modelling fatigue crack growth fcg in adhesively … • investigate the mechanical behaviour under...
TRANSCRIPT
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