is hardness of tool material and T is temperature of tool material at pin surface. 2.4 Modified Archard’s wear model The HTMF based wear model is developed by adapting Archard’s wear model. Modified Archard’s wear model is used to predict worn-out tool pin profile during FSW of CuCrZr alloy. Archard’s wear theory suggests that the volume of material removed due to wear is proportional to the work done by frictional force [33,37,38]. The basic Archard’s wear model depends on normal stress acting on interacting surfaces (σn), relative velocity at tool workpiece interface (Vr), hardness of material (H), and interaction time (t). The wear depth (h) can be given as
h=K
σ n .Vr t H
[13] 7
Several researchers have used modified Archard’s models for predicting wear during various other processes [39–41]. The generalized wear depth formula for modified Archard’s model is expressed as
σ . Vr h=K n d H(T) a
b
D U
c
[14]
where K is wear coefficient 8 × 10-6 for H13 steel tool [42,43], H(T) is temperaturedependent tool material hardness, D and U are tool traverse distance and traverse speed, respectively. Exponents a, b, c and d are constants that are calculated from regression analysis by using experimentally-measured wear depth and numerically-computed normal stress, relative velocity, hardness, traverse distance and traverse speed for tapered pin surface [34,44]. Wear depth measurement is done for fifteen combination of welding parameters (rotation speeds- 800 rpm, 1000 rpm and 1200 rpm, traverse speeds- 30 mm/min, 50 mm/min and 70 mm/min and traverse distances- 300 mm, 500 mm and 1000 mm). Around 240 measured wear depth data points are used for regression analysis for all fifteen experiments. Wear depth during FSW of CuCrZr alloy is measured experimentally and an example of that is explained in figure 2 for 1000 mm traverse distance at 1000 rpm rotation speed and 50 mm/min traverse speed [44]. Regression analysis is performed to incorporate the dynamic nature of wear; where the progressive wear rate reduces with traverse distance and reaches a constant value (known as self-optimized tool shape) [9,34]. Figure 2(a) shows the used tool pin image superimposed over unused tool pin line sketch [44]. The change in dimension (known as wear depth, h) is measured at various locations along the pin length by measuring the distance between two corresponding points. The variation of wear depth (h) as function of distance from shoulder shows that wear depth increases with increase in distance from shoulder due to elevation in stresses (figure 2(b)). The high stresses at the pin tip as compared to the pin root result in more wear at the tip. Average wear depth is used to compute exponents a, b, c and d of Eq. 14 during FSW of CuCrZr alloy. To avoid impact of localized variation, a straight line is fitted (upto 2.4 mm distance from shoulder) on experimental data to avoid the localized variation of average wear depth (figure 2(c)). The linearly fitted average wear depth is used to perform regression analysis in computing the value of exponents of normal stress, relative velocity,
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hardness and contact time. Linear fitted average wear depth regression analysis shows significant correlation (R2= 0.829 and p< 0.05).
Figure 2 (a) Superimposed image of used tool pin (b) variation of actual wear depth from pin root to pin tip (c) linear curve fitting for actual measured wear depth for regression analysis [44] The calculated values of constants a, b, c and d are 1.925, 1.394, 1.934 and 0.684, respectively, during FSW of CuCrZr alloy. The predicted modified Archard’s wear model with exponent values for tapered surface (Eq. 15) and bottom surface (Eq. 16) are given below respectively. The developed heat transfer and material flow based model does not consider the plunging stage. However, for wear calculation, the amount of wear during plunge (0.2 mm) is included in the wear depth calculations to validate the computed profile with the actual worn-out tool pin profile.
σn . Vr 1.935 H(T) 1.925
h=8 10
6
1.394
σn . Vr 1.935 H(T) 1.925
h=0.2 + 8 10
6
D U
0.684
1.394
[15]
D U
0.684
[16]
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3. Experimental procedure CuCrZr alloy (Cu-0.8wt%Cr-0.1wt%Zr) plates with 6 mm thickness were used in peak aged condition as workpiece material [34]. Bead-on-plate welding was performed to investigate the wear of H13 steel tool (Fe-5.27wt%Cr-1.25wt%Mo) during FSW of CuCrZr alloy. The tool with shoulder radius of 9.8 mm, tapered pin tip radius 5.2 mm to 2.2 mm at root and tip respectively and pin length of 4.6 mm is used for welding. The selected process parameters for welding are 800, 1000 and 1200 rpm rotation speed, traverse speed of 30, 50 and 70 mm/min with traverse distance of 140, 300, 500 and 1000 mm. A dedicated FSW machine was used to perform all experiments. Temperature was measured during the welding. However, tool wear and tool pin profiles were measured after the welding, to validate the model for FSW of CuCrZr alloy. The k type thermocouples were mounted at 12 mm from the weld center line to measure temperature disturbance during the process [34]. Tool wear during FSW of CuCrZr alloy using H13 steel tool revealed dependence on process parameters, tool rotational speed, tool traverse speed, and traverse distance [44]. H13 steel tool wear during FSW of CuCrZr alloy was measured using a shape measurement technique, which gauges change in dimension of the tool before and after welding. Tool pin profiles were analyzed at multiple traverse distances for welding with various tool rotational speeds, and traverse speeds. The parameters are tagged in the following combination (tool rotation speed (rpm)–tool traverse speed (mm/min)–traverse distance (mm)) for various figures in this article. 4. Results and Discussion 4.1 Validation of developed HTMF model based on temperature evolution The experimentally measured temperature is compared with the numerically computed values of temperature for various process parameters. Figure 3 shows a comparison of both experimentally measured and numerically computed thermal cycles for different tool rotation speeds and traverse speeds combinations. The numerically computed thermal cycles show reasonably good agreement with the experimentally measured thermal cycle for all process parameters. Slight disagreement at the start of heating and at the end of cooling is expected, as the numerical model considers steady state conditions whereas in experimental conditions achieving steady-state conditions is very difficult.
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Figure 3 Comparison of numerically computed and experimentally measured thermal cycles for FSW of CuCrZr for (a) various tool rotation speeds 800 rpm, 1000 rpm and 1200 rpm at constant traverse speed of 30 mm/min and (b) at constant rotation speed of 1000 rpm for various traverse speeds 30 mm/min, 50 mm/min and 70 mm/min. 4.2 Effect of process parameters on various variables at tapered tool pin surface In the present study, normal stress on the pin, relative velocity at the pin- workpiece interface, temperature-dependent hardness of tool pin and time of contact are used, as per equation 13, to compute tool wear during FSW of CuCrZr alloy. The effect of process parameters such as rotation speed and traverse speed on these variables can be explained using the numerically computed values of the variables. 4.2.1 Normal stress distribution At the tapered pin surface, tool translational motion results in normal and shear stresses due to bending and rotational motion results in torsional shear stress. The resultant effect of both stresses is incorporated to compute the maximum principal stress (normal stress) on the tapered pin surface [27]. Figure 4(a) shows the distribution of normal stress from pin root to pin tip for various rotation and traverse speeds. Normal stress increases from pin root to pin tip for all process parameters. The distribution of stresses depends mainly on the resistance offered by the workpiece material in front of the tool pin and geometry of the tool pin. Resistance offered along the pin length depends on the distribution of temperature along the pin length from pin root to pin tip. Figure 4(b) shows tool pin temperature decreases from pin root to pin tip as the majority of heat is generated near the pin root (at shoulder) and dissipated along the plate thickness. The resistance is relatively more at pin tip as compared to pin root due to this variation in temperature. For the tapered pin, stresses are 11
significantly more near pin tip (due to small diameter of pin at the tip) as compared to pin root. Hence, figure 4(a) shows a sharp increase in normal stress near pin tip due to considerable increase in stresses. Normal stress on tool pin surface, decreases with increase in rotation speed due to increase in temperature (figure 4(a)). The increase in temperature leads to reduced resistance offered by workpiece material on the tool pin. However, traverse speed shows a less significant effect on the variation of normal stress because of less variation in tool pin temperature with increase in traverse speed.
