Page in Car Body Development Process Simulation.
Page 2 Process pre-curing 2 C 2 min. Pressing Assembling final curing KTL oven 85 C 5 Min. Paint pre-treatment KTL-Coating ("Kathodische Tauchlackierung")
Page 3 Adhesive Curing (KTL Oven) Temperature Simulation. Relativ motions of the join partners...
Page 4 Process Damages. Problems with. typical fracture surface adhesive crack Abzeichnungen
Page 5 Process Simulation. Theory. Mechanical behaviour of adhesives during curing - as a function of a curing parameter (α =..) - as a function of temperature (T) Approach: viscoelastic behaviour, Theory by Adolf/Martin & Jendrny testing the curing for different heating rates (DSC) testing the thermomechanical behaviour (DMA)
Page 6 Theory - Testing Parameter Identification. Viscoelasticity. Final shear stiffness, at α = : Curing parameter, at gel point : Glass transition, at α = : Curve fitting parameters for T g (α) : G f α gel T g g, g 2 Quelle: Je. Quelle: Je. Quelle: Je. Quelle: Je. Curve fitting param. for shift function, at α = : c, c2, c3, c 4 Quelle: S.R. Prony data G i und τ i (measured at α =, T = T g ) G i, τ i Quelle: Je.
Page 7 Theory - Testing Parameter Identification. Curing. Betamate 48 Parallel kinetic: dα dt = k n 2 2 ( ) ( ) m T ( α) + k T α ( α n 2 ) A B B Totalseal 98 Serial kinetic: A B C D E
Page 8 Theory - Testing Parameter Identification. Thermo Mechanical Behaviour. DMA: Modulus of storage/loss as functions of the temperature Master curve: Modulus of storage/loss as functions of the frequency Time dep. relaxation function: E(t,T) prony funct. Transformation: from frequency dependence to time dep.
Page 9 Theory - Testing Parameter Identification. Viscoelasticity. Relaxation Functions. Standard: τ(t) = γ G(t) = γ G + n j= G j exp t τ j η η n Fully cured adhesive, temperature dependent: τ(t) = γ G(t,T) = γ G + n G exp j j= s= t ds τj(t) Relaxation time: τj = η j / E Adhesinve for different temperatures & curing parameters n t τ() t = γ α = γ α + G(t,T, ) G ( ) Gj exp j= s= τ j ds ( T, α) A modified integration scheme enables the simulation of plastic deformations as a result from the curing process!
Page Theory - Testing Parameter Identification. Viscoelasticity. Evaluation of the Relaxation Times τ j. dα Reaction kinetic: = dt f ( α,t) 8 2 2 2 => Final shear stiffness modulus: G G ( α α ) ( α ) 3 = f gel gel => Glass transition temperature: T g g α g 2 α ( α) = ( T + 273.5) exp 273. 5 g => Shift function: a a T T ( T,T ) g c(t Tg ) = exp c2 + T Tg T T ( T,Tg ) = exp[c3 ln{ c 4(T Tg )}], T < Tg, g => Relaxation times: τ ( T, α) = τ a ( T, α) i i T
Page Theory - Testing Parameter Identification. Viscoelasticity. Shear Stiffness and Tg.,8 BETAMATE 48 4 Shear Gleichgewichts stiffness modulus Modul,6,4 Gleichgew. Shear stiffness Mod. Tg 6 2 Tg,2-2,2,4,6,8 Conversion Level a α gel -6
Page 2 Theory - Testing Parameter Identification. Viscoelasticity. Relaxation Function for Betamate 48. Elastic Module [MPa α=, T=95 C (Master) α=, T=23 C α=.8, T=23 C.E+.E+3.E+5.E+7.E+9.E+.E+3 t [sec]
