Proportions of composite materials for aeronautic applications have dramatically increased over the last decades because of their inherent properties combining high mechanical properties with low mass. However, the major concern of the traditional 2D composites is the reduction of properties due to delamination between plies because of weak through-the-thickness properties. Three dimensional woven give the possibility to add a 3rd direction of reinforcement with the addition of yarns interlacing through the thickness. The main benefit of that additional direction of reinforcement is a better damage tolerance due to impact where delamination is the key failure mode. With the addition of that 3rd direction of reinforcement, possible combination of interlacement become extremely numerous. Different patterns commonly observed fall into 2 main categories:
- The orthogonal 3D woven, which is made of three different type of yarns, the warp (X direction), the weft (Y direction) and the binder (Z direction) which is placed through the thickness. The warp and wefts yarns are straight and perpendicular without interlacement and the binder is weaved in the X direction, interlacing on the top and the bottom surface with an angle of 90 degrees.
- The angle interlock 3D woven, which is made also of perpendicular and straight warp and weft yarns and with a binder weaved with an angle different from 90 degrees. It could also go through all the thickness or from layer to layer;
To support the development of 3D woven and to permit a quick screening of potential weave pattern properties, numerical tool must be proposed to designers. The last version of Digimat 2018.0 contains a complete workflow to analyze and predict stiffness, failure and thermo-mechanical behavior of any 3D woven representative volume element (RVE).
DIGIMAT FOR 3D WOVEN
- A micromechanics approach: Digimat computes the composite properties from the constituents’ properties and the description of the microstructure itself. In the context of 3D woven, fiber and resin material properties, yarn density, yarn section and finally weave pattern description are needed along the workflow.
- Performance prediction using homogenization: Based on the previous inputs, Digimat proposes two homogenization methodologies to compute the effective properties of the RVE: a mean-field homogenization algorithm and a full-field resolution. In the context of 3D woven, the complete analysis of the RVE requires a multi-step homogenization: first yarn properties are computed, then RVE properties are computed.
- Pre-defined and customizable weave pattern definition: Digimat 2018.0 proposes a user-friendly way to define any types of weave pattern based on the definition of the number of layers, the number of weft rows and the interlacement of each warp/binder within each warp section.
- Integrated workflow: Finally, the execution of the analysis work is totally integrated in a comprehensive workflow, with 4 mains steps (figure 1): 1. The weave pattern definition, 2. The weave pattern geometry creation, 3. The weave pattern mesh generation (in the case of the full-field approach), and 4. The resolution step.
The computation of the stiffness for three different types of weave pattern are compared. Input data regarding the weave pattern definition and test results can be found in  and the material properties in . The carbon fiber used is the HexTow IM7 and the resin is the MTM57. The yarn density is 12K, except for the binder of the orthogonal and angle interlock patterns which is 6K. Prediction of the stiffness using the mean-field homogenization and the full-field homogenization are given in the table 1.
Assessment of the strength of the weave pattern is also possible in Digimat using the full-field homogenization. In this context, the workflow is enriched with the failure prediction of the resin and the yarn. The failure envelop of the yarn is built using a micromechanic model that integrates the fiber volume fraction in the yarn, the stress limit of the resin alone and the strength of the fiber in tension and compression. That failure envelop differentiates the failure in the axial and transverse directions and in the shear plans of the yarn. During the loading of the RVE, that failure envelop is used to detect the damage initiation and a progressive failure mechanism is used to degrade the anisotropic stiffness of the yarn or of the resin (figure 2).
Residual stresses after cooling
Thermo-mechanical analysis can also be performed to evaluate the residual stresses during a cooling phase, at the end of a curing cycle for example. In a first approximation, the behavior of the carbon fiber and the resin becomes thermo-elastic with the addition of the anisotropic coefficient of thermal expansion (CTEs). A variation of temperature from curing temperature to room temperature is applied on the RVE without any mechanical boundary conditions (free stress state). Residual stresses are expected due to the mismatch of CTEs between the resin and the yarns and the evaluation of the risk of apparition of micro-cracks is done. To include the effect of hydrostatic pressure, a quadratic stress, combining the Von Mises stress and the hydrostatic stress is introduced  and compare to a classical approach based only on the Von Mises equivalent stress. Both criteria can be plotted to localize area prone to micro-crack apparition. Distribution of Von Mises stress or quadratic stress can be plotted over all the resin domain to assess risk of failure by comparing with a stress limit  (figure 4).