Figure 4 Distribution of (a) normal stress, (b) temperature, (c) hardness and (d) relative velocity on the tapered pin surface from the root to the tip for various process parameters during FSW of CuCrZr alloy
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4.2.2 Temperature distribution Distribution of temperature is shown in figure 4(b) from pin root to pin tip for various process parameters. It shows that temperature at pin-workpiece interface decreases from pin root to pin tip. Tool pin temperature increases with increase in rotation speed due to more heat generation at higher rotation speed. However, temperature decreases slightly with increase in traverse speed due to less heat input per unit length at higher traverse speed. 4.2.3 Hardness distribution Temperature-dependent hardness at each node of mesh is calculated (Equation 12). Based on the computed temperature, the variation of hardness from pin root to pin tip is shown in figure 4(c) for various parameters. It shows that hardness value increases from pin root to pin tip. Minimum hardness is observed at pin root, as corresponding temperature is more at pin root compared to the pin tip. However, maximum hardness at pin tip is due to less temperature. Tool pin hardness decreases with increase in rotation speed, as pin temperature increases with increase in rotation speed. However, hardness increases slightly with increase in traverse speed. 4.2.4 Relative velocity variation The magnitude of relative velocity at the tool-workpiece interface depends on tool tangential velocity, traverse speed and fraction of slip [30,45]. Figure 4(d) shows distribution of relative velocity from pin root to pin tip for various process parameters. The relative velocity at pin–workpiece interface decreases from pin root to pin tip for all process parameters. For rotation speed and welding speed being constant, relative velocity depends only on tool geometry. Maximum relative velocity is occurred at pin root due to highest radial distance at root and minimum at pin tip due to smallest radial distance. Relative velocity increases with increase in rotation speed at every location on the pin. However, it changes very little as a function of traverse speed (figure 4(d)). 4.3 Variation of various variables on bottom surface of tool pin Tool wear also occurs at pin bottom surface as a result of severe stresses acting on the bottom surface and leads to reduction in pin length. Tool wear is computed at each node of the mesh according to equation 13. Equation 10 is used to calculate distribution of normal stress at bottom surface is computed. Figure 5(a) shows the distribution of normal stress (contour plot) on the pin bottom surface for 800 rpm rotation speed and 30 mm/min traverse speed. It depicts, normal stress on the tool pin bottom surface increases with increase in radial 13
distance. This can be attributed to increase in shear stresses on the pin bottom surface. Normal stress increases from center to circumference and is maximum at the circumference of the pin bottom surface.
Figure 5 Distribution of (a) normal stress, (b) relative velocity, (c) temperature and (d) hardness on the pin bottom surface at 800 rpm rotation speed and 30 mm/min traverse speed during FSW of CuCrZr alloy. The relative velocity at the between pin-bottom workpiece interface increases with increase in radial distance and is maximum at pin circumference (figure 5(b)). The relative velocity between pin bottom surface and workpiece is governed by Equation 11. The distribution of temperature at pin bottom surface is shown in figure 5(c). It shows that temperature increases with increase in radial distance due to high heat generation at circumference. High heat is generated by high relative velocity between tool and workpiece material at circumference as compared to the pin center. The distribution of temperature affects variation of hardness on the tool pin bottom surface as shown in (Equation 12). Figure 5(d) shows the distribution of hardness on the pin bottom surface. Hardness is less at the circumference as compared to the pin center due to high temperature at pin bottom circumference. 14
4.4 Tool degradation- Wear/deformation The tool can degrade by either deformation or by wear. To examine the difference, we can compare shear stresses acting on the pin and shear strength of tool pin. Figure 6 shows the comparison of shear stress acting on tool pin and shear strength of H13 steel from pin root to pin tip during FSW of CuCrZr alloy. The maximum shear stress acting on the tool pin is computed by calculating the forces and torque on the tool pin. The shear strength of H13 tool material is calculated a function of by computed tool pin temperature [46]. It shows maximum shear stress acting on the tool pin profile increases from pin root to pin tip. The maximum shear stress at pin root is significantly less than the shear strength of tool material. Therefore, chance of deformation is very less near to pin root. However, near to the pin tip, shear stress is significantly more than shear strength of tool material. Hence, deformation may take place near to the tip. Based on this analysis, we can say that for most of the pin surface, deformation will not contribute to pin degradation. Only the pin bottom surface will be affected by deformation. However, wear is taking place at both the surfaces, vertical and bottom.
Figure 6 Comparison of shear stress acting on the tool pin with shear strength of H13 tool material from pin root to pin tip 4.5 Prediction of tool pin profile As we have found that only wear is responsible for pin vertical and bottom surface degradation, the modified Archard’s wear model is applied. The effect of wear on both 15
tapered vertical and bottom surface is computed. Figure 7(a) shows variation of computed wear depth as a function of distance from shoulder on pin tapered surface after traverse distance of 300 mm at 800 rpm rotation speed and 30 mm/min traverse speed. It shows that computed wear depth increases with increase in distance from the shoulder along pin length. The incremental rate is less near the pin root. However, wear depth increases with a higher rate near the pin tip due to higher stresses near pin tip as compared to pin root. Near the pin tip, higher stresses are due to small cross-sectional area as compared to pin root. Normal stress affects the wear depth more as compared to relative velocity near the pin tip.
Figure 7(a) Variation of computed wear depth from pin root to pin tip. (b) Distribution of wear depth at pin bottom surface for 300 mm traverse distance at 800 rpm rotation speed and 30 mm/min traverse speed. Variation of wear depth at the pin bottom surface shows wear depth increases from the center of pin bottom, radially out; and is maximum at the circumference (figure 7(b)). At the pin bottom surface, both normal stress and relative velocity are higher and hardness is minimum at the circumference as compared to center, which leads to higher wear depth at the circumference as compared to pin center. Subsequently, the computed worn-out pin profile is generated using computed wear depths at various points on the pin surface. Wear depth for tapered and bottom surfaces is combined near the pin tip to generate the complete computed worn-out pin profile for various process parameters.
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Figure 8(a) Numerically computed pin profile and (b) Comparison of computed and measured pin profile of H13 steel tool during FSW of CuCrZr alloy profile at rotation speed of 800 rpm, traverse speed of 30 mm/min and for traverse distance of 300 mm Figure 8(a) shows computed pin profile (red color profile) for traverse distance of 300 mm at 800 rpm rotation speed and 30 mm/min traverse speed during FSW of CuCrZr alloy. Wear increases from pin root to pin tip, and maximum wear occur near the pin tip. The amount of wear on tool pin depends on the distribution of normal stress, relative velocity and hardness for constant process parameters. The distribution of normal stress increases from pin root to pin tip and attains maximum value near the pin tip (figure 4(a)). However, relative velocity is greater at the pin root and decreases from pin root to pin tip as shown in figure 4(d). Hardness of tool pin also increases from pin root to pin tip and reaches maximum value at pin tip. The variation of relative velocity and hardness produces less wear near the pin tip. However, variation of normal stress produces more wear near the pin tip. The effect of normal stress dominates over the effect of relative velocity and hardness to produce more wear near the pin tip as compared to the pin root. Figure 8(b) shows the comparison of computed pin profile with the actual worn-out pin profile. For better comparison, computed and actual worn-out profiles are superimposed on each other. Computed pin profile is in good agreement with the worn tool pin geometry. The computed pin profile exposes some mismatch with the actual pin profile at certain locations because of localized deformation or dynamic behavior due to severe stresses at high temperature during FSW of CuCrZr alloy. The wear model has been validated for various process parameters to improve its reliability. 17
4.6 Validation of numerical model for tool wear The comparison of computed and actual worn-out pin profiles is shown in figure 9 for various process parameters. The parameters are included in each tool image in a sequence of rotation speed (rpm), traverse speed (mm/min), and traverse distance (mm). Numerically computed pin profiles depict reasonably good agreement with the worn-out tool pin profile for various parameters. The developed model is successfully able to predict the actual worn out tool pin profile. The worn out pin profile at bottom changes from flat tapered pin (unused tool) to curved cylindrical type shape (used tool) after wear for various traverse distances. The similar behavior is also computed through modeling of predicted tool pin profile. The gradual change in the shape of the tool pin from flat tapered to curved cylindrical pin is close to the self-optimized pin shape, which can be different at different process parameters. The predicted pin profile shows better agreement at the tapered surface closer to the pin root as compared to pin tip. The experimental profile shows more wear as compared to the computed pin profile near the pin tip. As shown earlier, the shear stress at the pin bottom is more than the shear strength of the tool. The tool degradation happens due to both wear and deformation. Thus, computed pin profile due to wear predicts less degradation at the tip.
