Behaviour of Bolted Joints Of FRP Composite Laminated Structures

By:Hitesh Parghi (13517012)Under Guidance ofDr. Anupam Chakrabarti

First Evaluation Presentation on

Presentation outline Factors affecting behavior of bolted joints in Fibre Reinforced Composites Model Development & Validation

Problem description Model development Validation

Implementation of Progressive Failure Introduction User subroutine : USDFLD USDFLD Validation

Parametric study Aspects Results & discussion

Future study scope Conclusions References

Factors affecting behavior of bolted joints in Fibre Reinforced

Composites

Failure modes and bearing strength - Important behavioural aspects to be studied for any bolted joint

By altering some factors - Desired failure mode and strength can be achieved

This factors are divided in Three distinct categories (Godwin et al. 1980) Material Parameters (i.e., Lamination scheme) Fastener Parameters (i.e., Tightening torque) Design Parameters (i.e., e/d ratio)

Need of the hour : Numerical models should be developed which can simulate behaviour of joints close to real life scenario

Model development & validation

Present study : A three dimensional finite element model – In Abaqus Verification against available results Development of user subroutine – Nonlinear model Validation of nonlinear model against available results Parametric studies

Problem description

Figure & Table 1. Joint geometry (McCarthy et al. 2004)

Length of each plate (l) 155 Diameter of bolt (d) 8Width of each plate (w) 48Thickness of each plate (t) 5.2Edge distance (e) 24Washer dimensions (OD, ID, Thickness)

15, 8.4, 1.2

Model Development : Parts

Figure 2. Parts

Composite Plate

Nut & HeadWasher

Bolt Shank

Figure 3. Assembly

• Bolted composite joint - - Three dimensional in nature (Padhi et al. 2002)• Clamping force, Bending of bolt, Delamination are

in third dimension• Plates also show out of plane deformations

• Three dimensional deformable solid parts

• Grip length excluded – Reduce analysis time

• Further partition of parts – Efficient meshing

• Parts are assembled together to form joint

Model development : Materials

Table 2. Mechanical Properties (McCarthy et al. 2004)

• Plates - CFRP (HTA/6376) - [45/0/-45/90]5s (Total 40 plies)• Bolt & nut - Aerospace grade Titanium alloy• Washer - Steel

CFRP (HTA/6376)E11

(Gpa)E22 (Gpa) E33

(Gpa)G12

(Gpa)G13

(Gpa)G23

(Gpa)ν12 ν13 ν23

140 10 10 5.2 3.9 3.9 0.3 0.3 0.5XT (Mpa) XC(Mpa) YT(Mpa) YC(Mpa) S12(Mpa) S23(Mpa)

2170 1600 73 250 83 50Titanium (Bolt) Steel (Washer)

E (GPa) ν E (GPa) ν110 0.29 210 0.3

Figure 4. Lamination scheme [45/0/-45/90]5s

90

- 45

0

45

Model development : Contact & Loadu=0,v=0,w=0 v=0,w=

0

Figure 5. Plate to Plate Contact

Figure 6. Bolt Contact with other Parts

Figure 7. Washer Contact with other

Parts

Figure 8. Uniaxial Displacement

Figure 9. Bolt preload

• Bolt preload• To simulate bolt tightening• 7.2 MPa (Identical to finger

tight bolt) (McCarthy et al. 2004)

Model development : Mesh

• Abaqus element C3D8R (8 node - 3 Dimensional solid elements)

• Finer mesh near hole• To accommodate higher stress concentrations

• No. of elements = 71252

Figure 10. Meshed parts & Model

-600-500-400-300-200-10001000

1

2

3

4

5

6

McCarthy et al. (2004)

Present

Stress (MPa)

Dist

ance

alo

ng p

ath

(mm

)

0 10 20 30 40 50 60 70 80

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

McCarthy et al. (2004)

Ekh et al. (2001)

Present

Distance along path (mm)

Out

of p

lane

disp

lace

men

t (m

m)

Model validation

McCarthy et al. (2004) Present Difference (%)

34.60 34.21 -1.12

1. Joint Stiffness (kN/mm)

2. Out of plane displacement ( u3 )

3. Stress variation

Table 3. Validation – Joint stiffness

Progressive failure analysis• Abaqus do not provide damage modelling for 3D solid elements of Fibre

reinforced composites therefore with default material library only linear analysis can be performed

• To implement damage models & non linear analysis one have to code user subroutines (UMAT, USDFLD, etc.)

