Creep Of A Tube

Chapter 51: Creep of a Tube

51

Creep of a Tube



Summary



Introduction



Modeling Details



Solution Procedure



Results



Modeling Tips



Input File(s)

1051 1052 1052

1055 1057 1057

1053

CHAPTER 51 1051 Creep of a Tube

Summary Title

Chapter 51: Creep of a Tube

Features

Real time creep analysis based on adaptive time stepping • Assumed strain formulation to ease bending locking

Geometry x-symmetry 0.26 in

y-symmetry pressure X Z

Y

1.9175 in

Material properties

4.51 · E = 21.46Mpsi ,  = 0.3 , Norton Creep  c = 4x10 – 24 

Analysis characteristics

Quasi static analysis using adaptive time stepping for real time creep with geometric and material nonlinearity due to large strain and creep

Boundary conditions

Only half of the tube is modeled due to symmetry. The symmetric conditions are applied to suppress rigid body motions

Applied loads

• A pressure of 66 psi is applied to the inner surface of the tube in the first load step within the second. This is to apply pressure load at the beginning of analysis. • At the second load step, the pressure load remains unchanged for 1000 hours during the creep step.

Element types

CQUAD4 with assumed strain formulation

FE results

Creep strain contours on deformed shape

1052 MD Demonstration Problems CHAPTER 51

Introduction This problem demonstrates the ability of the Nastran SOL 400 nonlinear solution sequence to perform a creep analysis using adaptive time stepping. A stainless steel oval is pressurized at a uniformly high temperature and over time allowed creep. The details of the finite element model, material and creep properties, load, boundary conditions, solution procedure, and adaptive creep stepping are discussed below.

Modeling Details Element Modeling The FE-mesh of the tube is shown in Figure 51-1. The model consists of 200 4-node plane strain elements and 255 nodes. Only half of the tube is modeled due to symmetry. The symmetric conditions are applied to suppress rigid body motions.

X Y

Figure 51-1

Z

The Finite Element Mesh of (half of) the Tube

Besides the standard options to define the element connectivity and grid coordinate location, the bulk data section contains various options which are especially important for nonlinear analysis. The nonlinear extensions to lowerorder plane strain element CQUAD4 can be activated by using the PSHLN2 property option in addition to the regular PLPLANE property option: PLPLANE 1 PSHLN2 1 + C4

1 1 PLSTRN

1 L

1.0

+

The PSHLN2 option allows the element to be used in both large displacement and large strain analysis and has no restrictions on the kinematics of deformation unlike the regular CQUAD4 elements with only the PLPLANE property entry. These standard elements are more suitable for large rotations but small strain analysis due to their linear formulation in the co-rotational system. While the difference may be small or even negligible in a truly linear analysis, nonphysical behavior may be seen in the results from analyses in which the linear assumptions are exceeded and these options are not used.

Material Modeling The isotropic, Hookean elastic material along with the creep properties are defined using the following MAT1 and MATVP options: MAT1 MATVP

1 1

2.14+7 4.e-24

.3 4.51,

CHAPTER 51 1053 Creep of a Tube

The Young's modulus is taken to be 21.4 Mpsi with a Poisson's ratio of 0.3. The Norton creep model is defined by 4.51 ·  c = 4x10 – 24  . The standard options to define the element connectivity, the grid locations, and the element properties are used in the bulk data section of the input: $ Elements and PSHELL 1 $ Elements in: CQUAD4 1 CQUAD4 2 ... $ Elements and PSHELL 2 $ Elements in: CQUAD4 169 CQUAD4 170 ... $ Nodes of the GRID 1 GRID 2

Element Properties for region : lower_plate 1 1.2 1 1 "lower_plate" 1 1 2 13 12 1 2 3 14 13 Element Properties for region : upper_plate 1 1.2 1 1 "upper_plate" 2 211 212 231 230 2 212 213 232 231 Entire Model 0. 10.

0. 0.

0. 0.

...

Loading and Boundary Conditions The symmetric conditions are defined to suppress the rigid motion motions: SPCADD SPC1 SPC1

2 1 216 3

1 1 226 2

3 81 236 16

91 246 32

101

111

121

48

64

80

206

A pressure of 66 psi, acting on the inner surface of the tube, is converted to a set of equivalent nodal forces: LOAD FORCE FORCE ...