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Figure 9 Comparison of computed and measured tool pin profiles for H13 steel tool during FSW of CuCrZr alloy at different traverse distances for various process parameters. 4.7 Validation of developed model by independent experiments The validated wear model is used to predict the tool pin profile for other random parameters that were not experimentally performed earlier and not used for regression analysis. Figure 10(a1-a3) show the effect of rotation speed and traverse speed for 140 mm traverse distance on predicted pin profile. Independent experiments are performed to compare the predicted pin profile with the actual pin profile for these new parameters. Figure 10(b1-b3) shows the comparison of predicted pin profile with the actual pin profile for various process parameters. It shows there is a reasonably good comparison between measured and predicted pin profile for new parameters. This comparison also improves the reliability of the wear model to 19
predict tool pin profile during FSW of CuCrZr alloy. The predicted profiles show some mismatch due to localized deformation at high temperature.
Figure 10(a1-a3) predicted pin profile for various process parameters and (b1-b3) comparison of these predicted pin profiles with actual pin profiles for various process parameters. 4.8 Effect of process parameters on predicted pin profile The developed tool wear model can be used to better understand the effect of process parameters on variation in tool pin profile. We have analyzed effect of traverse distance, rotation speed and traverse speed on the predicted tool pin profile. 4.8.1 Effect of traverse distances The effect of traverse distance on change in predicted tool pin profile for various traverse distances is shown in figure 11(a) during FSW of CuCrZr alloy. Overall size of the tool pin reduces with increase in traverse distance due to continuous wear. The wear depth increases with increase in traverse distance at each location due to continuous stresses on tool pin. Figure 11(b) shows wear depth as function of traverse distance at 0.1 mm, 1.1 mm, 2.1 mm and 3.1 mm from shoulder on the pin tapered surface. The rate of increment in wear depth is more near to pin tip (at 3.1 mm) as compared to pin root (at 0.1mm) i.e. slop for 3.1 mm is more than 0.1 mm. This mainly occurs due to more stresses on pin tip as compared to pin root (figure 4(a)). The developed model also has capability to compute the progressive wear rate for various traverse distance intervals. The reduction in pin size is more during initial traverse (figure 11(a)) due to severe wear. However, for longer traverse distance, reduction in pin size becomes less due to decrease in wear rate. Figure 11(c) shows wear rate as a function of traverse distance intervals at various locations on pin surface. It shows that progressive wear rate decreases with increase in the traverse distance intervals for all locations. However, wear 20
rate does not change much after long traverse distance (around 1000 mm) as tool pin approaches self-optimized pin shape and wear rate reduces. The developed model shows capability to predict self-optimized phenomena as observed by many researchers during FSW process.
Figure 11(a) Variation in predicted tool pin for various traverse distances of 200 mm, 600 mm, 1000 mm and 1400 mm at 800 rpm and 30 mm/min, (b) wear depth as a function of traverse distance and (c) progressive wear rate as a function of traverse distance intervals at various locations on the tool pin.
4.8.2 Effect of rotation speed The effect of rotation speed on predicted pin profile as shown in figure 12(a) confirms that wear increases with increase in rotation speed. Tool pin wear depends on stresses, hardness and the relative velocity at tool pin workpiece interface, as mentioned in Equation 13. With increase in rotation speed, stresses on the pin and pin hardness decreases as temperature around the pin increases (figure 4(a) and (c)). However, the relative velocity at the interface 21
increases with increase in rotation speed (figure 4(d)). The wear model suggests, wear should increase due to decrease in hardness and increase in relative velocity. Whereas, it should decrease due to reduction in stress. The computed pin profile shows wear increases (reduction in pin size) with increase in rotation speed as effect of relative velocity and hardness dominates over effect of stresses (figure 12(a)). The difference in tool wear due to rotational speed is not significant near the pin root, as the actual amount of wear is also low. However, the difference becomes clearly visible near the pin tip where wear is high; and significant change in the size of pin is seen due to increased tool rotation speed. The predicted pin size also reduces from the bottom and reflects the reduction in pin length with rotation speed. For 300 mm traverse distance, tool pin shape changes from completely flat bottom (unused) to curved bottom (used). Figure 12(b) shows effect of rotation speed on wear depth at 0.1 mm, 1.1 mm, 2.1 mm and 3.1 mm from shoulder on the pin tapered surface. Wear depth increases with increase in rotation speed for all locations on the pin due to increase in relative velocity between tool and workpiece.
Figure 12 (a) Predicted tool pin profiles for rotation speeds 600 rpm, 800 rpm, 1000 rpm and 1200 rpm with a constant traverse speed and distance of 30 mm/min and 300 mm, respectively (b) wear depth as a function of rotation speed at various locations on the tool pin.
22
4.8.3 Effect of traverse speed The effect of traverse speed on computed pin profile is shown in figure 13(a) for 1000 rpm and 300 mm traverse distance. Tool pin wear decreases with increase in traverse speed for all traverse distances. During FSW, stresses on the tool pin and pin hardness of tool pin slightly increases with increase in traverse speed due to slight reduction in temperature (figure 4(a) and (c)). However, traverse speed does not show significant variation on relative velocity (figure 4(d)). Hence, developed wear model suggests, wear does not affect much with slight variation in stresses, hardness and relative velocity. However, interaction time with tool pin and workpiece were affected significantly. Interaction time decreases with increase in traverse speed and results in less pin wear. The size of predicted pin reduced from the bottom reflects the reduction in pin length with traverse speed. For 300 mm traverse distance, tool pin shape changes from completely flat pin bottom to curved pin bottom.
Figure 13(a) Variation in size of computed tool pin for traverse speeds 10 mm/min, 30 mm/min, 50 mm/min, 700 mm/min and 90 mm/min with a constant rotation speed of 1000 rpm and traverse distance of 300 mm and (b) wear depth as a function of traverse speed at various locations on the tool pin.
