Meso-F E analysis of textile composites: Solutions, challenges, - - PowerPoint PPT Presentation

▶
meso f e analysis of textile composites solutions
SMART_READER_LITE
LIVE PREVIEW

Meso-F E analysis of textile composites: Solutions, challenges, - - PowerPoint PPT Presentation

Mar 27, 2024 187 likes •688 views

Meso-F E analysis of textile composites: Solutions, challenges, problems Stepan V. LOMOV, Dmitry S. IVANOV, Ignaas VERPOEST Department MTM, Katholieke Universiteit Leuven Hiroaki NAKAI, Tetsusei KURASHIKI, Masaru ZAKO Department of

slide-1
SLIDE 1

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 1

Meso-F E analysis of textile composites: Solutions, challenges, problems

Stepan V. LOMOV, Dmitry S. IVANOV, Ignaas VERPOEST Department MTM, Katholieke Universiteit Leuven Hiroaki NAKAI, Tetsusei KURASHIKI, Masaru ZAKO Department of Management of Industry and Technology, Osaka University

slide-2
SLIDE 2

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 2

C

  • ntents

1. Introduction: Road map for meso-FE modelling of textile composites 2. WiseTex/MeshTex/SACOM: specialised state-of-the-art FE package for textile composites 3. Boundary conditions: Periodic and not-that-periodic 4. Damage modelling: Paradoxes of stiffness degradation scheme and new damage mechanics approach 5. Conclusions

slide-3
SLIDE 3

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 3

1. Introduction: Road map for meso-FE modelling of textile composites 2. WiseTex/MeshTex/SACOM: specialised state-of-the-art FE package for textile composites 3. Boundary conditions: Periodic and not-that-periodic 4. Damage modelling: Paradoxes of stiffness degradation scheme and new damage mechanics approach 5. Conclusions

slide-4
SLIDE 4

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 4

A gallery

3-axial braid Knitted SMA plain weave 3D woven stitched NCF

slide-5
SLIDE 5

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 5

Textile C

  • mposite A

rchive

https://textilecomposite.tamu.edu/ Laboratoire de Mécanique des Contact et des Structures, LaMCoS, INSA Lyon School M3, University of Nottingham Department MTM, Katholieke Universiteit Leuven Texas A&M University Department of Management of Industry and Technology, Osaka University

slide-6
SLIDE 6

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 6

meso-F E : R

  • ad map

Geometric modeller Geometry corrector Meshing Assign material properties Boundary conditions FE solver, postprocessor Homogenisation Damage analysis

N+1 N N+2

slide-7
SLIDE 7

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 7

1. Introduction: Road map for meso-FE modelling of textile composites 2. WiseTex/MeshTex/SACOM: specialised state-of-the-art FE package for textile composites

  • Geometric preprocessor: WiseTex
  • Problem of interpenetration of the yarns and solution
  • MeshTex: specialised mesher and data assignment
  • SACOM solver and post-processing
  • Example: 3D woven fabric

3. Boundary conditions: Periodic and not-that-periodic 4. Damage modelling: Paradoxes of stiffness degradation scheme and new damage mechanics approach 5. Conclusions

slide-8
SLIDE 8

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 8

WiseTex–MeshTex/S A C O M

WiseTex, K.U. Leuven MeshTex, Osaka University

slide-9
SLIDE 9

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 9

Interpenetration of yarn volumes z

  • z

Deformation Splitting Separation

slide-10
SLIDE 10

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 10

MeshTex: Meshing, woven fabrics

imported WiseTex model mesh finesse, yarns added space between yarns total thickness mesh finesse, matrix actual VF mesh quality corrected interpenetrations

slide-11
SLIDE 11

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 11

MeshTex: Material properties

matrix data fibre data, imported from WiseTex VF in the yarn, imported from WiseTex Homogenised UD, Chamis

slide-12
SLIDE 12

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 12

MeshTex: H

  • mogenisation

Stiffness matrix and engineering constants matrix data

slide-13
SLIDE 13

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 13

MeshTex, Boundary conditions

identical mesh on the corresponding faces

slide-14
SLIDE 14

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 14

MeshTex: S tress analysis

slide-15
SLIDE 15

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 15

D amage model (built-in in S A C O M) –1

Damage initiation: Hoffmann

2 9 2 8 2 7 6 5 4 2 3 2 2 2 1

) ( ) ( ) (

LT ZL TZ Z T L T L L Z Z T

C C C C C C C C C F

  • 2

9 2 8 2 7 6 5 4 3 2 1

1 , 1 , 1 1 1 , 1 1 , 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1

s LT s ZL s TZ c Z t Z c T t T c L t L c Z t Z c T t T c L t L c T t T c L t L c Z t Z c L t L c Z t Z c T t T

