1. Finite Element Simulation Of Profile Rolling Of Wire Author: R. Iankov Presenter: Patrick Lewis Date: September 15, 2008

2. Introduction Investigate profile rolling of wire using 2 finite element model approaches.Investigate profile rolling of wire using 2 finite element model approaches. –3D –2D Compare model results to experimental data.Compare model results to experimental data. Determine applicability to Profile Rolling IndustryDetermine applicability to Profile Rolling Industry

3. Introduction - Cont. ReferencesReferences –W. Daves, F.D. Fischer, Drawing of a curved wire, in: Shen, Dawson (Eds.), Simulation of Materials Processing: Theory, Methods and Applications, NUMIFORM’95, A.A. Balkema, 1995, pp. 693–698. –W. Boris, A. Mihelic, Optimal design of the die shape using nonlinear finite element analysis, in: Shen, Dawson (Eds.), Simulation of Materials Processing: Theory, Methods and Applications, NUMIFORM’95, A.A. Balkema, 1995, pp. 625–630. –A. Skolyszewski, J. Luksza and M. Pasko, Some problems of multi-stage fine wire drawing of high-alloy steels and special alloys. J. Mater. Process. Technol. 60 (1996), pp. 155–160. –T.H. Kim, B.M. Kim and J.C. Choi, Prediction of die wear in the wire-drawing process. J. Mater. Process. Technol. 65 (1997), pp. 11–17. –MSC.MARC2000, User Manual 2000, MSC.Software Corporation. –Jan WINTERS Experimentele studie en alasto-plastische eindige-elementen-simulatie van de materiaalvloei bij het platwalzen van staaldraad, Kuleuven, 1989–1990 –M.A. Grisfield, Non-linear Finite Element Analysis of Solids and Structures, vols. 1 and 2, Wiley, New York.

4. Models & Design Principles Rolling is a metal forming process where the work piece is placed between opposing rollers. Rolling is a metal forming process where the work piece is placed between opposing rollers. Advantages over drawing: Advantages over drawing: Little motion between rollers Little motion between rollers High production speeds High production speeds No coating needed to improve application of lubricant No coating needed to improve application of lubricant Improved measurement and control of the final product Improved measurement and control of the final product No traction forces – no risk of a wire break No traction forces – no risk of a wire break No slippage between drawing disks = no surface damage No slippage between drawing disks = no surface damage

5. Models & Design Principles Cont. Advantages of the Cold Rolling Process Advantages of the Cold Rolling Process Higher productivity due to continuous rolling process Higher productivity due to continuous rolling process Tighter tolerances are attainable Tighter tolerances are attainable Immediate detection of shape defects. Immediate detection of shape defects. Driven rolling machines automatically pull the material Driven rolling machines automatically pull the material Finished wires can either be spooled or cut to length with flying shears Finished wires can either be spooled or cut to length with flying shears Purposeful hardening of materials that can’t be achieved through other processes. Purposeful hardening of materials that can’t be achieved through other processes.

6. Models & Design Principles Cont. Finite Element Model Finite Element Model Used to predict the force parameters, as well as to control and optimize many other parameters. Used to predict the force parameters, as well as to control and optimize many other parameters. Advantages of the Finite Element approach: Advantages of the Finite Element approach: Elimination of physical modeling, as well as material and energy costs of physical prototypes. Elimination of physical modeling, as well as material and energy costs of physical prototypes. Optimization of the technological parameter of the forming process. Optimization of the technological parameter of the forming process. “Choice of suitable material and predict the stress and strain fields during the process, residual stresses in a final product, damage evolution, strain localization, spreingback effect and so on.” “Choice of suitable material and predict the stress and strain fields during the process, residual stresses in a final product, damage evolution, strain localization, spreingback effect and so on.”

7. Models & Design Principles Cont. Model Assumptions: Model Assumptions: Wire material is a continuum Wire material is a continuum Material is isotropic Material is isotropic Anisotropic effect due to high plastic deformation is ignored Anisotropic effect due to high plastic deformation is ignored Quasi-static loading condition Quasi-static loading condition Inertial effects are ignored Inertial effects are ignored Material is elastic-plastic with hardening Material is elastic-plastic with hardening