23
Figure 13(b) shows wear depth as a function of traverse speed on tool pin at various locations. It shows that wear depth decreases with increase in traverse speed at 0.1 mm, 1.1 mm, 2.1 mm and 3.1 mm distance from shoulder on pin surface. The difference in wear depth becomes insignificant for high traverse speed (90 mm/min). Wear depth shows more difference at 0.1mm (near to pin root) to 3.1 mm (near to pin tip) for low traverse speed (10 mm/min) as compared to high traverse speed (90 mm/min). The difference is more for low traverse speed due to more interaction time in stress condition for 300 mm traverse distance. 5. Conclusions A three-dimensional heat transfer and visco-plastic material flow based model is developed to predict tool wear and pin profile using modified Archard’s wear model. Following are the major highlights of this research. 1. Numerical model is validated for thermal cycles and pin profile for various process parameters to show model reliability. The predicted pin profiles are also validated by performing independent experiments. The developed model can be used to successfully predict the worn out pin profile. 2. From the validated numerical model, it can be shown that amount of wear is more near the pin tip compared to pin root due to higher order of stresses at the pin tip. At the pin bottom, the stresses are more at the periphery compared to the center leading to more wear at the edges of pin bottom. This wear behavior results in curved pin bottom, as compared to the initial flat bottom pin. 3. The predicted pin profiles show that wear increases with increase in rotation speed due to increase in relative velocity between tool and workpiece material. However, predicted wear decreases with increase in traverse speed due to less interaction time. The effect of rotation speed and traverse speed are significant near the pin tip as compared to the pin root due to higher stresses at the pin tip. 4. The wear model also shows that pin size decreases with increase in traverse distance due to continuous wear. The progressive wear rate is more in the beginning and becomes less for long traverse as tool approaches self-optimized shape. Developed wear model also predicts the self-optimized phenomena during FSW process. The developed model promotes understanding of tool wear during FSW process and further explains the effect of various process parameters. 24
Acknowledgement The authors would like to thank Dr. G. K Dey, Materials Science Division and Mr. Kaushal Jha, Engineering Design & Development Division, Bhabha Atomic Research Centre (BARC), Mumbai, India. Authors would also like to acknowledge the Board for Research in Nuclear Sciences (BRNS), (project number 36(2)/20/02/2014-BRNS/). They also would like to thank staff at BARC for helping in performing experiments.
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27
Highlights
A numerical model is developed for prediction of tool wear and worn out pin profile.
Wear is more near the pin tip compared to pin root due to higher order of stresses.
Predicted profiles show more wear for higher RPM due to increase in relative velocity.
The developed wear model also predicts the self-optimized phenomena.
28
www.elsevier.com/locate/wear
PII: DOI: Reference:
S0043-1648(17)31731-3 https://doi.org/10.1016/j.wear.2018.05.007 WEA102418
To appear in: Wear Received date: 3 December 2017 Revised date: 23 March 2018 Accepted date: 9 May 2018 Cite this article as: Pankaj Sahlot and Amit Arora, Numerical model for prediction of tool wear and worn-out pin profile during friction stir welding, Wear, https://doi.org/10.1016/j.wear.2018.05.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Numerical model for prediction of tool wear and worn-out pin profile during friction stir welding Pankaj Sahlot, Amit Arora* Advanced Materials Processing Research Group, Materials Science and Engineering, Indian Institute of Technology Gandhinagar, Palaj, Gandhinagar - 382355, India *Corresponding author: [email protected]
Abstract Understanding tool wear during friction stir welding (FSW) is important for joining of high melting point metallic (HMPM) materials. Heat transfer and material flow based models developed in past have improved understanding of the FSW process. However, numerical models to predict tool wear and pin profile during FSW of HMPM materials are not available. Thus, the current research has focused on developing a heat transfer and material flow based model to predict tool wear and worn-out tool pin profile of H13 steel during FSW of Cu-0.8Cr-0.1Zr (CuCrZr) alloy. Temperature evolution and material flow are computed by solving conservation equations of mass, momentum and energy. The model thus developed is validated for thermal cycles and tool pin profile for various process parameters. Tool wear is predicted based on forces and stresses acting on the tool. Modified Archard’s wear theory is applied to compute tool wear and worn-out tool pin profile. The wear model successfully predicts the worn-out tool pin profile and self-optimized phenomena for various process parameters. The model is also applied to understand the changes in worn-out pin profile during FSW process.
Keywords: Friction Stir Welding; Numerical modelling; Thermal cycle; Stresses; Wear depth; Tool pin profile
1
1. Introduction Friction stir welding (FSW) tool is the primary source for heat generation and material flow during the joining process. Several researchers have related tool design with heat generation rate, material flow and weld properties [1–3]. Some investigators also proposed and patented new non-trivial tool shoulder and pin shapes to improve weld properties such as tensile strength and hardness [3–5]. A change in tool shape due to wear results in unexpected weld joint properties [6–8]. Tool wear is not an issue during FSW of low melting point metallic materials such as aluminium and magnesium alloys, because not enough resistance to tool rotation occurs during FSW of these materials [9]. However, high melting point metallic materials such as steel, copper and titanium alloys lead to faster and more severe wear of FSW tools [10,11]. Tool wear not only affects weld properties but also increases processing costs and reduces tool life [12,13]. Tool wear during FSW of high melting point metallic materials is an important factor affecting tool life and usability. So, studying and understanding tool wear to obtain reliable weld properties and improve tool life for such materials are important. Several experimental tool wear studies were investigated to understand and reduce tool wear during FSW for various tool and workpiece material combinations. Jasthi et al. [14] observed less wear in pcBN tool as compared to W-25%Re during FSW of Invar (Fe-36%Ni), due to high strength of pcBN at elevated temperature. Miles et al. [15] compared 60% pcBN with 40%W-Re tool (Q60) and 70% pcBN with 30% W-Re tool (Q70) for friction stir spot welding (FSSW) of DP 980 steel. They reported that the Q60 tool survived lower welding distance due to low hardness at high temperature. Surekha et al. [16] used cryotreatment to improve wear resistance of H13 and powder metallurgically (P/M)- produced steel tool during FSW of copper. Wear resistance improved due to the formation of fine eta-carbide particles and transformation of retained austenite to martensite. These experimental studies have increased understanding of the tool wear during FSW. However, numerical studies to understand and predict tool wear during FSW of high melting point metallic materials are limited. An experimentally validated numerical model can provide a suitable explanation of the actual process, significant insight into the process, and reduce experimental cost [2,17–19]. Heat transfer and material flow (HTMF) based models can predict properties such as temperature distribution, material velocity, strain, torque, forces, and stress during FSW [20–24]. Nandan et al. [20] developed a three-dimensional model to compute temperature, material flow and 2
torque on tool. Arora et al. [25] computed strains and strain rates from a coupled heat transfer and visco-plastic material flow model during FSW. Gan et al. [26] presented a numerical model for selection of tool material for FSW of L80 steel to avoid tool degradation. Their investigation of tool degradation of both commercial pure tungsten (CPW) and W–25%Re revealed that latter produced less degradation due to high temperature strength as compared to CPW. Arora et al. [27] developed a numerical model to compute the load-bearing capacity of the tool pin to improve pin geometry and selection of tool material to avoid tool degradation. These models have successfully predicted experimental observations during FSW of various alloys [20–22,24,28]. However, numerical models are not available to predict tool wear and a worn-out tool pin profile during the FSW process. Thus, a numerical model to predict tool wear and worn-out tool pin profile during FSW will be of great importance. Here we present a three-dimensional HTMF based numerical model to predict tool wear and tool pin profile during FSW of CuCrZr alloy. Numerically computed and experimentally measured thermal cycles are compared to validate HTMF-based model for FSW of CuCrZr alloy. These temperature values are used to compute the forces and stresses acting on the tool. Regression analysis is used to modify Archard’s wear model for FSW of CuCrZr alloy. Modified Archard’s wear hypothesis is applied to predict tool wear based on stresses acting on tool pin surfaces. Predictions of tool pin profiles from the modified Archard’s model are compared with experimentally observed tool pin profiles for various parameters. The wear model successfully predicts post-wear tool pin profile for various process parameters. The model is also applied to explain the effect of various process parameters on predicted worn-out tool pin profiles and also computed self-optimized phenomena. An HTMF-based numerical model would provide a broader picture to understand tool wear during FSW of various materials without performing experiments.
