When a crack propagates in a composite material perpendicularly to the reinforcing fibers, a substantial part of the energy is dissipated in the frictional debonding and sliding of the bridging fibers located behind the advancing crack front.
The primary objective of this project, supported by the NSF Mechanics and Materials Program, is to investigate these two energy absorption mechanisms.
A special numerical tool, referred to as the cohesive/volumetric finite element scheme is being developed and implemented to simulate the spontaneous crack initiation and propagation along the fiber/matrix interface.  Special emphasis is placed on the precise capture of the frictional contact taking place between the crack faces.  A thermal component is introduced in the dynamic code to capture the frictional heating which has been shown in some experiments to play a major role in the fracture resistance of the composites under dynamic loading conditions.
In this project, we collaborate with two experimental groups: Professor Nancy Sottos, from the Department of Theoretical and Applied Mechanics, and her students are conducting detailed quasi-static fiber pushout experiments on model composite systems.  Professor John Lambros, from the Department of Mechanical Engineering at the University of Delaware, and his student are investigating the dynamic fiber pullout and pushout process on similar model composite systems.
Excellent agreement with experimental observations has recently been achieved in the quasi-static case.
 
 

 
The method, called the Cohesive/Volumetric Finite Element (CVFE) scheme, is similar to that used in the composite impact induced delamination project.  The major differences are
• the axisymmetric geometry;
• the emphasis on the capture of crack face contact, including, in the dynamic case, the associated frictional heating;
• cohesive elements are only introduced at the interface between the matrix and the fiber.

Xiaopeng Bi (Ph.D. student)
Dr. Guoyu Lin (formerly part of the Center for the Simulation of Advanced Rockets, currently at ANSYS)
 
 

The following figure presents the result of a preliminary simulation of dynamic fiber pullout performed by Xiaopeng Bi.  The model composite is made of a single plyester "macro-fiber" embedded in an epoxy matrix.  At time t=0, the fiber is suddenly pulled from the bottom at a velocity of 6.5m/s.  The fracture toughness of the interface is chosen as 100N/m, which is similar to the values measured in quasi-static experiments.  The first picture shows the mesh used to discretize the fiber/matrix specimen.  The cohesive elements are introduced along the fiber/matrix interface.  The entire mesh is shown on the left figure, while detail on the interface region is shown on the right one.

The second figure shows two snapshot (after 4 and 100 microseconds) of the fiber debonding process, as the crack propagates upward along the fiber/matrix interface.  Dimensons are given in millimiters.  The contours present the distribution of shear stress (expressed in MPa), showing how the cohesive/volumetric finite element scheme captures the stress concentration present in the vicinity of the rapidly spontaneously propagating crack tip.
 

Dynamic fiber pullout in a model polyester/epoxy composite system.  Dimensions are given in mm and
stress values in MPa.

The next two figures present a comparison between numerical and experimental results for the quasi-static fiber pushout problem for the same polyester/epoxy model composite system.  The first figure shows the evolution of the punch force with the punch displacement (expressed in mm).  The second figure presents the crack location vs. punch displacement curve.  In both cases, the agreement between experimental and numerical results is excellent.  The numerical scheme is also able to predict the onset of unstable crack propagation characterized by a sudden drop in the punch load.  This work has been recently performed by Dr. Guoyu Lin.