The document discusses modeling friction stir welding and processing using smoothed particle hydrodynamics (SPH). SPH is a Lagrangian meshfree method that can simulate the large plastic deformation and material mixing of friction stir processes. Prior research has used SPH to study temperature distribution, grain size evolution, microhardness, and texture development during welding. The document outlines the governing equations of SPH and highlights several studies that have modeled friction stir welding and processing using this approach.

1. The Meshfree Simulation of Friction Stir
Welding/Processing
Abhishek Kumar Singh

2. 2
I. Introduction
Background
 Although the advantages such as low density and high st
J. Singh et al., J. Alloys Compd. 778 (2019) 124-133.
J. Singh et al., J. Alloys Compd. 708 (2017) 694-705.
* W. He et al., MSEA (2016)
* J.C.Baird et al., Scripta (2012)

3. 3
As the tool rotates and traverses, severely plasticized material migrates from ret
reating, to advancing side, and deposits in the wake of the tool.
nge phase,
ell or stabilization phase,
ding or advancing phase,
l removal or retraction phase.
I. Friction Stir Processing
Introduction
Ansari et al., Modelling Simul. Mater. Sci. Eng (2019)

4. 4
The physical principle of FSW has also been used to improve the microstructure of
the workpieces. In this technique, called friction stir processing (FSP), an FSW tool
is used to modify the microstructure of the material. The principal improvements ma
de by FSP are as follows:
• Creation of very fine microstructures to obtain super plasticity (nanograins can be
produced);
• Homogenization of the microstructure to reduce segregation, eliminate porosity, a
nd increase mechanical properties, ductility, and corrosion resistance;
• Introduction of particles to develop composite surface (metal matrix composite (M
MC)) and modify the elasticity, wear resistance, thermal and electrical conductivity,
or internal damping of the material.
The local modifications performed by FSP to the microstructure can be very benefic
ial in a zone of high stress, where a good ductility is needed, or where the fatigue lif
e should be increased.

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large plastic deformation and material mixing common to FSW are well captured by
the mesh-free method.
I. SPH Capabilities
This simulation approach allows the determination of temperature evolution, elastic
and plastic deformation, defect formation, residual stresses, and material flow all wi
thin the same model.

6. 6
Buffa et al. [3–5] used FEM to develop a hybrid model ca
pable of determining the residual
stresses in the resulting weld. They split the FSW proces
s simulation into two phases. In the
first phase, they model the plunge, dwell, and advance u
sing a rigid viscoplastic model (fluidbased)
that does not provide elastic stresses. Then, they switch
to an elastic-plastic model to
approximately calculate the resulting residual stresses d
uring weld cooldown. They are able
to obtain good correlation for the residual stresses. On th
e downside, their model does not
allow for tracking defects since the welding phase is bas
ed on a fluid model

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I. Incompressible Navier-Stokes equation

8. 8

9. 9
Vi= velocity of the particle
g- gravity
𝛻𝑷 − 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝒈𝒓𝒂𝒅𝒊𝒆𝒏𝒕
Smooth particle hydrodynamics is how to solve
incompressible N-S equation for single particle
Convective acceleration term

10. 10

11. 11
SPH uses an evolving interpolation scheme to approximate a field variable at any p
oint in a domain. The value of a variable at a particle of interest n be approximated
by summing the contributions from a set of neighboring particles, denoted by subsc
ript j, for which the “kernel” function, W, is not zero
The smoothing length, h, determines how many part
icles influence the interpolation for a particular point
W- Kernel (Smoothing) function,
In SPH, the material is discretized with separate sets of points or particle
s and a continuous field f(xi) is approximated at the discretization points

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The implementation is based on the classical smoothed particle hydrodynamic the
ory as outlined in the references
below. You also have the option of using a mean flow correction configuration upd
ate, commonly referred to in
the literature as the XSPH method (see Monaghan, 1992), as well as the correcte
d kernel of Randles and Libersky,
1997, also referred to as the normalized SPH (NSPH) method.
The characteristic length is half the length of the cube side.