2. Numerical Model 2.1 HTMF-based model for FSW of CuCrZr alloy A three-dimensional heat transfer and material flow (HTMF) based numerical model is developed to predict tool wear and tool pin profile during FSW of CuCrZr alloy. The model is developed in two stages; first, the HTMF based model is used to compute temperature distribution, material flow, forces and stresses acting on the tool pin are computed using solid mechanics approach. Finally, these computed parameters are used with modified Archard’s wear model to predict tool wear and tool pin profile during FSW of CuCrZr alloy.
3
An existing three dimensional HTMF based model is adapted where conservation equations of mass, momentum and energy are solved to compute the temperature evolution and material velocity [29–31]. The three conservation equations solved are as follows [20].
u i =0 x i
ρ
u i u j x i
ρCp
[1]
=-
P + x j x i
u j u j u +μ i -ρU μ x j x1 x i
[2]
(u i T) T T = +Sin +Sb k -ρCp U x i x i x i x1
[3]
Where i= 1, 2 and 3 represent the index notation for x, y and z direction respectively, ρ, µ, CP and k are density, non-Newtonian viscosity, specific heat at constant pressure, thermal conductivity of material. P is the pressure and U is the constant traverse speed. T is the temperature, Sin is the heat generation rate per unit volume due to both friction and plastic deformation at pin interface, and Sb is the heat generation rate per unit volume due to viscous dissipation. The details of the HTMF model are available in the previous literature [30]. Experimentally measured thermo-physical properties (k, Cp and yield strength) of CuCrZr alloy are used to adapt this model to estimate accurate and reliable temperature and material flow during FSW of this alloy [32]. The forces, stresses and torque acting on the tool pin lead to change in pin profile due to wear. In this study, Archard’s model is adapted to compute the tool wear and pin profile [33]. As per the adapted Archard’s wear model, the wear depth depends on the normal stresses acting on the tool, relative velocity between tool and workpiece, and temperature dependent hardness of the tool material. These variables can be computed using the numerical model. Arora et al. [27] proposed calculations to compute stresses acting on the simple cylindrical vertical pin surface leading to tool pin fracture. However, the stress calculations on pin bottom surface were not considered in that study. Wear occurs on both vertical and bottom surfaces, leading to change in the overall pin profile due to material removal [34]. So, it is also important to perform stress calculations on both the surfaces to compute tool wear and tool pin profile. In this study, stress calculations are carried out on both tapered cylindrical and flat pin bottom surfaces to predict the overall pin profile during the FSW process.
4
2.2 Stresses acting on tapered pin surface Rotational and translational motion of the tool during FSW results in bending and torsional stresses on the tool pin, respectively. At the tapered pin surface, translational motion generates normal and shear stresses due to bending. However, rotational motion generates torsional shear stress. Following equations are used for calculation of the stresses on tapered cylindrical pin as adapted from literature available for straight cylindrical pin [27]. The normal bending stress can be calculated as
b =
M y .x I yy
=
M y (r.cosθ) πr 4 /4
[4]
4cosθ L z.Fp (z) dz πr 3 z1
Where, σb , My, Fp(z) and Iyy are normal stress due to bending, bending moment at point y, axial force acting on the pin, and second area moment, respectively. The normal distance of the cord from the neutral axis of the pin is x, r is the radius of pin, and θ is the angle from the welding direction. The shear stress due to bending can be calculated as
Fshear .Q 4 sin 2 τb = I yy .n 3 r2
L
z1
Fp ( z ) dz
[5]
and the shear stress, τt, due to torsion can be calculated as
τt =
MT r MT r 2.MT = = J zz πr 3 /2 πr 2
[6]
Where, MT is the sticking torque experienced at a point and Jzz is the polar moment of area. The maximum normal stresses σ, at a point due to combined bending and torsional loading can be expressed as
σ=
σb σ ( b ) 2 +(τ b +τ t sinθ) 2 +(τ t cosθ) 2 2 2 5
[7]
2.3 Stresses on pin bottom surface Tool wear also occurs at the pin bottom surface due to severe stresses during FSW [27,34]. These stresses are mainly due to rotational and translational motion of the tool. The rotational motion produces torsional shear stresses on the pin bottom surface. The tool pin is also subjected to shear stresses due to shear force present on the pin bottom surface. Figure 1 is a schematic diagram sectional view of tapered tool pin and circular bottom surface of pin with distribution of shear stresses. Constant axial pressure on the tool also generates stresses on the pin bottom surface. The rotational motion of tool results in torsional shear stress, τt, at pin bottom surface and can be calculated as [35]
τt =
Tb r Tb r 2 Tb r = = J zz πrtip 4 /2 πrtip 4
[8]
Where r is the radius of a particular point at bottom surface, Tb is torque acting on tool pin bottom surface and rtip is radius of pin tip at bottom.
Figure 1 (a) Schematic diagram of FSW tool and (b) distribution of torsional shear stress at pin bottom surface The shear stress, τf at bottom surface due to frictional force and plastic deformation of material is defined by the following expression:
f [(1 ) f PN ]
[9]
6
where τ is temperature-dependent shear strength of workpiece material, PN is normal axial pressure acting on the tool, and δ and µf are spatially varying fractional slip and coefficient of friction, respectively, at tool and workpiece interface [30]. Maximum normal stress, σb, due to both shear stress and axial pressure on tool pin bottom surface is expressed as
P σb = N 2
2
2 PN + τ +τ f t 2
[10]
The relative velocity, Vr between tool pin bottom surface and workpiece material can be computed as
Vr =δ(ωr-Usinθ)
[11]
Where, ω is angular speed, r is radial distance from center, U is traverse speed and θ is the angle in the anticlockwise direction from the traverse direction [20]. Temperature-dependent hardness of H13 tool steel material is expressed as [36]
H (MPa)=6.3e10 T5 + 2.3e 6 T 4 +3.4e 3T 3 -2.4T 2 + 8.7e 2 T- 1.2e5 ,
for 300K T 1000K
H (MPa)= - 0.8T + 1.4e3 ,
for T 1000K
[12]
Where H is hardness of tool material and T is temperature of tool material at pin surface. 2.4 Modified Archard’s wear model The HTMF based wear model is developed by adapting Archard’s wear model. Modified Archard’s wear model is used to predict worn-out tool pin profile during FSW of CuCrZr alloy. Archard’s wear theory suggests that the volume of material removed due to wear is proportional to the work done by frictional force [33,37,38]. The basic Archard’s wear model depends on normal stress acting on interacting surfaces (σn), relative velocity at tool workpiece interface (Vr), hardness of material (H), and interaction time (t). The wear depth (h) can be given as
h=K
σ n .Vr t H
[13] 7
Several researchers have used modified Archard’s models for predicting wear during various other processes [39–41]. The generalized wear depth formula for modified Archard’s model is expressed as
σ . Vr h=K n d H(T) a
b
D U
c
[14]
where K is wear coefficient 8 × 10-6 for H13 steel tool [42,43], H(T) is temperaturedependent tool material hardness, D and U are tool traverse distance and traverse speed, respectively. Exponents a, b, c and d are constants that are calculated from regression analysis by using experimentally-measured wear depth and numerically-computed normal stress, relative velocity, hardness, traverse distance and traverse speed for tapered pin surface [34,44]. Wear depth measurement is done for fifteen combination of welding parameters (rotation speeds- 800 rpm, 1000 rpm and 1200 rpm, traverse speeds- 30 mm/min, 50 mm/min and 70 mm/min and traverse distances- 300 mm, 500 mm and 1000 mm). Around 240 measured wear depth data points are used for regression analysis for all fifteen experiments. Wear depth during FSW of CuCrZr alloy is measured experimentally and an example of that is explained in figure 2 for 1000 mm traverse distance at 1000 rpm rotation speed and 50 mm/min traverse speed [44]. Regression analysis is performed to incorporate the dynamic nature of wear; where the progressive wear rate reduces with traverse distance and reaches a constant value (known as self-optimized tool shape) [9,34]. Figure 2(a) shows the used tool pin image superimposed over unused tool pin line sketch [44]. The change in dimension (known as wear depth, h) is measured at various locations along the pin length by measuring the distance between two corresponding points. The variation of wear depth (h) as function of distance from shoulder shows that wear depth increases with increase in distance from shoulder due to elevation in stresses (figure 2(b)). The high stresses at the pin tip as compared to the pin root result in more wear at the tip. Average wear depth is used to compute exponents a, b, c and d of Eq. 14 during FSW of CuCrZr alloy. To avoid impact of localized variation, a straight line is fitted (upto 2.4 mm distance from shoulder) on experimental data to avoid the localized variation of average wear depth (figure 2(c)). The linearly fitted average wear depth is used to perform regression analysis in computing the value of exponents of normal stress, relative velocity,
8
hardness and contact time. Linear fitted average wear depth regression analysis shows significant correlation (R2= 0.829 and p< 0.05).