• In present study user subroutine UMAT (User material) & USDFLD (User defined field variables) are coded in Fortran compiler & coupled with Abaqus solver to enhance material modelling capabilities of Abaqus• UMAT – Can model complex material constitutive relations (Gave convergence issues)• USDFLD – Properties can be dependent on field variables (Used for Progressive failure

in present study)• Progressive failure analysis

• Failure mode is evaluated (Fibre failure or Matrix failure)• Corresponding properties are degraded• Redistribution of stresses to other elements

Hashin’s failure theory

• Classical failure theories do not distinguish between fibre and matrix failure

• Hashin (1980) proposed new failure criteria for unidirectional fibre reinforced composites

2 2 212 1311

212

1 failure 1 no failureTX S

2

11 1 failure 1 no failureCX

13

2 2 221222 33 23 22 33

2 2 223 12

1 failure 1 no failureTY S S

13

2 2 2 221222 3322 33 23 22 33

2 2 223 23 23 12

1 failure 1

1 no failure2 4C

C

YS Y S S S

Fibre Tension Failure- If σ11 ≥ 0,

Fibre Compression Failure- If σ11 < 0,

Matrix Compression Failure - If σ22 + σ33 < 0,

Matrix Tension Failure - If σ22 + σ33 > 0,

Property degradation

• If failure has occurred –• Gradual degradation • Instantaneous degradation (Identical to real life

scenario) • Reduction to 95% in original value of property

Property

Tensile

Fibre

Compressive Fibre

Tensile Matrix

Compressive Matrix

E11 X X - -E22 - - X XE33 - - X XG12 X X - -G13 X X - -G23 - X X X

Table 4. Property degradation rules

Get stresses from Abaqus

Check weather failure has occurred ?

Return values of field variable to

Abaqus

Field variable = 1Field variable = 0

If, yesIf, No

Check value of field variable

Continue analysis with

same properties

Reduction in properties

If, 0 If, 1

USDFLD

USDFLD

FLOW CHART

Get stresses

Check for failure

Update field variables

Property definition

Figure 11. USDFLD Flow Chart

USDFLD VALIDATION• Verification against –

• Plate (Reddy et al. 1995)• Experiments • Simulations

• Bolted joint (McCarthy et al. 2001)• Experiments • Nonlinear simulation

Model Lamination scheme Length (mm)

Width (mm)

Depth (mm)

L1 (45/90/-45/0)3s 76.2 25.4 6.35L2 (45/90/-45/0/0/0/-

45/0/0/0/45/0)s

76.2 25.4 6.35

L3 (45/90/-45/45/-45/0/45/-45/45/-45)s

76.2 38.1 6.35

Figure 12. Single bolted joint (McCarthy et al. 2001)

Figure 13. Composite plate (Reddy et al. 1995)

Table 5. Model description - Composite plate (Reddy et al. 1995)

USDFLD Validation (with Reddy et al. 1995)

L1

L2

L3

0 20 40 60 80 100 120 14078.819999999999

9

123.04

39.23

80.2

125.2

45.8

1.77

1.76

14.73

Comparision : Ultimate Load

Diff.(%)

Present (Simulation)

Experiments

Ultimate Load (kN)0 0.5 1 1.5 2 2.5

0102030405060708090

Experimental Ultimate Load

= [Y VALUE] kN

Load displacement curve (L1)

Reddy et al. (1995)Present

Displacement (mm)

Load

(kN

)

0 0.5 1 1.5 2 2.50

20

40

60

80

100

120

140Experimental Ultimate Load

= [Y VALUE] kN

Load displacement curve (L2)

Reddy et al. (1995)Present

Displacement (mm)

Load

(kN

)

0 0.5 1 1.5 2 2.505

101520253035404550

Experimental Ultimate Load

= [Y VALUE] kN

Load displacement curve (L3)

Reddy et al. (1995)Present

Displacement (mm)Lo

ad (k

N)

USDFLD Validation (with McCarthy et al. 2001)

0

5

10

15

20

25

30 27.03 27.39

1.33

Comparision : Ultimate Load

ExperimentsPresent (Simulation)Diff.(%)

Ult

imat

e lo

ad (

kN)

0

0.5

1

1.5

2

2.5

3 2.993.18Comparision : Displacement at ultimate Load

ExperimentsPresent (Simulation)D

ispl

acem

ent

at u

l-ti

mat

e lo

ad (

mm

)

0 0.5 1 1.5 2 2.5 3 3.5 405

10152025303540 Load displacement curve (Single

Bolt)

ExperimentsPresent (Simulation)McCarthy et al. (Non linear Simu-lation)

Displacement (mm)

Load

(kN

)

Parametric study• Linear and nonlinear models are in good agreement with past

experiments and simulations• So for further study parameters are varied and effect of these parameters

on behaviour of bolted joints of fibre reinforced composite material• Various factors affecting behaviour of bolted joints were listed in previous

slides• For current study following factors are varied

1. e/d • e/d = 1• e/d = 2• e/d = 3• e/d = 4• e/d = 5

2. Lamination

scheme• [0/0/0/0]5s• [0/45/0/45]5s• [0/-45/0/-45]5s• [0/90/0/90]5s• [45/-45/45/-45]5s• [45/0/-45/90]5s

