• Thomas Bro Henriksen
  • Brian Lau Verndal Bak
4. term , Design of Mechanical Systems, Master (Master Programme)
In this report a procedure for analyzing the fracture resistance of interface cracks between similar or dissimilar layers of fibrous composite materials is developed. This is intended for a detailed simulation of delamination defects using fracture mechanics, as they cannot be analyzed by use of point stress or strain based criteria.

In advanced composite structures a significant amount of resources are spent on inspection and repair of production errors like dry-spots, which are areas where fibers have not been wetted by the resin. The developed procedure is intended to be used to evaluate whether or not a dry-spot or another kind of detected delamination in a composite structure is critical for the structural integrity, and therefore has to be repaired.

The propagation of cracks in fibrous materials is considered to be dependent on the critical energy release rate $G_{c,0}$ at the crack tip, as well as the crack length and end-opening due to fiber bridging across the crack faces behind the crack tip. Fiber bridging increases the fracture resistance against crack propagation until reaching a steady state crack length for which it is assumed constant, and this is accounted for in the developed procedure.

The criteria for determining propagation implies that the energy release rate at the crack tip must reach a material dependent critical value $G_{0} \geq G_{c,0}$. The energy release rate $G_0$ is calculated from the stress intensity factors, and these are estimated by use of the analytical expression for crack face displacements near the crack tip. The increase in fracture resistance from fiber bridging influences this criterion by causing tractions between the crack faces and thereby reduce the relative crack displacement. This means that an increased load can be applied before the critical values are reached.

An extensive study of fracture mechanical theory concerning interface cracks between two isotropic or anisotropic materials, with focus on obtaining expressions for the relative displacement of the crack faces, has been conducted and is described in this report.

A numerical method for simulating this criterion for a specific delamination crack based on solving the structural response using a finite element model is described. Results for the relative crack face displacement near the crack tip are exported to a parameter estimation used for determining the stress intensity factors related to the analytical expressions. This parameter estimation is formulated as an optimization problem minimizing the least squares difference between the numerical results and the analytical expressions by use of the conjugate gradient method with a golden section search.

In fracture mechanics the expressions for the relative crack face displacement are derived as infinite series of eigenfunctions, but in most literature they are presented by the first eigenfunction which only applies very close to the crack tip. As this calls for using small elements compared to structural dimensions in order to yield reliable results in the numerical procedure, analytical expressions for the relative displacement including the second and third eigenfunctions are derived.
These are implemented in the parameter estimation, and studies of the determination of the stress intensity factors show that it yields reliable estimation results for elements up to 10-20 times larger than when using the expressions with the first eigenfunction only. Similar studies have been conducted for orthotropic materials with the same conclusion.

A simulation of propagation of a crack in two similar orthotropic fiber materials with bridging is conducted for a plane DCB model in order to verify the modeling of fiber bridging based on assumed test results. The resulting R-curves are compared to these and show good correlation for the pure mode I and mode II, while for a mixed mode case the steady state fracture resistance is overestimated.
Publication date2010
Number of pages121
Publishing institutionDepartment of Mechanical and Manufacturing Engineering, Aalborg University
ID: 32305486