JEC COMPOSITES MAGAZINE - Issue #108 - October 2016 - 53

Fatigue modelling of composite materials for industrial applications

a)

b)
Fig. 2: Mesoscopic
structure: a) textile
composite [5];
b) composite plate
lay-up

Tab. 1: Material properties

a)

b)
Fig. 1: Two modelling strategies implemented within the MAPICC3D project:
a) post-treatment model classified as a fatigue life approach; b) progressive
damage model

1) fatigue life models based on a stress/number of cycles (SN) curve
determined at the specimen level;
2) phenomenological models such as residual stiffness/strength approaches;
3) progressive damage models based on the definition of damage
mechanisms and their influence on the material's properties.
The MAPICC 3D project mainly considered the first and the third
models. The first approach is attractive because of its relatively
straight implementation into commercial software. The last one is
highly complex and requires a well-established material model.
It should be noted that the multi-scale methodology gained popularity during the past decade. This strategy can mainly be regarded as
the progressive damage model while introducing the microstructure
of composite materials into the material model definition which, in
turn, brings a physical interpretation of phenomenological parameters at the macroscopic scale. In the present work, multi-scale homogenization techniques were used to identify the elastic properties
of a given composite material.

Total fibre volume fraction

vf

0.6

Elastic modulus in warp direction

E11 [MPa]

17,700

Elastic modulus in weft direction

E22 [MPa]

15,400

Elastic modulus in thickness direction

E33 [MPa]

8140

Poisson's ratio (measured and estimated)

v12=v13

0.3

Poisson's ratio (estimated)

v23

0.4

In-plane shear modulus (measured and
estimated)

G12=G13 [MPa]

1695

Out-of-plane shear modulus (estimated)

G23 [MPa]

3130

Strength in warp direction

Xt=Xc [MPa]

300

Strength in weft direction

Yt=Yc [MPa]

197

Strength in shear direction

S [MPa]

57

Numerical implementation and strategies
From a standpoint of industrial applications, fatigue life models
and progressive damage models are the best candidates for implementation into a finite element code. Figure 1 shows numerical
algorithms of both models. A major difference between these two
models is that lifetime prediction in the fatigue life model is based on
the linear solution of a boundary value problem (BVP) by means of
the finite element method (FEM), whereas in the progressive damage
model, a BVP has to be solved every cycle (or block of cycles in the
case of cycle-jump techniques) in order to update the material properties and damage variables in every integration point (IP).
Various constitutive models and failure models for composites are
available in VPS, a FEM code from ESI Group [3], such as a continuous damage mechanics formulation coupled with a plasticity model
and widely used quadratic failure criteria. Lifetime prediction is based
on the modified Tsai-Hill quadratic criterion extended to three-dimensional cases. Each ply was considered as an equivalent homogeneous material whose properties are described in the following section.
No108 October 2016

/ jec composites magazine

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Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #108 - October 2016