8. Models & Design Principles Cont. The Mathematics The Mathematics Cauchy stress tensor (σ), Domain (Ω) Cauchy stress tensor (σ), Domain (Ω) ∇ σ = 0,σ = σ c ∇ σ = 0,σ = σ c Deformation gradient tensor (F) Deformation gradient tensor (F) F = ( ∇ 0 x) c F = ( ∇ 0 x) c Velocity gradient tensor (L) Velocity gradient tensor (L) L = ( ∇ 0 v) c = F’ * F -1 L = ( ∇ 0 v) c = F’ * F -1 Deformation rate tensor (D), Spin tensor(Ω) Deformation rate tensor (D), Spin tensor(Ω) L = D + Ω, D =.5(L + L c ), Ω =.5(L – L c ) L = D + Ω, D =.5(L + L c ), Ω =.5(L – L c ) Cauchy Green strain Tensor (B) Cauchy Green strain Tensor (B) B = F * F c B = F * F c Thermal heat transfer equation Thermal heat transfer equation ρc p T’ - λ ∇ 2 T = Q f σ : D p + q f ρc p T’ - λ ∇ 2 T = Q f σ : D p + q f Elastic (D e ) and Plastic (D p ) deformation rate tensor Elastic (D e ) and Plastic (D p ) deformation rate tensor D = D e + D p D = D e + D p σ J = C 4 : (D – D p) σ J = C 4 : (D – D p) Von Mises yield function (f), von Mises stress (σ), Yield stress (σ y ) Von Mises yield function (f), von Mises stress (σ), Yield stress (σ y ) f = σ 2 – σ y 2 f = σ 2 – σ y 2 Flow Rule, plastic strain rate (έ p ) Flow Rule, plastic strain rate (έ p ) D p = 3έ p σ / (2 σ y ) D p = 3έ p σ / (2 σ y ) Friction Force (F t ), Coulomb friction coefficient (μ), Normal reaction force (F n ), Relative Sliding Velocity (v r ), Tangent unit vector (t) Friction Force (F t ), Coulomb friction coefficient (μ), Normal reaction force (F n ), Relative Sliding Velocity (v r ), Tangent unit vector (t) F t = -μF n (2/π)arctan(v r /C)t F t = -μF n (2/π)arctan(v r /C)t t = v r / |v r |, C = constant t = v r / |v r |, C = constant Heat flux generated due to friction (q f ) Heat flux generated due to friction (q f ) q f = F t v r q f = F t v r

9. Models & Design Principles Cont. Numerical Simulation Numerical Simulation 3D Model 3D Model Quarter of wire and two rolls are modeled by eight nodes isotropic finite element. Quarter of wire and two rolls are modeled by eight nodes isotropic finite element. Rolls are assumed to be rigid bodies with prescribed rotating speed. Rolls are assumed to be rigid bodies with prescribed rotating speed. Each roll reduces the height/radius by 20%. Each roll reduces the height/radius by 20%. Wire length is 10x the radius. Wire length is 10x the radius. Simulation performed one roll at a time. Simulation performed one roll at a time. 2D Model 2D Model Generalized Plain Strain (GPS) approach using 4 node finite element analysis. Generalized Plain Strain (GPS) approach using 4 node finite element analysis. Deformation zone lies between two bounding plates (move as rigid bodies). Deformation zone lies between two bounding plates (move as rigid bodies). Element is allowed to grow in the z-direction. Element is allowed to grow in the z-direction. Simulation done with profile rolling of wire. Simulation done with profile rolling of wire. Material is elastic plastic with nonlinear hardening. Material is elastic plastic with nonlinear hardening. Each roll reduces the cross-sectional area by 12-15%. Each roll reduces the cross-sectional area by 12-15%.

10. Models & Design Principles Cont.

11. Results

12. Results Cont. 3D Model  Technique allows investigation of the influence of roll diameter, rotating speed, and tension force on final lateral spread of wire.  Lateral spread of the cross- section can be predicted.  Residual stress, equivalent strain, strain rate and equivalent stress distribution are obtained.  Fracture criteria can be incorporated during the rolling process. 2D Model  Equivalent plastic strain, total strain and stress can be obtained.  Spread of material as a function of the roll shape can be controlled

13. Conclusions 3D Model Application to a multi-pass profile leads to very long computational time. High accuracy is attainable 2D Model Shorter computing time and less computer memory are required. Useful when several passes are required May reduce the number of industrial trials.

14. Conclusions Cont. No technical advancement is created. Study simply verifies that the 2D FE approach is less time intensive then the 3D FE approach. Study does not investigate other programs, but does show that it is possible to predict the behavior/outcome when dealing with complicated profiles.