Shear localisation modelling of friction stir weld formation process X. J. Pei 1 and P. S. Dong* 2 This paper presents a shear localisation model for studying friction stir welding (FSW) formation process. With this model, shear band (SB) width, SB formation time, and SB propagation speed can be theoretically estimated. The SB propagation speed in this context serves as a theoretical estimate of the maximum welding speed possible for a given material and prescribed welding conditions, such as stir pin rotation speed and torque level. The model is shown to provide reasonable estimates of shear localisation parameters against a set of recent experimental data on FSW of titanium alloy Ti–6Al–4V. With this model, titanium alloy Ti–6Al–4V, high strength low- alloy steel 4340, and aluminium alloy 2024 are compared in terms of shear localisation parameters, such as maximum SB propagation speeds (or welding speeds). Keywords: Friction stir welding, Deformation localisation, Banded structure, Rotational speed, Translational speed List of symbols Dimensional parameters A yield strength, Pa B strain hardening strength, Pa C strain rate hardening coefficient c specific heat, J kg 21 K 21  f ~T=(2pR 2 h) frictional stress, Pa h height of the pin, m H length of physical domain modelled, m H c characteristic length in thermal diffu- sion, m k thermal conductivity m strain hardening exponent n temperature softening exponent q heat flux at workpiece/pin interface R radius of the pin, m  t time, s t c time per revolution, s T torque, Nm v velocity, m s 21 V pin pin surface velocity, m s 21 V W workpiece surface material velocity, m s 21 y physical coordinate in y,m  a~  k= r c thermal diffusivity, m 2 s 21 c shear strain c e elastic shear strain c p plastic shear strain _ c 0 ~V pin =H nominal strain rate, 1 s 21 h temperature, K h 0 ~ A=( r c) material reference temperature, K h r room temperature, K h m melting temperature, K  m shear modulus, Pa r density, kg m 23 t shear stress, Pa v angular velocity of pin, rev min 21 Non-dimensional parameters A  A=  A B  B=  A q  q=( _ c 0 H  A) t t _ c 0 y y=H h  h=h 0 l k=( r  c _ c 0 H 2 ) m  m=  A v v=V pin r rH 2 _ c 2 0 =  A Introduction Friction stir welding (FSW) is a relatively new solid state joining process, as first reported by Dawes and Thomas, 1 and has many advantages over traditional welding and joining processes as recently reviewed by Nandan et al. 2 It can be used either to join advanced high strength materials deemed not weldable or modify material surface conditions for improved fracture and fatigue resistance of a structure that may be subjected to a hostile service environment, such as space vehicle launch and operation, as discussed by Nandan et al. 2 and Nunes. 3 Recognising the needs for an improved understanding of weld formation process associated with FSW, there have been numerous investigations into various aspects of FSW process over the last decade, which resulted in many important findings as recently discussed elsewhere. 2 One significant finding that is of a particular interest to the authors of this paper is that plastic flow phenomena in form of shear banding seem 1 Ph.D. student, Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI, USA 2 Department of Naval Architecture and Marine Engineering, University of Michigan, Ann Arbor, MI, USA *Corresponding author, email dongp@umich.edu ß 2014 Institute of Materials, Minerals and Mining Published by Maney on behalf of the Institute Received 9 January 2014; accepted 11 March 2014 DOI 10.1179/1362171814Y.0000000207 Science and Technology of Welding and Joining 2014 VOL 19 NO 5 416