The role of curing stresses in subsequent response, damage and failure of textile polymer composites

Abstract

An integrated computational framework for textile polymer composites is introduced. A novel polymer curing model is used in connection with modeling the polymer curing process during manufacturing of textile composites. The model is based on the notion of polymer networks that are continuously formed in a body of changing shape due to changes in temperature, chemistry and external loads. Nonlinear material behavior is incorporated through nonlocal continuum damage mechanics that preserves mesh objectivity in calculations that go beyond maximum loads. The integrated model is applied to the curing of plain weave textile composites made from carbon fiber tows and $\mathrm{Epon}™862$ resin. The mechanical and chemical properties are measured during curing using concurrent Brillouin and Raman light scattering. It is shown that significant stresses can develop during cure. The effect of these stresses on the manufactured part performance, when subsequent service loads are applied, is evaluated and a reduction in ultimate load, in agreement with experimental observations, is observed.

Introduction

Textile composites manufactured from carbon fiber tows and epoxy matrix are finding wide use in aerospace and other industrial applications. Such composites include 2D and 3D woven and braided composites comprised of glass or carbon fiber and polymer matrix. In woven composites, the fibers are combined into fiber tows consisting of thousands of individual fibers. These fiber tows are woven or braided using many different weaving patterns. Of interest in this study are 2 dimensional, triaxially braided composites (2DTBC) (Song, 2007, Song et al., 2007, Song et al., 2008, Song et al., 2009, Song et al., 2010). In 2DTBC, bias tows are braided at an angle to an axial tow. What makes woven composites an interesting material for engineering applications is their increased fracture toughness compared to pre-preg and stitched composites due to the lack of a clear path for a macroscopic crack to progress. Due to an undulating textile architecture, cracks progressing in the matrix can be arrested at intersections of fiber tows. Thus, textile fiber composites are of great interest in the design of crashworthy vehicle structures.

Textile composites offer the added advantage that high volumes of parts can be manufactured at relatively reduced costs. In addition, textile preforms can be used for net-shape manufacturing which can lead to reduced part count. During the manufacturing of a composite part from textile fabrics, the dry fabric is placed in a mold and liquid resin is inserted into the mold afterwards using a resin transfer molding (RTM) process. The wetting of the fibers may be aided with the help of vacuum (VARTM). In VARTM, a vacuum is created inside the mold. Liquid epoxy resin is ejected through one or several ports on one side of the mold and pulled to other ports that are used to create the vacuum. RTM and VARTM can be performed at room temperature, thus eliminating the need for an oven and allowing to manufacture large parts such as wind turbine blades.

The design process with these materials remains challenging. Material properties need to be identified and the response up to and including failure needs to be investigated properly. During the characterization process of such a composite, Song et al. (2007), have noted that effective overall composite 2DTBC material properties are not in agreement with properties based on calculations with individual “virgin” constituent properties. The experimentally observed maximum service loads were found to be significantly lower compared to computational predictions. This disagreement has been attributed to changes in the state of the matrix due to curing in the presence of fibers. These changes are due to a mismatch in the thermal coefficient of expansion, cure shrinkage of the epoxy and thermal gradients causing different rates and degree of cure throughout the curing volume of matrix material. Stresses are present at the end of the cure cycle and these may reduce the margin of load that can be applied to the part before the onset of inelastic response and failure. To capture the correct stress state of the resin inside the fully relaxed (no external load applied) composite, attempts have been made to measure the “in situ” matrix properties (Song et al., 2009, Yerramalli and Waas, 2002). Here the material is treated to be stress free after cure and prior to loading, but effective or equivalent material properties are subsequently adopted. The “in situ” properties are extracted using an inverse modeling approach. The idealized complex geometry of the textile composite is created in a finite element (FE) model. Then the material properties of the matrix material in the computational model are altered until the simulation results agree with the experimental results of a suitable coupon level test. Such an approach, which finds engineering utility, is suitable to investigate the response of a specific textile composite, and to obtain the “in situ” material properties. However, this inverse modeling procedure to find the “in situ” properties has to be repeated each time the properties of the textile composite constituents and parameters of the curing process are changed. A more fundamental approach is described in this paper.

An integrated computational modeling approach that considers the textile composite manufacturing process and its subsequent service performance is presented in this paper. Material properties of fiber and matrix material including the evolution of material properties of the matrix during cure are found from the constituents individually. As in previous studies that investigated the cure of epoxy resins, it is necessary to include various physical concepts to properly determine the importance of the various curing parameters. The curing of epoxy is a highly exothermic reaction (Ramakrishnan et al., 2000, Shanku et al., 1997, O'Brien and White, 2003) that can lead to appreciable temperature gradients in thick composites. The chemical evolution is tightly linked to the temperature and finally the evolution of stresses and material properties of the bulk composite depends on both the temperature history and curing history of the resin.

In developing a model for the cure generated stresses, the possibility of matrix failure during cure and prior to the onset of service load application must be considered. The computational models for failure prediction employed in the past can roughly be divided into two categories. On the one hand macroscopic cracks and failure have been captured through the use of discrete cohesive zone models (DCZMs) (Xie and Waas, 2006, Xie et al., 2006). These models usually require a-priori knowledge of the intended crack path. The other major model to capture failure is the continuum damage model (CDM) (Chaboche, 1981, Lemaitre and Desmorat, 2005). In CDM, micro-cracks and voids are not explicitly modeled. Instead damage due to microstructural changes are accounted for in an average sense by degrading material properties. CDM models do not predict the formation of macroscopic cracks. On the other hand, when modeling failure with CDM, the location where damage will occur does not need to be known. Therefore, CDM within a nonlocal computational framework is employed to model failure of epoxy during and after cure.

