Un esempio di materiale avanzato: le leghe a memoria di forma

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1 Un esempio di materiale avanzato: le leghe a memoria di forma F. Auricchio Dipartimento di Meccanica Strutturale, Università degli Studi di Pavia, Italy European Centre for Training and Research in Earthquake Engineering (EUCENTRE), Pavia, Italy Istituto di Matematica Applicata e Tecnologie Informatiche, CNR, Pavia, Italy Centro di Simulazione Numerica Avanzata, CESNA-MECMA, IUSS, Pavia, Italy auricchio@unipv.it Acknowledgments : G.Attanasi $, M. Conti ^, A.Reali ^, U.Stefanelli * $ European Centre for Training and Research in Earthquake Engineering (EUCENTRE), Pavia, Italy ^ Dipartimento di Meccanica Strutturale, Università degli Studi di Pavia, Italy * Istituto di Matematica Applicata e Tecnologie Informatiche, CNR, Pavia, Italy

2 Presentation outline 3D constitutive models SE + SME time-continuous constitutive models Algorithmical / mathematical considerations Algorithm numerical validation (uni-axial & multi-axial) A home-made round-robin test 3D numerical simulations SE: stents [ free-expansion / crush test ] SME: actuators / intervertebral spacers Hybrid composites New areas of research / application Micro-actuators SMA Isolation Bearing Biomedical applications (peripherical stents, embolic filters, wallstent)

3 Shape memory alloy: an introduction Shape memory alloys (SMA) : materials with an intrinsic ability to recover initial shape also after severe deformations Macroscopic point of view : two unusual effects, in general non available in traditional materials Superelastic effect Shape memory effect

4 Shape memory alloy: an introduction Superelastic effect Shape memory effect Mechanical recovery Thermal recovery

5 Application fields Macroscopic effects non available in traditional materials Innovative and commercially valuable applications Biomedical area : orthodontics, orthopedics, guidewires, stents, eyeglasses, micro-actuators Mechanical area : actuators, thermal valves, connectors, closing/opening systems Structural area : shape & vibration control, energy dissipation (civil engineering, aeronautics, car industry)

6 Superelasticity: applications Superelastic effect (SE) :

7 Superelasticity: orthodontics Orthodontic archwires for the correction of tooth malposition [ results in only 3 weeks of therapy!! ] Advantages : application of a constant and low intensity force reduced tissue damage and increased remodeling speed

8 Shape-memory effect: applications Shape-memory effect (SME) :

9 Shape-memory effect: connectors Best known application: constrained recovery Recovery constrained by a rigid element Different materials High precision Easy use

10 Shape-memory effect: orthopedics Cambers : elements to help bone healing Spinal fixtures: devices for the treatment of herniated disks

11 A collaboration with an Italian company: SAES getters

12 Coupling between : a wire with shape-memory effect a spring-like deformable element Two-way SME ( repeatable ) Shape-memory effect: automotive Linear actuators Angular actuators Current EM actuator Shape memory actuator

13 A collaboration with an Italian company: SAES getters

14 SAES getters: some ideas in automotive industry From concept design Mechanical opening from the outside Rigid flaps Mirror support Shape memory wires Internal electrical and mechanical opening based on SMA bowden to prototypes: Shape memory wire

15 Shape-memory effect: actuators

16 Shape-memory alloys: micro-mechanics Key aspect : reversible crystallographic transformation solid-solid phase transformation martensitic phase transformation [no diffusion] Martensite : Austenite : stable at lower temperatures lower crystallographic symmetry stable at higher temperatures higher crystallographic symmetry

17 Shape-memory alloys: micro-mechanics Thermo-elastic martensitic transformation crystallographically reversible (diffusionless, first type, athermal, two phases, hysteresis) Austenite stable at higher temperatures T>A f Martensite stable at lower temperatures T<M f single/multi variant multi-variant martensite single-variant martensite austenite A-B D-A B-C C-D-A A-B-C C-D austenite single-variant martensite single-variant martensite

18 Shape-memory alloys: micro-mechanics Single crystal transformation: change of crystallographic group Crystallographic theories : compute the deformation gradient to obtain the change of group symmetry ( Wayman 1964 ) PROBLEM : interaction between product and parent phase Single-variant martensite i.e. with a preferred direction (stress) Multiple-variant martensite i.e with no preferred direction PROBLEM : interaction also between different grains and other microstructure Approach the problem from the micro-mechanics level to build a macroscopic model is quite complex

