Outline Erweiterte Kontaktformulierung, User-Reibmodell und thermische Analyse Simulationsmöglichkeiten zur Werkzeugauslegung mit LS-DYNA Workshop Simulation in der Umformtechnik Institut für Statik und Dynamik, Universität Stuttgart K. Schweizerhof, D. Lorenz & A. Haufe Universität Karlsruhe, DYNAmore GmbH. Motivation Forming including the TRIP-effect 2. User defined interface for friction law in LS-DYNA 3. Thermo-mechanical coupling exemplified at S-rail part 4. Future: Smooth contact formulation 5. Conclusions Dynamore GmbH Industriestraße 2 70565 Stuttgart http://www.dynamore.de 2 Forming including the TRIP-effect Tension test of stainless steel type 30 Acronym: TRIP TRansformation Induced Plasticity Initially, the specimen is purely in austenitic phase The TRIP-effect: The austenitic phase is transformed to the stronger martensite phase through deformation of the material. The TRIP-effect is sensitive to the amount of deformation, temperature, and initial martensite content The TRIP-effect is of considerable amount in low alloy austenitic stainless steel (e.g. AISI 30, AISI 304 8% Cr, 8% Ni ). The deformation of the specimen transforms the austenite to martensite, i.e. it hardens. Martensite content 33 % The TRIP-effect can have a dramatic influence on the hardening behavior during bending, stamping etc. because a large percentage of the material may be transformed to martensite. 0 3 5
Typical stainless steel with extreme TRIP effect Objective of TRIP-effect simulation HytensX: Experimental stress/strain curve Yield stress: 32 MPa Failure strain: 37% Failure stress can be as high as 2000 MPa! True Stress (Mpa) 600 400 200 000 800 600 400 200 Test temperature 28 C Predict formability Good accuracy possible with standard practice: Standard forming simulation and Forming Limit Diagram Predict component hardness/hardening after forming Requires a good material model able to predict martensite formation Necessary to be able to predict component crash performance in subsequent analysis Hänsel et al. material model for TRIP-effect Predicts the martensite formation as function of temperature and deformation Determines the hardening curve/yield stress as function of effective plastic strain volume fraction martensite V B -V = exp(q/t) A V ε m ( B+ ) / B 2 p ( V ) ( tanh (C DT)) m m m + 0 0,0 0, 0,2 0,30 0,4 True effective plastic strain σ = y ε n (B HS-(BHS-AHS ) exp(-m ))(K K2T) Hγ α ' + + V m [see Hänsel, Hora & Reissner 998] 6 7 Good and fast thermal contacts required Test on a specific forming part Standard thermal contacts in LS-DYNA have been too slow to perform stamping simulations: New faster thermal contacts Use keyword CONTACT_THERMAL_SURFACE_TO_SURFACE (No input changes required to enable the faster contacts) Segment to segment contact Contact search using pinball type algorithm Support for thermal adaptive mesh refinement (open) VAMP 2 B VAMP 2: Research collaboration on hydroformingand stamping, between IVF and Swedish industry Part B in VAMP 2: double curved pan Part is deep drawn Tools are initially at room temperature Blank a 0 C Part geometry Model setup Information provided by: Engineering Research Nordic AB, Linköping, AvestaPolarit AB, Avesta Research, Sweden Part after stamping, before trimming 40 234 404 [Figure from Pressnigsförsök i VAMP 2: Konventionell djupdragning, IVF report, 2002] 8 9
VAMP 2 B - Performance benchmark Evolution of martensite volume fraction Model and process setup 50 000 Belytschko-Tsay elements, 5 IP through the thickness 00 explicit cycles per single thermal time step Including the thermal effects (i.e. thermal solver and thermal contacts) adds only slightly to computational cost 42 % Case Conventional stamping simulation Stamping simulation with thermal effects Relative solution time 00 % 0 % 0 0 Temperature after forming Hardening - yield limit Information provided by: Engineering Research Nordic AB, Linköping, AvestaPolarit AB, Avesta Research, Sweden 35 C 300 N/mm 2 0 30 2 3
Open issues Further validation of the specific material model (Hänsel) necessary Forming of a muffler Energy absorption behavior of component in subsequent analysis Hardening parameters from stamping (Volume fraction of martensite and effective plastic strain) Hardening parameters together with thickness distribution are transferred to crash mesh using *INCLUDE_STAMPED_PART 2. User defined interface friction Improvement of the Hänsel model (Institut für virtuelleproduktion, ETH Zürich) Optimization of material parameter identification process Identification of material parameters for specific steels Further temperature effects due to heating of the tools Frictional effects temperature induced effects by friction 4 5 Standard frictional