Jae Noh

Concise Derivation of Formulas for 3D Sublaminate Homogenization

Typically, lamina by lamina modeling of thick composites is excessively expensive. Although formulas for sublaminate homogenization appear in the literature, there are discrepancies and the derivations are either not given or are complex. Herein, a simple, concise derivation of homogenization formulas is presented. The formulas are easily specialized for special classes of laminates. The formulas are expressed in an efficient form, which makes them suitable for use in numerical simulations. Three-dimensional finite element analysis was used to demonstrate that the formulas are exact.

Effect of Various Parameters on the Effective Properties of a Cracked Ply

Damage in composite materials accumulates in a diffuse manner. Accounting for this damage in a progressive failure analysis requires an accurate measure of the degraded stiffness coefficients. This paper describes micromechanics models for predicting the effect of distributed cracks on the engineering properties (extensional moduli, shear moduli, and Poisson’s ratios). Quasi-3D and 3D finite element methods were employed to determine the effective material properties of the cracked ply. Analyses were performed for various material systems, damage states, and adjacent (to the cracked ply) ply properties. The results show that the effective properties of cracked ply are very sensitive to the initial properties of a cracked ply. These properties are also found to be sensitive to the adjacent ply properties and orientation. However, they are not much affected by cracks in the adjacent plies. Relationships describing the sensitivity of the effective properties to the adjacent ply properties and the initial properties of a cracked ply were obtained. These relationships are useful for explaining the degradation behavior of laminates. Quantitative measures are presented for the errors introduced when shear-extension-coupling terms are ignored when calculating effective properties. Also, it was proven that transverse matrix cracks only affect the diagonal terms in the effective compliance matrix for certain configurations.

Prediction of Cryogen Leak Rate through Damaged Composite Laminates

The structural weight of a cryogenic propellant tank for reusable launch vehicles (RLV) can be effectively reduced by the use of advanced composite materials. However, microscopic damage such as transverse matrix cracks (TMC) and delaminations are prone to develop in composites well below the load levels that would result in mechanical failure. This microscopic damage leads to a leakage path for the fuel. The leakage is influenced by many factors, including pressure gradients, microcrack density, connectivity of the cracks, residual stresses from manufacture, service-induced stresses from thermal and mechanical loads, and composite stacking sequence. It is expected that there is a direct relationship between leakage and damage opening but the connectivity of matrix cracks is also a major factor affecting the leakage. In this article, the leakage rate through the damage network is discussed based on earlier studies for the opening of damage paths due to TMC and delamination, including the TMC intersection area. In order to examine the leakage process, numerical simulations are performed using the computational fluid dynamics software (FLUENT) and the effective conductance of the leakage paths is estimated. A simplified model is also developed to predict the effective conductance. The flow resistance in the TMC and the resistance of the TMC intersection area are accounted for in the calculation of the effective conductance of the leakage path through the entire laminate using the simplified model. Comparisons between the numerical solution for a five-ply composite with interconnected leakage paths and the prediction of the simplified model are presented for gaseous hydrogen flow through the thickness of the composite at room and cryogenic temperatures.

EFFECT OF LAMINATE DESIGN AND LOADS ON CRACK OPENING VOLUME IN LAMINATES USED IN CRYOGENIC TANKS

The use of advanced composite materials for cryogenic fuel tanks reduces the mass of the structure but the leakage of fuel can become a problem. Since the amount of leakage will increase with crack opening volume, it is essential that we understand the factors that affect the crack opening. In a previous study by the authors, the degradation behavior of lamina properties due to cracking was studied extensively. The study examined the effects of a variety of parameters such as adjacent ply orientation, material properties of adjacent plies, initial properties of the cracked ply, and cracks in adjacent plies on the effective properties of the cracked ply. It was shown that the rate of degradation is not very sensitive to these parameters. In the current paper, it will be shown that the crack opening volume can be directly related to changes in effective moduli. A simple calculation of the crack opening volume for a laminate based on the degradation of the E22 of a cracked lamina is presented. The effect of various parameters on the crack opening volume shows a similar pattern as the E22 degradation of a cracked ply. This suggests that the opening volume is expected to also be quite insensitive to the laminate design parameters listed above.

Evaluation of Various Approximate Analyses for Plain Weave Composites

The literature contains a variety of analyses for analyzing plain weave composites. These differ in both geometric approximation and assumptions about stress and strain distribution. Herein the weave geometry for a wide range of waviness was described using three-dimensional finite element meshes. These meshes were used with various stress and strain assumptions to determine how these assumptions affect predicted in-plane extensional stiffness. Assumptions about stress and strain can be tied to whether an analysis is equivalent to a virtual work, complementary virtual work, or hybrid formulation. Since these variational principles have well understood convergence behavior, it is easy to explain the observed effects of the various assumptions. The results indicate that sometimes accurate predictions for particular cases result from cancellation of errors, rather than sound formulation.