Figure 2 (a) Superimposed image of used tool pin (b) variation of actual wear depth from pin root to pin tip (c) linear curve fitting for actual measured wear depth for regression analysis [44] The calculated values of constants a, b, c and d are 1.925, 1.394, 1.934 and 0.684, respectively, during FSW of CuCrZr alloy. The predicted modified Archard’s wear model with exponent values for tapered surface (Eq. 15) and bottom surface (Eq. 16) are given below respectively. The developed heat transfer and material flow based model does not consider the plunging stage. However, for wear calculation, the amount of wear during plunge (0.2 mm) is included in the wear depth calculations to validate the computed profile with the actual worn-out tool pin profile.
σn . Vr 1.935 H(T) 1.925
h=8 10
6
1.394
σn . Vr 1.935 H(T) 1.925
h=0.2 + 8 10
6
D U
0.684
1.394
[15]
D U
0.684
[16]
9
3. Experimental procedure CuCrZr alloy (Cu-0.8wt%Cr-0.1wt%Zr) plates with 6 mm thickness were used in peak aged condition as workpiece material [34]. Bead-on-plate welding was performed to investigate the wear of H13 steel tool (Fe-5.27wt%Cr-1.25wt%Mo) during FSW of CuCrZr alloy. The tool with shoulder radius of 9.8 mm, tapered pin tip radius 5.2 mm to 2.2 mm at root and tip respectively and pin length of 4.6 mm is used for welding. The selected process parameters for welding are 800, 1000 and 1200 rpm rotation speed, traverse speed of 30, 50 and 70 mm/min with traverse distance of 140, 300, 500 and 1000 mm. A dedicated FSW machine was used to perform all experiments. Temperature was measured during the welding. However, tool wear and tool pin profiles were measured after the welding, to validate the model for FSW of CuCrZr alloy. The k type thermocouples were mounted at 12 mm from the weld center line to measure temperature disturbance during the process [34]. Tool wear during FSW of CuCrZr alloy using H13 steel tool revealed dependence on process parameters, tool rotational speed, tool traverse speed, and traverse distance [44]. H13 steel tool wear during FSW of CuCrZr alloy was measured using a shape measurement technique, which gauges change in dimension of the tool before and after welding. Tool pin profiles were analyzed at multiple traverse distances for welding with various tool rotational speeds, and traverse speeds. The parameters are tagged in the following combination (tool rotation speed (rpm)–tool traverse speed (mm/min)–traverse distance (mm)) for various figures in this article. 4. Results and Discussion 4.1 Validation of developed HTMF model based on temperature evolution The experimentally measured temperature is compared with the numerically computed values of temperature for various process parameters. Figure 3 shows a comparison of both experimentally measured and numerically computed thermal cycles for different tool rotation speeds and traverse speeds combinations. The numerically computed thermal cycles show reasonably good agreement with the experimentally measured thermal cycle for all process parameters. Slight disagreement at the start of heating and at the end of cooling is expected, as the numerical model considers steady state conditions whereas in experimental conditions achieving steady-state conditions is very difficult.
10
Figure 3 Comparison of numerically computed and experimentally measured thermal cycles for FSW of CuCrZr for (a) various tool rotation speeds 800 rpm, 1000 rpm and 1200 rpm at constant traverse speed of 30 mm/min and (b) at constant rotation speed of 1000 rpm for various traverse speeds 30 mm/min, 50 mm/min and 70 mm/min. 4.2 Effect of process parameters on various variables at tapered tool pin surface In the present study, normal stress on the pin, relative velocity at the pin- workpiece interface, temperature-dependent hardness of tool pin and time of contact are used, as per equation 13, to compute tool wear during FSW of CuCrZr alloy. The effect of process parameters such as rotation speed and traverse speed on these variables can be explained using the numerically computed values of the variables. 4.2.1 Normal stress distribution At the tapered pin surface, tool translational motion results in normal and shear stresses due to bending and rotational motion results in torsional shear stress. The resultant effect of both stresses is incorporated to compute the maximum principal stress (normal stress) on the tapered pin surface [27]. Figure 4(a) shows the distribution of normal stress from pin root to pin tip for various rotation and traverse speeds. Normal stress increases from pin root to pin tip for all process parameters. The distribution of stresses depends mainly on the resistance offered by the workpiece material in front of the tool pin and geometry of the tool pin. Resistance offered along the pin length depends on the distribution of temperature along the pin length from pin root to pin tip. Figure 4(b) shows tool pin temperature decreases from pin root to pin tip as the majority of heat is generated near the pin root (at shoulder) and dissipated along the plate thickness. The resistance is relatively more at pin tip as compared to pin root due to this variation in temperature. For the tapered pin, stresses are 11
significantly more near pin tip (due to small diameter of pin at the tip) as compared to pin root. Hence, figure 4(a) shows a sharp increase in normal stress near pin tip due to considerable increase in stresses. Normal stress on tool pin surface, decreases with increase in rotation speed due to increase in temperature (figure 4(a)). The increase in temperature leads to reduced resistance offered by workpiece material on the tool pin. However, traverse speed shows a less significant effect on the variation of normal stress because of less variation in tool pin temperature with increase in traverse speed.
Figure 4 Distribution of (a) normal stress, (b) temperature, (c) hardness and (d) relative velocity on the tapered pin surface from the root to the tip for various process parameters during FSW of CuCrZr alloy
12
4.2.2 Temperature distribution Distribution of temperature is shown in figure 4(b) from pin root to pin tip for various process parameters. It shows that temperature at pin-workpiece interface decreases from pin root to pin tip. Tool pin temperature increases with increase in rotation speed due to more heat generation at higher rotation speed. However, temperature decreases slightly with increase in traverse speed due to less heat input per unit length at higher traverse speed. 4.2.3 Hardness distribution Temperature-dependent hardness at each node of mesh is calculated (Equation 12). Based on the computed temperature, the variation of hardness from pin root to pin tip is shown in figure 4(c) for various parameters. It shows that hardness value increases from pin root to pin tip. Minimum hardness is observed at pin root, as corresponding temperature is more at pin root compared to the pin tip. However, maximum hardness at pin tip is due to less temperature. Tool pin hardness decreases with increase in rotation speed, as pin temperature increases with increase in rotation speed. However, hardness increases slightly with increase in traverse speed. 4.2.4 Relative velocity variation The magnitude of relative velocity at the tool-workpiece interface depends on tool tangential velocity, traverse speed and fraction of slip [30,45]. Figure 4(d) shows distribution of relative velocity from pin root to pin tip for various process parameters. The relative velocity at pin–workpiece interface decreases from pin root to pin tip for all process parameters. For rotation speed and welding speed being constant, relative velocity depends only on tool geometry. Maximum relative velocity is occurred at pin root due to highest radial distance at root and minimum at pin tip due to smallest radial distance. Relative velocity increases with increase in rotation speed at every location on the pin. However, it changes very little as a function of traverse speed (figure 4(d)). 4.3 Variation of various variables on bottom surface of tool pin Tool wear also occurs at pin bottom surface as a result of severe stresses acting on the bottom surface and leads to reduction in pin length. Tool wear is computed at each node of the mesh according to equation 13. Equation 10 is used to calculate distribution of normal stress at bottom surface is computed. Figure 5(a) shows the distribution of normal stress (contour plot) on the pin bottom surface for 800 rpm rotation speed and 30 mm/min traverse speed. It depicts, normal stress on the tool pin bottom surface increases with increase in radial 13
distance. This can be attributed to increase in shear stresses on the pin bottom surface. Normal stress increases from center to circumference and is maximum at the circumference of the pin bottom surface.
