Development, implementation and Validation of 3-D Failure Model for Aluminium 2024 for High Speed Impact Applications

Transcription

1 Development, implementation and Validation of -D Failure Model for Aluminium 2024 for High Speed Impact Applications Paul Du Bois, Murat Buyuk, Jeanne He, Steve Kan NCAC-GWU th International LS-DYNA Users Conference June Dearborn, Michigan, USA Introduction FAA William J Hughes Technical Center (NJ) conducts a research project to simulate failure in aeroengines and fuselages, main purpose is blade-out containment studies material testing performed by OSU ballistic testing performed by NASA/GRC numerical simulations performed by GWU-NCAC involved the implementation in LS-DYNA of a tabulated generalisation of the Johnson-Cook material law with regularisation to accommodate simulation of ductile materials previously published results in : A Generalized, Three Dimensional Definition, Description and Derived Limits of the Triaxial Failure of Metals, Carney, DuBois, Buyuk, Kan, Earth&Sky, march 2008

2 FAA engine safety working group NASA Glenn Cleveland OH GWU-NCAC Sterling VA FAA Seattle W FAA Atlantic City NJ LSTC Livermore CA OSU Columbus OH penetration failure modes /6 05. ft/s /8 42 ft/s / ft/s Petaling Bending ecking Plugging Shearing Spaling

3 Part : OVERVIEW OF MAT_224 Development of MAT_224 in LS-DYNA The Johnson-Cook material law is based on a multiplicative decomposition of strain hardening, strain rate hardening and thermal softening : σ y m n εɺ T TR = ( a+ bεp) cln + εɺ T T A similar formulation is used for the plastic failure strain in function of state of stress (triaxiality), temperature and strain rate ε pf p D εɺ T T = σ ( + ) + + A damage variable with scalar accumulation is used as failure criterion : Exactly the same approach is followed in MAT_224 analytical formulations are replaced by tabulated generalisation 0 R D De vm D ln D εɺ 0 T m T R d dε ε p = pf m R

4 Development of MAT_224 in LS-DYNA regularisation of the displacement at failure is added to account for the inevitable mesh-dependency of the simulations after necking in ductile materials started development in november 2006 production version available in ls97-r4.2 current presentation is based on implementation in ls97-r5.0 developed on the basis of MAT_024 with VP= available for fully and underintegrated shell and solid elements full keyword code : *MAT_TABULATED_JOHNSON_COOK MAT_224 : material law k : table of rate dependent isothermal hardening curves or load curve defining quasistatic hardening curve kt : table of temperature dependent quasistatic hardening curves σ = k ( ε, εɺ ) kt( ε, T) y p p p ε = εɺ p β T= TR+ Cρ p p σεɺ y p

5 MAT_224 : failure model f : table of load curves giving failure plastic strain in function of triaxiality at constant Lode angle g : scaling function for rate effects h : scaling function for temperature i : regularisation curve ε pf p = f g( εp) h( T) i( lc) σ ɺ vm MAT_224 : material law : basic example σ = k ( ε, εɺ ) kt( ε, T) y p p p 000 Yield Stress (MPa) Plastic Strain T ε σ TR σy= k ( εp, εɺ p) TM 0 TR = 00 K TM = 775 K

6 MAT_224 : failure law : basic example E q. P l a s ti c S tr a i n Triaxiality E q. P l a s ti c S tra i n εɺ εf TR 0 TM Triaxiality ε d TR = 00 K TM = 775 K 0 l max p = f g( ε ) h( T)( i l ) σ ɺ vm dεp = ε pf p c pf MAT_224 : Verification Process extensive verification needs to be performed some elementary single solid element tests are shown next resuls must be compared to reliably implemented material laws in LS-DYNA : natural choices are MAT_024 and MAT_05 in particular verify the influence of thermal softening and stress triaxiality

7 A B C D Ζ/ Τ E F A B C D Ζ/ Τ E F

8 A B C D Ζ/ Τ E F A B C D Ζ/ Τ E F

9 Once and for all : the history variables : HV Shell Solid Plastic strain rate 5 Plastic strain rate 7 Plastic work 8 Plastic strain/failure strain Plastic failure strain 9 Element size triaxiality 0 temperature Lode angle Plastic failure strain Plastic work 2 Triaxiality Plastic strain/failure strain Element size 4 temperature Part 2 : FAILURE MODEL DESCRIPTION THE PLANE STRESS CASE

10 Characterisation of the state-of-stress general state of stress : σ 0 0 σ < 2 0 σ 0 σ 0 2 = σ < 0 0 σ State-of-stress is compression only unless the first principal stress is strictly positive σ σ > 0 0 σ 0 σ 0 a 0 = σ 0 0 b parameters are needed to characterize the state-of-stress up to a multiplicative constant, one valid choice is : σ σ a= b= σ σ 2 Plane stress general state of plane stress : σ aσ 0 a σ σ σ 0 0 σ σ σ 0 0 σ σ a invariants : 0 0 aσ σ+ σ2 p σ + a + a p= = = 2 2 σvm σ + a a + a a p σ + a + a σ = σ + σ σσ = = + + a a vm σvm σ a a

11 Important cases of plane stress overview of plane states of stress : p σ vm σ 0 0 σ 0 0 σ 0 0 σ 0 0 σ σ σ σ 0 0 σ 0 0 σ a= a= /2 a= 0 a = a σ = 0 Example of a minimal test program for metal sheet : notched sample smooth sample? shear sample FKP GP SZP η Courtesy Adam Opel AG0