F C F C F C F F C F F C F F C F F F F F F C F F F F F F C F F F F F F C

Definition of the damage mode

L T Z

slide-16
SLIDE 16

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 16

D amage model (built-in in S A C O M) –2

slide-17
SLIDE 17

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 17

E xample: 3D woven fabric

eps_X in collaboration with A.E. Bogdanovich, D. Mungalov (3Tex)

slide-18
SLIDE 18

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 18

3D woven fabric –Tensile diagram

50 100 150 200 250 300 350 400 450 500 0.5 1 1.5 2 2.5 3 eps, % sig, MPa exp MeshTex 0.1 MeshTex 0.01

correct change of stiffness strength prediction depends on the assumed L-strength for UD

slide-19
SLIDE 19

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 19

P redictions of the damage onset

bundle-boundary cracks in Z-yarns transverse cracks in fill Experiment FE, strain 0.22% Damage starts at Z-yarn locations:

  • T-mode at the edges of fill
  • Z-mode in Z-yarns

FE, strain 0.30% T-mode in fill

slide-20
SLIDE 20

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 20

D eveloped damage

Experiment: strain 0.5% fill Z warp warp FE

slide-21
SLIDE 21

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 21

SACOM , Visu a l SACO M M esh Tex W iseTex

C

  • nclusions: WiseTex–MeshTex/S

A C O M

State-of-the-art numerical tool for preparation of FE models and FE analysis of textile composites on meso-structural level Geometric modeller Geometry corrector Meshing Assign material properties Boundary conditions FE solver, postprocessor Homogenisation Damage analysis

slide-22
SLIDE 22

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 22

1. Introduction: Road map for meso-FE modelling of textile composites 2. WiseTex/MeshTex/SACOM: specialised state-of-the-art FE package for textile composites 3. Boundary conditions: Periodic and not-that-periodic

  • Periodic BC for symmetry-reduced unit cells
  • Periodic BC for non-orthogonal unit cell
  • Deviation from periodicity: stress-strain fields near free surface

4. Damage modelling: Paradoxes of stiffness degradation scheme and new damage mechanics approach 5. Conclusions

slide-23
SLIDE 23

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 23

S ymmetry of a unit cell and reduction of size of the F E problem

1 Unit cell 2 Half of the UC Rotation around the x3 axis by 3 Quarter of the UC Rotation around the x1 axis by x1 -x2 coordinate plane coincides with the mid-plane of the braid

slide-24
SLIDE 24

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 24

d1 d2 P eriodic boundary conditions (translational symmetry)

slide-25
SLIDE 25

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 25

J.D.Witcomb et al. Derivation of boundary conditions…, J Compos Mat, 34, 9, 2000, 724-747

E quivalent co-ordinate systems

1 2 3 2 1 3

3 3 2 2 1 1

x x x x x x

  • 1

1 1

ij

a

i ij j

x a x

  • u i

(j k) (1) – i n u n (j k) (2) = j i d k (j k)- fixed indexes –point out the

macro deformation (6 boundary value problem to solve)

slide-26
SLIDE 26

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 26

BC : ¼of unit cell

un =0 uz (2) + uz (1) =0 uz (1=2) = 0 ut (2) – ut (1) =0 ut (1=2*) = 0 “B” and “C” un =0 uz (2) -– uz (1) =0 ut (2) + ut (1) =0 ut (1=2*) = 0 “A” normal, n thickness, z in-face, t

slide-27
SLIDE 27

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 27

N

  • n-orthogonal unit cell does not “forgive” errors in boundary conditions

UD - hexagonal packing

Dirichlet

u(x) = x x u(x) - = x x

Periodic BC Dirichlet = periodic

slide-28
SLIDE 28

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 28

D ifferent tricks Layered composite

Dirichlet Self-consistent Embedded

C x x x x C x x y y C y y y y C x y x y C x y y y C x y x x

Dirichlet Self-cons. Embedding

10 20 30 40 50 60 Dirichlet Self-cons. Embedding

Errors against the analytical solution,%

slide-29
SLIDE 29

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 29

C

  • rrect boundary conditions

d = { , b, 0} Periodicity vectors: kI = 2{a; 0, 0} =a(1+cos()), b= a sin() kII =2{c-a; b, 0} Two co-ordinate transformations: Rotation about the x3 axis of : Mirroring about the plane x1 -x2 and translation

