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Determining the mechanism of defect formation and material flow characteristics in underwater stationary shoulder friction stir welding using coupled Eulerian-Lagrangian simulation

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Abstract

The coupled Eulerian-Lagrangian (CEL) method was used to simulate underwater friction stir welding with rotational shoulder (RFSW) and stationary shoulder (SSFSW) tools. New equations for time-dependent pressure distribution and heat transfer coefficients and temperature-dependent friction coefficient were used. In simulation results, the SZ width had the maximum error of 2.5 % compared to experimental measurement. Material flow during SSFSW was divided into two categories: horizontal flow (HF) and backflow (BF). The result of collision of material flows was the formation of an upward material flow that was concentrated in the middle of the thickness. Consequently, an elliptical stir zone was produced in SSFSW. However, the intense material flow of the shoulder in RFSW produced a downward flow orientation. The maximum welding forces along the x, y, and z axes for the SSFSW are about 44, 25, and 31% higher than the RFSW, respectively. The increase in welding forces in SSFSW increased the material flow velocity around the pin and caused a higher intensity in BF and HF. The interfacial force applied to the surrounding material in the low temperature sample was decreased by 55% compared to the moderate temperature sample, and a cavity defect was formed.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Amirkabir University, Tehran, Iran

    Akbar Hosseini

  2. Department of Mechanical Engineering, Amirkabir University, Tehran, Iran

    Alireza Fallahi Arezoudar

Authors
  1. Akbar Hosseini
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  2. Alireza Fallahi Arezoudar
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Contributions

All authors contributed to the study conception and design. The first draft of the manuscript was written by Akbar Hosseini based on PHD thesis and under supervision of Dr Alireza Fallahi Arezoudar. All authors read and approved the final manuscript.

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Correspondence to Alireza Fallahi Arezoudar.

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Appendix. User subroutine VFRIC

Appendix. User subroutine VFRIC

figure afigure a

The variables used in the subroutine are introduced in this section for information [from the Abaqus 6.14 documentation: http://130.149.89.49:2080/v6.14/]:

 

Description

statev(nstateVar, nSlvNod)

This array contains the user-defined solution-dependent state variables for all the nodes on the slave surface

kStep

Step number

kInc

Increment number

nContact

Number of contacting slave nodes

nFacNod

Number of nodes on each master surface facet

dtimCur

Current increment in time

timGlb

Value of total time

timStep

Value of step time

jConMstid(nFacNod, nContact)

This array lists the surface node numbers of the master surface nodes that make up the facet with which each contact point is in contact

nMstNod

Number of master surface nodes

jMstUid(nMstNod)

This array lists the user-defined global node numbers of the nodes on the master surface

jSlvUid(nSlvNod)

This array lists the user-defined global node numbers of the nodes on the slave surface

numDefTfv

Equal to nContact if the master surface is made up of facets

nPred

Number of predefined field variables

jConSlvid(nContact)

This array lists the surface node numbers of the slave surface nodes that are in contact

nTemp

1 if the temperature is defined and 0 if the temperature is not defined

nSlvNod

Number of slave nodes

nProps

User-specified number of property values associated with this friction model

nStateVar

Number of user-defined state variables

nDir

Number of coordinate directions at the contact points

nFricDir

Number of tangent directions at the contact points

surfInt

User-specified surface interaction name, left justified

shape(nFacNod, nContact)

For each contact point this array contains the shape functions of the nodes of its master surface facet, evaluated at the location of the contact point

frictionWork

This variable contains the value of the total frictional dissipation in the entire model from the beginning of the analysis

fNormal(nContact)

This array contains the magnitude of the normal force for the contact points applied at the end of current time increment

fTangPrev(nDir, nContact)

This array contains the values of the frictional force components calculated in the previous increment but provided in the current local coordinate system [zero for nodes that were not in contact]

fStickForce(nContact)

This array contains the magnitude of frictional force required to enforce stick conditions at each contact point

dSlipFric(nDir, nContact)

This array contains the incremental frictional slip during the current time increment for each contact point in the current local coordinate system

lContType

Contact type flag

surfMst

Master surface name

surfSlv

Slave surface name

tempSlv(nContact)

Current temperature at the slave nodes

coordSlv(nDir, nSlvNod)

Array containing the nDir components of the current coordinates of the slave nodes

coordMst(nDir, nMstNod)

Array containing the nDir components of the current coordinates of the master nodes

dirCosSl(nDir, nContact)

Direction cosines of the incremental slip at the contact points

dircosN(nDir, nContact)

Direction cosines of the normals to the master surface at the contact points

props(nProps)

User-specified vector of property values to define the frictional behavior between the contacting surfaces

areaSlv(nSlvNod)

Area associated with the slave nodes

preDefSlv(nContact,nPred)

Current user-specified predefined field variables at the slave nodes

tempMst(numDefTfv)

Current temperature at the nearest points on the master surface

preDefMst(numDefTfv,nPred)

Current user-specified predefined field variables at the nearest points on the master surface

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Hosseini, A., Fallahi Arezoudar, A. Determining the mechanism of defect formation and material flow characteristics in underwater stationary shoulder friction stir welding using coupled Eulerian-Lagrangian simulation. Int J Adv Manuf Technol 127, 1755–1778 (2023). https://doi.org/10.1007/s00170-023-11513-y

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