Figure 5 Distribution of (a) normal stress, (b) relative velocity, (c) temperature and (d) hardness on the pin bottom surface at 800 rpm rotation speed and 30 mm/min traverse speed during FSW of CuCrZr alloy. The relative velocity at the between pin-bottom workpiece interface increases with increase in radial distance and is maximum at pin circumference (figure 5(b)). The relative velocity between pin bottom surface and workpiece is governed by Equation 11. The distribution of temperature at pin bottom surface is shown in figure 5(c). It shows that temperature increases with increase in radial distance due to high heat generation at circumference. High heat is generated by high relative velocity between tool and workpiece material at circumference as compared to the pin center. The distribution of temperature affects variation of hardness on the tool pin bottom surface as shown in (Equation 12). Figure 5(d) shows the distribution of hardness on the pin bottom surface. Hardness is less at the circumference as compared to the pin center due to high temperature at pin bottom circumference. 14
4.4 Tool degradation- Wear/deformation The tool can degrade by either deformation or by wear. To examine the difference, we can compare shear stresses acting on the pin and shear strength of tool pin. Figure 6 shows the comparison of shear stress acting on tool pin and shear strength of H13 steel from pin root to pin tip during FSW of CuCrZr alloy. The maximum shear stress acting on the tool pin is computed by calculating the forces and torque on the tool pin. The shear strength of H13 tool material is calculated a function of by computed tool pin temperature [46]. It shows maximum shear stress acting on the tool pin profile increases from pin root to pin tip. The maximum shear stress at pin root is significantly less than the shear strength of tool material. Therefore, chance of deformation is very less near to pin root. However, near to the pin tip, shear stress is significantly more than shear strength of tool material. Hence, deformation may take place near to the tip. Based on this analysis, we can say that for most of the pin surface, deformation will not contribute to pin degradation. Only the pin bottom surface will be affected by deformation. However, wear is taking place at both the surfaces, vertical and bottom.
Figure 6 Comparison of shear stress acting on the tool pin with shear strength of H13 tool material from pin root to pin tip 4.5 Prediction of tool pin profile As we have found that only wear is responsible for pin vertical and bottom surface degradation, the modified Archard’s wear model is applied. The effect of wear on both 15
tapered vertical and bottom surface is computed. Figure 7(a) shows variation of computed wear depth as a function of distance from shoulder on pin tapered surface after traverse distance of 300 mm at 800 rpm rotation speed and 30 mm/min traverse speed. It shows that computed wear depth increases with increase in distance from the shoulder along pin length. The incremental rate is less near the pin root. However, wear depth increases with a higher rate near the pin tip due to higher stresses near pin tip as compared to pin root. Near the pin tip, higher stresses are due to small cross-sectional area as compared to pin root. Normal stress affects the wear depth more as compared to relative velocity near the pin tip.
Figure 7(a) Variation of computed wear depth from pin root to pin tip. (b) Distribution of wear depth at pin bottom surface for 300 mm traverse distance at 800 rpm rotation speed and 30 mm/min traverse speed. Variation of wear depth at the pin bottom surface shows wear depth increases from the center of pin bottom, radially out; and is maximum at the circumference (figure 7(b)). At the pin bottom surface, both normal stress and relative velocity are higher and hardness is minimum at the circumference as compared to center, which leads to higher wear depth at the circumference as compared to pin center. Subsequently, the computed worn-out pin profile is generated using computed wear depths at various points on the pin surface. Wear depth for tapered and bottom surfaces is combined near the pin tip to generate the complete computed worn-out pin profile for various process parameters.
16
Figure 8(a) Numerically computed pin profile and (b) Comparison of computed and measured pin profile of H13 steel tool during FSW of CuCrZr alloy profile at rotation speed of 800 rpm, traverse speed of 30 mm/min and for traverse distance of 300 mm Figure 8(a) shows computed pin profile (red color profile) for traverse distance of 300 mm at 800 rpm rotation speed and 30 mm/min traverse speed during FSW of CuCrZr alloy. Wear increases from pin root to pin tip, and maximum wear occur near the pin tip. The amount of wear on tool pin depends on the distribution of normal stress, relative velocity and hardness for constant process parameters. The distribution of normal stress increases from pin root to pin tip and attains maximum value near the pin tip (figure 4(a)). However, relative velocity is greater at the pin root and decreases from pin root to pin tip as shown in figure 4(d). Hardness of tool pin also increases from pin root to pin tip and reaches maximum value at pin tip. The variation of relative velocity and hardness produces less wear near the pin tip. However, variation of normal stress produces more wear near the pin tip. The effect of normal stress dominates over the effect of relative velocity and hardness to produce more wear near the pin tip as compared to the pin root. Figure 8(b) shows the comparison of computed pin profile with the actual worn-out pin profile. For better comparison, computed and actual worn-out profiles are superimposed on each other. Computed pin profile is in good agreement with the worn tool pin geometry. The computed pin profile exposes some mismatch with the actual pin profile at certain locations because of localized deformation or dynamic behavior due to severe stresses at high temperature during FSW of CuCrZr alloy. The wear model has been validated for various process parameters to improve its reliability. 17
4.6 Validation of numerical model for tool wear The comparison of computed and actual worn-out pin profiles is shown in figure 9 for various process parameters. The parameters are included in each tool image in a sequence of rotation speed (rpm), traverse speed (mm/min), and traverse distance (mm). Numerically computed pin profiles depict reasonably good agreement with the worn-out tool pin profile for various parameters. The developed model is successfully able to predict the actual worn out tool pin profile. The worn out pin profile at bottom changes from flat tapered pin (unused tool) to curved cylindrical type shape (used tool) after wear for various traverse distances. The similar behavior is also computed through modeling of predicted tool pin profile. The gradual change in the shape of the tool pin from flat tapered to curved cylindrical pin is close to the self-optimized pin shape, which can be different at different process parameters. The predicted pin profile shows better agreement at the tapered surface closer to the pin root as compared to pin tip. The experimental profile shows more wear as compared to the computed pin profile near the pin tip. As shown earlier, the shear stress at the pin bottom is more than the shear strength of the tool. The tool degradation happens due to both wear and deformation. Thus, computed pin profile due to wear predicts less degradation at the tip.
18
Figure 9 Comparison of computed and measured tool pin profiles for H13 steel tool during FSW of CuCrZr alloy at different traverse distances for various process parameters. 4.7 Validation of developed model by independent experiments The validated wear model is used to predict the tool pin profile for other random parameters that were not experimentally performed earlier and not used for regression analysis. Figure 10(a1-a3) show the effect of rotation speed and traverse speed for 140 mm traverse distance on predicted pin profile. Independent experiments are performed to compare the predicted pin profile with the actual pin profile for these new parameters. Figure 10(b1-b3) shows the comparison of predicted pin profile with the actual pin profile for various process parameters. It shows there is a reasonably good comparison between measured and predicted pin profile for new parameters. This comparison also improves the reliability of the wear model to 19
predict tool pin profile during FSW of CuCrZr alloy. The predicted profiles show some mismatch due to localized deformation at high temperature.