19 Shape-memory alloys: thermodynamical aspects Strong thermo-mechanical coupling : balance between chemical (thermal component) and mechanical (elastic component) thermodynamical forces characterize PTs temperature and stress are thermodynamically equivalent driving forces

20 Shape-memory alloys: thermomechanical coupling Latent heat release/absorption as well as body thermal exchange with surroundings may strongly influence body temperature ΔH cooling ΔT Cooling Ni50.35Ti M f M s A s A f Heating ΔH heating

21 Versus SMA constitutive models Important to have a 3D computational tool to perform structural analysis of existing devices to perform structural analysis of new possible devices Complex constitutive behavior Mechanical response Thermo-mechanical coupling We prefer to approach the problem directly from a macroscopic phenomenological point of view Few models available in commercial codes Engineers play a fundamental role correct design

22 Nitinol biomedical devices An investigation through Finite Element Analysis Investigated Devices Laser cut stent Self-expandable braided stent Embolic filter design analysis Use Abaqus superelastic model: Auricchio et al (CMAME 1995) (isothermal simulations) In collaboration with Institute of Biomedical Technology (Ibitech) Ghent University M. De Beule, B. Verhegghe, P. Mortier, R. Van Impe, P. Verdonck

23 Laser cut stent: realistic 3D model generation Ad hoc microct scanner (Ghent) Catheter diameter = 2 mm CAD 3D model

24 Laser cut stent: possible parametric investigation Software devoted to mesh generation (PyFormex) Stent diam:9 mm Strut number: 12 Model paramerts Stent diameter Stent length Number of rings Number of struts/ring Strut thickness... Number and type of bridges Stent diam:4.5 mm Strut number: 18 Strut along length: 6 Stent diam:3 mm Strut along length: 9

25 Laser cut stent: from laser cutting to delivery Shape setting Shape setting after laser cutting Release in a curved vessel

26 Laser cut stent: patient specific simulation ECA ICA Vessel centerline CCA Medical imaging 3D vessel modeling (Patient-specific) Implant simulation

27 Laser cut stent: patient specific simulation Objective: perform realistic simulation of nitinol stent implant in a patient specific carotid artery model ICA ECA Vessel Stent 1 Catheter 2 3 CCA Keypoints Splines + surfaces Simulations Data elaboration, surface & mesh generation using GO-MESH Nurbs based sofware by AAPS Informatica (

28 Evaluation of design impact: straight vs tapered NO Stent XACT Tapered XACT Straight

29 Evaluation of design impact: straight vs tapered NO Stent ACCULINK Straight XACT Straight

30 Evaluation of design impact: lumen gain PRE Cutting planes POST

31 Evaluation of design impact: centerline evaluation Numerical simulation ECA ICA CCA Inner surface of the vessel STENTING NO STENT ICA Centerline of the vessel vessel CCA

32 Braided wirestent: free-expansion simulation Real device Parametric Geometrical model FEA

33 Braided wirestent: apposition in a idealized vessel Partially expanded stent Totally Expanded Stent

34 Embolic protection devices: many possible devices SPIDERx (EV3) AccuNET Rx (Guidant) Emboshield (Abbo?) Several Stent designs FilterWire (Boston ScienGfic) Angioguard (J&J) Trap NFS (Microvena)? Interceptor (Medtronic) Rubicon (Rubicon- medica)

35 Angioguard XP: simulation & 1 st model validation Micro- CT Filter Free Deployment Micro-CT VS Finite Element Analysis Simulazione Good agreement between Experimental and Numerical data Filter Release in the vessel Simulation 2 steps Filter insertion in delivery system + vessel expansion (systolic pressure) Filter releasing

36 Angioguard XP: simulation on vessel asymmetry Clinic study: factoid/caro1d%20artery%20stenosis.pdf SIMULATION: 4mm filter released in 3mm circular vessel (on the let) e 3 mm vessel having 0.75 ovality (on the right). Wall apposigon (Numerical results) Filter size [mm] Ovality Gap [% vessel lumen] Vessel ovality has a major impact on wall appoition than oversizing

37 3D effective constitutive models SE + SME time-continuous constitutive models ROBUST: Algorithmical / mathematical considerations ROBUST: Algorithm numerical validation (uni-axial & multi-axial) ACCURATE: Home-made & international round-robin tests Several 3D numerical simulations SE: stents [ free-expansion / crush test ] SME: actuators / intervertebral spacers / Micro-actuator Biomedical device investigations Laser cut stent (patient specific simulations) Braided wirestents Embolic stents Conclusions Possible accurate design process for devices (biomedical or not) exploiting shape memory alloy material features Simulations of actual devices in realistic situations are quite complex