Prediction of Leakage Rate through Damage Network in Cryogenic Composite Laminates

The structural weight of a cryogenic propellant tank for reusable launch vehicles (RLV) can be effectively reduced by the use of advanced composite materials. However, microscopic damage such as transverse matrix cracks (TMC) and delaminations are prone to develop in composites well below the load levels that would result in mechanical failure. This microscopic damage leads to a leakage path for the fuel. The leakage is influenced by many factors, including pressure gradients, microcrack density, connectivity of the cracks, residual stresses from manufacture, service-induced stresses from thermal and mechanical loads, and composite stacking sequence. It is expected that there is a direct relationship between leakage and damage opening but the connectivity of matrix cracks is also a major factor affecting the leakage. In this paper, the leakage rate through the damage network is discussed based on the earlier studies for the opening due to TMC and delamination, including the TMC intersection area. The leakage path is expressed as a function of crack density (ply by ply) and the number of TMC intersections. In order to examine the leakage process, numerical simulations were performed using a computational fluid dynamics program (FLUENT). A formula based on series and parallel models was developed to predict the leakage rate. The flow resistance in the TMC and the resistance of the TMC intersection area are accounted for in the calculation of the effective conductance of the leakage path through entire laminate. The paper discusses how the number of TMC intersections is related to the leakage rate.

Numerical Modelling of Cryogen Leakage Through Composite Laminates

*† ‡ § Cryogenic composites find critical application in the manufacture of fuel tanks for reusable launch vehicles due to significant reduction in overall structural weight of the tank. These fuel tanks contain pressurized cryogen such as hydrogen at cryogenic temperatures. Exposure to varying temperatures and mechanical loads resulting from flight cycle, containment of pressurized cryogen causes thermo-mechanical loading of the composite. The thermo-mechanical loading cycles combined with mismatch in the thermal and mechanical properties of fibers and matrix lead to transverse matrix cracks (TMC) in each ply of the composite. TMC in adjacent plies intersect in localized regions at ply interfaces called crack junctions, which open up due to delamination on application of thermo-mechanical load. TMC and crack junctions usually form a network of leakage paths that assists leakage of cryogen through the composite. In this study, the volumetric flow rate of cryogen leaking through a damaged composite is determined by estimating the effective conductance of the leakage paths. For a given damage state and applied load, crack junction and TMC openings are obtained by finite element analysis as described in the first paper on this subject by the same authors. A computational fluid dynamics model is first used to estimate the effective conductance of a leakage path and then a simplified analytical model is used to compute the effective conductance from individual conductances of each crack junction and TMC through a series-parallel combination. A single phase flow model is considered for the numerical analysis of cryogen flow through TMC and crack junctions. The simulations are carried out using the commercial computational fluid dynamics software, Fluent. The simplified model predictions of the effective conductance for a five ply composite show good comparison with numerical simulations.

Efficient techniques for predicting viscoelastic behavior of sublaminates

Even for linear elastic behavior, stress analysis of thick laminated composites can be very computation intensive if every lamina is modeled discretely. In such cases, modeling of individual lamina is impractical and the homogenization method for sublaminates becomes essential. In the current work, 3D homogenization formulas for an elastic sublaminate, which were derived by the authors in previous work, were utilized to determine the 3D effective properties for a viscoelastic sublaminate. The properties were determined by three methods that exploited the 3D elastic homogenization formulas: (i) quasi-elastic method, (ii) correspondence principle, and (iii) direct time integration of the incremental viscoelastic equations. The finite element method with discrete modeling of the plies was used to obtain reference solutions. The effective viscoelastic properties obtained using the three methods based on the elastic homogenization formulas were in very good agreement with the reference solution. Among these methods, the quasi-elastic method was found to be both accurate and the simplest method in determining the effective properties. The methods were also used to predict the stress response of a sublaminate to different strain histories. The direct time integration method using the 3D elastic homogenization formulas performs accurately and efficiently for this problem.

Prediction of Delamination Growth and Opening Near Intersection of Transverse Matrix Cracks and Delamination

The use of advanced composite materials for cryogenic fuel tanks reduces the mass of the structure but microscopic damage can cause fuel leakage. The amount of leakage depends on the connectivity of the damage and crack opening displacements. In this paper, the damage growth and the opening near the intersection of transverse matrix cracks (TMC) and a delamination are discussed. Three-dimensional finite element analysis (FEA) was used to analyze cross-ply and angle-ply graphite/epoxy laminates. The strain energy release rates (SERR) along the delamination front were calculated based on the virtual crack closure technique. The strain energy release rate has a very large variation along the delamination front and is sensitive to a variety of geometric and load parameters. There is an extreme gradient of the strain energy release rate near the intersection of the delamination front and the TMC. Based on the SERR results, likely delamination shape and size for cross- and angle-ply laminates were determined. Prediction of the likely shape and size will help one to understand the conduit for leakage. The opening near the intersection of the TMC and the delamination was calculated. The effect of ply thickness on the SERR and the opening is also discussed.

Effect of Transverse Matrix Cracks on the Relaxation Moduli of Linear Viscoelastic Laminates

A finite element based degradation model was employed to study the effect of cracks on the relaxation moduli of linear viscoelastic laminates. In the current study, the relaxation moduli are expressed in terms of the elastic moduli, the fully relaxed moduli, and the relaxation functions. The degradation behavior of a viscoelastic lamina due to cracks was examined and compared with that of an elastic lamina. The study shows that the degradation behavior of a viscoelastic lamina can be predicted by that of an elastic lamina. The effect of other parameters such as adjacent lamina orientation on the properties of a cracked lamina in a viscoelastic analysis is found to be very similar to that for an elastic analysis. It was found that the cracks affect the elastic and fully relaxed moduli but do not affect the relaxation functions. The study also shows that the variation of the stress state of a viscoelastic laminate depends on the instantaneous crack density, not on the time-history of cracking. Based on the study, an efficient method has been developed for the progressive damage analysis of viscoelastic materials. The method allows accurate prediction of the stress state of a viscoelastic laminate utilizing the degradation information obtained from an elastic analysis. This method is very efficient and accurate.