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For these methods you do not define nodes and elements as you would nor
mally define in a finite element analysis; instead, only a collection of points a
re necessary to represent a given body. In smoothed particle hydrodynamics
these nodes are commonly referred to as particles or pseudo-particles.
Smoothed particle hydrodynamics is a fully Lagrangian modeling scheme permitting the
scretization of a prescribed set of continuum equations by interpolating the properties di
ctly at a discrete set of points distributed over the solution domain without the need to d
ne a spatial mesh

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Mixing flow during FSW
Pan et al. / International
Journal of Plasticity (2013)

15. 15
Literature
W. Pan et al. / International
Journal of Plasticity 48 (2013)
 The retreating side (RS) shows finer grain size than
the advancing side (AS)
 high-translational and low-rotational tool speeds
are ideal to cause effective grain refinement and
higher hardness of the material
Pan et al. studied the friction stir welding (FSW) using smoothed particle
hydrodynamics (SPH) model and studied the temperature history and
distribution, grain size, microhardness as well as the texture evolution
Mixing flow during FSW

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• Pan et al. (2013) considered each SPH particle to represent a polycrystalline re
presentative volume element (RVE), and we assume a weak coupling between
the SPH simulations and crystal plasticity modeling.
• Particle velocities obtained from the SPH solution at each time step are used t
o calculate the plastic velocity gradient for the polycrystalline deformation beh
avior. Texture evolution is then computed using crystal plasticity modeling
Conti..
TMAZ particle pole Fig.
W. Pan et al. / International
Journal of Plasticity 48 (2013)
Simulation of texture evolution

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Literature
 Ansari et al. (2019) studied the plunging phase friction stir welding of Al 6082 all
oy using SPH modeling with different rotational speed and plunging phase and s
tudied the stress and strain distribution near tool pin
 The force and tarque from simulation were compared with experimental and the
results were in close agreement.
 They studied the effect of tool rotational speed on the force field, stress, and eq
uivalent plastic strain at different tool depth in the plunging stage.
 Increasing the plunge depth, the stress, strain, and force field is increased.
 Furthermore, increasing rotational speed from 600 to 1200 rpm, stress, and equi
valent plastic strain increased by about 3% and 19%, respectively, while the force
decreased by 22%.

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Xiao et al. (2016) studied the heat transfer during friction stir welding using a
modified SPH model
heat source model based on sticking friction is implemented to describe the heat
generation of FSW

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Coupled Eulerian Lagrangian Method

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Simulation of FSP
Tool
Backing Plate
Locking Strips
A, B, n, C and m are the five material constants
JC
Parameter
A (MPa) B (MPa) C n m
324 114 0.002 0.42 1.34
Shear Modulus
(GPa)
Density (Kg/m3)
(Al-6061T6)
Cut-off Pressure
(MPa)
27.6 2700 1200
Johnson-Cook material model
Constitutive Equation Al Plate
Gruneisen EOS Units
0 2700 Kg/m3
C 5328 m/s
0 1.97 -
S1 1.4 -
a 0.48 -
Al-6061T6 Thermal Parameters
Cv k
Values 875 175
Units J/KgK W/mK

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Distribution of state variables
Plunging stage

23. 23
Conti..
After process completion

24. 24
3
4
5
RS AS RS AS
RS AS
RS AS
RS AS
1 2
Mixing of particles and Nodal Tracking

25. 25
Advancing/Welding Phase
Plunge phase Dwell phase
Tool Force

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Conclusions
• hello

27. Scope of novelty
 Limited research is available on modeling FSW of Ti alloy
 Very limited (4-5) study is available on SPH modeling of FSP and nil on
Ti alloy
 Modification of more stable Kernal function (for SPH modeling )using su
broutine
 The combined study of SPH and VPSC simulation to study texture predi
ction

28. 28
Future Work
• SPH model benchmarking
• Selection and Implementation of a proper smoothing (Kernal) fu-
nction
• SHP simulation and analysis for FSP of CP Ti
• Texture analysis (ODF) of FSP CP Ti material
• Texture Simulation using VPSC
• Manuscript writing