Void-Growth Model

Let the initial void content of the representative volume element, a , equal the initial average void content of the composite, a . That is. 

Let the initial fiber volume fraction of the volume element, pj, equal that of the composite pj, 

Since the matrix melt has both elastic and viscous properties, it can be described by a constitutive law of viscoelasticity. The non-linear Kelvin-Voigt equation is employed here 

Suppose that the elastic stress-strain relation of the matrix melt can be described by a linear function, 

Tq is the initial temperature, is the initial pressure of the air inside the void.po is the external pressure, which is normally 1 atm (1.03x10 MPa), Ap denotes the controllable external applied pressure in processing, 5 is the surface tension coefficient, (0 = p K, and 

---

In developing the void growth model, the following simplifying assumptions were made ... 

In the development of the computer code for the void growth model, the following input relationships are provided in the program. These could, of course, be modified to account for different cure cycles or different material systems. The values used in this study are provided as default options in the code. 

The main assumptions in building a general void growth model are... 

The model framework for describing the void problem is schematically shown in Figure 6.3. It is, of course, a part of the complete description of the entire processing sequence and, as such, depends on the same material properties and process parameters. It is therefore intimately tied to both kinetics and viscosity models, of which there are many [3]. It is convenient to consider three phases of the void model void formation and stability at equilibrium, void growth or dissolution via diffusion, and void transport. 

A model and attendant computer code have been constructed to describe time-dependent void growth and stability for any processing cure cycle. Although the analysis is approximate, it does account for the moving void-resin boundary layer and its effect on the concentration profile and diffusion of water in the resin. It was found that for the duration of the cure cycle it makes little difference whether the initial small voids contain pure water or mixtures of air and water. 

Furthermore, the model makes it possible to separate the contributions of the three toughening mechanisms as a function of temperature (Fig. 13.6). At high temperatures, the crack-bridging mechanism plays a minor role the void-growth mechanism is very sensitive to temperature and can be completely suppressed at low temperatures. Shear yielding is the main mechanism, except at very high test temperatures where cavitation plays the major role. The contribution of shear yielding depends on the difference between the test temperature and Tg, as discussed in Chapter 12. 

In order to start the multiscale modeling, internal state variables were adopted to reflect void/crack nucleation, void growth, and void coalescence from the casting microstructural features (porosity and particles) under different temperatures, strain rates, and deformation paths [115, 116, 221, 283]. Furthermore, internal state variables were used to reflect the dislocation density evolution that affects the work hardening rate and, thus, stress state under different temperatures and strain rates [25, 283-285]. In order to determine the pertinent effects of the microstructural features to be admitted into the internal state variable theory, several different length scale analyses were performed. Once the pertinent microstructural features were determined and included in the macroscale internal state variable model, notch tests [216, 286] and control arm tests were performed to validate the model s precision. After the validation process, optimization studies were performed to reduce the weight of the control arm [287-289]. 

Crack growth models in monolithic solids have been well document-ed. 1-3,36-45 These have been derived from the crack tip fields by the application of suitable fracture criteria within a creep process zone in advance of the crack tip. Generally, it is assumed that secondary failure in the crack tip process zone is initiated by a creep plastic deformation mechanism and that advance of the primary crack is controlled by such secondary fracture initiation inside the creep plastic zone. An example of such a fracture mechanism is the well-known creep-induced grain boundary void initiation, growth and coalescence inside the creep zone observed both in metals1-3 and ceramics.4-10 Such creep plastic-zone-induced failure can be described by a criterion involving both a critical plastic strain as well as a critical microstructure-dependent distance. The criterion states that advance of the primary creep crack can occur when a critical strain, ec, is exceeded over a critical distance, lc in front of the crack tip. In other words... 

Figure 3.9. Section view of unit cell model displaying void growth around a particle at macroscopic longitudinal strains of (a) 0, (b) 0.1 and (c) 0.6. [Adapted, by permission, from Ognedal, A. S., Clausen, A. H., Berstad, T, Seeling, T., Hopperstad, O. S.,Int. J. Solids Structures, rapiess, 2014.]...

This chapter sununarizes some recent research advances in the understanding of deconsolidation and reconsolidation, which include (i) a mechanistic model for void growth, in term of the degree to which thermal deconsolidation can be evaluated, (ii) an analysis based on transient heat transfer consideration for the so-called propagating fronts of both deconsolidation and reconsolidation, (iii) an indicative void-closure model relevant to reconsolidation, and (iv) a squeezed creep flow model. 

Thus, it appears that the traction induced by the decompaction of the fiber reinforcement network plays a major role in void growth at thermal deconsolidation, and a relevant model is discussed in the next section. 

---