Shape Memory Analysis Of A Stent

Chapter 48: Shape Memory Analysis of a Stent

48

Shape Memory Analysis of a Stent 

Summary



Introduction



Modeling Details



Solution Procedure



Results



Modeling Tips



Input File(s)



Reference

985 986 987

990 991 992 992

990

CHAPTER 48 985 Shape Memory Analysis of a Stent

Summary Title

Chapter 48: Shape Memory Analysis of a Stent

Features

Shape memory material model, both mechanical and thermo-mechanical.

Geometry

Material properties

AS

E a = E m = 50000Mpa ,  a =  m = 0.33 ,  s AS

SA

f

= 1931.4Mpa , C a = 8.66 ,  s C m = 6.66

= 1631.7Mpa , SA

= 1688.7Mpa ,  f

= 1558.8Mpa ,

Analysis characteristics

Quasi-static analysis using: fixed time stepping and material nonlinearity due to plastic or thermoelastic behavior

Boundary conditions

Tangential displacement is fixed

Applied loads

Prescribed displacements at the end nodes of the stent

Element type

8-node solid elements

FE results

History plots of stress versus strain (z-components) for a specific node for both the mechanical and thermo-mechanical model Stress Strain Relation for Mechanical and Thermo-Mechanical Model

Stress Strain Relation for Thermo-Mechanical Model 800

800 T=-150 Vol_mart=100%

Therm-Mech T=0

T=-150

700

Therm-Mech T=30 700

T=-70

Thermo-Mech T=50

T=0

Mech T=0

T=10

600

Mech T=30

T=30

600

Mech T=50

T=50

500

500

400 Stress ZZ

Stress ZZ

400

300

200

300

200

100

100

0 0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

0 0

0.002

0.004

0.006

0.008

-100 -100

-200 Strain ZZ

-200 Strain ZZ

0.01

0.012

0.014

0.016

0.018

986 MD Demonstration Problems CHAPTER 48

Introduction This problem demonstrates the ability of MD Nastran SOL 400 to model shape memory materials. The most common materials which have shape memory properties are alloys of nickel and titanium. The shape memory effect is due to a phase change between martensite and austenite phases in the alloy. These phases have identical chemistry but different crystalline structures; body-centered-tetragonal for martensite and face-centered-cubic for austenite. Transitioning between these two phases requires only a small amount of activation energy giving the transformation. A cold collapsed stent sheathed in a catheter can be deployed in a plaque lined blood vessel by the self-expansion caused by the change in room to body temperature, with the stent expansion keeping the vessel open and blood flowing properly. In other words, the stent’s “remembered” shape keeps the blood vessel open.The martensite phase forms when the material is cooled down, or it can form when stress is applied to a hot material. In this phase extensive deformation can occur as a thermoelastic martensitic shear mechanism. This deformation can be undone when the material is reheated, or at simple unloading of a hot material. When a hot (unstrained) specimen is cooled it is initially in the austenite phase. Upon cooling between martensite start M s and martensite finish M f temperature the specimen will change to the martensite phase. Conversely starting from a cold specimen which is in a martensic phase upon heating between austenite start A s and austenite finish A f temperatures, the specimen will change to the austenite phase. Different temperature ranges can be distinguished T  M s , M s  T  A f , A f  T  T c , where T c is defined as the temperature above which the yield strength of the austenite phase is lower than the stress required to induce the austenite-martensite transformation. Uniaxial tensile tests will show the following responses. For T  M s , the specimen is completely in the martensite phase. The stress versus strain curves will display a smooth parabolic type behavior, the deformation is caused by the movement of defects such as twin boundaries and the boundaries between variants. Unloading occurs nearly elastically and the accumulated deformation caused by the reorientation of the existing martensite and the transformation of any pre-existing austenite, remains after the specimen is completely unloaded. Note that the deformation is entirely due to oriented martensite and this would be recoverable upon heating to temperatures above the ( A s – A f ) range. This would show the shape memory effect. For A f  T  T c , the specimen shows pseudo elastic behavior. In this range the specimen is in the austenite phase, and stress induced martensite is formed, along with the associated deformation; upon unloading the martensite is unstable and reverts to austenite thereby undoing the accumulated deformation. For T  T c when the stress is higher than the yield stress no phase transition takes place, and the austenite phase will deform plastically which cannot be undone. Figure 48-1 shows thermo-mechanical response of NiTi, the data is of Miyazaki et al. (1981). In this case, M s = 190K , M f = 128K , A s = 188K , and A f = 221K . Two different models are available to simulate the shape memory behavior: a mechanical model, and a thermo-mechanical model. The thermo-mechanical model describes the complete behavior as discussed before. The mechanical model only describes the super elastic behavior, and thus can only be used at higher temperatures. In this example, a stent will be analyzed at different ambient temperatures. Simple loading and unloading is applied. Stress-strain graphs will show the response at the different ambient temperatures.