12 f Failure model : step sdehnung ε pl [ - ] plastische Dehnung ε pl [ - ] bzw. Versagens Triaxialität [ - ] FKP_R FKP_R8 FKP_R0 GP DSP_ DSP_7 DSP_0 SZP Versagen Courtesy Adam Opel AG0 Failure model : step 2 ε pl Failure strain? average triaxiality Failure curve Iterative improvement η f η mittel η First estimate : Courtesy Adam Opel AG0

13 f Failure model : step : regularisation Sollwerte (Versuchs-Versagensmesslänge erreicht) Simulation.2 7,5 mm 5 mm 4 mm mm 2 mm mm 0,5 mm - ] Versagensdehnung ε pl [ Elementkantenlänge l ele [mm] Courtesy Adam Opel AG0 Plane stress Failure criterion for Aluminium 2024

14 Plane stress Failure criterion for Aluminium 2024 Comparison to JC failure criteria In fact the JC criterion usually cannot handle petaling ( tensile) and plugging (shear) failure simultaneously Example of AL2024, the physical failure criterion is more complex then JC

15 Part 2 : FAILURE MODEL DESCRIPTION THE D CASE dependency upon the state of stress : D case in a D state of stress ( solid elements ) it cannot be assumed that the third invariant of the stress tensor is zero, 2 invariant parameters are needed to characterize the state of stress : p σ vm σ + a+ b = σ + + I σσσ σ σ σ 2 2 a b ab a b 2 = = vm vm σ 2 2 ab ( + a + b ab a b) Lode angle is often used since it varies between - and /2 J I p p = + σvm σvm σvm σvm 27J 27sss = 2σ 2 2 vm σvm

16 material tests for failure criterion I σ vm failure criteria for solid elements 27J 2σ = vm 27J σ = 2 vm 27J 0 σ = 2 vm t p = σ vm

17 Dynamic punch testing on the SHB Controlled dynamic testing is performed on a SHB to examine failure of Aluminium 2024 before assessing the ballistic testing by NASA SHB at OSU is used for dynamic punch testing at 20 m/s using different punch shapes and a circular sample with D=4.56 mm and t=.456 mm (0%) different punch shapes were selected these tests allow validation of the failure criteria determined from quasistatic testing on samples with different shapes also failure criterion can be extended to states of stress lying on the compressive meridian crack patterns corresponding to different failure modes ( petaling, plugging and combined ) can be examined stop collars were used to arrest the impactor bar at predetermined values of the displacement allowing to study the crack growth in the samples dynamic punch testing on the SHB Punch Punch 4 Punch 6

18 what happens during a punch test? I σ vm top side of sample biaxial compression bottom side of sample biaxial tension σ σ 2 σ 00 0σ p t= σ vm extension meridian : a=b cilinder gets longer Lode= compression meridian : a= cilinder gets shorter Lode=- ~Lode ~Triaxiali ty -0.8 Cylinder G6 Grooved Plate G Cylinder G5 Grooved Plate G2 Punch Cylinder G4 Dogbone G4 Grooved Plate G 0.49 Cylinder G Dogbone G -0.4 Cylinder G2 Dogbone G2-0. Cylinder G Dogbone G Tension/Torsi on Tension/Torsi on 0 Torsion Punch 6 Spline-4 Punch 4 0. Compression Spline- Free Points Spline-2 Spline-

19 Basic splines for the D failure model -D Failure criterion for Aluminium 2024

20 preliminary simulation results : punch

21 preliminary simulation results : punch bottom view top view preliminary simulation results : punch 4-0.6

22 preliminary simulation results : punch 4 preliminary simulation results : punch 6

23 preliminary simulation results : punch 6 Comparison to SHB test results : mm displacement bottom no cracks yet top

24 Comparison to SHB test results :.7mm displacement circumferential crack at bottom side Comparison to SHB test results : 2.4mm displacement radial cracks also appear at the bottom side

25 animated simulation results Comparison to SHB test results : 2.4mm displacement radial cracks also appear at the bottom side

26 Part : CONCLUSION Continuation further iterations using the material and punch test results to refine the failure model simulation of the ballistic tests performed at GRC to assess the current model

27 Limitations of the current method material may not yield according to the von Mises yield surface : σt σc > σt σs < material may be anisotropic damage accumulation may need to be tensorial if cyclic loading is considered regularisation may not be uncoupled from the state of stress, the current approach will fail to correctly simulate failure induced by plastic instability some of these considerations will need to be assessed when titanium is investigated next Mesh dependent orientation of the localized neck Equivalent Plastc strain Messlängen- Dehnung 0,000 l =,6 mm 0,056 0, 0,67 0,222 0,278 0, 0,89 l =,68 mm 0,444 0,500 Courtesy Adam Opel AG0

28 Conclusions predictive analysis of failure is desribale for materials used in aeronautical structures to achieve maximum flexibility in the numerical models a tabulated and regularized generalisation of the Johnson-Cook material law was implemented in LS-DYNA a comprehensive testing program was used to create a material data card for aluminium 2024 it proved possible to predict the complicate crack pattern in a dynamic punch test the results of the punch tests can be used for further fine tuning of the material dataset