Unidirectional fibers strength predictions

Strength predictions are based on the equations provided in [4].

The tensile strength in the fiber direction is calculated by assuming that under longitudinal tension, the phase (fiber or matrix) with the lower strain fails first. For perfectly bonded fibers, the average longitudinal stress in the composite, σ1, is given by the rule of mixtures as:

Where Vf and Vm correspond respectively to the volume of the fiber and the volume of the matrix and σf and σm correspond to the stress in the fiber and the stress in the matrix, respectively. Under the simple deterministic assumption of uniform strengths, two cases are distinguished depending on the relative magnitudes of the ultimate tensile strains of the constituents.

In the case in which the ultimate tensile strain of the fiber is lower than that of the matrix, that is, when:

the composite fails when its longitudinal strain reaches the ultimate tensile strain in the fiber. The longitudinal tensile strength of the unidirectional ply can be approximated by the relationship:

Where XT corresponds to the longitudinal tensile strength of the unidirectional ply, XfT is the ultimate strength of the fibers, and σ’m is the average longitudinal matrix stress when ultimate fiber strain is reached. Assuming linear elastic behavior for the constituents, the last equation can be written as:

When, on the other hand, the ultimate strain of the matrix is lower than that of the fiber, that is, when:

the composite fails when its longitudinal strain reaches the ultimate tensile strain of the matrix. Then, the longitudinal tensile strength of the composite can be approximated by the relation:

which can be further approximated as:

XmT is the tensile strength of the matrix and σ’f is the longitudinal fiber stress when ultimate matrix strain is reached. For compressive strength in the fiber direction, two idealized microbuckling patterns are assumed and two different strength values are predicted. For low values of fiber volume ratio, the extensional or out-of-phase mode of microbuckling is predicted with a corresponding compressive strength:

For higher values of Vf, the shear or in-phase mode is predicted with a compressive strength:

Finally, another measure of the compressive strength can be obtained:

XC,1 , XC,2 and XC,3 are calculated by Laminate Composites and the strength of the ply is taken to be the lowest of the three.

Tensile strength perpendicular to the fibers is assumed to be:

Compressive strength perpendicular to the fibers is assumed to be:

Finally, the shear strength is given by:

How do I

Create a fiber-reinforced ply material

Look up more details

Micromechanics

Unidirectional fibers

Woven fibers

Woven fibers strength predictions

Sheared woven fibers

Sheared woven fibers thermal properties

Sheared woven fibers strength predictions

Randomly oriented short fiber reinforced ply

Randomly oriented short fiber reinforced ply strength predictions

Particulate reinforced ply

Particulate reinforced ply strength predictions

Micromechanics references

Fiber-reinforced ply material

Fiber-reinforced ply material types

Quick links

Command reference

Pre/Post video examples

Bulk Entry Descriptions

Simcenter 3D tutorials

Browse Simcenter 3D help by product area

Unidirectional fibers strength predictions, Simcenter 3D 2021.1 Series

© 2020 Siemens

window.mainLanguage="en_US"

window.delivId=""

window.projectId=""

MathJax.Hub.Config({ TeX: { extensions: ["autoload-all.js"] }, tex2jax: { displayMath: [ ] }, "SVG": { scale: 125 } });