CHAPTER 48 987 Shape Memory Analysis of a Stent

(b) 153K

(a) 77K

(c) 164K

300 200 100

Tensile Stress (MPa)

0 400

0 (d) 224K

0 (e) 232K

(f) 241K

300 200 100 0

0

0

600 (g) 263K

(h) 273K

(i) 276K

400

200

0

Ms = 190K AF = 221K 2

Figure 48-1

4 0 2 4 Strain (%)

0

2

4

Thermal history

Modeling Details Figure 48-2 shows a representation of the stent which is modeled. At a prescribed ambient temperature the stent is loaded and unloaded by prescribing the displacement in the z-direction. For modeling reasons isotropic material is chosen at the end parts of the stent. In this way no local effects will occur where the displacements are prescribed. Smaller steps are chosen during the unloading part. Small steps are also needed to capture the shape memory behavior.

Figure 48-2

Model of the Stent

988 MD Demonstration Problems CHAPTER 48

The case control section of the input file contains the following options for nonlinear analysis: ENDC TEMPERATURE(INITIAL) = 1 DISPLACEMENT(SORT1,REAL)=ALL SPCFORCES(SORT1,REAL)=ALL STRESS(SORT1,plot,REAL,VONMISES,BILIN)=ALL NLSTRESS(SORT1,plot,REAL,VONMISES,BILIN)=ALL SUBCASE 1 STEP 1 TITLE=Loading. ANALYSIS = NLSTATIC NLPARM = 1 SPC = 2 LOAD = 3 STEP 2 TITLE=Unloading. ANALYSIS = NLSTATIC NLPARM = 2 SPC = 4 LOAD = 3 Two STEPS are defined to do the loading and the unloading. It is possible to obtain extra post quantities to examine the behavior of the shape memory material. To do this, the NLOUT option should be used in combination with the NLSTRESS option in the following way: NLSTRESS(NLOUT=10)=ALL BEGIN BULK NLOUT 10 VOLFMART

CPHSTRN

See the MD Nastran Quick Reference Guide for which output quantities can be selected. In this case the volume fraction of martensite and the phase transformation strain tensor will be printed in the .f06 file and can be postprocessed in SIMX.. Large displacement effects are included in the nonlinear analysis using the large strain option: NLMOPTS LRGS

1

For the mechanical model the multiplicative decomposition formulation is used, this is set automatically for the elements using this material behavior. It can be activated for the whole model using NLMOPTS LRGS

2

Element Modeling Besides the standard options to define the element connectivity and grid coordinate location, the bulk data section contains various options which are especially important to do nonlinear analysis, and are needed to be able to use shape memory material. The nonlinear extensions to lower-order solid element, CHEXA can be activated by using the PSLDN1 property option to the regular PSOLID property option in the manner shown below: PSOLID PSLDN1 + C4

1 1

1 1 SOLI

0 1 L

+ +

CHAPTER 48 989 Shape Memory Analysis of a Stent

The PLSLDN1 option allows the element to be used with different kinds of inelastic material models, one being the shape memory model. This element is also used in both large displacement and large strain analyses and has no restrictions on the kinematics of deformation unlike the regular CHEXA elements with only PSOLID property entry.

Material Modeling The material properties for the thermo-mechanical model is given using the MATSMA option. The mechanical model uses a subset of these properties. The following material properties for the shape memory material are used:

E a = E m = 50000Mpa

Young’s modulus

 a =  m = 0.33

Poisson’s ratio

AS

s

AS

f

= 1631.7Mpa

Starting tensile stress in austenite-to-martensite transformation

= 1931.4Mpa

Finishing tensile stress in austenite-to-martensite transformation

C a = 8.66 SA

s

SA

f

Slope of the stress dependence of austenite

= 1688.7Mpa

Starting tensile stress in martensite-to-austenite transformation

= 1558.8Mpa

Finishing tensile stress in martensite-to-austenite transformation

C m = 6.66

Slope of the stress dependence of martensite

This data corresponds to temperature ranges where the martensite  austenite phase transformations take place at o

o

o

o

o

M s = – 45 C , M f = – 90 C , and A s = 5 C , A f = 20 C , where T 0 = 200 C . The initial volume fraction of o

martensite is taken M f ra c = 0 for all cases except for the case where T i n it = – 150 C , then the volume fraction of martensite is M f ra c = 1 . The corner parts of the stent are modeled using isotropic material properties using the MAT1 option. MATSMA

MAT1

1 50000. 50000. 0. 300. 2

2 0.33 0.33 0. -4. 50000.