  • 1

1 1

=

  • 1

1 1

= x i = i j xj x i =i j xj + i

U(mt)

p (x ) – p i U (mt) i ( j xj) = dm t p

U (mt)

p (x ) – p i U (mt) i ( j xj + i) = m t p

2= kI if x1= ctg( ) x2+const 2= kII if x2=const

slide-30
SLIDE 30

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 30

Boundary conditions for the quarter of the unit cell

slide-31
SLIDE 31

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 31

H

  • w different are stress-strain fields near the surface and inside?

Full “reference” problem Unit cell carbon/epoxy VF inside yarns 60% Ply thickness 0.49 mm Unit cell width 5.56 mm Tension in the direction x1:

  • BC in x1 direction: periodic
  • BC in x2 direction:

(Poisson from homogenisation solution)

11 12 22

  • Tension in the direction x1:
  • BC in x1 direction: periodic
  • BC in x2 direction:

(a) periodic (b) best to correspond to the reference solution near the surface 2D finite element solution

slide-32
SLIDE 32

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 32

P eriodic BC vsreference

Distribution of the relative volume of elements, where transverse stress in the 90 yarns lies within the interval in the N-ply laminate (N=2,4, ). NB: maximum differs 2 times!

40 / ) (

min max

  • (periodic)
slide-33
SLIDE 33

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 33

H

  • w to formulate correct boundary conditions for the surface plies?

Scheme I (=1) Scheme II

inner inner inner ij ij inner

  • uter
  • uter
  • uter

ij ij

  • uter
  • uter

inner

E E E E N E

11 11 11 11

min 2 ) 2 (

  • 1.15

1.19 1.25 1.37 1.71 unit cell 1.16 1.21 1.27 1.38 1.72 RS 6 5 4 3 2 N

slide-34
SLIDE 34

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 34

C

  • rrected boundary conditions vsreference, 6-ply laminate –1
slide-35
SLIDE 35

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 35

C

  • rrected boundary conditions vsreference, 4-and 6-ply laminate –2
slide-36
SLIDE 36

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 36

C

  • nclusions: Boundary conditions

1. Method of equivalent co-ordinate systems (J. Whitcomb) can efficiently handle difficult non-orthogonal configurations of textile composites. 2. Reduction of the model size can be effectively done using symmetry transformations of the unit cell 3. Promising new approach for correction of periodic boundary conditions for near-free-surface locations

slide-37
SLIDE 37

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 37

1. Introduction: Road map for meso-FE modelling of textile composites 2. WiseTex/MeshTex/SACOM: specialised state-of-the-art FE package for textile composites 3. Boundary conditions: Periodic and not-that-periodic 4. Damage modelling: Paradoxes of stiffness degradation scheme and new damage mechanics approach

  • Stiffness degradation scheme: reasonable prediction of damage initiation
  • Very bad prediction of damage propagation in case of prevailing shear
  • Inconsistency of damage mechanics (distributed cracks) and actual brittle

cracking in anisotropic fibrous material

  • Damage parameters based on overall damage development in structural

elements of the unit cell (rather then in individual finite elements)

5. Conclusions

slide-38
SLIDE 38

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 38

D amage initiation in 3-axial braided composite

3.25mm

slide-39
SLIDE 39

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 39

D amage propagation in 3-axial braided composite

Stiffness degradation scheme: same as in SACOM real damage: transverse cracks, propagating along braiding yarns Stiffness degradation scheme, applied to individual elements, leads to unphysical direction of propagation

  • f damage: across the fibres inside

the yarns damage zone

slide-40
SLIDE 40

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 40

A lso seen (but left without comments) by others…

Tang X., Whitcomb J. “Progressive failure behaviours of 2D woven composites” Journal of Composite Materials, 37, No 14 (2003), 1239-1259.

slide-41
SLIDE 41

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 41

The reason: intrinsic feature of local (element related) degradation

2 22 / F

  • 12

12 / F

  • 12

12 / F

  • Analytical solution

FE modelling Test problem: damaged “element” – small zone in UD composite. Q: Where the next damage initiation will be registered? A: When applied shear – at a position across fibres

Gorbatikh, L., D. Ivanov, S.V. Lomov, and I. Verpoest On modelling of damage evolution in textile composites on meso-level via property degradation approach. Composites Part A, 2007; 38: 2433-2442

slide-42
SLIDE 42

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 42

The paradigm of damage mechanics (D M) is not really applicable…

Damage mechanics:

  • degradation of microstructure occurs volume-wide and damage tensor is

representative of that volume wide degradation.

