Delamination Behaviour of Composites

Srinivasan Sridharan

• Publisher: Woodhead Publishing
• Year: 2008
• Print ISBN:
  9781845692445
• eBook ISBN:
  9781845694821
• Topic: Technology & Engineering
• Subtopic: Materials Science
• Index: Technology & Engineering

Given such advantages as low weight compared to strength and toughness, laminated composites are now used in a wide range of applications. Their increasing use has underlined the need to understand their principal mode of failure, delamination. This important book reviews key research in understanding and preventing delamination.The first part of the book reviews general issues such as the role of fracture mechanics in understanding delamination, design issues and ways of testing delamination resistance. Part two describes techniques for detecting and characterising delamination such as piezoelectric sensors, the use of lamb waves and acoustic emission techniques. The next two sections of the book discuss ways of studying and modelling delamination behaviour. The final part of the book reviews research on delamination behaviour in particular conditions such as shell and sandwich structures, z-pin bridging and resin bonding.With its distinguished editor and international team of contributors, Delamination behaviour of composites is a standard reference for all those researching laminated composites and using them in such diverse applications as microelectronics, aerospace, marine, automotive and civil engineering. - Reviews the role of fracture mechanics in understanding delamination, design issues and ways of testing delamination resistance - Discuss ways of studying and modelling delamination behaviour - A standard reference for all those researching laminated composites

Part I

Delamination as a mode of failure and testing of delamination resistance

1

Fracture mechanics concepts, stress fields, strain energy release rates, delamination initiation and growth criteria

I.S. Raju; T.K. O’Brien NASA-Langley, Research Center, USA

1.1 Introduction

A complete understanding of composite delamination requires an appreciation for the fundamental principles of fracture mechanics and how these principles have been extended from the original concepts developed for isotropic materials to include the anisotropy typically present in composite materials. These extensions include the complexities of oscillatory singularities that occur for interface cracks in anisotropic media, and how these singularities are resolved for delamination growth prediction. Furthermore, full implementation of Interlaminar Fracture Mechanics (ILFM) in design requires development of composite delamination codes to calculate strain energy release rates and advancements in delamination growth criteria under mixed mode conditions for residual strength and life prediction.

The chapter is organized as follows. First, fracture mechanics concepts for isotropic materials are presented. The stress field near a crack tip and the concept of the stress-intensity factor are introduced. Next, the evaluation of the strain energy release rate for self-similar crack growth, which is a measure of the crack driving force, through Irwin’s crack closure concept and the near-tip stress and displacement fields is presented. Cracks in orthotropic and anisotropic materials are considered next. A bi-material problem with an interface crack is considered as a precursor to cracks in layered media. In Section 1.3, the problem of delaminations in composite laminates is discussed. Mixed-mode behavior, determination of interlaminar fracture toughness, fatigue characterization, delamination onset are treated next. The process of evaluation of strain energy release rates in two- and three-dimensional finite element analyses is discussed. Two examples of delamination prediction and their validation with test data are presented next. Finally, future work needed to achieve a fully mature methodology for use in design certification of composite structures is outlined.

1.2 Fracture mechanics concepts

Consider a crack in a homogeneous isotropic linear elastic infinite plate as shown in Fig. 1.1(a). The crack lies on the y = 0 line and in the region x = ± a. This line discontinuity with zero thickness and with sharp ends is defined as a crack. A crack can also be thought of as a limiting case of an elliptical hole with a major axis of 2a and minor axis approaching a zero value. Under external loading the crack faces at θ = ± πin Fig. 1.1(a) can displace relative to each other. Figure 1.1(b) shows a crack in an infinite solid. The two- and three-dimensional stress states are also shown in Fig. 1.1. Any complex deformation of the crack faces can be described by a combination of three fracture modes, Mode-I, Mode-II, and Mode-III as shown in Fig. 1.2. Mode-I represents the opening mode of the crack faces, Mode-II represents the sliding mode, and Mode-III represents the tearing mode (out-of-plane shear mode) deformation.

