بحث بعنوان Phase Field Fracture Predictions of Microscopic Bridging Behaviour of Composite Materials
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 بحث بعنوان Phase Field Fracture Predictions of Microscopic Bridging Behaviour of Composite Materials

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بحث بعنوان
Phase Field Fracture Predictions of Microscopic Bridging Behaviour of Composite Materials
Wei Tan a, Emilio Martínez-Pañeda b,∗
a School of Engineering and Materials Science, Queen Mary University London, Mile End Road, London, E1 4NS, UK
b Department of Civil and Environmental Engineering, Imperial College London, London SW7 2AZ, UK

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A R T I C L E I N F O
Keywords:
Fracture toughness
Polymer-matrix composites (PMCs)
Finite element analysis (FEA)
Damage mechanics
Phase field method
A B S T R A C T
We investigate the role of microstructural bridging on the fracture toughness of composite materials. To achieve
this, a new computational framework is presented that integrates phase field fracture and cohesive zone
models to simulate fibre breakage, matrix cracking and fibre–matrix debonding. The composite microstructure
is represented by an embedded cell at the vicinity of the crack tip, whilst the rest of the sample is modelled as
an anisotropic elastic solid. The model is first validated against experimental data of transverse matrix cracking
from single-notched three-point bending tests. Then, the model is extended to predict the influence of grain
bridging, brick-and-mortar microstructure and 3D fibre bridging on crack growth resistance. The results show
that these microstructures are very efficient in enhancing the fracture toughness via fibre–matrix debonding,
fibre breakage and crack deflection. In particular, the 3D fibre bridging effect can increase the energy dissipated
at failure by more than three orders of magnitude, relative to that of the bulk matrix; well in excess of the
predictions obtained from the rule of mixtures. These results shed light on microscopic bridging mechanisms
and provide a virtual tool for developing high fracture toughness composites.
Conclusions
We have proposed a novel computational framework capable of
modelling the influence of matrix–fibre microstructures on the crack
growth resistance of composites. This is achieved by combining phase
field fracture, to capture matrix and fibre cracking, with a cohesive
zone model, to simulate matrix–fibre debonding. Fibre–matrix interaction mechanisms, such as fibre-bridging, are explicitly resolved in
both 2D and 3D for the first time. Several boundary value problems
with various microstructures are simulated to showcase the capabilities of the framework and gain physical insight into the roles of
constituent properties and matrix–fibre interactions on macroscopic
fracture resistance.
Firstly, the model is validated against data from single-edge notched
beam bending experiments. Our predictions are in very good agreement
with the experimental results, in terms of both the load–displacement
response predicted and the crack trajectory. The role of different microstructures on crack growth resistance is subsequently explored. We
show that the use of bridged fibres of rectangular prismatic shape
(‘‘grains’’) is a very efficient strategy to enhance fracture resistance as
a significant amount of energy is dissipated via fibre–matrix debonding
and fibre breakage. The design of brick-and-mortar microstructures also
shows a noticeable elevation in the fracture toughness, comparable to
the continuous fibre reinforcement with a much smaller fibre volume
fraction, due to a significant amount of crack deflection and crack
branching events.
The simulation of 3D boundary value problems enables gaining
a unique insight into fibre toughening mechanisms. Energy dissipating mechanisms such as fibre bridging, fibre–matrix debonding, fibre
breakage and matrix cracking can notably elevate toughness predictions. We quantify the role of the fibre fracture toughness, the fibre
volume fraction and the fibre–matrix interface toughness. A significant
increase in crack growth resistance is observed when weakening the interface, due to increased fibre–matrix debonding, and when increasing
the fibre volume fraction and toughness. Toughness values predicted
shortly after the onset of crack growth turn out to be several orders of
magnitude larger than those predicted using the rule of mixtures.
The computational framework presented provides a powerful virtual tool to investigate the role of the microstructure and material
properties on the fracture behaviour of composite materials and structures of arbitrary geometries and dimensions. This will promote a
more efficient design paradigm for improving the fracture toughness
of damage-tolerant or energy-absorbing composites.


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