Figure 10(a1-a3) predicted pin profile for various process parameters and (b1-b3) comparison of these predicted pin profiles with actual pin profiles for various process parameters. 4.8 Effect of process parameters on predicted pin profile The developed tool wear model can be used to better understand the effect of process parameters on variation in tool pin profile. We have analyzed effect of traverse distance, rotation speed and traverse speed on the predicted tool pin profile. 4.8.1 Effect of traverse distances The effect of traverse distance on change in predicted tool pin profile for various traverse distances is shown in figure 11(a) during FSW of CuCrZr alloy. Overall size of the tool pin reduces with increase in traverse distance due to continuous wear. The wear depth increases with increase in traverse distance at each location due to continuous stresses on tool pin. Figure 11(b) shows wear depth as function of traverse distance at 0.1 mm, 1.1 mm, 2.1 mm and 3.1 mm from shoulder on the pin tapered surface. The rate of increment in wear depth is more near to pin tip (at 3.1 mm) as compared to pin root (at 0.1mm) i.e. slop for 3.1 mm is more than 0.1 mm. This mainly occurs due to more stresses on pin tip as compared to pin root (figure 4(a)). The developed model also has capability to compute the progressive wear rate for various traverse distance intervals. The reduction in pin size is more during initial traverse (figure 11(a)) due to severe wear. However, for longer traverse distance, reduction in pin size becomes less due to decrease in wear rate. Figure 11(c) shows wear rate as a function of traverse distance intervals at various locations on pin surface. It shows that progressive wear rate decreases with increase in the traverse distance intervals for all locations. However, wear 20
rate does not change much after long traverse distance (around 1000 mm) as tool pin approaches self-optimized pin shape and wear rate reduces. The developed model shows capability to predict self-optimized phenomena as observed by many researchers during FSW process.
Figure 11(a) Variation in predicted tool pin for various traverse distances of 200 mm, 600 mm, 1000 mm and 1400 mm at 800 rpm and 30 mm/min, (b) wear depth as a function of traverse distance and (c) progressive wear rate as a function of traverse distance intervals at various locations on the tool pin.
4.8.2 Effect of rotation speed The effect of rotation speed on predicted pin profile as shown in figure 12(a) confirms that wear increases with increase in rotation speed. Tool pin wear depends on stresses, hardness and the relative velocity at tool pin workpiece interface, as mentioned in Equation 13. With increase in rotation speed, stresses on the pin and pin hardness decreases as temperature around the pin increases (figure 4(a) and (c)). However, the relative velocity at the interface 21
increases with increase in rotation speed (figure 4(d)). The wear model suggests, wear should increase due to decrease in hardness and increase in relative velocity. Whereas, it should decrease due to reduction in stress. The computed pin profile shows wear increases (reduction in pin size) with increase in rotation speed as effect of relative velocity and hardness dominates over effect of stresses (figure 12(a)). The difference in tool wear due to rotational speed is not significant near the pin root, as the actual amount of wear is also low. However, the difference becomes clearly visible near the pin tip where wear is high; and significant change in the size of pin is seen due to increased tool rotation speed. The predicted pin size also reduces from the bottom and reflects the reduction in pin length with rotation speed. For 300 mm traverse distance, tool pin shape changes from completely flat bottom (unused) to curved bottom (used). Figure 12(b) shows effect of rotation speed on wear depth at 0.1 mm, 1.1 mm, 2.1 mm and 3.1 mm from shoulder on the pin tapered surface. Wear depth increases with increase in rotation speed for all locations on the pin due to increase in relative velocity between tool and workpiece.
Figure 12 (a) Predicted tool pin profiles for rotation speeds 600 rpm, 800 rpm, 1000 rpm and 1200 rpm with a constant traverse speed and distance of 30 mm/min and 300 mm, respectively (b) wear depth as a function of rotation speed at various locations on the tool pin.
22
4.8.3 Effect of traverse speed The effect of traverse speed on computed pin profile is shown in figure 13(a) for 1000 rpm and 300 mm traverse distance. Tool pin wear decreases with increase in traverse speed for all traverse distances. During FSW, stresses on the tool pin and pin hardness of tool pin slightly increases with increase in traverse speed due to slight reduction in temperature (figure 4(a) and (c)). However, traverse speed does not show significant variation on relative velocity (figure 4(d)). Hence, developed wear model suggests, wear does not affect much with slight variation in stresses, hardness and relative velocity. However, interaction time with tool pin and workpiece were affected significantly. Interaction time decreases with increase in traverse speed and results in less pin wear. The size of predicted pin reduced from the bottom reflects the reduction in pin length with traverse speed. For 300 mm traverse distance, tool pin shape changes from completely flat pin bottom to curved pin bottom.
Figure 13(a) Variation in size of computed tool pin for traverse speeds 10 mm/min, 30 mm/min, 50 mm/min, 700 mm/min and 90 mm/min with a constant rotation speed of 1000 rpm and traverse distance of 300 mm and (b) wear depth as a function of traverse speed at various locations on the tool pin.
23
Figure 13(b) shows wear depth as a function of traverse speed on tool pin at various locations. It shows that wear depth decreases with increase in traverse speed at 0.1 mm, 1.1 mm, 2.1 mm and 3.1 mm distance from shoulder on pin surface. The difference in wear depth becomes insignificant for high traverse speed (90 mm/min). Wear depth shows more difference at 0.1mm (near to pin root) to 3.1 mm (near to pin tip) for low traverse speed (10 mm/min) as compared to high traverse speed (90 mm/min). The difference is more for low traverse speed due to more interaction time in stress condition for 300 mm traverse distance. 5. Conclusions A three-dimensional heat transfer and visco-plastic material flow based model is developed to predict tool wear and pin profile using modified Archard’s wear model. Following are the major highlights of this research. 1. Numerical model is validated for thermal cycles and pin profile for various process parameters to show model reliability. The predicted pin profiles are also validated by performing independent experiments. The developed model can be used to successfully predict the worn out pin profile. 2. From the validated numerical model, it can be shown that amount of wear is more near the pin tip compared to pin root due to higher order of stresses at the pin tip. At the pin bottom, the stresses are more at the periphery compared to the center leading to more wear at the edges of pin bottom. This wear behavior results in curved pin bottom, as compared to the initial flat bottom pin. 3. The predicted pin profiles show that wear increases with increase in rotation speed due to increase in relative velocity between tool and workpiece material. However, predicted wear decreases with increase in traverse speed due to less interaction time. The effect of rotation speed and traverse speed are significant near the pin tip as compared to the pin root due to higher stresses at the pin tip. 4. The wear model also shows that pin size decreases with increase in traverse distance due to continuous wear. The progressive wear rate is more in the beginning and becomes less for long traverse as tool approaches self-optimized shape. Developed wear model also predicts the self-optimized phenomena during FSW process. The developed model promotes understanding of tool wear during FSW process and further explains the effect of various process parameters. 24
Acknowledgement The authors would like to thank Dr. G. K Dey, Materials Science Division and Mr. Kaushal Jha, Engineering Design & Development Division, Bhabha Atomic Research Centre (BARC), Mumbai, India. Authors would also like to acknowledge the Board for Research in Nuclear Sciences (BRNS), (project number 36(2)/20/02/2014-BRNS/). They also would like to thank staff at BARC for helping in performing experiments.
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Highlights
A numerical model is developed for prediction of tool wear and worn out pin profile.
Wear is more near the pin tip compared to pin root due to higher order of stresses.
Predicted profiles show more wear for higher RPM due to increase in relative velocity.
The developed wear model also predicts the self-optimized phenomena.
28