1.1 Cracks in plates and solids.

1.2 The three fracture modes.

1.2.1 Crack-tip stress field

The elastic stress field around a crack tip has been well characterized and documented in research monographs and reference books (see Paris and Sih, 1965; Parker, 1981; Broek, 1982; Ewalds and Wanhill, 1984; Tada et al., 2000; Sanford, 2003; Anderson 2005). The stress field in the immediate vicinity of a crack tip can be written as (see Fig. 1.1(a))

$\begin{array}{l}{\sigma }_x=\frac{K_I}{\sqrt{2\pi r}}cos\left(\frac{\theta }{2}\right)⌊1-sin\left(\frac{\theta }{2}\right)sin\left(\frac{3\theta }{2}\right)⌋\\ -\frac{K_{II}}{\sqrt{2\pi r}}sin\left(\frac{\theta }{2}\right)⌊2+cos\left(\frac{\theta }{2}\right)cos\left(\frac{3\theta }{2}\right)⌋\\ {\sigma }_y=\frac{K_I}{\sqrt{2\pi r}}cos\left(\frac{\theta }{2}\right)⌊1+sin\left(\frac{\theta }{2}\right)sin\left(\frac{3\theta }{2}\right)⌋\\ +\frac{K_{II}}{\sqrt{2\pi r}}sin\left(\frac{\theta }{2}\right)cos\left(\frac{\theta }{2}\right)cos\left(\frac{3\theta }{2}\right)\\ {\tau }_{xy}=\frac{K_I}{\sqrt{2\pi r}}cos\left(\frac{\theta }{2}\right)sin\left(\frac{\theta }{2}\right)cos\left(\frac{3\theta }{2}\right)\\ +\frac{K_{II}}{\sqrt{2\pi r}}cos\left(\frac{\theta }{2}\right)⌊1-sin\left(\frac{\theta }{2}\right)sin\left(\frac{3\theta }{2}\right)⌋\\ {\sigma }_z=0\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{plane}\mathrm{stress}\mathrm{and}{\sigma }_z=v\left({\sigma }_X+{\sigma }_y\right)\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{plane}\mathrm{strain}\mathrm{conditions}\text{,}\end{array}$

1.1

and

$\begin{array}{l}{\tau }_{yz}=\frac{K_{III}}{\sqrt{2\pi r}}cos\left(\frac{\theta }{2}\right)\\ {\tau }_{zx}=-\frac{K_{III}}{\sqrt{2\pi r}}sin\left(\frac{\theta }{2}\right)\end{array}$

1.2

Clearly, from Eqs 1.1 and 1.2, the stresses are singular at the crack tip (r = 0) and the stresses have a square-root singularity. The constants K_I, K_II, and K_III are termed as the Mode-I, Mode-II and Mode-III stress-intensity factors, respectively. The stress-intensity factors describe the intensity of the stress field and are a measure of the severity of the crack.

The displacements (u, v) that correspond to the stresses in Eq. 1.1 can be written as

$\begin{array}{l}u=\frac{K_I}{2\mu }\sqrt{\frac{r}{2\pi }}cos\left(\frac{\theta }{2}\right)⌊\kappa -1+2{sin}^2\left(\frac{\theta }{2}\right)⌋\\ +\frac{K_{II}}{2\mu }\sqrt{\frac{r}{2\pi }}sin\left(\frac{\theta }{2}\right)⌊\kappa +1+2{cos}^2\left(\frac{\theta }{2}\right)⌋\\ v=\frac{K_I}{2\mu }\sqrt{\frac{r}{2\pi }}sin\left(\frac{\theta }{2}\right)⌊\kappa +1-2{cos}^2\left(\frac{\theta }{2}\right)⌋\\ -\frac{k_{II}}{2\mu }\sqrt{\frac{r}{2\pi }}cos\left(\frac{\theta }{2}\right)⌊\kappa -1-2{sin}^2\left(\frac{\theta }{2}\right)⌋\end{array}$

1.3

and the out-of-plane displacement (w) corresponding to the tearing mode in Eq. 1.2 is

$w=\frac{2K_{III}}{\mu }\sqrt{\frac{r}{2\pi }}sin\left(\frac{\theta }{2}\right)$

1.4

where μ is the shear modulus, κ = (3 – v)/(1 + v) for plane stress, κ = (3 – 4v) for plane strain, and v is the Poisson’s ratio of the material.

1.2.2 Strain energy release rate, G

Utilizing the near tip str...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright page
• Contributor contact details
• Introduction
• Part I: Delamination as a mode of failure and testing of delamination resistance
• Part II: Delamination: detection and characterization
• Part III: Analysis of delamination behaviour from tests
• Part IV: Modelling delamination
• Part V: Analysis of structural performance in the presence of delamination, and prevention/mitigation of delamination
• Index