Energy absorption and damage propagation in 2D triaxially braided carbon fiber composites: effects of in situ matrix properties

Abstract

Results from an experimental program to investigate the propagation of damage and energy dissipation in 2D triaxially braided carbon fiber textile composites (2DTBC) under static conditions are reported. A methodology is presented in which classical concepts from fracture mechanics are generalized to address damage growth in an orthotropic and heterogeneous structural material. Along with results from the experimental program, a novel numerical technique that employs ideas from cohesive zone modeling, and implemented through the use of finite-element analysis, is also presented. The inputs that are required for the discrete cohesive zone model (DCZM) are identified. Compact tension specimen fracture tests and double notched tension tests were carried out to measure the fracture energy (G _Ic), and the maximum cohesive strength (σ _c), of the 2DTBC. The DCZM modeling strategy was independently verified by conducting single edge notched three-point bend tests using a modified three-point bend test fixture. The experimental and numerical analyses were carried out for two different types of 2DTBC made from the same textile architecture but infused with two different resin systems to validate the proposed methodology.

Appendix: measurement of the plasticity parameter a 66

The plastic response of braided composites was characterized by carrying out off-axis compression tests. Rectangular composite coupons were cut in such a way that the axial fiber tow makes an angle with the direction of loading as shown below.

A three-strain gage rosette was used to measure the global strains that are then transformed to get the local strains in the specimen principal material directions. Axial stress is also measured during the test. A yield function or plastic potential that is quadratic in stresses for a orthotropic composite gives an equivalent stress and a work conjugate equivalent plastic strain as

$$ \ifmmode\expandafter\bar\else\expandafter\=\fi{\sigma } = {\sqrt {\frac{3} {2}{\left( {a_{{22}} \sigma _{{22}} ^{2} + 2a_{{66}} \sigma _{{12}} ^{2} } \right)}} }, $$

(6a)

$$ {\text{d}}\ifmmode\expandafter\bar\else\expandafter\=\fi{\varepsilon }^{p} = \frac{2} {3}{\left( {a_{{22}} \sigma _{{22}} ^{2} + 2a_{{66}} \sigma _{{12}} ^{2} } \right)}{\text{d}}\lambda , $$

(6b)

$$ {\text{d}}\lambda = \frac{3} {2}{\left( {\frac{{{\text{d}}\ifmmode\expandafter\bar\else\expandafter\=\fi{\varepsilon }^{p} }} {{{\text{d}}\ifmmode\expandafter\bar\else\expandafter\=\fi{\sigma }}}} \right)}{\left( {\frac{{{\text{d}}\ifmmode\expandafter\bar\else\expandafter\=\fi{\sigma }}} {{\ifmmode\expandafter\bar\else\expandafter\=\fi{\sigma }}}} \right)}, $$

(6c)

where, $\ifmmode\expandafter\bar\else\expandafter\=\fi{\sigma }$ is the Von Mises type equivalent stress, ${\text{d}}\ifmmode\expandafter\bar\else\expandafter\=\fi{\varepsilon }^{p}$ is the equivalent plastic strain increment, and dλ is a scalar factor of proportionality. The parameters a ₂₂ and a ₆₆ are the material constants that characterize orthotropy of the plastic response.

Substituting, using stress transformations, into Eq. 6a–c to specialize to the off-axis compression test configuration, results in

$$\ifmmode\expandafter\bar\else\expandafter\=\fi{\sigma } = {\sqrt {\frac{3} {2}{\left( {\sigma_{y} ^{2} n^{4} + 2a_{{66}} \sigma_{y} ^{2} m^{2} n^{2} } \right)}} }$$

(6d)

or

$$ \ifmmode\expandafter\bar\else\expandafter\=\fi{\sigma } = \sigma _{y} h{\left( \theta \right)}. $$

Similarly,

$$ \ifmmode\expandafter\bar\else\expandafter\=\fi{\varepsilon }^{p} = \frac{{\varepsilon _{y} ^{p} }} {{h{\left( \theta \right)}}}, $$

where, m = cos(θ), n = sin(θ), and $h{\left( \theta \right)} = {\sqrt {\frac{3} {2}{\left( {n^{4} + 2a_{{66}} m^{2} n^{2} } \right)}} }.$

Off-axis tests were carried out on 30, 60, and 75° specimens. Thus, from experimental measurement of σ _y and ε _y, the equivalent stress and equivalent plastic strain are plotted for every off-axis angle. For each test, a value of a ₆₆ is selected such that the curves of equivalent stress versus equivalent plastic strain for each off-axis angle collapses to one. Test data for different off-axis angles for Epon specimens are given in Fig. 10. The value of a ₆₆ corresponding to this converged behavior was found to be 1.1. Similarly, value of a ₆₆ for Hetron specimens was found to be to be 1.2.

Fig. 10

Collapsed equivalent stress versus equivalent plastic strain Epon specimen (a ₆₆ = 1.1)