3 2 2

1. 1 2

1.

2 1.573 1.573

1. 1.

0. 0.

Solution Procedure Control Parameters Creep and large strain effects are included in the nonlinear analysis using the option: NLMOPTS,CREEP, ,LRGSTRN,1, ,ASSM,ASSUMED

0. 0.

1054 MD Demonstration Problems CHAPTER 51

The CREEP field activates the creep analysis. The LRGSTRN field indicates the use of large displacement, large rotation kinematics and large strains of the element. Because it is an analysis with isotropic, elastic Hookean material, and the large strain option is on, the assumed strain formulation is toggled on with the NLMOPTS input. The assumed strain formulation provides better bending behavior for the continuum elements.

Solution Parameters The case control section of the input contains the following options for nonlinear analysis: SUBCASE 1 STEP 1 TITLE=This is a default subcase. ANALYSIS = NLSTATIC NLSTEP = 1 SPC = 2 LOAD = 3 DISPLACEMENT(SORT1,REAL)=ALL NLSTRESS(SORT1,REAL,NLOUT=101)=ALL STEP 2 TITLE=This is a default subcase. ANALYSIS = NLSTATIC NLPSTEP = 2 SPC = 2 LOAD = 3 DISPLACEMENT(SORT1,REAL)=ALL NLSTRESS(SORT1,REAL,NLOUT=101)=ALL $ BEGIN BULK NLOUT 101 CCASTRSS CCRPSTRN $

EQCRSTRN

The analysis contains a single subcase with two steps. The internal pressure of the tube is applied in the first load step in one increment. The real time in the first load step is second implying (nearly) no creep in the step. In the second load step, the pressure remains unchanged for seconds to allow the material to creep. Each step has a convergence control via NLSTEP, single point constraints via SPC, load via FORCE, and the displacements and stress results for the .f06 (output) file. The NLOUT entry specifies the quantities of output sought via Cauchy stress, creep strain, and equivalent creep strain. The nonlinear procedure used is defined through the following NLSTEP entry. In the first load step: NLSTEP

1 1.00E-09 GENERAL 40 FIXED 1 MECH PV 0.00

0 1

10 .100E-010.00

0 PFNT

0

3

$ The total time of this step is 1.0E-09 with fixed stepping of one increment. The PV method is used for convergence control with the tolerance as 0.01 and with stiffness update method as PFNT signifying full Newton Raphson procedure with stiffness being updated during every iteration.

CHAPTER 51 1055 Creep of a Tube

In the second load step, the load stepping is controlled by the following NLSTEP entry: NLSTEP

2 3.47e6 GENERAL 40 0 ADAPT 5.0E-06 1.0E-12 .500 0 .200E-03 MECH PV 0.00 .100

$ TABSCTL ENCSI

10 1 0.00

1 6 1.50 -1 999999 1 1 .100 10.0 PFNT -1 3

1 5.00E-011.00E+30

The NLSTEP entry for the second load step has the total time as 3.47e6. Adaptive time stepping is employed in this step with user-driven criteria using the option CRITID=1 (5th field in second line of the ADAPT entry). The TABSCTL entry specifies the user criteria for load step control which is referred to by the NLSTEP entry for the second load step. The data ‘ENCSI’ specifies the type of user criterion to use followed by the first and second target values (5.00e-1 and 1.00e+30).

Results Figure 51-2 shows the original and deformed tube at the end of simulation. The x-displacements of node 80, node with largest displacement, after the two load steps are 5.486e-3 and 2.083e-1 in, respectively (Figure 51-3). About 98% deformation comes from the material creep.

Figure 51-2

Original and the Deformed Tube

1056 MD Demonstration Problems CHAPTER 51

Figure 51-3

X Displacement History for Node 80

A curve of the equivalent von Mises stress with respect to the creep strain at node 80 is given in Figure 51-4. The significant stress relaxation over time due to creep effects can be observed.

Figure 51-4

Curve of Equivalent Stress via Creep Strain at Node 80

CHAPTER 51 1057 Creep of a Tube

Modeling Tips There are three critical inputs for a creep analysis. • Activate creep analysis using NLMOPTS,CREEP, • Input creep material properties using MATVP (and MATEP for implicit creep). • Define real time adaptive stepping for creep using NLSTEP.

Input File(s) File nug_51.dat

Description MD Nastran input