  • generally applicable when damage consists of a very large number of defects

that are more or less uniformly distributed throughout the considered volume.

  • riginally intended for modelling of damage accumulation in the material prior to

formation of detectable defects. Damage mechanics cannot be applied rigorously to modelling of damage evolution in textile composites

slide-43
SLIDE 43

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 43

… apply damage mechanics to larger, non-local volumes in yarns

averaging in the cross-sections 1. Damage initiation is assessed using Puck criterion 2. Damage parameter d is assigned for each zone, rather then for individual elements 3. Stiffness of all the elements in the zone is reduced according to d.

slide-44
SLIDE 44

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 44

D amage parameter: calculation

  • 13

2 13 12 23 2 23 12 12 2 12 1 33 11 13 2 2 22 33 23 2 2 22 11 21 3 2 33 2 2 2 2 22 1 2 11

1 1 2 1 2 1 2 1 2 1 G d G d G E d E d E E d E E

  • 1-3: directions of the most probable crack plane
  • 12

12

d Sup Y

t

  • Sup => non-healing damage
  • 23

2 23 12 2 12 2 12 33 23 11 21 2 2 22 12 2 2 2 2 12 12

1 2 1 1 1 1 G G d d d d d E d Y

  • X

X X X

d d if d d d d d d if d d

12 12 12 12 2 12 12 12 12 12 2

) ( 1 ) ( 1 2 1 Transverse damage parameter relates to shear damage parameter, which is the only one independent damage parameter

  • 2

23 23 2 12 12 13 33 12 11 2 22 22 22 2 12 2 12

2 1 1 1

  • G

G C C d C d d d Y

slide-45
SLIDE 45

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 45

D amage parameter: Identification

carbon/epoxy master curve for different VF

slide-46
SLIDE 46

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 46

R esults: 3-axial braid

experimental damage initiation Damage development (shear degradation parameter d12) in MD tensile test

Principal levels of applied strain and stress at failure: 1 - damage initiation; 2 –crack density increase (delamination onset); 3 – ultimate failure;

slide-47
SLIDE 47

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 47

C

  • nclusions: D

amage modelling

1. Continuum damage mechanics cannot be applied rigorously to modelling

  • f damage evolution in textile composites

2. Stiffness degradation scheme: Presence of shear leads to physically wrong predictions of the damage patterns, even if the stress-strain diagram is calculated correctly 3. Non-local damage model, based on thermodynamic (Ladeveze-type) approach gives good prediction for the stress-strain curve and threshold loads for damage development

slide-48
SLIDE 48

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 48

1. Introduction: Road map for meso-FE modelling of textile composites 2. WiseTex/MeshTex/SACOM: specialised state-of-the-art FE package for textile composites 3. Boundary conditions: Periodic and not-that-periodic 4. Damage modelling: Paradoxes of stiffness degradation scheme and new damage mechanics approach 5. Conclusions

slide-49
SLIDE 49

Downloaded from http://www.mtm.kuleuven.ac.be/Research/C2/poly/index.htm 49

S tate of the A rt

WiseTex – MeshTex (SACOM) – ANSYS/ABAQUS… Software Handled automatically in MeshTex “Separate and compress” algorithm: effective but difficult Contact pairs work OK for “wire” fabric Interpenetrations “Ivanov-Gorbatikh” paradox: wrong damage propagation for stiffness degradation model, prevailing shear Ladéveze-type approach more physically sound? Statistical difference: unit cell modelling and real sample Stiffness degradation OK Damage propagation Uncertainty in local (UD) strength Mesh issues can make a priori predictions questionable In general OK Damage initiation Mesh superposition is promising Meshes are generally bad. Need for a dedicated mesher? Strain fields OK for trends Local maxima may be artifacts of the bad mesh Homogenised properties OK. No need for FE Elastic deformation