200. 1.E-05 1.E-05 100. 2.

0.008573 1.E+20 1.E+20 1.E+20 0. 2.75 .33

1.

1631.7 1688.7

1931.4 1558.8

8.66 6.66

0.

3.

1.

990 MD Demonstration Problems CHAPTER 48

Loading and Boundary Conditions The loading is prescribed by a displacement of 0.008m in the z-direction. For unloading, the displacement goes back to zero. To improve stability, the nodes are only allowed to move in the radial and axial direction. To obtain this, a cylindrical coordinate system is applied to each node using the CORD2R option, and the tangential movement is fixed. The ambient temperature is prescribed on all nodes using the TEMP option, and is activated in the case control file using TEMPERATURE(INITIAL)=1.

Solution Procedure The nonlinear procedure used is defined through the following NLPARM entry: NLPARM NLPARM

1 2

30 60

PFNT PFNT

PV PV

ALL ALL

30 Increments are used for the loading and 60 increments for the unloading. Two STEPS are defined to do the loading and unloading. The analysis is performed at different ambient temperatures to study the material behavior, respectively.

Results Analyses are performed for the thermo-mechanical and mechanical models at different temperatures. Figure 48-3 shows the stress-strain relationship for one node (node number 1292) at different ambient temperatures for the thermomechanical model. The z-component of the stress and strain of this node is collected during the loading and unloading o

and plotted in the figure. At T = – 150 C an analysis is performed with a martensite volume fraction of 0% and an analysis with a volume fraction of 100%. Note that for 0% martensite no plastic behavior occurs. If no martensite is present no plastic behavior can occur, and due to the low temperature no martensite can form due to stress. Physically this would however be an unstable situation, and the martensite volume fraction should be set. This is different for o

T = – 75 C where martensite will form if none is present, and the material will show plastic behavior. Also note that o

since these are temperatures below A f = 20 C the plastic deformation cannot be undone. This only happens for the o

o

o

case where T = 30 C , and T = 50 C . The simulation for T = 10 C stops prematurely, because it cannot find convergence. The material behavior can be sensitive during unloading, in this case reducing the timestep further did not help. What would help to get convergence in this case is to refine the mesh. Figure 48-4 compares the results of the mechanical model with the thermo-mechanical model. The mechanical model is designed to simulate the super-elastic behavior, so it should be used for higher temperatures. The results show a similar response.

CHAPTER 48 991 Shape Memory Analysis of a Stent

Modeling Tips The behavior of the shape memory material can be quite sensitive to the loading. Therefore, the user must use sufficiently small timesteps, and the mesh should be fine enough. It is best to use the PFNT option of NLPARM for stability. Stress Strain Relation for Thermo-Mechanical Model 800 T=-150 Vol_mart=100% T=-150

700

T=-70 T=0 T=10

600

T=30 T=50

500

Stress ZZ

400

300

200

100

0 0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

-100

-200 Strain ZZ

Figure 48-3

Results for the Thermo-Mechanical Model (Node Number 1292) Stress Strain Relation for Mechanical and Thermo-Mechanical Model

800 Therm-Mech T=0 Therm-Mech T=30 700

Thermo-Mech T=50 Mech T=0 Mech T=30

600

Mech T=50

500

Stress ZZ

400

300

200

100

0 0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

-100

-200 Strain ZZ

Figure 48-4

Comparison of the Mechanical and Thermo-mechanical Model (Node Number 1292)

992 MD Demonstration Problems CHAPTER 48

Input File(s) File

Description o

nug_48a.dat

Mechanical model with ambient temperature of T = 0 C

nug_48b.dat

Mechanical model with ambient temperature of T = 30 C

nug_48c.dat

Mechanical model with ambient temperature of T = 50 C

nug_48d.dat

Thermo-mechanical model with ambient temperature of T = – 150 C

nug_48e.dat

Thermo-mechanical model with ambient temperature of T = – 70 C

nug_48f.dat

Thermo-mechanical model with ambient temperature of T = – 0 C

nug_48g.dat

Thermo-mechanical model with ambient temperature of T = 10 C

nug_48h.dat

Thermo-mechanical model with ambient temperature of T = 30 C

nug_48i.dat

Thermo-mechanical model with ambient temperature of T = 50 C

o o

o

o

o

o o o

Reference Miyazaki, S., Otsuka, K., Suzuki, S. 1981. Transformation pseudoelasticity and deformation behavior in a Ti50.6at%Ni alloy. Scripta Metallurgica, 15 (3); 287-292.