Modelling fatigue crack growth FCG

in adhesively bonded composite materials

Azhar Jamil, Department of Mechanical Engineering, AMU, Aligarh

POLITECNICO DI MILANO Technical University of Milan, Milan, Italy

Parma, Italy

Objectives

• Investigate the mechanical behaviour under fatigue loading, of

adhesively bonded composite materials.

• Based on the state of art, implementation of the principles of

fracture mechanics like virtual crack closure technique VCCT,

using numerical models based on commercial FE codes of

Abaqus® and Ansys® for modelling FCG.

• The ultimate goal of this work was to implement a crack

modelling technique in real industrial problems, where the

conventional methods fail to provide solution.

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Methodological approach

Modelling FCG is generally based on the implementation of the Paris law or its modified expressions, which maybe represented as

𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅

= 𝑩𝑩∆𝑮𝑮𝒅𝒅

where, da/dN is the advance of crack length per cycle, ΔG is the change in maximum SERR for that cycle, at the crack front

corresponding to peak loading. B & d are parameters depending on the material and load mixity ratio which are

generally obtained by fitting the experimental test data. Once the SERR values are known the procedure for the prediction becomes a simple numerical integration between the initial crack length a0 and the final crack length af of the inverse of the crack growth rate:

𝑁𝑁𝑓𝑓 = �1

𝐵𝐵 ∆𝐺𝐺 𝑑𝑑 𝑑𝑑𝑑𝑑 = 𝑎𝑎𝑓𝑓

𝑎𝑎𝑜𝑜�

1𝑑𝑑𝑑𝑑

𝑑𝑑𝑁𝑁�𝑑𝑑𝑑𝑑

𝑎𝑎𝑓𝑓

𝑎𝑎𝑜𝑜

Typical Paris Curve showing linear region

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Virtual Crack Closure Technique (VCCT)

Nomenclature b Element thickness ∆a Element length

Xi Force per unit length on node i in x-direction

Yi Force per unit length on node i in y-direction

Δul Difference of displacements between nodes l1 and l2

Δvl Difference of displacements between nodes l1 and l2

VCCT is a technique for the evaluation of strain energy release rate of a specimen using the principles of LEFM. It is based on the assumption that the strain energy released, when a crack is extended by a certain amount is the same as the energy required to close the crack by the same amount.

Basic Equations

𝐺𝐺𝐼𝐼=12𝛥𝛥𝑑𝑑

𝑌𝑌𝑖𝑖 𝑣𝑣𝑙𝑙2 − 𝑣𝑣𝑙𝑙1 ; 𝐺𝐺𝐼𝐼𝐼𝐼 =12𝛥𝛥𝑑𝑑

𝑋𝑋𝑖𝑖 𝑢𝑢𝑙𝑙2 − 𝑢𝑢𝑙𝑙1 Total energy release rate is : -

𝐺𝐺𝑇𝑇𝑇𝑇𝑇𝑇 = 𝐺𝐺𝐼𝐼 + 𝐺𝐺𝐼𝐼𝐼𝐼 𝐺𝐺𝐼𝐼𝐼𝐼𝐼𝐼 is the energy release rate for third mode of fracture which is zero for a 2D case

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Preliminary Analysis

Fatigue tests conducted on Double Cantilever Beam (DCB)

FCG experimental data from previous DCB Tests

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T300 Woven and Unidirectional Prepregs

T45 / UD45 / T0 / T45×2/ T0 / UD5 / T45

Paris Law in Mode I

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Preliminary Analysis

Numerical Modelling

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(a) Experimental FCG and VCCT

based GT and the Geq results. (b) VCCT and J-Integral Results

(c) VCCT results with different Paris

law parameters, for TLJ specimen (d) SERR distribution in 3D TLJ

(a) DCB Model (b) 2D TLJ Model (c) 3D TLJ Model

1. Bernasconi, A. Jamil, F. Moroni, A. Pirondi “A study on fatigue crack propagation in thick composite adhesively bonded joints’’, International Journal of Fatigue 50 (2013) 18–25.

• Based on the state of art, VCCT was used as implemented in Abaqus®, initially for static conditions in 2D and 3D for double cantilever beam DCB and single lap joint SLJ .

• The expertise gained during this activity was utilised for modelling tapered lap joint TLJ, both in two and three dimensions

Discrepancies between the FEA and analytical Results

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Results DCB

3Point Bending Tests

Emean & Gmean

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Further Tests

Data Reduction Scheme

Implementation of Timoshenko Beam on Winkler Elastic Foundation

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Results DCB

1. Bernasconi, A. Jamil, “Choice of an analytical scheme in correlating strain energy release rate, crack length & opening of the faces of an adhesively bonded, thick composite DCB specimen”, CompTest 2013, 6th International Conference on Composites Testing & Model Identification, Aalborg, Denmark, ISBN: 87-91464-49-8.

Observations

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0

10

20

30

40

50

60

0 10000 20000 30000 40000

a m

m

N

19kN VCCT Single Crack

VCCT Adhesive

Exp

0

20

40

60

80

100

120

0 50000 100000 150000 200000 250000

a m

m

N

14kN

VCCT Composite

VCCT Adhesive

EXP

Observations

These preliminary analyses were affected by the following limitations:

• FCG data were obtained in mode I, whereas FCG in TLJ takes place with varying

mixed mode ratio values, which depend on crack length.