contact Frictional algorithm Friction in LS-DYNA is based on a Coulomb formulation *CONTACT... Card 2 Variable Type Default FS FD DC VC FS F 0. FD F 0. DC F 0. µ s VC Static coefficient of friction Dynamic coefficient of friction µ d Exponential decay coefficient c Coefficient for viscous friction κ F 0.......... ( ) cv d s d e µ = µ + µ µ... ( κ ) f = min f, A Coulomb master (friction force can be limited to a maximum to account for yield stress of contacted material) 6. Update the interface force to a trial value, trial n f = f k e 2. Compute the tangential part 3. Compute coefficent of friction and yield force c v µ = µ d + ( µ s µ d) e fy = µ fn 4. Determine frictional force ( ) f = f f n= f f n n, trial, trial, trial t n f = f k... penalty stiffness Δe... incremental displacement v... velocity, trial, trial t t y t f y, trial, trial f if n, trial t ft > f + y ft if f The frictional algorithm uses the equivalent of an elastic-plastic spring f "stick" "slip" 7
User defined friction User subroutine arguments This standard algorithm can be modified via user subroutine A subroutine "usrfrc" is provided in fortran file dyn2.f, where the frictional algorithm can be modified. The whole algorithm is given, i.e. modifications can be quite general. Main idea is the user defined modification of friction coefficients, e.g. friction coefficients as function of temperature, pressure,... Other friction models (than Coulomb) could be implemented, e.g. "interface constitutive models" or "asperity-lubricant models" on micro-scale. A lot of input parameters can be used: sliding velocity, contact pressure, temperature, sliding displacement, etc. old friction force slave node coordinates slave node area time step size penalty stiffness slave node relative displacement normal vector temperatures user constants user history variables friction coefficients from input... INPUT user subroutine OUTPUT new friction force components new slave node force components updated history... arguments are extensively described in comments in user subroutine 8 9 Thermo-mechanical coupling In forming processes with high strength steels considerable thermal effects can occur. 3. Thermo-mechanical coupling exemplified at S-rail part Thermal effects can be caused by dissipation of plastic work and sliding friction energy. The dissipation of plastic work is proportional to the flow stress The frictional energy increases with contact pressure and friction coefficient. LS-DYNA can account for thermal effects within a coupled simulation. The thermal part of the problem is solved using an implicit conjugate gradient solver. A sequential coupling method is used between the explicit mechanical solver and the implicit thermal solver. 20 2
Thermo-mechanical coupling Time Scaling of the thermal problem Simulation process with explicit time integration (specifics) Mechanical Solver Based on the actual temperature the mechanical solver calculates: Plastic work Contact gap and contact pressure Temperature dependent constitutive material properties Thermal expansion Update of the actual geometry Explicit (SMP & MPP) Thermal Solver based on the actual geometry the thermal solver calculates: Heat source from plastic work Heat generated by sliding friction Contact heat transfer coefficient based on actual contact gap and pressure Update of the actual temperature. Implicit (SMP& MPP) Thermal time step is typically some orders of size bigger than the mechanical time step. One thermal step after 0 00 explicit mechanical time steps necessary. besides mass scaling a common approach to reduce CPU cost in sheet metal forming simulations is the application of time scaling time scaling is done by increasing the tool velocity since the elastic-plastic material model used for the blank do not account for strain rate effects the tool velocity has no physical meaning all thermal velocity terms like conductivities, heat transfer coefficients etc. have to be scaled according to the mechanical problem the scale factor is the tool velocity ratio of simulation compared to the real metalforming process unlike in conventional sheet metal forming simulations the tool velocity has a physical meaning in coupled simulations, thus the correct tool velocity of the real forming process MUST be considered 22 23 Thermo-mechanical Coupling Effects S-Rail Model Description Conversion of sliding friction energy into heat heat is divided equally between contact surfaces energy calculation with W fric = µf N d d is relative displacement F N d Blank material TRIP700, 2.0 mm non-quadratic yield locus (*MAT36) phase change not considered in material model (not *MAT_TRIP) Coulomb friction law µ=0.5 Die velocity 0 m/s Blank Hardening curve