Page 3 Simulation D Material Behaviour. System, Boundary Conditions. adhesive γ 3, σ 3 D C applied motion 3 2 relative displacement 2 8 temperature (applied) : Temperatur 2.8.5 motion (applied) 6 : Aushärtegrad.6 T [ C] 4 2 8 6 4 simuliert.4.2.8.6.4 Aushärtegrad [mm].5 -.5 t [sec] 2 3 4 5 6 2 2 3 4 5 6 t [sec].2 - -.5
Page 4 Simulation D Material Behaviour. Results. T [ C] [Mpa] 2 8 6 4 2 8 6 4 2 5 5-5 - temperature (applied) 2 3 4 5 6 t [sec] shear stress simulated : Temperatur : Aushärtegrad simulated t [sec] 2 3 4 5 6 2.8.6.4.2.8.6.4.2 Aushärtegrad [mm].5.5 -.5 - -.5.8.6.4.2 -.2 -.4 -.6 -.8 - motion (applied) t [sec] 2 3 4 5 6 simulated strain 2 3 4 5 6 t [sec]
Page 5 FE Model for. Automatic Assembling of Joints in ANSA. initial: final: outer sheet: shell elements grids RBE3 HEXA D RBE2 inner sheet: shell elements automatically added D elements RBE3: distributed coupling RBE2: cinematic coupling
Page 6 FE Model for. Automatic Assembling of Joints in ANSA. FE Model (symmetric) TOTALSEAL 98 z.b. 3 rows solid HEXA elements Dachaußenhaut roof bow roof liner
Page 7 ABAQUS Implementation. User Subroutines. UMAT, UEXPAN. User subroutines will be called by the main solver ABAQUS at each time step, each iteration, each iintegration point... main solver ABAQUS T ε ( t), T ( t + Δt), Z( t) () t, ε( t + Δt), σ() t σ( t + Δt) Z Δ α, ΔT Δε vol ( t + Δt) ( Δσ) ( Δε) UMAT update state variables: Z ( t + Δt) = { α G, T g, a, τ, τ,...} adaptive time stepping: Δt next = viscoelast. material law: σ, T 2 ( t + Δt) =... UEXPAN Δ ε = Δ Δα vol ath T acure therm. expansion adhesive shrink
Page 8 ABAQUS Implementation. User Subroutines. Parameters. ** *MATERIAL,NAME=matname *USER MATERIAL, CONSTANTS=4, TYPE=MECHANICAL alpha, compr_mode, init_compr_factor, dt_ctrl *EXPANSION, TYPE=ISO, USER *DEPVAR 54, ** initial curing param.: α( t = ) x = K Method for adhesive compressibility: =... linear approach f. literature BETAMATE48 or TOTALSEAL98 adaptive time stepping = 2... constant Poisson's Number: 2G (+ ν) K ; G = G ( α) K 3( 2ν) K f K = ( α) K + αk f = K = ( α) Warning: do not use only one adhesive element row because of incompressibility...
Page 9 ABAQUS Implementation. Sequential Thermomechanical Coupling. Thermal analysis (initially) - simulates temperatures t = 65sec t = 24sec t = 43sec t = 629sec... T(t ) T(t 2 ) T(t 3 ) T(t 4 ) step step 2 step 3 step 4 Structure mechanical analyse (ABAQUS with User Subr.) - reads in: temperature fields - simulates curing,..., stresses, strains, displacements
Page 2 Validation. '5er Touring' - Roof Bow rel. displacement measurement Measurement instrumentation (temperature and relative displacement)
Page 2 Validation. '5er Touring' - Roof Bow relative Connector displacement Öffnung (mm), [mm] Aushärtung () 2,5,5 -,5 W3 mess W3 sim Aushärtung (bei W/3) T-T2 sim T2 mess (Spriegel) T sim (aussen) T2 sim (Spriegel) rel. displ (mes.) rel. displ (sim.) curing dt (outer - inner) inner temp. (mes.) outer temp. (sim.) inner temp. (sim.) 2 5 5-5 Temperatur ( C) - - 2 3 4 5 Zeit (s)
Page 22 Thank you very much... Freude am Fahren