38 Aortic valve: research activity Riprodurre gli effetti di un allargamento patologico della radice a partire dalla condizione di valvola sana: Cosa siamo in grado di fare Vista dal basso Si simula un allargamento patologico della radice Vista dal basso Si valuta l incompetenza della valvola in fase diastolica

39 Aortic valve sparing: an engineering support Vista dall alto Vista dal basso Ciclo simulato diastole-sistole-diastole da cui è possibile desumere la localizzazione degli sforzi

40 Crack placement Modify mesh to introduce master and slave surfaces ABAQUS pyformex ABAQUS Creazione dei set di elementi che serviranno per definire le due superfici Scrittura del file di input e esportazione in pyformex Creazione di 3 parti distinte: 1) master 2) slave 3) parte rimanente dell anello Creazione di un nuovo file di input e importazione in ABAQUS Unione delle 3 parti Selezione dei nodi per il debond Modifica del file di input per inserire il criterio VCCT

41 Stain energy release rate for crack propagation Robertson e Ritchie (2006) caratterizzazione di Kc di un tubo super elastico in Nitinol (come quelli usati per realizzare gli stent) campioni CT ricavati seguendo direzioni diverse rispetto all asse del tubo ( longitudinali, circonferenziali e a 45 ) Risultati ottenuti per le tre configurazioni. Valore di K affinchè l estensione della cricca inizi NOTA: Cricche circonferenziali causano il maggior numero di fratture a fatica o per sovraccarico Kc = 16 Mpa mm

42 Fatigue life analysis Fatigue life analysis following Lemaitre/Deisborat (Spinger) Numerical/experimental investigation: Accumulation of plastic deformation Crack nucleation at the microscopic level Crack evolution from microscopic to macroscopic level Macroscopic crack propagation Structural failure Finite element analysis (FEM) Continuum Damage Mechanics (CDM) Fracture Mechanics (FM)

43 Fatigue life analysis: Cypher stent as example Cypher Stent (Cordis Corporation, NJ, USA) Materiale: acciaio SS316L Ghent Stent Research Unit (Belgium) (http ://www:stent-ibitech.ugant.be) Abaqus v. 6.8 C3D8R (Stent) SFM3D4 (Cilindro) Abaqus Standard Grandi Deformazioni Diametro ext. Iniziale : d 0 = 1.15 mm Diametro ext. Espanso : d exp = 3.0 mm Dimetro Recoil : d recoil = 2.95 mm Spessore: th = 0.3 mm Lunghezza Iniziale: l i = 8.4 mm Lunghezza Finale: l f = 7.6 mm

44 Cypher stent: elasto-plastic analysis Espansione: lo stent viene sovra-espanso locali deformazioni plastiche mantengono la configurazione aperta Elastic Recoil: rimosso il palloncino lo stent diminuisce il proprio diametro Risultati

45 Cypher stent: systolic-diastolic cycling Risultati Stress Equivalente Massimo (von Mises) : 375 MPa Stress Principale Massimo : MPa Stress Range 110 MPa

46 Cypher stent: material failure test Modulo di Young: MPa Modulo di Poisson: 0.3 Tensione di snervamento: 380 MPa Ultimate Stress: 474 MPa ε(σ u ) = 0.15 Rupture Stress: σ R = 330 MPa Rupture Strain: ε pr = 0.32 Coefficiente di strizione: Z = (S 0 S R )/S 0 = 0.6 Rupture Strain in zona di strizione: ε* pr = 0.6 Accumulo Plastico di soglia: ε pd = ε p (σ = σ u ) 0.15

47 Cypher stent: material fatique failure test Limite di Fatica : σf = 220 MPa (10 6 cicli) Δε p1 = N R = 10 ; σ M1 = 450 MPa Δε p2 = N R = 100 ; σ M2 = 340 MPa integrando sul periodo di innesco della cricca Risolvendo per i due valori sperimentali s = 2.4 m = 6

48 Cypher stent: conclusions Estrapolare da dati sperimentali N R per un generico valore di (Δε p - σ M ) Effettuare un test per un numero di cicli pari ad N R Interrompere il test e portare il provino a rottura per carico monotono Misurare il modulo di Young ( ) Quantificare il danno prodotto

49 185 Cypher stent: conclusions a 0 = δ 0 a f = 80% larghezza stent