TRIP700 200 00 000 900 800 700 600 500 0 0, 0,2 0,3 0,4 0,5 0,6 contact heat transfer coefficient 3000 W/m 2 K Belytschko-Tsay shell for mechanical part Binder Z-force 800kN Planar anisotropy TRIP700,20 Dissipation of plastic work into heat commonly 80 90 % of plastic work are converted thick shell elements for thermal calculations shell thickness for tools 4 mm Punch fix r-value,0,00 0,90 0,80 heat calculation using w pl = ρc T = η p ε σ dε eq eq eq quadratic shape functions for temperature through thickness blilinear shape functions in plane 0 45 90 rolling direction contact plane used in thermal contact using thermal thickness offset ITHOFF in *CONTROL_CONTACT card Two nodes to model the temperature gradient normal to shell surface 24 25
Influence of real tool velocity on final Influence of real tool velocity on final temperature after forming temperature after forming tool velocity has considerable impact on final temperature high local temperature gradients on tool surface for the faster process at higher real tool velocity the time scaling factor for thermal is rather low negligible heat conduction in tool for the higher velocities fast forming process has a more adiabatic character only little difference between the maximum computed temperatures temperature [ C] temperature [ C] Tmax = 05 C Tmax = 5 C real velocity 250 mm/s simulation velocity 0 m/s time scale factor ft = 40 simulation time 6.75 ms real velocity 25 mm/s simulation velocity 0 m/s time scale factor ft = 400 simulation time 6.75 ms die temperature for 250 mm/s 26 Influence of contact heat transfer for 250 mm/s die temperature for 25 mm/s 27 Influence of Coulomb friction coefficient almost no heat transfer from the heating blank to the colder die friction coefficient has a strong influence on the thermal tool loading process can be considered as adiabatic for the high tool velocity friction can cause a noticeable increase of the tool temperature if a real production sequence with a high production rate is considered tool temperature increase only caused by frictional energy temperature [ C] temperature [ C] Tmax = 66 C die temperature for 250 mm/s contact heat transfer coefficient 3000 W/m2K die temperature for 250 mm/s and die temperature for 250 mm/s m = 0.5 Tmax = 78 C die temperature for 250 mm/s and m = 0.2 without contact heat transfer the friction coefficient can also be a function of temperature 28 29
Temperature-dependent friction coefficients in reality the static and dynamic friction coefficients are temperature sensitive quantities Version 97 of LS-DYNA offers the possibility to describe the static as well as the dynamic friction coefficient as a function of temperature $--------------------------------------------------- *CONTACT_(option)_THERMAL_FRICTION $ LCFS LCFD FORMULA a b c d { } $--------------------------------------------------- Contact area Slave segment Master segment 4. Future: Smooth contact formulation Friction is a function of temperature static µ s = µ s * lcfs(t) dynamic µ d = µ d * lcfd(t) lcfs and lcfd are load curves vs. temperature ( ) c v d s d e µ = µ + µ µ 30 3 Smooth contact formulation Conclusions Problem: Contact surfaces contain artificial edges and corners mostly only C0 continuous surfaces friction is not correct Alternatives to improve friction in simulation models Statics Represent geometry as correctly as possible Variables have to be correctly transported between contact segments (Konyukhov/Schweizerhof International Journal for Numerical Methods in Engineering, 66(9): 432--465, (2006)) In implicit solution tangent matrices have to be carefully set up - convergence issues Dynamics Any artificial geometry fault in particular linear contact segments as surfaces of FE meshes - introduce also artificial dynamics into the system Removal by A) using CAD geometry of tools for contact (requires correct CAD surfaces without holes and edges) B) smoothing contact surfaces by interpolation of linear segments of FE like contact surface BUT non unique interpolation still in its infancy for general cases C) contact damping only for minor vibrations useful Thermal effects become nowadays more important in metalforming simulations Generation of temperature by friction has to be considered Available algorithms in LS-DYNA are able to capture major effects in coupling friction and temperature analysis Users can implement own friction models depending on many parameters Experience of engineers or experiments are necessary to provide a) correct data for temperature distribution between contact partners b) generation of temperature by plastic work c) temperature sensitivity of friction coefficients Future improvements with smooth contact surfaces possible 32 33