• Results obtained in pure mode I and II did not allow for simulation of the

mixed mode FCG of the TLJ.

• Delamination of the first ply of the laminate took place in DCBs, followed by

severe fibre bridging; this might have affected values of the parameters of the

Paris Law.

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Observations

Simpler VCCT Mesh in the adhesive layer.

Enlarged Area

14 Variation of mixed mode ratio w.r.t. crack length

In order to overcome these limitations, a new

experimental plan was drawn, with FCG tests on

DCB (Mode I), ENF (Mode II), TLJ (all woven

laminate) and with different adherends

(unidirectional, woven, all woven laminate).

In order to improve the modelling phase, the

VCCT was adopted and carefully analysed.

Simpler VCCT Mesh in the adhesive layer.

Determination of Mixed mode Paris Parameters

• Experimental tests were conducted on Tapered Lap Joints TLJ on two different loads and the Paris Parameters were extracted from the data.

• In order to simulate FCG in real structures, a 3D model is required. Therefore, the Paris parameters for both plane stress and plane strain so obtained were compared with simulation of the FCG of TLJ obtained with 3D models.

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Fatigue tests conducted on Tapered Lap Joints (TLJ)

Determination of Mixed mode Paris Parameters

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TLJ test data with curve fitting along with Mode I and II Paris laws

Schematics of the methodology of evaluating mixed mode Paris Law. 1.5 Scaled MM Paris law parameters

VCCT models and comparison with CZM Modelling FCG using Abaqus® requires the ‘Direct Cyclic’ procedure VCCT based FCG models were developed & compared with Cohesive Zone Method

CZM • Double Cantilever Beam DCB geometry, for pure Mode I loading. • End Load Split ELS geometry, for pure Mode II loading. • Mixed Mode End Loaded Split MMELS geometry, for mixed mode I/II loading. • Single Lap Joint SLJ geometry, representing real geometry having Mixed mode I/II

loading with crack on a single side of the joint.

(a) DCB geometry

(b) ELS geometry

(c) MMELS geometry

(d) SLJ geometry

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VCCT models and comparison with CZM

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VCCT models and comparison with CZM

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1. A. Pirondi, G. Giuliese, F. Moroni, A. Bernasconi, A. Jamil,. “Simulation of fatigue delamination/debonding using cohesive zone and virtual crack closure, in Woodhead (Ed.), Fatigue and fracture of adhesively bonded composite joints: Behaviour, simulation and modeling.

2. G. Giuliese, A. Pirondi, F. Moroni, A. Bernasconi, A. Jamil, Comparative study of cohesive zone and virtual crack closure techniques for three-dimensional fatigue debonding, Journal of Adhesion

(a) DCB Specimen, Mode I (b) ELS Specimen, Mode II

(c) MMELS Specimen, Mixed Mode (d) SLJ Specimen, Mixed Mode

VCCT models and comparison with CZM

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1. G. Giuliese, A. Pirondi, F. Moroni, A. Bernasconi, A. Jamil, Three-dimensional fatigue debonding simulation: comparison of a cohesive zone- and a virtual crack closure-based techniques, AB 2013 Porto, Portugal, July 2013.

2. G. Giuliese, A. Pirondi, F. Moroni, A. Bernasconi, A. Jamil, A. Nikbakh, Fatigue delamination: A comparison between virtual crack closure and cohesive zone simulation techniques, 19th ICCM Canada, July 2013.

• A very good correspondence in the values of SERR obtained by VCCT along with the comparison with CZM, and J-integral (stationary crack).

• In the result of a vs. N, a small difference of about 2.5% was observed. • In terms computational times the following were observed

VCCT(Direct Cyclic) 676.2 mins

CZM 9.1 mins

Implementation in an Industrial Problem

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Implementation in an Industrial Problem

DIRECT CYCLIC 1. An industrial boom section was modeled using the ‘Direct Cyclic’ procedure for

modelling FCG in Abaqus®.

2. The section is composed of the following parts: • Inner Tube • Outer Tube

(a) Inner Tube (b) Outer Tube (c) Assembly of the Section

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DIRECT CYCLIC

(b) Detail of the size and position of the initial crack in the Direct Cyclic (a) Meshed assembly with SC8R continuum

shell elements

Implementation in an Industrial Problem

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Implementation in an Industrial Problem

DIRECT CYCLIC

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Implementation in an Industrial Problem

DIRECT CYCLIC

(a) Initial crack front in the

section (b) Propagated crack front in the

section

(c) Final simulation result plot depicting crack depth as a function of the

number of cycles

Conclusions Effective method in predicting the life of the component, however, involves enormous computational times which on average lasted for weeks on a workstation

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Ansys Solver (Static Analysis)

• Offers the same implementation of VCCT in static loading. • The structure of Ansys® is more flexible and can be employed in automating the

simplified static approach developed in Abaqus®, which still had the problems of modifying the mesh and repeating the solution with manual integration of SERR values over the Paris law.

• Flexibility in the Ansys® Advanced Parametric Design Language APDL, lead to the development of a user subroutine in Ansys® for automated mesh modification and automated integration of the Paris law.

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Ansys Subroutine

• Based on the drawbacks in the ‘Direct Cyclic’ algorithm, particularly concerning the computational times

• Subsequent manual mesh modifications and manually integrating the results are quite cumbersome.

Subroutine Flowchart

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Conclusions

Comparison of SERR values extracted

Comparison of a-N values

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Thank You