Delamination

 ( Composite Materials ) 

$G\_Q\; =\; \backslash frac\{3mP^\{2\}\_\{\backslash max\}a^\{2\}\_\{0\}\}\{2B\}$

where $B$ is the thickness of the specimen and $P\_\{\backslash max\}$ is the max load and $m$ is a fitting parameter. $m$ is determined by experimental results with a least squares fit of compliance $C$ vs. the crack length cubed $a^3$ with the form of

$C\; =\; A\; +\; ma^3$.

The candidate fracture toughness $G\_Q$ equals the mode II fracture toughness $G\_\{IIc\}$ if strain energy release rate falls within certain percentage of $G\_Q$ at different crack lengths specified by ASTM.

Interlaminar [[shear strength]] is used as an additional measure of the strength of the fiber-matrix bond in fiber-reinforced composites. Shear-induced delamination is experienced in various loading conditions where the [[bending moment]] across the composite changes rapidly, such as in pipes with changes in thickness or bends. Multiple test architectures have been proposed for use in measuring interlaminar shear strength, including the short beam shear test, Iosipescu test, rail shear test, and asymmetrical four-point bending test. The goal of each of these tests is to maximize the ratio of [[shear stress]] to [[tensile stress]] exhibited in the sample, promoting failure via delamination of the fiber-matrix interface instead of through fiber tension or [[buckling]]. The orthotropic symmetry of fiber composite materials makes a state of pure shear stress difficult to obtain in sample testing; thin cylindrical specimens can be used but are costly to manufacture. Sample geometries are thus chosen for ease of machining and optimization of the stress state when loaded.
     

In addition to manufactured composites such as glass fiber-reinforced polymers, interlaminar shear strength is an important property in natural materials such as wood. The long, thin shape of floorboards, for example, may promote deformation that leads to vibrations.

Asymmetric four-point bending (AFPB) may be chosen to measure interlaminar shear strength over other procedures for a variety of reasons, including specimen machinability, test reproducibility, and equipment availability. For example, short-beam shear samples are constrained to a specific length-thickness ratio to prevent bending failure, and the shear stress distribution across the specimen is non-uniform, both of which contribute to a lack of reproducibility. Rail shear testing also produces a non-homogeneous shear stress state, making it appropriate for determining shear modulus, but not shear strength. The Iosipescu test requires special equipment in addition to the roller setup already used for other three- and four-point flexural tests.
     

ASTM C1469 outlines a standard for AFPB testing of advanced ceramic joints, and the method has been proposed to be adapted for use with continuous ceramic matrix composites.ASTM C1469 - 10: Standard Test Method for Shear Strength of Joints of Advanced Ceramics at Ambient Temperature, West Conshohocken, PA: ASTM International, 2015 Rectangular samples can be used with or without notches machined at the center; the addition of notches helps to control the position of the failure along the length of the sample, but improper or nonsymmetrical machining can result in the addition of undesired normal stresses which reduce the measured strength. The sample is then loaded in compression in its test fixture, with loading applied directly to the sample from 4 loading pins arranged in a parallelogram-like configuration. The load applied from the test fixture is transferred unevenly to the top two pins; the ratio of the inner pin load $P$ and outer pin load $Q$ is defined as the loading factor $\backslash lambda$, such that

$\backslash frac\{P\}\{Q\}\; =\; \backslash frac\{S\_2\}\{S\_1\}\; =\; \backslash lambda$,

$\backslash sigma\_\{xx\}\; =\; \backslash frac\{6(\backslash lambda-1)FL\}\{(1+\backslash lambda^2)bt\}$,

where $F$ is the total applied load on the sample, $L$ is the sample length, $b$ is the sample width (into the page as seen in a 2D free-body diagram), and $t$ is the sample thickness. The shear stress $\backslash sigma\_\{xz\}$ in the sample is maximized in between the inner span of the pins and is given by

$\backslash sigma\_\{xz\}\; =\; \backslash frac\{3(1-\; \backslash lambda)F\}\{2(1+\; \backslash lambda)bt\}$.

$C\; =\; \backslash frac\{\backslash sigma\_\{xx\}\}\{\backslash sigma\_\{xz\}\}\; =\; \backslash frac\{4L\}\{(1+\backslash lambda)t\}$.