Variation of e/d• Up to certain value of e/d, increase in strength with increasing

e/d ratio

e/d Edge distance (e)

Hole diameter (d)

Length of each plate (l)

1 8 8 482 16 8 643 24 8 804 32 8 965 40 8 112

1 2 3 4 5

Table 5. Model dimensions for different e/d ratios

Results & Discussion

1 2 3 4 520

25

30

35

40

23.65

34.71 34.2132.12

30.38

Joint Stiffness

e/d ratio

Join

t st

iffne

ss

(kN

/mm

)

0 0.08 0.16 0.24 0.32 0.4 0.48 0.56 0.64 0.72 0.8 0.88 0.96 1

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

Out of plane displacement (For 1 mm axial displacement)

e/d=1e/d=2e/d=3e/d=4e/d=5

Normalised Distance, Along Length (mm)

Out

of

plan

e di

stan

ce

U3

(mm

)

1 1.5 2 2.5 3 3.5 4 4.5 512.5

17.5

22.5

27.5

15.58

25.9727.39 27.78 27.49

Ultimate load

e/d ratio

Ult

imat

e lo

ad (

kN)

• After e/d > 2 • Ultimate load gets stable• Decrease in joint stiffness

e/d = 1

e/d = 2

e/d = 3

e/d = 4

e/d = 5

Final failure – Total failure mode (Fibre + Matrix)

Figure 14. Total failure mode

Variation of Fibre orientation (Lamination scheme)

• Fibre orientation – Mainly effects failure mode of bolted connection

0

0

0

45

45

00

0

-45

45

-45

90

45

-450

0

0

-45

45

90

0

0

90 -45

• 6 different ply stacking sequence (e/d = 3)• 5 layers of above lamination scheme & a symmetric layer of same 20 plies – Total

of 40 plies

Figure 15. Variation of fibre orientation

Results and discussion : Ultimate load

0

5

10

15

20

25

30

18.5620.11

21.5923.55 23.62

27.39

Comparision : Ultimate load

[45/-45/45/-45]5s[0/0/0/0]5s[0/90/0/90]5s[0/-45/0/-45]5s[0/45/0/45]5s[45/0/-45/90]5s

Ultim

ate

load

(kN

)

• Laminate without 0° plies – • Very low load bearing capacity & a

stable failure • Laminate with only 0° plies –

• Little higher strength but early but catastrophic failure

• Asymmetric laminate – • Highest strength and stable failure

mode

For uniaxial loading,

Results & discussion : Failure modes

[0/-45/0/-45]5s [0/45/0/45]5s

[0/90/0/90]5s [0/0/0/0]5s [45/-45/45/-45]5s

[45/0/-45/90]5s

Figure 16. Total failure mode

Future study scope

• Detailed analysis of results obtained• Combined study of e/d ratio & fibre orientation• Variation of tightening torque & Temperature• Application of progressive failure to multi bolt joint

Conclusions• Linear & Non linear models – Good agreement with

experiments & other simulations• Parametric study – e/d ratio & Fibre orientation• Following observations are made -

For e/d>2 o No major change in strength of jointo Stable failure mode is achieved

Composite with no 0° fibres – Very low strength Asymmetric fibre orientation – 50 % Higher strength then

laminate without 0° fibres and a stable failure mode is achieved Use of 45° or -45° fibres – No noticeable change in strength and

failure mode

References• Abaqus CAE user’s manual , (2013), Version 6.13, Dassault systems.• Godwin E.W., Matthews F.L. , (1980), A Review of the strength of joints in fibre-

reinforced plastics , Composites, Vol. 10, pp. 155-160.• Padhi G.S., McCarthy M.A., (2002), McCarhty C.T., BOLJAT : a tool for designing

composite bolted joints using three-dimensional finite element analysis, Composites Part A : applied science & manufacturing, Vol. 33, pp. 1573-1584.

• McCarthy M.A., McCarthy C.T., Lawlor V.P., Stanely W.F. , (2004), Three-dimensional finite element analysis of single-bolt, single-lap composite bolted joints:P1—Model development and validation, Composite structures ,Vol. 71, pp. 140-158.

• Reddy Y.S.N., Dakshina Moorthy C.M., Reddy J.N., (1995), Non-linear progressive failure analysis of laminated composite plates, Int. J. Non-linear Mechanics, Vol. 30, pp. 629-649

• Lawlor V.P., McCarthy M.A., Stanely W.F., (2001), Experimental study on the effects of clearance on single-bolt, single-shear, composite bolted joints, J. Plastic rubber and composites, Vol. 31, pp. 405-411.

• Z. Hashin, (1980), Failure criteria for unidirectional fibre composites, J. of applied mechanics ASME, Vol.47, pp. 329-334.

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