Whoever is careless with the truth in small matters cannot be trusted with important matters. -Albert Einstein\
Microstructural modeling is often viewed as an extraneous activity when analyzing the behavior of composites. Many engineers use the “system” properties as the inputs for their part design, without considering what contributes to that overall “system” response.
In this post, we will look at the anatomy of a composite microstructure to better understand how mechanical and geometric properties come together to influence overall behavior.
For UD composite the following items have been shown to impact the overall system response, so let’s take a close look and understand how we characterize each within a virtual model.
- Fiber Volume Fraction
- Fiber Size and Orientation
- Fiber Strength (Tension Compression Shear)
- Strength and Geometric Distributions
- Resin Behavior
- Interface Strengths
- Voids, Defect, Particles within Resin
Fiber Volume Fraction
The fiber content and alignment is the single most important aspect of any composite system.
Depending on the alignment and orientation of your fibers, your part can either behave like steel or like wood. And may even behave like both in different regions of a part.
Unidirectional Composites are not nearly as complex as injection molded composites, which can vary in both the alignment and orientation of the fibers.
In a Unidirectional composite, like a laminate or filament wound part, orientation still does play a major role. For laid up composites, the layup pattern and drape angles need to be accounted for in the model. For Filament wound parts, the wind pattern can be imported from winding tools like FiberGrafix, which will drive the microstructure orientation. Further, a custom specification could be imported to account for voids or residual stresses that result from manufacturing induced variations.
Even a 10% different in orientation within a Unidirectional composite can mean the difference between the system failing predominately at the matrix (in shear) or at the fiber (in tension) – resulting in a 40% reduction in ultimate strength.
Modeling Variability and Stochasticity
There is no question that there exists variability in composites – both in their geometric configurations and in their properties. Both of these variations influence the system behavior – and thus should be reflected in virtual predictions.
To do this, stochastic modeling is used to capture the variability. From a geometry perspective, size spatial configurations can be modeled according to distribution. This means that things like fiber size and length variations can be captured.
The distribution of fiber can play a role in the introduction of failure, because regions of high stress between inclusions will cause strain gradients and premature failure. Depending on your material and application, this could either result in improved properties (hardening effects) or decreased properties (crack onset).
In addition to fiber orientation, for some composite systems, you want to take into account the strength distribution in your fiber or matrix or at the fiber-matrix interface. These strengths often follow the well-documented Weibull distribution, governed by the equation above. Using experimental data, the Weibull modulus (m) and scaling parameter (A) can be obtained for a given phase of your material and input into the model. To obtain this data for your fibers for instance, a single filament test could be performed to generate a Weibull distribution curve for fiber tensile or compressive strengths.
Another important and often overlooked feature of composites is the response of the resin.
As some may know, viscoelastic materials exhibit different behavior at different loading rates and exhibit some energy dissipation and stress relaxation characteristics. Most resin systems have some viscoelastic or viscoplastic behavior. While rate dependency may not be a concern for quasi-static analysis, strain-induced stiffening or stress relaxation may be.
The image below show the loading of UD composite both along and transverse to the fiber. Notice that along fiber you get a primarily linear stress-strain response, as the stress is fiber dominated. However, transverse to the fiber we see non-symmmetric behavior in loading and unloading. This is a characteristic of a viscoelastic material, where the area under this curve is the energy dissipated by the material.
When using a single analytical model to capture your composite behavior, this seems like a difficult problem that is ignored in most analytical models. However using the MultiMech software, it's possible to generate accurate viscoelastic material cards for the different phases of your material. These models easily capture the strain-dependent and energy dissipating characteristics of the materials.
A major consideration when designing a composite material is “How will these materials maintain adhesion throughout a load and fatigue cycle.” The mechanisms of failure in this case is debonding and pullout and can be captured in a virtual model through the use of cohesive zones between the different phases.
For complex biaxial cases, where shear forces are present, debonding can be a major area of damage onset. As seen in the image below, a 45 degree test on a unidirectional coupon yields a stair-stepping crack, working its way around the fiber-matrix interface and through the matrix.
While it may be difficult to obtain interface properties experimentally, MultiMech has developed techniques to reeverse engineer these properties, given that the other facets of your system are understood.
Voids and Toughening Particulates
A hot area of research is in the effects of voids and toughening particulates within a composite matrix phase. These microscopic occurrences can have tremendously beneficial or deleterious effects, depending on their size, distribution, adhesion, and mechanical properties.
Using MultiMech, these inclusions or voids could be explicitly modeled using MultiMech and their effects could be studied using the same principles used to study the interactions of fiber and resin. We have previously discussed modeling voids within CMCs, but more to come on toughening nano-particles in a future post.
Putting Together the Pieces
When you put all of this together you get some very interesting results.
You can have the viscoelastic resin, interacting with an orthotropic fiber. The stress gradients between the two phases causes some initial fiber debonding. That debonding then distributes stress into the matrix region, where matrix cracks start to form and propagate. Eventually, the composite system loses stability.
Validations of models such as this have achieved experimental correlations in the 1% range. But more importantly, clearly see the progression of damage within the microstructure. It isn’t a smearing of behaviors, but different, distinct interacting mechanisms; all of which are physically verifiable.
This post focused mainly on the behavior of unidirectional composites, but a similar story can be told for other types of heterogeneous materials. If you would like more info on how to accurately model the behavior of your advanced materail, reach out!