Finally, it is noted that the curing process can produce self-equilibrating internal stresses within the material. If the process is modeled and understood properly, then the desired internal stress state can be “designed” so that subsequent part performance is optimized. Such an approach has precedent in the manufacturing process of auto-glass, where compressive surface stresses are “built-in” by tailoring the manner by which the cooling process is controlled, as shown in the pioneering work by Lee et al. (1965). In that work, it is shown that different cooling rate histories can produce undesired surface tensile stresses, which if present, can accelerate the propagation of surface flaws like cracks, when tensile service loads are experienced.

In this paper, a novel model is introduced to capture the effects of the manufacturing process on the state of the cured matrix within a plain weave composite. This model is used to evaluate the mechanical response of the plain weave composite when subjected to service loads. The maximum applicable service load is dependent on the curing related properties of the polymer matrix material. The holistic computational modeling procedure introduced here (manufacturing and subsequent service loads) shows the need for an approach that integrates materials science and engineering, leading to the title of this paper—“integrated computational materials science and engineering of textile polymer composites”.

The mechanical properties of textile composites have been extensively studied in the past and a summary can be found in the work by Song (2007). Early investigations were aimed mostly at predicting elastic properties of plain weave composites (Ishikawa and Chout, 1983, Naik and Shembekar, 1992, Sankar and Marrey, 1993, Naik and Ganesh, 1992, Zhang and Harding, 1990). The onset of inelastic response of plain weave composites was considered by Karkkainen and Sankar (2006). They constructed the failure envelope of a plain weave woven unit cell and noted a close relation to the Tsai–Wu failure criterion (Tsai and Hahn, 1980). Whitcomb and Srirengan (1996) investigated progressive damage of plain weave composite. They used a static finite element simulation to determine the locations of largest stress and failure onset. At these points the material properties were modified and a new equilibrium state was calculated. This process was repeated until no further damage occurred and the global strain was increased until the next onset of damage. Song and co-workers investigated the compressive response of 2DTBC experimentally and through finite element simulations (Song, 2007, Song et al., 2007, Song et al., 2008, Song et al., 2009, Song et al., 2010). The finite element model used was of an idealized representative unit cell (RUC) consisting of fiber tow and matrix. The fibers were treated as elastic and the matrix material was treated as plastic or plastic-damaging. The resulting nonlinear fiber tow behavior was modeled using Hill's theory of anisotropic plasticity (Hill, 1948).

Manufacturing induced effects have usually been studied in the context of cure induced stresses and potential failure during cure. Rabearison et al. (2009), gives an example of how stress gradients in cure develop in a thick carbon epoxy tube and subsequently cause defects such as cracks. In a similar fashion Corden et al. (1998) have developed a curing model to predict the residual stresses in thick resin transfer molded laminated cylinders to identify chemical shrinkage due to cure as a major contributing mechanism for stress build up. Plepys and Farris (1990) noted the creation of cracks during isothermal cure of three-dimensionally constrained epoxy resin in a glass cylinder, and Chekanov et al. (1995) have identified different defect types that may occur during the constrained cure of epoxy resins. Besides stress generation and possible cracking during cure, geometric tolerances are also important. For example, a thick composite may be cured on a metal tool with two perpendicular side faces to give an L-shaped composite part. Upon removal of the part from the mold, a “spring-in” can be observed. Here, the two sides of the L-shaped part bend inwards giving a smaller angle than the anticipated 90° (Darrow and Smith, 2002, Fernlund et al., 2002, Albert and Fernlund, 2002, Johnston et al., 2001). Equivalently, when a composite part is cured on a flat tool, bending or warpage can be observed due to thermal gradients and residual stresses build up during cure (Kim et al., 2006, Kim and Hahn, 1989, White and Hahn, 1993, Shrotriya et al., 2001). Proper knowledge of curing induced distortion can be used to design a mold that will compensate for such effects, as demonstrated by Capehart et al. (2007). Various studies have also been performed to optimize aspects of the curing cycle and these are described in Li et al. (2001), White and Hahn (1993), Gopal et al. (2000), and Zhu and Geubelle (2002).

Studies that investigate the curing process of composites are commonly broken down into two parts: chemical reaction, heat generation and heat conduction, and, the evolution of stress and development of structural integrity. In order to understand and optimize the manufacturing process, both issues must be understood well. The temperature field is usually modeled using the standard heat equation and Fourier's law. The cure kinetics is usually modeled using a phenomenological model proposed by Kamal (1974). The evolution of stress on the other hand is modeled through a variety of approaches, as described in Plepys and Farris (1990), Plepys et al. (1994), Bogetti and Gillespie (1992), Adolf et al. (1998), Adolf and Chambers (1997), White and Hahn (1992), and Lange et al. (1995).

The approach that will be used in this study for the cure of the matrix is based on previous work by Mei et al. (1998) and Mei (2000), who investigated solidification of epoxies using a novel network forming model where networks are continuously created in a new reference configuration as cure progresses and each network had different visco-elastic material properties.